Advances In Geophysics, Volume 04

ADVANCES IN

GEOPHYSICS VOLUME 4

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Advunces In

GEOPHYSICS by H. E. LANDSBERG Edited

U. S. Weother Bureou Woshingfon, D. C.

J. VAN MIEGHEM Royal Belgion Mefeorological Institute

Uccle, Belgium

Editorial Advisory Committee BERNHARD HAURWITZ WALTER D. LAMBERT

ROGER REVELLE R. STONELEY

VOLUME 4

ACADEMIC PRESS INC

PUBLISHERS

NEW Y O R K , 1 9 5 8

COPYRIGHT @ 1958, B Y ACADEMIC PRESS INC. 111 Fifth Avenue, New York 3, N. Y.

All Rights Reserved No part of this book may be reproduced in any form, by photostat, microfilm, or any other means, without written permission from the publishers.

Library of Congress Catalog Card No. 52-12266 PRINTED I N T H E UNITED STATES OF AMERICA

LIST OF CONTRIBUTORS JOSEPHW. CHAMBERLAIN, Yerkes Observatory, University of Chicago, Williams Bay, Wisconsin J. LEITH HOLLOWAY, JR., General Circulation Research, U. S. Weather Bureau, Suitland, Maryland CHRISTIAN E. JUNGE,A i r Force Research Center, Bedford, Massachusetts LINCOLNLAPAZ,Director, Institute of Meteoritics, University of New Mexico, Albuquerque, New Mexico PAUL MELCHIOR,Obsereatoire Royal de Belgique, Reporter General f o r earth tides of the International A ssociations o f Geodesy and Seismology, Uccle, Brussels, Belgium

V

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FOREWORD As this fourth volume of Advances in Geophysics finds its way t o our colleagues, a fifth volume is being assembled and a sixth is through the planning stages. This reflects the rapid progress in our field. The International Geophysical Year-and the public interest in it-has also served to promote a once rather obscure area of science into the limelight. Also, more departments and institutes of geophysics or earth sciences are being established in universities the world over. Thus it has become one of our aims, among others, to bring in these volumes, to professors and advanced students alike, broad reviews of sectors of our science where new knowledge has accumulated fastest or where perhaps neglect has relegated an important facet into the background. I n all our contributions the authors not only report the solid progress but also point toward the great questions which remain open and where the avenues of future research lie. Wherever possible, we want also to show how other sciences impinge on the quest for knowledge about the physics of our planet. The meteoritical article in this volume reflects this concept. We are also always interested in discussions of analytical techniques for the rapidly accumulating data collections. I n the search for suitable topics the editor has had again the good advice of the editorial committee. This is gratefully acknowledged. Reviewers have voiced however, an important criticism of our past volumes. This is the preponderance of American authors for our articles. Although we are quite aware of the universality of geophysics the problem of language difficulties has loomed large. I n Volume IV we are trying our hand for the first time with a translated contribution. I n a limited way, this may provide an answer. We have been fortunate enough t o obtain a distinguished European colleague as associate in the editorship. Dr. J. Van Mieghem of Uccle, Belgium, is joining me in the editorial responsibility, and his active participation will be apparent beginning with Volume VI. A preview of Volume V indicates that the article on model experiments, already announced in the foreword to Volume 111, will be in it. Other titles will include cloud physics, atmospheric tides, photochemical problems of the high atmosphere, and the shape of the earth.

H. E. LANDSBERG August, 1957 vii

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CONTENTS LIST OF CONTRIBUTORS . . . . . . . . . . . . . . . . . . . . . . .

v

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

Atmospheric Chemistry

CHRISTIANE . JUNGE 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. TraceGases . . . . . . . . . . . . . . . . . . . . . . . . . . 44 71 4. Precipitation Chemistry . . . . . . . . . . . . . . . . . . . . . 5 . Air Pollution and Its Role in the Chemistry of Unpolluted Air . . . . 94 List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 101 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Theories

of the Aurora

.

JOSEPH W CHAMBERLAIN 1 . Introduction . . . . . . . . . . . . . . . . . . . . 2. The Motions of Charged Particles in Magnetic Fields . 3 . Stormer’s Theory of Aurorae . . . . . . . . . . . . 4. Electric Currents bctween the Sun and Earth . . . . . 5. The Chapman-Ferraro Stream and Ring Current . . . 6 Other Electric-Field Theories of Aurorae . . . . . . . 7 Additional Mechanisms for the Production of Aurorae . 8. Theories of Auroral Excitation . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . .

. .

. . . . . . 110 . . . . . . . 116 . . . . . . . 127 . . . . . . . 146 . . . . . . . 158 . . . . . . . 173 . . . . . . . 183 . . . . . . . 191 . . . . . . 206 . . . . . . 207 . . . . . . 210

The Effects of Meteorites upon the Earth (Including Its Inhabitants. Atmosphere. and Satellites)

LINCOLN LAPAZ 1. The Effects of Typical Meteorite Falls . . . . . . . . . . . . . . 218 2. Number. Classification. and Weights of Recovered Meteorites . . . . . 235 3 . Metcoritic Abundnnws and Terrcstrid Meteorit.ic Accretion . . . . . 240 4 . The Hyperbolic Meteorite Velocity Problem . I . . . . . . . . . . . 273 5 . The Hyperbolic Meteorite Velocity Problem . 11. . . . . . . . . . . 292 6. Crater-Producing Meteorite Falls . . . . . . . . . . . . . . . . . 307 Appendix I . Meteoritical Pictographs and the Veneration and Exploitation of Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . 329 ix

CONTENTS

X

Appendix I1. Basic Meteoritic Data and in Section 5 . . . . . . . . . . . List of Sym6oIs . . . . . . . . . . . References . . . . . . . . . . . . .

Classificational Criteria Employed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

336 339 341

Smoothing and Filtering of Time Series and Space Fields

J . LEITHHOLLOWAY. JR. 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Time Smoothing and Filtering . . . . . . . . . . . . . . . . . . 3. Equalization, Pre-emphasis, and Inverse Smoothing . . . . . . . . 4. Smoothing and Filtering Functions . . . . . . . . . . . . . . . . 5. Frequency Response of Smoothing Functions and Other Filters . . . . 6. Design of Smoothing Functions and Filters with Specified Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. High-Pass and Band-Pass Filtering Functions . . . . . . . . . . . 8 . Elementary Smoothing and Filtering Functions . . . . . . . . . . 9 . Design of Inverse Smoothing Functions . . . . . . . . . . . . . 10. Design of Pre-emphasis Filters . . . . . . . . . . . . . . . . . 11. Filtering by Means of Derivatives of Time Series . . . . . . . . . 12. Space Smoothing and Filtering . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

351 352 353 354 355 363 365 369 372 376 378 380 386 387 388

Earth Tides

PAULJ . MELCHIOR 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 392 2. Static Theory of the Tides . . . . . . . . . . . . . . . . . . . 394 3 . Definition of Love’s Numbers . . . . . . . . . . . . . . . . . . 400 4 Studs of the Amplitude of Oceanic Tides . . . . . . . . . . . . . 401 5 Periodical Deflections of the Vertical with Respect to the Crust . . . . 403 6 Measurement of Elastic Tensions and Cubic Dilatations Due to Deformations Produced by the Earth Tides . . . . . . . . . . . . . . . 418 7 . Deflections of the Vertical with Respect to the Axis of the Earth . . . 423 8 . Variations in the Intensity of Gravity . . . . . . . . . . . . . . . 426 9. The Role of the Geologic Structure of the Crust in the Indirect Effects 432 10. Theory of Elastic Deformations of the Earth . . . . . . . . . . . . 435 11 . Effect of Earth Tides on the Speed of Rotation of the Earth . . . . . 439 12. Program of the International Geophysical Year . . . . . . . . . . . 440 List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 452

.

. . .

ATMOSPHERIC CHEMISTRY Christian E. Junge Geophysics Research Directorate, Air Force Cambridge Research Center, 1. G. Hanscom Field, Bedford, Massachusetts

Page 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 2.1. General Comments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Size Distribution of Natural Aerosols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3. Physical Constitution of Natural Aerosol Particles. . . . 2.4. Nature and Origin of Aitken Particles,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 20 2.5. Sea-Salt Aerosols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Continental Aerosols. . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ 29 3. Trace Gases.. . . . . . . . . 3.1. General Comment 3.2. Carbon Dioxide.. . . . . . . . . . . 45 3.3. Ozone .............................. 3.4. Nitrous Oxide.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 59 3.5. Nitric Oxide, Nitrogen Dioxide, and Ammonia.. . . . . . . . . . . . . . . . . . . . . . ............................. 64 3.6. Sulphur Dioxide, Hydrogen Sulfide. ............................. 66 3.7. Halogens ........................ 67 3.8. Methane, Carbon Monoxide, and Formaldehyde.. . . . . . . . . . . . . . . . . . . . . 3.9. Ratio of Gaseous to Particulate Matter for Some Chemical Components 68 4. Precipitation Chemistry.. . . . ............................. 71 4.1. The Removal of Trace Substances from the Atmosphere.. . . . . . 4.2. Physical and Chemical Processes of Wash-Out by Precipitation.. . . . . . . . 73 4.3. The Content of Rain Water with Respect to the Predominantly Continental Components NH4+, NO,-, NOz-, SOa-- and Ca++. . . . . . . . . . . . 81 4.4. The Content of Rain Water with Respect to the Predominantly Maritime Components C1-, Na+, Kf, Mg++ and the Role of Precipitation in the 88 Natural Cleansing Process of the Atmosphere.. . . . . . . . . . . . . . . . . . . . . . . 5. Air Pollution and Its Role in the Chemistry of Unpolluted Air. . . . . . . . . . . . . 94 5.1. The Main Components in Polluted Air. .................... 94 5.2. The Area of Influence around Pollution Centers., . . . . . . . . . . . . . . . . . . . . 98 List of Symbols ................................................ 101 ...... ..... . 101

1. INTRODUCTION

Atmospheric chemistry, if it is to be comprehensive, must treat such varied problems as the origin of our atmosphere as a phenomenon of general geochemistry, the temporal changes and geochemical cycles of its components, the effects of biological processes at the earth’s surface and 1

2

CHRISTIAN E. JUNGE

in its oceans, and finally, the photochemistry of the upper atmosphere. Space limitations preclude any such comprehensive treatment here; our discussion will center, therefore, on one particular field of atmospheric chemistry, the chemistry of active trace substances in the troposphere. Active trace substances may be defined as those atmospheric constituents which form but an infinitesimal part of the total atmosphere, and which are continually in the process of being removed and added to the atmosphere by chemical or meteorological processes. As a result their concentration varies greatly with time and space, in contrast to the permanent gases, including the rare ones, which we will regard here as the given carrier gas. Trace substances comprise primarily compounds of nitrogen, sulphur, chlorine, carbon, and oxygen, as well as all substances present in the form of aerosols. We consider COz a borderline case because of its comparatively large concentration, small fluctuations, and relatively passive role in the atmosphere. Water, though it undergoes rapid changes, will not be treated here. We will restrict our discussion to the troposphere, since its chemistry is t o a large degree independent of, and different from, that of the stratosphere. A number of the trace substances to be treated here are formed at the earth’s surface and will be confined to the troposphere by the limiting action of the tropopause. On the other hand, a large number of the products formed photochemically at high altitudes will remain a t these levels, being unable to penetrate downwards through the tropopause. Our knowledge of tropospheric trace substances is quite fragmentary; there are, however, a number of vague hypotheses, most of which have been formulated on the basis of only a very few measurements. Therefore, our first concern will be to summarize as comprehensively as possible the most reliable factual material and to point out in what respect it is inadequate. Hypotheses and assumptions regarding the nature of the chemical decompositions and the cycle of the substances will be mentioned only insofar as they appear to be reasonably supported by observation, or possess a certain degree of probability on the basis of our present knowledge. In our description of the chemical components (Sections 2 and 3) we will distinguish them according to phase, i.e., whether they are present in particle form, as an aerosol, or as a gas. This appears to be the most reasonable division, and is of fundamental importance for those substances which may occur in both forms. Section 2 will therefore start with a detailed discussion of the physics and meteorology of natural aerosols, since it is only on this basis that we will be able to understand properly the behavior of certain chemical compounds and their role in cloud and precipitation chemistry.

3

ATMOSPHERIC CHEMISTRY

I n Section 4, cloud and precipitation chemistry will be discussed. These processes take on particular importance in a n age of increasing industrial pollution of the atmosphere, for they provide the major means whereby numerous chemical components are removed from the atmosphere. Again we feel the need for a careful discussion of the physicochemical processes involved in order to attempt a proper interpretation of the extensive observational data from rain-water analyses. Finally, in Section 5 we will discuss air pollution briefly in terms of its significance for the general chemistry of the troposphere. The role of these anthropogenic trace substances in the troposphere has occasionally been overestimated, though in certain cases their influence has been found to attain a continental scale. 2. AEROSOLS 2.i. General Comments I n view of their special importance for numerous branches of meteorology, we will begin our discussion of trace substances with the aerosol. T o provide the necessary basis for a proper understanding of the chemical composition of the aerosol particles we will first give a complete survey of their physical properties, size distribution, and concentration under various conditions. The concept of the aerosol is generally understood as the disperse state of matter in a gaseous medium, in our case the air. All sizes of particles, ranging from air molecules all the way to raindrops, appear in the atmosphere (see Fig. 1). However, our interest will be confined t o parand 20 p. Particles in this ticles in the size range between about 5 X size range a t relative humidities below water saturation are defined here as natural aerosols. I n meteorology they are labeled condensation nuclei, or just nuclei. This designation is fundamentally correct, since these particles are all capable of acting as condensation nuclei for water vapor. However, usually in the atmosphere only a small fraction of these potential nuclei (preferably the largest) actually take part in the formation of droplets. Thus i t is preferable t o speak of aerosol particles generally and refer t o them specifically as condensation nuclei only in those cases ere tJheyreally form the starting point for condensation or sublimation Certain regions of the aerosol spectrum, which extends over lmost four orders of magnitude, are well known from the investigations of special branches of meteorology. We might draw an analogy here between the spectrum of the aerosol particles and that of the electromagnetic waves. Similar t o the specific and quite different properties of the various wavelength regions, distinct size classes of particles are responsible for certain physical processes in the atmosphere (Fig. 1).

?

4

CHRISTIAN 1. JUNGE

For example, particles smaller than 0.1 p play a significant role with respect to the electrical conductivity of the air and thus the potential gradient. When charged these particles are called large ions. Particles in the range between about 0.08 p and 1.0 p are most important for light scattering. Beyond these limits the product of the particle concentration and the Mie scattering coefficient becomes so small under normal conditions in the atmosphere that their optical effect is practically zero. A third example is that of cloud formation. The main portion of true condensation nuclei, at least over land, consists of particles above approximately 0.1 p . Particles above about 5 p probably play an important role in the formation of rain. Particles below 0.1 1.1 may act as condensation nuclei only in areas with quite low aerosol concentrations, i.e., at high altitudes or over the oceans.

p radius FIa. 1. Nomenclature of natural aerosols and the importance of particle sizes for various fields of meteorology.

For convenient characterization, the over-all range of aerosol particles has been broken down into three parts, namely, the Aitken, the large, and the giant particles (see Fig. 1). Particles outside the range of the Aitken and the giant nuclei normally are not important carriers of chemical substance in the atmosphere. The small ions, which are very important for atmospheric electricity, have a different physical constitution than the Aitken nuclei and are separated from these by a distinct gap in the size distribution. They consist of about 10 to 30 molecules and have an average concentration of some hundreds per cm3. This is equivalent to a substance concentration of 10-7 ylmeter3, a value several orders of magnitude smaller than the corresponding value of all the other chemical components. On the other hand, particles larger than 20 p can remain airborne for only a limited time and their occurrence is therefore restricted to the vicinity of their source.

ATMOSPHERIC CHEMISTRY

5

With rising humidity the aerosol particles gradually change, both in size and physical properties, into either cloud droplets, fog droplets or ice particles, and possibly even into raindrops. I n the process of growing, these particles may accumulate chemical materials in addition to the original condensation nuclei around which they formed, and their composition therefore differs from that of the aerosol particles. However, in view of the fact t ha t they cannot exist a t relative humidities below loo%, they will be treated in connection with precipitation chemistry. If not otherwise stated, we will use y/meter3 (i.e., grams per meter3) as the unit of concentration for both aerosols and gases. This amount of material is represented, e.g., by a water droplet of 0.12-mm diameter in a cubic meter of air. 2.2. Size Distribution of Natural Aerosols

For a better understanding of the results of the size-distribution measurements, we will briefly discuss the methods which are used for this investigation. The well-known Aitken nuclei counter, which operates on the principle of the Wilson cloud chamber, determines only the total number of particles. With proper adjustment of the expansion ratio (see, e.g., [l]) small ions are not counted. This total particle number is approximately identical t o that below 0.1 1.1 radius, since the number of the large and giant particles is comparatively low (hence the designation of the Aitken size range). Data on the size distribution below 0.1 p can be obtained by measuring the coefficient of diffusion due to Brownian motion [2], or the mobility of the charged particles in an electric field [3]. The latter method permits a quite accurate size resolution, which refers, of course, to thc charged Aitken nuclei (large ions) only. Findings indicate th a t the size distribution of large ions frequently resembles a “line spectrum”; i.e., the particles are concentrated around discrete sizes (Fig. 2). The reason for this phenomenon is unknown. To convert a n “ion spectrum” into a n “aerosol spectrum,” it is necessary t o know the charge of the particles as well as the fraction of particles charged. Both quantities are functions of the particle size. These functions are approximately known for natural ionization conditions 141. Size determinations based on measurements of diffusion and ion mobility can be carried out only up to a radius of 0.08 to 0.1 p and are not, applicable for larger particles. I n fact no satisfactory method is available for the size range between 0.08 and 0.8 p. It is not difficult t o obtain somewhat representative samples of these particles with the Dessens spider thread method [ 5 ] , with an impactor [ 6 ] , or with thermal precipitation, the latter method being not very appropriate because of the low concen-

6

CHRISTIAN E. JUNGE

trations of aerosols in the atmosphere. The difficulty lies rather in the evaluation itself: the limit of measurement with the optical microscope is already reached a t 0.3 1.1. The application of the electron microscope, on the other hand, is unsatisfactory because the size and the shape of the particles change considerably with the evaporation of water and other volatile substances due to heating by the electron beam in the vacuum.

4o

t

p radiusFIG.2. Zon spectrum a t various places (solid columns) according to Israel and Schuls [3] in per cent of the total ion population. The total height of the columns indicates the calculated size distribution of the corresponding aerosol spectrum (ions plus uncharged particles) in arbitrary units.

The light microscope is an ideal instrument for evaluating giant nuclei, which can easily be collected on spider threads or with an impactor. For instance, Woodcock [7] collected giant particles on small glass plates, which he exposed to the wind or air stream from an aircraft. Also gravity deposits on horizontally exposed plates yield good samples of aerosol particles [7, 81. The advantage of this method lies essentially in the simplified evaluation. All particles appear in the samples in

ATMOSPHERIC CHEMISTRY

7

about equal amounts due to the opposite trends exhibited by particle concentration and fall speed. We see from this brief survey that a determination of the entire size range requires the simultaneous use of several methods, but even then the range around 0.1 to 0.3 1-1 remains hard to cover. In view of the difficulties involved, very few measurements of the complete size distribution have been made t o date. On the other hand, extensive data have been obtained with single instruments, e.g., the Aitken nuclei counter, Owens dust counter, and other types of impactors. However, because these instruments cover only a narrow, poorly defined portion of the total size distribution, the measurements are only of relative value. As a consequence of the independent use of these various instruments, the view prevailed for a long while that the natural aerosols consisted of fairly independent groups of particles, e.g., the hygroscopic, in contrast to the dust particles counted by the impactor or the Owens “dust counter.” The realization that the natural aerosols form essentially a coherent size distribution is relatively new. A few words about the appropriate representation of the size distribution curves will be helpful here. A fundamental requirement of such representations, whether histogram or continuous distribution curve, is that the number of particles within a radius interval Ar or dr be represented not by the value of the abscissa, but by the surface area enclosed by the particular interval and the distribution curve. Unfortunately, this has not always been taken into account in the literature, making a comparison of values difficult or even impossible in some cases. Considering the wide range of particle sizes and concentrations, it seems advisable to use logarithmic scales. The log-radius distribution can thus be defined by (2.1)

n(r) = dN/d(log

r)

where N is the total concentration of aerosol particles (per cm3) from the lowest size limit up to size r. Therefore, dN = n(r)d(log r ) is the particle number per om3 found between the limits of the interval d(1og r ) . The log-radius distribution is not as important for atmospheric-chemical considerations as is the log-volume distribution dV/d(log r ) . Multiplying the log-radius distribution by r . r 3 we obtain (2.2)

dV/d(log r)

=

?.$ ?r * r3 dN/d(log r )

Knowing the density, from the volume distribution we can immediately estimate the maximum amount of substance which may be present in any size range of the aerosol. This value is maximal because of the possible presence of other components in the particles.

CHRISTIAN E. JUNGE

8

104

103

102

f

10'

0 L Q)

0. L

lo(

10-

lo-:

10-:

FIQ.3. Complete size distributions of natural aerosols, average da ta [4,81. Frankfurt/Main, curves 1, 2, and 5. Curve 1: ion counts converted to nuclei numbers. Curve 2: data from impactors. The point below 0.1 /I radius was obtained from the total Aitken-nuclei number under the assumption that the radius interval of the Aitken nuclei is A log r = 1.0. Curve 5: average sedimentation data over a period of I1 days. Curves 1, 2, and 5 are not simultaneous. Zugspitze, 3000 meters above m.s.1.: curves 3 and 4 correspond to curves 1 and 2 for Frankfurt and were obtained at approximately the same time. The figures in parentheses give the number of individual measurements. The dashed curves between 8 x 10-2 and 4 X 10-1 /I are interpolated.

Results of the measurements of the complete size distribution are shown in Fig. 3 for a densely populated area and for an elevation of 3000 meters [4,81. The curves were obtained by the combined use of ion counters, nuclei counters, impactors, and sedimentation chambers; they represent mean values from which the individual values can depart considerably. These curves exhibit the following main features: the lower

ATMOSPHERIC CHEMISTRY

9

limit of the particle size, which may vary greatly from day to day, lies a t about 4 X p and is separated by a break from the small ions. The upper limit of 10 p for curve 2 is incorrect, because the observational procedure precluded detection of the few still larger particles. Curve 5 places the true value in the neighborhood of 20 1.1. The maximum of the logradius distribution lies between 0.01 and 0.1 p, usually a t 0.03 p , This has been repeatedly confirmed by Nolan and his co-workers [2] and also by other investigators. The most striking feature of the size distributions is their almost straight-line segment extending over two orders of magnitude from 0.1 to 10 p . It can be approximated by (2.3)

dN/d(log r )

=

const/ro

where p is equal to about 3. I n the log-volume representation this would correspond t o a constant value (Fig. 4).The interpretation important for atmospheric chemistry is that the large and giant particles represent approximately equal as well as the major amounts of substance, while the Aitken nuclei, despite their large number, are unimportant with respect to mass. The curve obtained on the Zugspitze shows that these features are valid for the 3000-meter level as well; however, the concentrations there are by one order of magnitude smaller and the upper radius limit is possibly somewhat lower. The contradiction between the continuous distribution curves in the Aitken nuclei range in Fig. 3 and the line spectrum in Fig. 2 is only apparent, being the result of a different method of representation. In Fig. 3 the ion numbers were evaluated from certain intervals of the Aitken particle range, so that the position and intensity of the ‘(lines” could not be detected. Moreover, the observational material seems to indicate that as the radius grows the line structure tends to disappear. It is hardly detectable in the region of the larger nuclei. The small number of direct measurements of the complete size distribution does not permit any conclusions about the general validity of these results. However, the optical behavior of atmospheric haze gives added confirmation that the exponential law is in any case valid within the optically effective p?rticle range between 0.08 to 0.8 p for a /3 approximately equal t o 3 [4]. Angstrom found that the pure haze extinction is almost inversely proportional to the wavelength of light. Theoretically it follows from our distribution law that with /3 = 3 the extinction is exactly inversely proportional to the wavelength. Numerous observers have confirmed h g s t r o m ’ s law [9] and their findings imply that the corresponding p values of the aerosol distribution must lie between 2.5 and 3.5. We might therefore infer that the aerosol distribution law for the

10

CHRISTIAN E. JUNGE

optically effective size range between 0.08 and 0.8 p has a wide validity. Observations of the scattered light around the sun lead t o a similar conclusion, as the detailed investigation by Volz [lo] has shown. All measurements of the entire size distribution as well as the optical observations cited above have thus far been made only over land. The

I0-

l o

FIG.4. Log-volume distribution curves for various aerosols [ll-131. Curve 3B is extended to a point determined by chemical analysis. The curve of Frankfurt is approximated by a “model” distribution, which is used for calculations in Fig. 5. (By courtesy of Tellus.)

conditions above the ocean appear to be fundamentally different [ll].Unfortunately, size-distribution measurements over the ocean have so far been made for giant particles only. Woodcock [la] has made the most extensive observations. The log-volume curves obtained by different observers above the ocean (Fig. 4) indicate that) with average wind forces, the giant nuclei exhibit nearly the same distribution as over land, i.e., approximately the same total concentration, identical upper limit, and a mean 0 of 3 (see also Fig. 10). However, all maritime curves show a defi-

11

ATMOSPHERIC CHEMISTRY

nite decrease as the radius approaches 1 to 2 p , where the measuremeilts end. This is confirmed by data which have been obtained in chemical analyses and included in Fig. 4. The fundamental difference between continental and purely maritime aerosols is immediately evident. The sharp drop of the extrapolated curve reflects the small content of both the Aitken and the large particles above the ocean, a fact that was already well known. The extrapolated maritime distribution curve is valid for extremely pure sea air. A large variety of transitions between continental and maritime curves may therefore be expected over a wide area along the coast and seem to be implied in some observations obtained over the East Atlantic [13]. These general features in the size distribution of natural aerosols establish the framework within which the numerous individual observations of limited size ranges must be fitted. Table I contains a compilaTABLE I. Number concentration of Aitken particles per cm3 in different types of localities [I 1. Locality City Town Country (inland) Country (sea shore) Mountain 500-1000 meters 1000-2000 meters >2000 meters Islands Ocean

Number of Places Observations

Average

Average Max Min 379000 49100 1140OO 5900 66500 1050 33400 1560

28 15 25 21

2500 4700 3500 2700

147000 34300 9500 9500

13 25 16

870 1000 190 480 600

6000 2130 950 9200 940

7 21

36000 9830 5300 43600 4680

1390 450 160 460 840

tion of data on A i t k e n particles after Landsberg [l];it shows the considerable decrease in the concentrat,ions as one approaches the sea. In entirely undisturbed areas (i.e., in marine areas far from continents) particle numbers of only 100 to 200/cm3 have usually been observed. The particle numbers obtained by the various dust counters and impactors (conimeter) depend to a great degree on the lower precipitation limit (-0.1 p ) of these instruments, because of the steep slope of the size distribution curve in this range. Naturally, this limit fluctuates with instrument type and operating conditions; however, it generally lies around a few tenths of a micron. Moreover, when the particles are precipitated on normal glass surfaces or hygroscopic films rather than on hydrophobic surfaces, the true nature of atmospheric particles, as mixed particles, remains concealed; indeed, only a fraction of them may even

12

CHRISTIAN E. JUNOE

become visible. The numerous reported concentrations vary over a wide range between ten and a few hundreds of particles per cma (see, e.g., Effenberger [14]). Giant nuclei counts above the ocean 1121 lie between about 0.1 and l/cm3; similar concentrations in this size range were also found over land [8]. The question now arises as to the physical processes underlying the observed size distributions. There is a comparatively simple explanation for the lower and upper limits of the aerosol distributions. The lower limit results from coagulation (due to Brownian motion) of the small Aitken particles with larger particles. This process causes the number of the smallest particles to decrease very rapidly; it can be computed with good approximation 1151. Figure 5 shows how a given model size distribution, which follows closely the Frankfurt values (Fig. 4), changes with time. The decrease of the small Aitken nuclei number is rapid, compared t o meteorological processes, and results in a displacement of the size-distribution maximum toward larger particle radii. Because of the minute size of the small Aitken nuclei, this process brings about no noticeable change in the size and concentration of the particles larger than 0.1 p. From Fig. 5 it must be concluded that a decrease in the total particle concentration should be related to an increase in the average particle size. This can actually be verified statistically on the basis of numerous measurements made at various places throughout the world [4]. The corresponding representation of these results by a log-volume distribution (Fig. 5) shows that the decrease in the volume of the Aitken particles corresponds to an equal increase in volume above 0.1 p, which occurs preferably in the large-nuclei range, Hence, one should expect that the Aitken and the large nuclei have some chemical components in common, and that the individual particles consist of a mixture of various substances (mixed particles). The upper limit is established by the fall-out due t o gravity. Since the fall speed increases, according to Stokes’ law, with the square of the radius, we may expect this limit to be comparatively abrupt. The sources of aerosols are usually to be found right at the earth’s surface (above ocean and land), or a t any rate, quite near to it, as in the case of the various types of smoke and dust sources. The upper size limit is then determined by the equilibrium between the upward flux of particles (due to eddy diffusion) and the downward sedimentation flux. It can be computed under simplified conditions, as e.g., above the sea where the water surface is a uniform source of sea-salt particles [15]. If the eddy diffusion is represented by the wind speed a t a 5-meter height, the roughness parameter of the sea surface, and the constant austausch coefficient a t a relatively great height, the fraction E of the par-

ATMOSPHERIC CHEMISTRY

13

ticles produced at the sea surface which can penetrate to various heights are given in Fig. 6 as a function of their radius. The variation of the individual parameters obviously exerts little influence. Above about 20 p radius, E drops rapidly to zero, indicating that this size is virtually the

FIG. 5. Calculated change in the size and volume distribution of natural aerosols, due to coagulation resulting from Brownian motion. The size distribution at the beginning (Oh) is the model distribution of Fig. 4. ( h = hours, d = days.)

upper limit for aerosols present for any considerable length of time in the atmosphere under normal conditions. The conditions over land are more complex, but estimations show that the same, or a somewhat higher upper limit, may be expected. Although it is possible to explain the limits of the size distribution on the basis of well-known physical laws, there is no satisfactory explana-

14

CHRISTIAN E. JUNGE

tion of the distribution law between these limits. As becomes evident from Figs. 5 and 6, the effects of coagulation and sedimentation do not extend far enough into the range between 0.08 and 10 p t o exert any great influence on shaping the size distribution in this range. Figure 4 seems to point to the nearly constant log-volume distribution as the basic phenomenon requiring clari$cation. As far as we can see, there are two processes that could be responsible. First, the large-scale mixing of innumerable small aerosol sources everywhere over the continents may result statistically RADl US I .o

I

I

I

I

I I

l0P l l l

1

I

I

I l

'OP l l l

I

I

I

I

10P

I , I ,

1

I

1

,,,,,

w 0.4 0.2

b =4crn

RADIUS-

b =4cm u5 = 5 rn/sec

FIG.6. Calculated concentration t of sea-spray particles as a function of the radius a t altitudes of 10, 50, and 250 meters if the concentration at the surface of the sea is 1.0. In the upper part of the figure the wind speed, u6,a t 5 meters altitude is varied, while the austausch coefficient for high altitudes ( A , ) and the roughness parameter of the sea surface ( b ) remain constant. I n the lower part of the figure A , and b are varied.

in a constant log-volume distribution. This could easily explain the relatively large deviations in time and place. Second, the formation, coagulation, and re-evaporation of cloud and raindrops in the atmosphere might exert an effect which tends to re-establish a constant log-volume distribution. Nevertheless, our present knowledge is still too inadequate for anything beyond a suggestion. 2.8. Physical Constitution of Natural Aerosol Particles

The physical properties of the particles are just as important relative to their role in air chemistry as is their size distribution. The particles in

ATMOSPHERIC CHEMISTRY

15

natural aerosols can consist of solid material or droplets, or of a mixture of both. It is well known that a considerable portion of the natural aerosols are droplets of a solution of hygroscopic matter which grow with increasing humidity [16]. On the other hand, insoluble particles are very widespread, e.g., the soot particles in smoke, or the mineral dust over large land masses. A great variety of mixtures is encountered, depending upon the geographical location and the history of the air masses. The factors determining the physical characteristics of the particles are their content of soluble substances, the relative humidity at which these substances form a saturated solution (usually somewhat unclearly termed hygroscopicity) and the relative humidity of the air itself. The vapor pressure above a solution droplet is reduced by the dissolved substances and increased by the curvature of the surface. For particles with radii above 0.1 p, the latter effect is smaller than 1% relative humidity and may thus be disregarded here. Aerosol particles of salt solution then assume such a volume that the concentration of the solution is in a vaporpressure equilibrium with its surroundings. The corresponding growth of the particles with rising humidity depends only slightly on the temperature and the type of the dissolved substance. I n computing such growth curves one should use the measured data of the water-vapor partial pressure for different concentrations of solution, and not Raoult’s law, which holds true for dilute solutions only. Figure 7 gives some examples of growth curves for various substances. An NaCl crystal becomes a droplet at, or a little below, 75% relative humidity, which is the relative humidity of a saturated solution. However, crystallization with decreaszng humidity does not occur until 40 %50% relative humidity is reached, i.e., not until the solution becomes considerably supersaturated. The same holds true for other salts as well. The growth curves of mixed particles show all transitions between a pure droplet of solution and the straight line of a completely dry particle. The computed growth curves have by and large been confirmed by measurements [17]. The measured mean growth curves for natural aerosols over land [Fig. 7(d)] are not much different for giant and Aitken particles [17, 181. We see immediately that they agree well with those of mixed particles which contain a noticeable amount of insoluble substance. Growth curves of indiuidual giant aerosol particles show great variety, indicating fairly comulex chemical compositions 1171. The predominance of mixed particles over land is confirmed by direct observations. Figure 8 shows electron microscope pictures of large and giant particles, a considerable number of which were obviously droplets before they evaporated in the vacuum [19]. Impaction of particles on dif-

16

CHRISTIAN E. JUNGE

2

3

4

6

0

1

0

2

3

4

6 0 1 0 0

radius 4

FIG.7. Growth of aerosol particles with relative humidity. The curves are valid for the size range of the large particles, but are not very different for other sizes. With the logarithmic radius abscissa, the curves are almost independent of the absolute size of the particles. (a) NaC1. The solid curve is calculated. At 75% the crystal goes into solution, increasing the radius by a factor of about 2. The dashed lines represent observations made in the size range of the giant particles. With increasing humidity the crystal goes into solution somewhat earlier than the calculated value; with decreasing humidity a considerable salt supersaturation in the droplet delays the crystallization. (b) Calculated growth curves for various hygroscopic substances. 1 = HNOa, 2 = CaCL (the arrow indicates the expected crystallization point), 3 = H2S04. The differences are small. (0) Calculated growth curves for mixed particles composed of a solid spherical core (indicated by the hatched areas) and of a liquid layer of HtSOn of varying thickness (indicated by the length of the solid line). (d) Measured average growth curves of continental giant (1) and Aitken (2) particles. The hatched area indicates the size of the solid core, which agrees best with curves in (c).

ferent type surfaces has provided additional confirmation. Using alternately clean dry glass plates (which catch only droplets) and plates covered with a viscous film (which catch both droplets and dry particles) in an impactor has shown that below 70% relative humidity a noticeable fraction of the particles are dry, but that above 70% almost all of the particles have assumed the properties of a droplet 1171. The sea-salt nuclei in pure maritime air contain practically no insoIuble components. If the relative humidity rises to more than 70%, the crystals go into solution, as may be expected from their chemical composition [20]. Figure 7 shows that mixed nuclei and pure solution droplets grow with increasing rapidity and gradually become fog and cloud droplets when water saturation is approached. But even dry dust particles will be covered by several layers of water vapor below water saturation, due

.ITMOSPHERIC CHEMISTRY

17

to physical adsorptioii. In the presence of soluble gas traces the water coiitrwt of aemhol particles may be important for proiiiotiiig chemicd reactions betwer.11 such gas traces aiid the inaterial of the particles t heriiselves. S..4. NatiirP a d Origin of ,titlietL Particles

The history of twearvh iiito the nature of iiatural aerosols is esseiitially the history of the study of the Xitkeii nuclei, iiiitiated by the famous iiivestigatioiis of Aitken. These particles attracted particular attention because of the high values and pronounced fluctuations of their number (ionrelitrations wider various geographical and atmospheric conditions, hecause of their significance for air electricity, and last but not least, herause the iiuclei counter provided such a handy iiistrumeiit to count them. ,Is a result of these investigations the natural aerosol was for a loiig time considered to be identical with the Aitken iiuclei. The importance of the less numerous, but much bigger particles above 0.1 p for such fields as air chemistry, cloud physivs, and atmospheric optics

18

CHRIRTIIN E. J U N O E

was for a long time completely overlooked, or at, least underestimated. To a certain extent this resulted in a vonsiderahle delay in a proper approach t o the problems of the natural aerosol. ,111 this research into Aitken nuclei, however, was far more concerned with the origin and the geographical distribution rather than with the chemical composition of the particles, the importance of which was stressed almost exclusively by bioclimatologists, as indicated by the work of Cauer [2l, 221. Since the extremely small amounts of material represented by the Aitken nuclei excluded and still exclude today any direct analytical method, indirect methods mere tried to obtain information on the nature of these particles. I t was, for instance, attempted to determine to what degree the nuclei counter responded to soluble, hygroscopic substances only, and not to dry and insoluble ones. But this approach failed after it became evident that all substances can act as condensation nuclei provided that they are of the proper size. Another approach was to investigate the most efficient processes of Aitken-nuclei formation. A considerable amount of effort was devoted t o these studies, the results of which are summarized in excellent# monographs [l, 231. The large number of such processes can be divided into three major groups: (1) Condensation and sublimation of substaiices in rapidly cooled airgas mixtures. This group includes all smokes produced b y heat and combustion. Typical substances formed in large quantities in this way are ashes, soot, tar products, as well as sulphuric acid and sulfates in cases where the fuel contains sulphur. The variety of particles which can be formed in this way by industrial installations is, of course, enormous and of considerable importance for the production of aerosols in continental atmospheres. The sizes of these particles cover a wide range, but are primarily within that of the Aitken nuclei. ( 2 ) Reactions between trace gases through the action of heat, radiation, or humidity. Examples are the formation of NH&1 in the presence of NH, and HC1 vapors, the oxidation of SOt to SO3, and the oxidation processes yielding higher iiitrogeii oxides by the action of heat, ozone or short -wave radiation. ,111 these processes are efficient sources of Aitken nuclei. Because of the small size of the particles formed in most of these reactions, even large particle concentrations represent only minute fractions of the reacting gases. This is best illustrated by the careful investigatioii of SO? ouidation. Gerhard [24] found that SO2is directly oxidized to so3 by solar radiation at a rate of 0.1% to 0.2% per hour. This SO3 immediately forms droplets of H2S04in the presence of watcr vapor in normal air. An SO2 concentration of 10 y 'meter3, which can be considered average for coun-

ATMOSPHERIC CHEMISTRY

19

try air, would yield about 0.03 y/meter3 H2SO4per hour. This value corresponds approximately to the following particle concentrations: 106/cm3 with a radius of 5 X p, 104/cm3with p, and 3 X 102/cm3with 3 X p. These concentrations are quite high, though we should bear in mind that they would actually be reduced considerably due to rapid coagulation with each other, or with larger particles already present. Though this photochemical process is apparently a very efficient Aitkennuclei producer, it is still of minor importance compared with the sulphate formation resulting from oxidation of SO2 in cloud and fog droplets (see Section 3.9). (3) Dispersion of material a t the earth’s surface, either a s sea spray over the oceans, or as mineral dust over the continents. I n contrast t o processes 1 and 2, which generally yield particles below 1 1.1 radius, the mechanical and chemical processes considered here usually produce much coarser particles, of which only those with radii below 10 to 20 p remain as aerosols for any appreciable length of time. While the sea-salt mechanism has been fairly well investigated, very little is known about the role of mineral dust and soil particles in the aerosols. This is partly due t o the fact that dust and soil particles consist for the most part of insoluble matter, which makes quantitative analyses in the microgram range very difficult. It becomes quite obvious from this brief survey that the numerous possible sources of natural aerosols do not permit us to draw any conclusions as t o the composition of aerosols in general and of the Aitken particles in particular. A third indirect method to obtain information on the composition of the Aitken nuclei was by statistical correlations between the concentrations of Aitken nuclei and the geographical location, season, wind direction, and general weather situation. The large number of observations have been carefully examined by Flohn, Burckhard, and Landsberg [ l , 251. All the interrelationships found thus far point t o continental areas with dense populations and much industry as the major sources of Aitken nuclei. The Aitken nuclei turn out to be a very sensitive index of air pollution, though they in no way represent an important pollub ant themselves. But again the results of these investigations fail to answer the question of their general composition. Despite the development of the electron microscope and of advanced microchemical techniques, this situation has not changed in recent years. It is true that some of these methods are well suited for the analysis of particles above 0.1 p radius; however, identification of particles below this size by examination of electron micrographs becomes nearly impossible. Moreover, the amount of material in the Aitken particle range is

CHRISTIAN E. JUNGE

20

so small and its precipitation and separation from the much larger amount of aerosol material above 0.1 p radius so difficult, that the chemical composition of the Aitken nuclei in our atmosphere is still an open question. Two facts may be of some help in this situation: the similarity in the respective growth curves of the Aitken and the giant particles in Fig. 7 and the mass exchange by coaguIation between the Aitken and the large particles according to Fig. 5. From these we may infer that there probably is not very much difference between the composition of particles with radii smaller and larger than 0.1 p. This conclusion is supported by the observation that a large number of aerosol sources produce particles over a wide size range from about 0.01 p up to 1.0 p . However, for particles above 0.1 p some results on their chemical composition are available, which will be discussed in the next sections.

2.6.Sea-Salt Aerosols Until recently it was generally assumed that the foam from breaking waves, as wind-carried spray, provided the main source of sea-salt nuclei.

I

,. 9

Water Surface

FIG.9. The formation of sea-salt particles from the bursting of bubbles. The large droplets ( W ) originate upon disintegration of the jet; they have been investigated thoroughly by Woodcock 1261. More numerous, though much smaller, particles (M)formed from the bursting bubble jilm have been assumed by Mason [27].

However, apart from those that originate in surf, such particles are not very numerous and are also too large to remain in the air for any considerable length of time. Woodcock and his co-workers were able to show that the numerous small air bubbles bursting in the foam of waves represent a much more effective source of sea-salt nuclei [26].Figure 9 shows schematically how the bursting of a bubble creates a small jet, which shoots high into the air and breaks up into about 5 t o 10 droplets of nearly the same size. The droplet size is about %,J that of the air bubbles,

ATMOSPHERIC CHEMISTRY

21

so that the size distribution of the particles is determined t o a large extent by that of the bubbles. Woodcock suggests that the lower size limit of the bursting bubbles is determined by the solution of the smallest bubbles if the sea water is not saturated with atmospheric gases. So far it has not been determined whether this, or a purely mechanical process, limits the size of the droplets. After their formation the droplets of sea water shrink to about one-third their original size, due to evaporation, until they are in equilibrium with the humidity of the surrounding air. Besides the particles formed in the jet of bursting bubbles, Mason [27] suggests that about 100 much smaller particles are formed from the remnants of the thin liquid film which covers the bubble prior to breaking. Researchers who have supported the thesis that the sea-salt particles play a n important role not only with respect to the amount of substance but also in terms of particle number have always been disturbed by the fact that considerably more Aitken nuclei are found over land than above the ocean. They therefore welcomed observations which indicated tJhe possible subsequent occurrence of an increase in the sea-salt nuclei. For instance, some have claimed that when a sea-salt particle dries and crystallizes very rapidly, it shatters into several fragments; more recently it has been stated that the drying of sea-salt particles which were attached t o spider threads produced a large number of very small particles [28]. The first process was not verified by a careful check [29]; nor did unpublished investigations of the author substantiate the second process when spider threads were not used. Rau’s measurement [30] in Central Europe certainly prove that the number concentration of chloride particles is of no importance in the interior of a continent. It might very well be th a t a fraction of the chloride particles which Rau counted in the range of the large nuclei are still of continental origin (see Section 2.6). The question now arises a,s to whether the sea-salt particles produced in this manner havc and maintain the same composition as sea water. Our information is quite poor on this question. Neither Facy’s notion [31] that there is an increase of Mg in the particles produced by bursting of bubbles, nor Cauer’s view [21] that C1 is released from the sea-salt partoiclesthrough the action of ozone, are anything more than hypotheses. More impressive is the finding made by Swedish researchers and others [32] that in rain water the ratio of C1 to Na over land deviates considerably from that of sea water. But we will see in Section 4 that this is probably due t o additional Na and C1 sources over land rather than t o a decomposition. The few direct analyses of marine aerosols so far do not indicate a decomposition. Twomey [20] found that sea-spray particles undergo a phase change from crystal to droplet a t the expected relative humidity and concluded that their composition must be the same as sea

22

CHRISTIAN E. JUNGE

water. Junge [ l l ] analyzed sea-salt nuclei in Florida for C1, Na, and in some cases, also for Mg, and found agreement with the composition of sea water within the limits of accuracy of his analytical method. Very good agreement of the C1, Na, and Mg ratio with that of sea water was found in rain water by Gorham in North England [33]. Since the air masses which arrive there from the Atlantic are influenced very little by the European continent, these data are of special significance. It appears from these measurements that any decomposition of sea-salt particles, if it occurs a t all, can only take place very slowly. Additional studies along this line are necessary. Of basic importance for the role which the sea-salt particles play within the natural aerosols is their size distribution. Data above or near the ocean for different wind forces and at various heights have been obtained by Woodcock, Moore, Fournier D’Albe and Lodge [12, 34-36]. All these researchers were primarily interested in the giant nuclei because of their importance for cloud physics. Woodcock and Moore collected particles on small plates which they exposed to the wind or the air stream from an aircraft. Aerodynamic conditions restricted this collection to particles above 1 p radius. Fournier d’Albe used a cascade impactor, but counted only particles above 2 p radius. The particles counted in these investigations were assumed to consist of sea salt. The circumstances of the investigations as well as the physical behavior of the particles certainly justify this assumption. Lodge employed a microchemical method specific for chloride. The particles were collected on the surface of fine membrane filters and identified by their reaction with mercurous fluosilicate. The size of the resulting color spots can be calibrated in terms of the original particle size. The results of the various sea-salt-particle counts agree quite satisfactorily (see Fig. 4).Some of Woodcock’s measurements, which he made a t a height of about 600 meters and primarily in the region of the trade winds of Hawaii, are also plotted in Fig. 10. With increasing wind speed the increase in the concentration of the largest particles is somewhat more pronounced than that of the smaller ones; however, on the whole, the character of the size distribution changes only slightly. Unfortunately, a t present there are no measurements of marine aerosols below a radius of 1 to 2 p. Based on chemical analyses, Junge [37] found that in the pure sea air of Hawaii the C1 concentration of nuclei with radii between 0.08 to 0.8 p amounts to only 1.501, of that of the nuclei with radii between 0.8 to 8 p. This result was used in Fig. 4 and Fig. 10 for extrapolation of the curve for Beaufort 3. According to this tentative extrapolation, the most frequent size of the sea-salt particles should lie around a radius of about 0.5 p. This seems t o agree with Isono’s

23

ATMOSPHERIC CHEMISTRY

L

=T I -B 0

1.0-2

10-1 1,oo 10' .lo2 PI radius at 993 relativle humidikv 10-1"

1043

10-10

10-7

I

Iwelghf of ska,sal/ inlpo,rtir+e gr FIG.10. Average size distribution of sea-salt particles according to Woodcock [12] for wind forces 1, 3, 5, and 7 Beaufort. The dotted line, a, gives the size distribution at Frankfurt (Fig. 3) for comparison. The dashed line, b, is the extrapolated size distribution of marine particles according to Fig. 4. The various scales a t the bottom allow a comparison of the different units used in the literature to indicate the size of sea-spray particles.

24

CHRISTIAN E. JUNGE

observations [38] that the residues of evaporated snow crystals contain many NaCl crystals of this size. The total number of sea-salt nuclei estimated from Fig. 10 is 2 per cms for Beaufort 3 and is not expected t o exceed 10 to 20 per cms a t higher wind speeds. The data on total sea-salt nuclei are compiled in Table 11. There is strong evidence that the majorTABLE 11. Data on the total concentration of sea-salt particles.

0b ser v er Woodcock

Fournier d’Albe

Moore

Rau

Junge Moore

Remarks

Total number concentration/cms

Beaufort 1 0.05 3 0.15 5 0.30 7 0.36 12 20 All particles larger than I p radius a t 80% 2 X 10-4 to 0.3 relative humidity in Pakistan a t various distances from the coast. The particles probably predominantly of marine origin. All particles larger than 2 p a t 80% relative humidity over the Atlantic a t 10.5 meter/sec wind 0 . 3 15 meter /sec wind 0 . 8 Maximum numbers during 0 months of Max. . . . . . . . . 18 observation in Central Europe of all 96% of all chloride particles larger than 0.25 p observations, . f 1 radius a t 80 %, relative humidity. Estimated total number of sea-salt nuclei 2-10 for average wind speeds (Fig, 10). Lowest Aitken counts over the Atlantic 77 during 3 weeks of observation Average 703 All particles larger than 1.5 p radius a t 80 % relative humidity for various wind speeds.

..

ity of the Aitken nuclei, even over the ocean where they reach their minimum concentrations, is not of maritime origin. This is confirmed by Moore [34] who found no relationship between the Aitken nuclei and the wind force or wave height over the Atlantic Ocean, quite in contrast to the giant particles. It is probable that these Aitken nuclei are remnants of continental aerosols. I n this connection, a few words should be said about the controversy between Wright [39] and Simpson [40] over the role of sea-salt nuclei with respect t o visibility in marine air. Simpson claims that the constancy of visibility with humidity below 70% precludes any change in particle size in the optically important size range. If the particles were composed of sea salt, the process of crystallization, even if distributed over the humid-

ATMOSPHERIC CHEMISTRY

25

ity range between 40% and 70% due to supersaturation of the solution [Fig. 7(a)] would cause a significant variation in visibility. This variation, however, is not observed. It must therefore be concluded, in agreement with Simpson, that the major part of the large particles in Valentia even with west winds are not of maritime origin [41]. This appears t o be probable, because, according t o Fig. 10, the concentration of sea-salt particles below 1 p is small compared to that of continental aerosols and because continental aerosols penetrate far over the oceans as we shall see later.

W I N D FORCE

FIG.11. Sea-salt concentration over the ocean (Woodcock [12],Moore [34]) or a t the coast (Fournier d’Albe, cited in [34], Junge [49]) as a function of the wind force.

On the basis of the data in Fig. 10 we may infer a close relationship between the total content of sea salt in the air and the wind force. Woodcock [12] showed that all his measured values fall between the two dashed lines in Fig. 11. His observations were usually made slightly below the base of the clouds (at a height of approximately 600 meters) in the tradewind regions of Florida, Hawaii, and Southern Australia. We have supplemented his data with the values of Fournier d’Albe, Moore and Junge [42], obtained at sea level. Considering the different conditions under which these observations were obtained, the agreement is quite surprising and indicates a generally valid relationship. As this relationship permits quite reliable estimates of the amount of airborne sea salt under

26

CHRISTIAN E. JUNQE

varying conditions, an attempt will be made t o explain this phenomenon. To do this we must examine more closely the vertical distribution of the sea-salt nuclei above the ocean. Figure 12 represents some examples of the vertical distributions under trade-wind conditions, which Lodge [36] obtained near Puerto Rico. We see that the number of particles decreases exponentially with height, independent of particle size. The slope

2000

* .-c d 1000

E

lo-’

part i d e s per cm3

-

10-3

FIG. 12. Average vertical distribution (based on data from 5 flights) of sea-salt particles of various sizes on the windward sidc of Puerto Rico, according to Lodge [36]. These observations are compared with calculated distributions under the assumption of a production of 5 X loT3 cm-2 sec-1 particles at the surface of the sea, a n average austausch coefficient of 255 gm om-2 sec-1, and an inversion layer a t 2000 meters. At time 1 = 0 the particle concentration was assumed to be zero a t all altitudes.

of the curves varies with the individual measurenients and is sometimes only weakly indicated. Lodge’s measurements are the only ones available which cover the space below the cloud base (which is particularly important here). On the basis of the available observational material (including Figs. 10, 11, and 12) the following main features become evident for the height distribution of sea-salt nuclei and their dependence on the wind: (1) A fairly good relationship between wind force and total salt content in the mixing layer over various parts of the oceans. (2) A more or less well-pronounced exponential decrease with height of the particle numbers with varying slope. (3) Independence of the vertical distribution of particle sizes.

ATMOSPHERIC CHEMISTRY

27

These features, established predominantly on data from regions of the trade winds, can be adequately explained by the following model. The surface of the ocean produces a constant amount of particles per unit surface and unit time for each wind force. If these particles are smaller than the critical fall-out radius, a large percentage of them penet.rates into higher layers. Given the vertical distribution of the eddy diffusion, the nuclei concentration can be computed as a function of height and time [42]. Such computations show that the time-dependent vertical particle distribution is little influenced by the assumed vertical distribution of eddy diffusion but depends almost entirely on the average austausch coefficient. The calculations in Fig. 12 are based on an eddy diffusion (represented by the austausch coefficient) which a t first increases linearly with height and later approaches a convection-controlled constant value, thus approximating the actual conditions quite closely. We see how the concentration increases rapidly at first and then more slowly with time and how the vertical gradient is approximately exponential, becoming increasingly steeper with time. Naturally, below the size limit of 10 to 20 p this process must be independent of the particle size. The calculation was based on the assumption that the trade-wind inversion, which stops further vertical mixing, was situated a t an altitude of 2000 meters. However, the result would not be essentially different without this assumption. After a certain initial time has elapsed, the concentration in Fig. 12 increases only slowly with time and height and then becomes essentially proportional to the wind-force-dependent particle production rate. Generally we should thus find a relationship between the salt content and the wind force as indicated in Fig. 11. Naturally, in the atmosphere there are further complicating factors such as time and space variations of the wind force, cloud formation, and precipitation. Hence, we can expect this model to conform only approximately to natural conditions. Observations show that sea-salt particles can penetrate far into the interior of the continents. On a flight over the USA at a height of 3000 meters, Seely and his colleagues [43], employing a microchemical method, counted chloride particles larger than about 10-13 gm (= 0.5 p radius at 80 % relative humidity). The highest number concentration of 0.46/cm3 was encountered in an air mass of marine origin. On a 600-mile flight over the southeastern corner of Australia at a height of 700 to 2700 meters, Twomey [44] counted hygroscopic salt particles (probably all sea-salt nuclei) which were larger than 10-lo gm (= 4 p at 80% relative humidity). He found little correlation between the particle number and the watervapor mixing ratio, the distance of the trajectory of the air mass over land, and the length of time since the air mass had crossed the coast.

28

CHRISTIAN E. JUNGE

However, his values show that convection over land rapidly works toward the creation of a uniform vertical distribution of sea-salt nuclei. The basic difference in the vertical distribution of sea-salt particles over land as a result of mixing is best demonstrated by Fig. 13. On several flights in Illinois and southward toward the Gulf of Mexico, Byers and his group [45] measured the size distribution of salt particles with Lodge’s microchemical filter methods. Figure 13 gives their mean concentrations for particles with a dry radius larger than 3 p. For comparison

FIG. 13. Vertical distribution of the number of sea-salt particles having a dry radius 23 p (equivalent to a radius of 7 p at 80% relative humidity and a mass of 5X gm). The curves marked W are measured by Woodcock [12] in regions of the trade winds; the portion of the curve beween the ocean surface and the measured values around 0.5 km is assumed. The values show the rapid decrease a t the level of the trade-wind inversion. The curves marked B are given by Byers [45]. B 1is a n average of three soundings made in Illinois. Bz are average concentrations for four overland flights southward from Chicago. The lengtth of the bar indicates the altitude range during each flight.

we have also plotted Woodcock’s figures for the corresponding particle size [12], which he obtained in the trade winds, and which are probably also representative of the Gulf of Mexico. Lodge’s absoEute numbers obtained in Puerto Rico are not reliable enough for comparison here. The main finding of Byers’ flights is that in general the particles are fairly uniformly distributed horizontally and vertically, with a mean value of approximately 300/meters. The sharp drop in the lowest 200 meters apparently caused by fall-out and impaction of particles on trees, etc., is an interesting phenomenon. It shows that the earth’s surface can act as

ATMOSPHERIC CHEMISTRY

29

a sink for aerosols, a t least for giant particles, so that surface measurements must be interpreted with caution. The total number of sea-salt particles above 1 meter2 over land and ocean can be estimated on the basis of Fig. 13. From Woodcock’s data we obtain a value of 1.8 X lo8per meter2 and from Byers’ data, 2.3 X lo6 per meter2.’ The approximate agreement of the two figures indicates that the loss of sea-salt nuclei due to precipitation is small, even in air masses which are 1000 miles from the coast. We will return to this question in Section 4.4. A marked increase in sea-salt nuclei has been observed in the immediate vicinity of the coast, a phenomenon which can lead to chloride values of 50 to 1000/metera [46]. Due to fall-out, impaction, and vertical mixing the concentration of these local and shallow sea-spray clouds from surf areas rapidly decreases inland by approximately 1 to 2 orders of magnitude in about 10 km. 2.6. Continental Aerosols The invention of the electron microscope presented new possibilities for obtaining information on the nature of the natural aerosol particles. Such investigations were made primarily in Japan. Kuroiwa [47] obtained evidence on the origin of particles by observing the changes of their structure after repeated exposures to humidity; Yamamoto and Ohtake [48] obtained similar information from observing evaporation of nuclei substance in connection with an intensity increase of the electron beam; Isono [38] made electron diffraction diagrams of individual aerosol particles. These researchers investigated exclusively particles found in fog or cloud elements, i.e., true condensation nuclei. Among these particles, which were in the main larger than 0.1 p, they found many minerals from the soil, combustion products, as well as sea salt. Jacobi and Lippert [8] determined the presence of ammonium sulfate in continental aerosols by electron diffraction. The electron microscope, however, as an instrument for investigating aerosols has its limitations. The shape of the particles and their physical behavior under electron bombardment preclude any definite conclusions about their chemical composition. Even the electron diffraction method can detect, of course, only those components which are present in a crystallized form, but even for these no quantitative data can be obtained on the actual amount of material. On the basis of these shortcomings of electron-microscope techniques, it proved advisable to employ more direct microchemical methods. TWO 1 Here, we assume a uniform mixing over an altitude range of about N of the atmosphere.

30

CHRIBTIAN E. JUNQE

particles size ranges, 0.08 S r 4 0.8 1.1 and 0.8 5 T 5 8 p, which represent approximately large and giant particles, respectively, were separately collected in a cascade impactor [8]. I n accordance with Fig. 4 both size ranges should yield about an equal mass in continental aerosols. The aerosol samples were precipitated on Plexiglas plates, dissolved with a drop of distilled water, and then analyzed for NH4+, Na+, Mg++, Sod--, C1-, NO3-, and NOz- by spot test, turbidity, or in case of Na, by polarographic methods [49, 111. The selection of these chemical components for test was partly determined by the sensitivity of available methods, so as to make possible the detection and determination of a few tenths of a y of material with a reasonable accuracy of +20%. The first measurements were carried out in densely populated areas of West Germany. They confirmed the electron diffraction pattern with respect to the ammonium sulfate content [8]. In the large particles NH4 and SO4 were apparently essential constituents of the soluble material. The ratio of these components was approximately that of (NH4)zS04. On the other hand, in the giant-nuclei range only a small amount of NH4 was found and it must be assumed that a considerable fraction of the SO4 was bound to another cation. In Frankfurt no analysis was made for NO,, and the analyses for NO2 invariably gave negative results in both size ranges. The C1 analyses confirmed its presence in both size ranges. With advection of maritime air the C1 concentration increased in the giant particles and decreased in the large particles. This indicates that the seaspray component of the natural aerosol is limited to particles larger than 0.8 p, and that smaller C1 particles are of continental origin. These findings have been completely confirmed by measurements made at Round Hill on the east coast of the USA [49]. I n contrast to the site in Germany this coastal setting is entirely rural, although air masses in this area are to a certain degree still influenced by the industrial and more densely populated regions of the northeastern part of the United States. Analyses were made for NH4+, Na+, Mg++, SO4--, C1-, NO3-, and NOz-. Figures 14 and 15 give the daily values of the analyses. Here, NH4 and SO4 again predominate in the large nuclei and show about the same mass ratio as in Frankfurt. In Fig. 16 the NHa values are plotted against the SO4. It appears that they are present as (NH4),S04 and NH4HSOI (with the exception of one value in sea fog). Here, C1 and Na were found almost exclusively in the giant nuclei, even when the wind came directly from the ocean, which was not more than 100 meters away. The large nuclei contained C1 and Na in amounts above the limit of detection in only a few cases. This shows that the sea-salt component was quantita-

-

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IY I* 0

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C w / r e +01

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t

ATMOSPHERIC CHEMISTRY

t n * N

E

n

ii

6 0

L

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o

$ 0 " Y

a 0

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z

2

4

2

4 2

t

SEA FOG

JUNE

t

t

SEA FOG SEAFOG

JUNE

t

JULY

SEA FOG

FIQ.15. The same as Fig. 14, but for giant particles. (By courtesy of the Journal of Meteorologg.)

ATMOSPHERIC CHEMISTRY

33

I

I

I

I

I1

0

E

‘ f a

0

.I ’ In

E

5

4

3

2

I

NH.‘

10-8~r/m’

FIQ.16. Relation between SO1-- and NH4+ content for large particles a t Round Hill. Each set of values is represented by a line indicating the limits of accuracy. The line corresponds to (NH4)zSOn. (By courtesy of the J O U T n d of Meteorology.)

tively confined t o giant nuclei, a fact that has been confirmed in all subsequent measurements. Again, no NO2 was found; however, the results of the NO3 analyses were surprising. Similarly t o C1, NO3 was limited almost exclusively to giant nuclei and a relationship between the C1 and NO3 contents seemed indicated. These findings at Round Hill were later confirmed in the trade winds

34

CHRISTIAN E. JUNGE

of southeastern Florida and also in Hawaii [ll].The data obtained in Florida are plotted in Fig. 17, together with the values of gas traces, which will be discussed later. With the exception of sea salt, all components show essentially smaller concentrations. We note that, when obtained under like geographical conditions, the C1 and Na analyses agree well with those of Woodcock and others (Fig. 11). All results for large and giant particles are summarized in Figs. 18 and 19 and are arranged by sampling sites in order of increasing maritime influence with arbitrary equal spacing. The figures contain mean concentrations and, in the case of the maritime sites with their low values, also the average detection limits of the various components. For the sake of clarity, the difference between the two is indicated by hatching. An NH4 value for large nuclei, obtained above the trade-wind inversion in Hawaii (Mauna Kea 3200 meter), is included. Figure 18 shows a decrease of all values with increasing maritime influence. Here, SO4 and NH4 follow nearly a parallel course up to the Florida notation; from there on the determination of SO4 was no longer possible, due to the comparatively high detection limit. The line “b-b” represents the sulfate content, which corresponds to the observed NH4 content and the formula (NN4)zS04.The actual SO4 values are a little higher; however, the major portions of NH4 and SO4 are reciprocally bound. Very likely a corresponding SO4 content would have been found on Hawaii and on Mauna Kea also, had a more sensitive method been employed. Chlorine decreases up to the Florida line and then starts to rise. The line “u-a” corresponds to 1.5% of the C1 content of the giant nuclei of Fig. 19 and thus gives the average maritime C1 component in the large nuclei range. The difference between the actual C1 values and the line “ a-u” indicates the continental C1 component in the large-particle size range. The nitrate content of the large particles is small and there are no figures available for Frankfurt. The giant-nuclei composition curves shown in Fig. 19 present a similar picture for NH4 and sod, the only difference being that the SO4 surplus is essentially more marked at all sites. I n Hawaii the SO4 content increases again due to its presence in sea water. This maritime SO, content is computed on the basis of the C1 values and represented by line “a-a.” The trend of the C1 values is completely different from that of all the other components, indicating at once its marine origin. The NOs exhibits a surprising feature: the results from Round Hill point to a marine origin, but the curve in Fig. 19 does not. Summarizing, we can state that the sea-spray component can clearly be distinguished from that of continental origin, and that the injluence

'C

It

LARGE PARTICLES

GIANT PARTICLES

GAS

10

LARGE PARTICLES I

GIANT PARTICLES I

IC

LARGE PARTICLES

.

n

€

5

GIANT PARTICLES

k .

ul

t

3 z

w 2 4

0

1

cn

GAS

5

I LARGE PARTICLES

I GIANT PARTICLES I

10

DUST

RAIN

rzm==--

JULY I AUG FIG.17. The chemical composition of large and giant particles in Florida [ll]and the concentration of the gases NH,, NOZ,Clt, (?) and SOZ, measured simultaneously and plotted as NH,, NOI, C1, and SO1 for better comparison. 8 and L indicate sea and land breeze, respectively. Note the different scales for gases and aerosols! (By courtesy of Tellus.)

35

36

CHRISTIAN E. JUNOE

of the latter can be traced as f a r as the middle of large oceans. This is the counterpart to the penetration of the sea-salt particles into the interior of the continents. On Mauna Kea, above the trade-wind inversion, ammonia was detected in the large particles, but no C1. This might well indicate a continental rather than a marine history for these air masses.

n

E

\

h

0.01

CONTINENTAL

c-----)MARITIME

sites are arranged with respect to their continental and maritime character. The shaded areas indicate the difference between tho actual values and the corresponding limits of detection, Lines "a-a" and "b-b" are explained in the text. (By courtesy of Tellus.)

However, more observations are necessary to confirm this interesting observation. Figures 18 and 19 give a clear answer to the old controversy over the role of continental and marine aerosols. It is emphasized that the components quantitatively determined may not represent the total soluble substance of the aerosols, For instance, rain-water analyses show that con-

37

ATMOSPHERIC CHEMISTRY

siderable amounts of Ca are encountered over land, and that additional amounts of Na, C1, and Mg also occur. However, NH4 and SO4 certainly appear among the prevailing components in the large-particle range. As for NO3,its continental origin is not as evident as, e.g., for NH, and Sod. Additional investigations in the vicinity of Boston show that during advection of air from the interior of the continent the NO8 content

B

GIANT PARTICLES

SO;-

+

0 NU4

A

-!-I

O.O1

t

I

t

WINTER SUMMER FRANKFURT

t

ROUNDHILL

CO NTINE NTALC------,

NO; I

CL-

t

FLORIDA

,-T

t

HAWAII

MARITIME

FIQ.19. The same as Fig. 18, but for giant particles. (By courtesy of Tellus.)

decreases to values comparable to those in Fig. 19 for Hawaii; and that with the influx of marine air the NO3values become comparable to those from Round Hill. Furthermore, parallel measurements of the NO3 content in the center of Boston and in the suburban area show that urban atmospheres are not an important source of NO3. We can summarize the facts on the NOS content of the aerosols as follows: (1) With a few exceptions in or near Boston, NO3 was always confined t o the giant nuclei.

38

CHRISTIAN E. JUNGE

(2) The smallest concentrations were found at the center of the ocean and in pure continental air masses. (3) The largest concentrations were found in marine air masses on the northeast coast of the USA. (4) The increase of the NO3 content in the polluted atmosphere of Boston compared to the level of the unpolluted atmosphere in its suburbs was much less than, say, that of NH4. These observations suggest that NOs possibly forms in sea-salt particles in coastal areas when they come in contact with the higher NO2 concentrations of continental air. Woodcock has personally suggested to the author that nitrate may be formed in sea-spray droplets by decomposition of marine micro-organisms. At certain seasons the marine areas along the east coast of the USA are rich in these micro-organisms. However, the available observational material is still too sparse for such speculations; besides, the rain-water analyses, which we discuss below, present a different picture. A comprehensive study of the composition of aerosols in polluted atmospheres was recently undertaken by the U.S. Public Health Service [50]. This study is important for the problems under discussion, since a considerable fraction of the continental aerosols come from these sources. Under this program, in thirty cities for a little more than a year, aerosol particles larger than about 0.3 p were collected on glass filters. The numerous chemical components determined were selected with regard for their importance to air hygiene. Tables I11 and IV give the average values for medium-sized cities and nonurban areas. These nonurban areas are mostly suburbs and, therefore, may not be quite representative of the undisturbed background of country air. The only components which were also investigated by Junge are SO4 and NO3. The reported concentrations agree satisfactorily with the corresponding values of Figs. 18 and 19. So far as can be concluded from the few NO3values, the cities are less efficient sources for NO3 than for so4 and NH3, a conclusion which is in agreement with the observations in Boston. There are two interesting exceptions with respect to the NO3 content in the Public Health network; the high values in San Francisco (3.4?/meter3) and in Los Angeles (14.4 ?/meter3). Both are coastal cities and it is very tempting to regard these data as confirmation of the abovementioned conditions for the formation of nitrate in areas near the coast. The other components show the strong influence of certain industries, (e.g., the relative high F1 values) and of automobile traffic (Pb). The high percentage of acetone-soluble organic components shows that the

39

ATMOSPHERIC CHEMISTRY

TABLE111. Particulate analyses from cities having populations between 500,000 and 2,000,000. (Average values in ?/meters.) Cineinnati Total load Acetone soluble Fe Pb

F-

176

PortKansas land City (Oregon) Atlanta 146

143

137

31.4 4.5 1.6 0.21

Mn

cu V Ti Sn As Be

sod-N01-

San Francisco

Houston 129

18.4 24.2 S9.1 4.1 6.1 3.3 1.2 1.o 1.8 0.01 Nil 0.05 0.23 0.12 0.94 0.08 0.01 0.18 0.04 0.05 0.09 0.002 0.024 0.009 0.24 0.06 0.21 0.12 0.01 0.0s 0.0s 0.0s 0.02 0.09 0.09 <0.01 0.0002 0.0003 0.0003 0.0002 6.6 1.5 0.8 1.o 1.o 0.6 0.2 0.8

104

18.5 4.0 1

19.4 2.4

.o

9.4

Nil 0.23 0.02 0.001 0.29 0.02 0.01 0.0002 2.4 1.o

0.ST 0.11 0.07 0.002 0.04 0.02 0.01 0.0001 1.8 3.4

Minneapolis 120 15.8 4.4 0.5 0.06 0.08 0.60 0.002 0.11 0.01 0.01 0.0002 0.8 1.3

TABLE IV. Particulate analyses from nonurban areas. (Average values in ?/meters.) Boonsboro Salt Lake City Atlanta Total load Acetone soluble Fe Pb FMn

cu V Ti Sn As Be Sod--

NO$-

68

8.7 3.7 0.1

-

0.00 Nil 0.003 0.26 <0.01

0.01 0.0001 0.3

-

55 6.2 4.1 0.1 0.04 0.28 Nil Nil <0.01 0.03 <0.0001 <0.01 -

71 9.3 2.7 0.9 Nil 0.11 0.01 0.004 0.13 <0.01 0.01 0.0002 0.5 -

Cincinnati 45 9.0 2.4 0.4 0.26 0.07 0.19 <0.001 0.01 0.01 <0.01 0.0001 1.9

0.7

Portland (Oregon) 86 12.6 3.6 0.3

-

0.04 <0.01 0.002 Nil <0.01 0.04 0.0001 0.4

-

main part of the collected material comes from combustion processes and other artificial sources, even in the nonurban areas, But by and large the composition of the aerosols seems to be strikingly uniform. The average concentration of the total particulate material is 65 and 136 ?/meter3 for nonurban areas and medium-sized cities, respectively.

40

CHRISTIAN E. JUNGE

A comparison with the log-volume distribution of Fig. 4 proves to be quite interesting. The curve for Frankfurt gives a total volume of 80 X cm3/meter3. If we assume a density of 1.5 for the aerosol material a t medium relative humidities, which seems to be a reasonable value, the concentration of the total particulate material is 120 y/meter3, in good agreement with the values of Table 111. Nonurban observations a t the Taunus Observatory in Central Europe (800 meters above m.s.1.) give volume concentrations of 50 X cm3/meter3, a value which would correspond to 75 y/meter3 total material. This figure agrees closely with the nonurban values in Table IV. This confirms the experience of the author that the total particular material fluctuates much less with time and space than does the number of Aitken nuclei. Unfortunately, no data on the total amount of water-soluble material is given in the report of the U. S. Public Health Service. Judging from the data of Tables I11 and IV, the soluble portion of the material is small. The same conclusion was drawn from the growth of aerosol particles with humidity (Fig. 7) and from our findings in Frankfurt, where only 10% to 20% were soluble. The major insoluble substances are probably soot, tar, and ashes in polluted areas (see Section 5 ) , substituted by mineral dust (i.e., disintegration products from the earth’s surface) outside densely populated areas. Both rain-water analyses and investigations of Kumai, Isono, and others indicate that the role of this dust apparently has been underestimated. Water-insoluble substances are unfortunately difficult t o analyze quantitatively, so that more detailed data on these chemical components are almost completely lacking. Moreover, nothing is known about the particle size distribution of these dust components in the atmospheric aerosol. The airborne dust particles represent the lowest end of a very broad particle size distribution of soil material, i.e., that below 10 p, and are, therefore, primarily found in the size range of the giant and large particles. The significance of this size limit for airborne transport of soil particles is well demonstrated by the particle sizes in loess deposits. Loess deposits in Illinois, for instance, show an average particle radius of 15 p near the source area; this radius decreases rapidly and then more slowly to 8 p over a distance of 100 km [51]. Considering the density of the soil material, which is greater than that of water (the basis for the calculations of Fig. 6), we should expect an upper limit of T = 6 to 11 p , which conforms well to the observed values. That particles below this size limit can cover great distances in the atmosphere is substantiated by the frequently observed Sahara-dust falls on islands west of Africa and in South and Central Europe. The following data on this dust have been taken from an investigation made by Glawion [52]:

ATMOSPHERIC CHEMISTRY

Particle size: 68%

I 1 p, 24% 5 1-2

p,

41

8 % I 2 p.

Chemical composition : SiOz 37-75 %, Fez03 6-22%,

&03 0-20 %, Mn304 2-4%,

1-16 % Ma0 0.&3%

CaC03

I n addition, small amounts of K, Na, Cu, HzS04, and HCI. Certain components (e.g., the oxides of iron and of manganese) appear strongly enriched compared to the source rock. Probably each chemical component in stone and soil disintegrates in its own peculiar way, a process which then determines the size of the particles and the frequency of their occurrence in the aerosol. In other words, the physical and, above all, the chemical disintegration process acts selectively with respect t o the production of dust, so that its composition is not the same as th a t of the source material. Unfortunately nothing is known about these processes. Brief mention must also be made of meteoric dust, which has importance for some geochemical relationships. Spherical and angular particles, which are magnetic and contain iron-nickel compounds, have been observed a t the earth’s surface and in deep-ocean sediments (see e.g., [53]). Their concentration in the atmosphere is very small, so that a collection is possible from comparatively large samples of rain water only, The particle radii vary from a few microns up to 150 p. The most frequent value is about 5 p. However, this lower size limit may be determined by the collection process. Observations of greater concentrations of “spherules” a few days after meteor showers confirms their cosmic origin; but Schaefer [54] has pointed out that industrial products with similar properties predominate in certain regions, so th at any interpretation of meteoric dust must be undertaken with great caution. On the basis of data for the total annual amount of meteoric dust, we may expect a tropospheric concentration of 5 p part,icles amounting t o about 1 per 100 meter3. Such quantities are unimportant for atmospheric chemistry. Some researchers found also evidence for the presence of meteoric particles below 1 p a t high altitudes; however, such particles can have no significance either for air chemistry, in as much as only very small concentrations of particles of this size have been observed in the upper part of the troposphere. This question leads to a discussion of the vertical distribution of continental aerosols. Basically the following process is involved : maritime air masses move in over a continent and receive from the earth’s surface additional aerosols, which penetrate into higher layers as a result of mixing. Mixing in the trade-wind areas, discussed in the previous section,

42

CHRISTIAN E. JUNGE

FIG.20. Average vertical distribution of natural aerosol particles in relative number concentrations, according to various investigators (551. All data refer to Central Europe. Curves a and f represent Aitken particles; all other curves, large particles. (a) 28 balloon flights, condensation nuclei (Wigand), (b) 12 summer flights, and (c) 8 winter flights, impactor (Siedentopf), (d) 18 flights, impactor (Rossmann), (e) calculated curves from observations on the attenuation of solar radiation (Krug, Penndorf), (f) calculated curve from 22 flights based on potential-gradient measurements (Rossmann), and ( g ) calculated curve from zenith sky luminance measurements obtained on 18 flights (Siedentopf). Curves e' and g' represent a constant mixing ratio for comparison.

was confined to a relatively shallow layer of 1 to 2 km; mixing over the continents, on the contrary, normally reaches much greater heights, due to the more intense convection, the lack of persistent inversion layers, and the large-scale mixing in the circulation of high- and low-pressure systems. If in a first rough approximation we assume that the resulting eddy diffusion is constant with height, the concentration in an air mass crossing a continent would increase with time and height in a manner

43

ATMOSPHERIC CHEMISTRY

N, x

IONS/C M 3

NORMALIZED PROFILE OF LARGE ION OlSTRlBUTlON

FIQ.21. Aircraft altitude, h, divided by the height of the exchange layer, H, vs positive large-ion concentration, N+, according to Sagalyn and Faucher [56]. (By courtesy of the Journal of Atmospheric and Terrestrial Physics.) DATE 1. 2. 3. 4. 5. 6. 7. 8. 9.

Dec. 29, 1952 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan. 5, 1953. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Feb. 10, 1953. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Feb. 18, 1953. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mar.3, 1953. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Apr.15,1953 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aug. 18, 1953.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aug. 28, 1953 (1400-1445).. . . . . . . . . . . . . . . . . . . . . . . . . . . . Aug. 28, 1953 (1900-1945) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

H

(FEET)

5500 8200 4300 4500 3200 7000 8200 9400 8000

similar to that shown in Fig. 12. We should therefore expect approximately a log-height distribution. Various observations of the mean vertical distribution over Central Europe [ 5 5 ] , given in Fig. 20, generally agree with this conclusion. The decrease in concentration, which is logarithmic, a t least in certain layers, almost ceases a t a height of about 4 to 5 km. The height of 5 km is, therefore, the upper boundary of the Central European mixing layer. Most of the curves in Fig. 20 relate to large particIes; however, the curves for the Aitken and the giant particles are nearly identical. The computation of mean curves, as in Fig. 20, obscures the marked

44

CHRISTIAN E. JUNGE

stratification in individual profiles. The surface layer in particular shows a fairly constant concentration due to intense mixing. This is demonstrated by the observations of Sagalyn and Faucher [56], who measured the charged Aitken nuclei (large ions). To emphasize the typical characteristics of stratification they normalized the height scale according to the upper boundary of the mixing layer and obtained Fig. 21. We see how little the processes of daily convection and mixing influence the atmospheric aerosols above this level. It must be kept in mind, however, that the measurements given in Figs. 20 and 21 were obtained primarily under fair-weather conditions.

3. TRACE GASES 3.1. General Comments Prior to our treatment of atmospheric trace gases, a few remarks should be made about the units used and the selection of gases treated in this paper. The content of gas traces, especially in air pollution, is usually expressed by the ratio of the volume of gas t o that of air (molecular ratio) in terms of parts per million (ppm) or parts per hundred million (pphm). These mixing ratios do not depend on the pressure or temperature of the air and are therefore independent of altitude. To permit comparison with aerosol data, however, the gases in this paper will, as a rule, be expressed in y/meter8 for standard temperature and pressure (STP). I n contrast to the mixing ratio, this unit of concentration depends on pressure and temperature and therefore on altitude. Sometimes the concentrations of gases are expressed in millimeters of gas at STP per kilometer (mm STP/km), which is numerically equal t o 1 ppm at STP. The total amount of gas in the atmosphere is often given by the thickness of the layer of this gas in mm at STP. Since the height of the homogeneous atmosphere is equal t o 7.991 km, this thickness in mm is equal to 7.991 X ppm or 7.991 X mm STP/km, given a constant mixing ratio throughout the atmosphere. The conversion factors for various units including the partial pressure in mm Hg of the gases discussed here are contained in Table V. A closer examination of the substances included in this section reveals that our definition of active trace substances is not rigorous in respect to such gases as COZ and NOz. On the one hand, these gases are quite uniformly distributed and very rarely take part in reactions in the troposphere, thus exhibiting a behavior similar to that of permanent gases. On the other hand, they experience a fairly rapid exchange a t the earth’s surface, resulting in a cycle shorter by several orders of magnitude than that of any permanent gas. Their treatment here thus seems jus-

45

ATMOSPHERIC CHEMISTRY

tified; however, our discussion of COz will be brief, dealing only with the major facts and problems. TABLE V. Conversion factors for mixing ratio, concentration, and partial pressure of trace gases.

Gas

coz Oa N20

NO NOz NHs

so2 SH, c12 I2

co C& CHyO

x y/meter3 STP

1 ppm =

1 y/meter3 STP = x PPm

1 ylmeters STP = X mm Hg partial pressure

1960 21 40 1960 1340 2050 760 2850 1520 3165 11300 1250 712 1340

5.10 x 10-4 4.67 5.10 7.46 4.88 13.15 3.51 6.58 3.16 0.885 8.100 14.05 7 . 4 6 x 10-4

3.87 x 10-7 3.55 3.87 5.67 3.71 10.00 2.61 5.00 2.41 0.672 6.10 10.70 5.67 x 10-7

3.2. Carbon Dioxide

As already mentioned, the presence of COZhas little significance for the chemistry in the troposphere: COZ is very uniformly distributed, is not involved in important reactions with aerosols and gases, and has not very much bearing on rain-water chemistry. The primary reason for our treatment of COZin this paper is its interesting cycle and its apparent increase during the last fifty years [57]. Because of the role of COZ in the heat budget of our atmosphere, this increase should raise the average temperature of the atmosphere by a small, though measurable, amount. Such a phenomenon has actually been observed in various parts of the world; the problem of a COz increase, therefore, is of basic importance for meteorology. The average concentration of COS is generally fairly constant and exhibits only small variations as Table VI indicates [57, 581. Larger, more local fluctuations of COZconcentrations ranging from 200 t o 600 ppm occur in the layers near the ground as a result of the exchange of COS with soil and vegetation. This process has a very pronounced daily cycle. A considerable fraction of the COz cycle takes place directly between the ground and the vegetation and is thus confined t o the lowest layers near the ground. Excess consumption of COz by photosynthesis during the day and excess production during the night give rise

46

CHRISTIAN E. JUNGE

t o a vertical C02 gradient which depends t o a large degree also on the vertical distribution of the eddy diffusion. The amount of data on the height distribution of C02 above these low layers is still very sparse and not reliable enough t o permit conclusions. Of course, no noticeable departures of the mixing ratio with height should be expected since the cycle of atmospheric C02 is estimated t o be of the order of 10 to 20 years and since its horizontal distribution is quite uniform. The representative C02 content a t the present time is about 320 ppm. The COz content of the atmosphere is controlled to a large extent by the composition and the temperature of the water at the surface of the TABLE VI. Average variation (in per cent) of the average COP concentration of different air masseR (Europe [57]), seasons (Europe [57]), and geographical locations [581.

-1 .I

Maritime air Continental air Polar air Tropical air

+'-0.7" +2.5 +0.8

Spring Summer Autum Winter Rural France West Indies South America Cape Horn

average 293.6 ppm

-1.4 -0.1 $0.6 64' N 20" N 40" S 56's

average 294.6 ppm

+4.4

'3

-1.0 -6.9

average 274.8 ppm

ocean. Generally, the partial pressure of CO2 in air seems to be in equilibrium with that dissolved in sea water. Because of the temperature variations of the ocean's surface, this partial pressure is higher in the low latitudes and lower over the polar regions. Buch [59] found the lowest C 0 2 concentrations in equilibrium with the water (150 ppm) in the vicinity of Spitsbergen. A similar low value has been observed near Cape Horn [60].Positive deviations have been found primarily over the COzrich upwelling waters along the coast of West Africa. These observations show that the C02 exchange of the atmosphere with the surface layer of the ocean seems to occur comparatively rapidly. On the whole, however, the exchange between air and ocean is slow because a complete turnover of the ocean water is estimated to be of the order of several thousands of years. The estimates on the various components of the COScycle seem to

ATMOSPHERIC CHEMISTRY

47

agree fairly well. For instance, Hutchinson [58] gives the following mean values : (1) Fixation of COZby photosynthesis over land during the day and release of COz through soil respiration as well as by organic decomposition, preferably at night: 100 X 10l6gm/year for thewhole earth (about 98% of total cycle). (2) Fixation of COZin bicarbonate a t the earth’s surface, subsequent transport in river water t o the oceans and release into the air from the ocean: 2 X 10l6gm/year (about 2% of total cycle). (3) Fixation of COZ in sediments in the ocean and release through volcanoes: 0.5 X 10l6gm/year (0.05% of total cycle). The dominant influence of the biological processes on land, in which the forests and the cultivated areas have the greatest share (90%) is immediately evident from the table. Since this exchange is confined solely to the atmosphere, any upset in the biological cycle will immediately affect the COz concentration in air. The ocean with its long cycle can only exert a damping effect on such variations. Callendar in his well-known surveys of the secular trend of COz [57, 611 found a 10% increase during the last fifty years. Although this result has generally been accepted by others as reliable, Slocum [62] in a more recent and very careful review concludes that, although he cannot refute Callendar’s thesis, “the available data merely fail to confirm it.” In fact, Callendar in his survey rejected a few sets of observations which would have changed the trend considerably. In Fig. 22 the data of Slocum are plotted with the omission only of those sets in which the number of individual observations is unknown, or which are documented as anomalous data. The data used by Callendar are specially marked. They show a definite increase beginning around 1900 as well as a narrow grouping around the indicated line. Four sets of measurements with more than 200 observations show considerable deviations toward higher values. The impression gained is that these deviating mean values may be due t o local differences in the “COZ climate,” or t o a systematic error in the method; the latter, of course, is now hard to check. However, those values which show a fairly close grouping around the indicated line must be weighted more heavily in terms of reliability than the others. Therefore, we feel that there is evidence in support of Callendar’s thesis, although this matter has yet t o be definitely decided. Callendar claimed that the 10% increase of COZ, which raises the total weight of COZby 200 X 10l6 gm, is caused by fuel consumption. The total amount of fossil carbon consumed up to the present time corresponds t o 150 X 10l6gm COz. The agreement between these two values

48

CHRISTIAN E. JUNGE

is not as good as it first appears to be. Two objections can be raised against the fuel hypothesis : (1) The ocean should absorb a portion of the additional COz, so that the agreement of the two values (200 and 150 X 10I6 gm) would become even poorer [58, 631. (2) An increase in the COz content would immediately intensify the rate of the photosynthetic fixation, the result being the same as in objection (1) above [58]. The fossil carbon of fuel (coal, oil, etc.) contains no C14. Therefore, a passive accumulation of such fossil carbon in the atmosphere should X <50 Observations

x

a

400

loo-zoo 200-500

-

3001 200

-x

1060

ld00

I

I

I

1900

I920

1940

I

FIG.22. Cai Jon dioxide data as a function of time according to Slocum 621. The uncircled values were used by Callendar as the most reliable oms. The value marked B represents recent measurements by Buch (cited in [631) in Scandinavia and was not included in Slocum's paper.

have modified the C14/C12 ratio in the atmosphere as well as in the recently formed organic material. Measurements made so far apparently show ambiguous results [62, 631. Slocum, however, points out that a decrease of this ratio would not confirm an increase in the total COZ content of the atmosphere, so that no decision on the question of a COZ increase can be expected on this basis. Hutchinson suggests that the increasing area of cultivated land, which has accompanied the growth of population and industrial development, is mainly responsible for the COz increase. It is known that cultivated land releases COz at a higher rate than uncultivated land. If the annual release of COZ from the soil is increased by only 4% during a 50-year period, this would account for the total accumulation of 200 X 1 0 1 6 gm. It may be that the combined effect of fuel consumption and the

ATMOSPHERIC CHEMISTRY

49

change in soil structure will account for the observed COz increase. However, both effects are anthropogenic. Since no attempt has been made t o explain the COz increase as the outcome of natural processes, it must be concluded that with respect to COz the effect of man’s activity has assumed global dimensions. The influence of man’s activity on the heat budget of the atmosphere can, therefore, no longer be disregarded. A few interesting papers on atmospheric COz appeared recently, which might be summarized a t the end of this section, Fonselius et al. [64] discuss some new results of COz measurements from a Scandinavian network, and compare them with the older measurements in a diagram similar to Fig. 22. It is emphasized that a definite confirmation of a world-wide increase needs still further data, obtained under standard conditions over various parts of the world. Plass [65J reconsiders the role of COz in the radiation balance of the earth’s atmosphere on the basis of new calculations. Due t o the better knowledge of the fine structure of the absorption spectra of HzO, 0 3 , and COz it appears that there is less effective overlapping of the spectra than previously thought, resulting in a higher influence of the C02 in the heat budget. If the COz concentration would change by a factor of 46 or 2, the average temperature a t the earth’s surface would change by -3.8 and +3.G°C, respectively. He emphasizes further the considerable consequences for our climate by human activities, assuming with Callendar that the combustion is the major source of the apparent COz increase. Eriksson and Welander [66] investigated the COZ fluctuations by using a simplified mathematical model for the system atmospherebiosphere-sea. It appears that this system is capable of self-sustained oscillations due t o the presence of the sea and the existence of time lags in the biosphere of the order of a few decades. On the other hand, this model shows the important feature that the COz concentration in the air is not increased very much by additional COz injection corresponding t o the present rate of combustion, because of storage in the biosphere. Thus the observed COz fluctuations would be the result of natural oscillations rather than the result of human activities. 3.3. Ozone

Ozone has been investigated more fully than any other of the trace gases treated in this survey, with the exception, perhaps, of C02. The greatest amount of ozone, i.e., about 90%, is concentrated in the stratosphere, where it is confined to a layer a t an altitude of about 20 km. The essential features of the stratospheric ozone distribution are fairly well known, thanks to spectroscopic observations from the ground (Umkehr effect of Goetz), from balloons and rockets [67], and more recently from

50

CHRISTIAN E. JUNOE

the earth’s shadow during lunar eclipses [68]. The determinations show that both the height of the ozone maximum and the total quantity of ozone are subject to considerable fluctuations. In regions near the equator the maximum usually lies above a height of 17 km; in northern latitudes, however, especially in the spring, a considerable amount of ozone can also be found below 17 km. The effect of this additional ozone is to increase the total amount of ozone in a vertical column. The total ozone content shows a maximum in the spring and a minimum in late autumn, increasing rapidly at the end of winter, particularly in the upper latitudes. The latitudinal distribution of the total ozone exhibits a minimum at the equator with values decreasing almost t o zero [69]. As a consequence of the latitudinal distribution of the stratospheric ozone considerable variations are observed during the passage of high- and low-pressure systems over a fixed point. I n the middle latitudes these variations are strongly correlated with tropospheric and stratospheric mean temperatures [70]. The main features of the stratospheric ozone distribution can be quantitatively interpreted as a photochemical equilibrium. The ozone is formed from photochemically dissociated oxygen by the action of radiation below 2530 and is in turn decomposed photochemically by strong absorption in the Hartley bands between 2000 and 2900 A. Dissociation also occurs to a small degree at longer wavelengths. The vertical distribution of ozone depends, therefore, on the interaction of both the concentration of the ozone formed and its short-wave absorption and subsequent decomposition. The calculated form of the ozone distribution and also the height and amount of the maximum agree approximately with the observed data [69, 711. However, there are considerable discrepancies, especially below 20 km. These can be explained by the large-scale horizontal, and possibly vertical, stratospheric circulations when the rates of the photochemical reactions are taken into account. Calculations of these rates show [69] that the ozone equilibrium is established very rapidly above 30 km, but that the process occurs at an increasingly slower rate a t lower altitude, so that below 20 km even slow movements of the air prevent an equilibrium from being reached. Below this altitude there is hardly any ozone formation and decomposition. Ozone which is transported down into the substratosphere and troposphere by any meteorological process is protected against photochemical decomposition and can only be destroyed through reaction with other substances. This basic fact must be kept in mind in any attempt to explain tropospheric ozone distributions. Interest in ozone research was at first concerned only with the stratosphere. The methods employed in its measurement did not permit a

ATMOSPHERIC CHEMISTRY

51

reliable determination of the small ozone concentrations in the troposphere. A successful investigation of tropospheric ozone was not possible until more sensitive chemical methods, in particular, the potassium iodide method, had been developed [72]. Potassium iodide may to a certain degree react with nitrogen dioxide and other oxidizing compounds [73]; however, if applied under carefully controlled conditions, this effect appears to be negligible [74]. The first to advance the thesis [75] that tropospheric ozone originates in the stratosphere were probably E. Regener and his co-workers. The downward flow of ozone is dependent on its rate of production at the photochemically active height as well as on the vertical distribution of small, medium, and large-scale turbulent motions in the stratosphere and troposphere. Once the ozone has been injected into the troposphere, it will be decomposed by gaseous and particulate trace substances and in clouds. The vertical distribution of ozone in the troposphere is thus the result of a complicated process, which is still very poorly understood, and, therefore, no quantitative check of Regener’s views has been possible up to now. Qualitatively the observed tropospheric distributions can be interpreted, though sometimes with difficulty, on the basis of the stratospheric origin of ozone. Exceptions are observed in certain polluted atmospheres [76]. The number of available measurements of the vertical tropospheric ozone distribution is still small. The data obtained by spectroscopic methods and extrapolated from stratospheric distribution curves are too uncertain for any detailed consideration [75]. The only reliable data on the free atmosphere have been obtained by Ehmert ([77], 4 ascents by aircraft) and, more recently, by Kay ([78], 13 ascents) and Brewer ([79], 4 ascents), using the iodide method. Ehmert measured the ozone distribution up to 4 km at the northern edge of the Alps during stable highpressure weather situations; in most cases he found that the highest values occurred immediately above the subsidence inversion layer at 500 meters above the ground. The explanation of this phenomenon on the basis of the stratospheric origin of ozone is somewhat forced. Kay’s soundings in England, carried out apparently without any particular regard for the weather, reached an average altitude of 12 km and represent at present the most comprehensive data available. Figure 23 shows two of Kay’s soundings and his average curve. The individual flights agree generally with those of Ehmert. The increase of the mean ozone concentration from 23 ?/meter3 at the ground to 43 y/meter3 at the tropopause corresponds to an increase in the ozone/air mixing ratio by 43/23 X 3 = 5.5. This average increase in the mixing ratio offers confirmation that the stratosphere is the main source of the tropospheric ozone.

62

CHRISTIAN E. JUNGE

Recently Brewer [79], who measured the vertical distribution of ozone in Norway during the summer, has questioned Kay’s findings. Brewer found that the apparatus used by Kay was contaminated; after improving the equipment he obtained higher values, especially above the tropopause. Brewer’s mean values are included in Fig. 23. Future measurements must decide if the differences are due to the defects in Kay’s procedure or to the difference in season and geographical location. The increase of the ozone content above the tropopause in Brewer’s data is interesting and important in this connection.

-

y Ozone per m 3 Fro. 23. Vertical distribution of ozone concentration in the troposphere. (a) average of 13 flights over England October, 1952 to November, 1953, after Kay [78]. (b) average of 4 flights over Norway, June-July, 1955, after Brewer [79]. (c) and (d) individual flights of Kay.

The two individual soundings included in Fig. 23 are typical. I n contrast to the average values they do not show a steady gradient, but rather pronounced layers of low and high concentrations. The ozone-depleted layers have a tendency to coincide with clouds, especially in the cirrus level. This stratified vertical structure may have different causes: it may reflect the different “ozone history” of the various layers, or it may correspond to the stratification of destructive materials, such as water clouds and dust. Very little is known about the extent of ozone decomposition in the atmosphere. In Arosa, Volz [80] observed that in orographic clouds the ozone content dropped by 30% to 50%; he also obtained some experimental data for the decomposition rate of ozone on contact with various surfaces, which data indicate a fairly rapid decay. Many more ozone observations are available from mountains and from near the ground. Among the more recent and longer series of measure-

ATMOSPHERIC CHEMISTRY

53

ments are those of Gotz and Volz [81], who made hourly measurements for a period of over a year at Arosa, a village located in an Alpine valley at an elevation of 1860 meters above m.s.1. In order to eliminate the ozone-destroying effects of the earth’s surface and to obtain fairly representative values in the free atmosphere, only maximum values have been selected from the hourly observations. Figure 24 shows these values together with the total ozone content. They fluctuate generally between 30 and 60 ?/meter3, with minimum and maximum values of 19 and 80 ?/meter3. A slight maximum appears in May, and a minimum in December and January. The maximum of the total ozone content appears nearly 0,350 0,300

cmo, 0.250 0,200

rvs 30 5

Fro. 24. Daily ozone maximum concentration in Arosa [Sl], April, 1950, through March, 1951, in ?/meters for an average pressure of 608 mm Hg. The dashed line for the winter months represents approximately the upper level of other observations; they are higher than the Arosa data because of only little subsidence during the winter 1950/1951 in Arosa. The upper curve represents the total amount of ozone for comparison. (By courtesy of zehchrift f u r Nuturforschung.)

two months earlier. This gives us a rough estimate of the time lag of the ozone transport across the tropopause, due to vertical circulation and turbulence. The ozone content was recorded simultaneously by V. Regener at various places in New Mexico, e.g., on Mt. Capillo (3070 meters above m.s.1.) and near Albuquerque (1700 meters above m.s.l.), for intervals over a two-year period [82]. The values for Mt. Capillo are more representative of the free atmosphere than are those for Arosa, considering that the latter site is surrounded by higher mountains. Because of less influence from the ground they are also more constant than those in Arosa. Some short-period fluctuations can be attributed, as in Arosa, to the passage of fronts; others cannot be explained in this way, but are hardly due to local sources. Because of gaps in the observations, annual variations cannot be derived. By carrying out parallel measurements on the Pfaender (1064 meters above m.s.1.) and on the Bodensee (404meters above m.s.l.), Ehmert and Ehmert [83] were the first t o demonstrate that the ozone content near the

54

CHRISTIAN E. JUNGE

ground is greatly reduced, in comparison t o the values at higher levels. On the shore of the Bodensee during calm weather situations, they found a diurnal variation with low values during the night, a rapid rise in the forenoon, and maximum values in the afternoon. This marked diurnal variation is limited to the lowest air layers and is due to the interaction between the diurnal variation of the eddy diffusion and of the ozone decomposition near the ground. On the Pfaender they found no diurnal variation and smaller fluctuations. These results have been confirmed by various observers, for example, Regener in New Mexico [82] and Teichert in Lindenberg [84].Teichert made comparative measurements at the surface and on an 80-meter-high radio tower for a period of several months. Table VII gives the hourly means for different months and shows the characteristic features of such measurements. The values at 80 meters are always higher or equal to those at the ground. Due to more stable weather, the diurnal variation for September is much more pronounced than for July, but the diference between the two levels is smaller in September, even during the morning hours. This finding seems to indicate that the main destruction of the ozone occurs here because of the accumulated pollution within the stable layer rather than contact with the ground. Similar results were obtained by V. Regener, who measured ozone on the open plains of Nebraska at altitudes of 12.5, 6.3, 1.6, and 0.4 meters above the ground [85]. The vertical gradients in this boundary layer are almost always very slight and become noticeable only during periods of very small eddy diffusion at night. He estimates the ozone flux towards the ground at 1.3 X 10" molecules per cm2 and sec, a value that differs from other evaluations by one to two orders of magnitude. Table VIII attempts to give a survey of reliable recent measurements of representative tropospheric ozone values. The mean concentrations and also the maxima exhibit a fairly uniform level when one considers that these observations relate to different seasons, latitudes, and altitudes. The minima, of course, decrease rapidly to zero on approaching the earth's surface. Despite the interaction of various factors the over-all distribution of the tropospheric ozone content seems on the average to be fairly uniform. A general tropospheric gradient from higher to lower latitudes (not apparent from Table VIII) is sometimes indicated [Sl], but reliable data from polar, tropical, and oceanic regions are still lacking. Although the majority of the findings seem to support the thesis of the stratospheric origin of tropospheric ozone, some observations point t o sources in low tropospheric layers. For instance, the measurements from Albuquerque [82] show certain short-term maxima (see, e.g., the relatively high maxima values for Albuquerque in Table VIII) of 1 to

TABLE VII. Average hourly concentrations of ozone in r/meter3 according to Teichert [84]. Hour 80 meters Ground Hour 80 meters Ground

7-8 25 18

7-8 2 2

8-9 28 19 8-9 6 5

9-10 24

21 9-10 11 9

June/July 12-13 13-14 32 33 30 31

10-11 27 25

11-12 28 28

10-11 18 17

September 11-12 12-13 13-14 33 24 30 33 24 28

14-15 33 29

15-16 34 33

16-17 29 26

17-18 30 30

%*is 18-19 34 29

19-20 29 26 d

m

14-15 31 28

15-16 29 28

16-17 33 34

17-18 33 28

18-19 28 26

Fi

t: e

56

CHRISTIAN E. JUNGE

2 hr, which appear around noon with values approximately twice as large as concurrent values for Mt. Capillo. The effect is much more pronounced in the highly polluted atmospheres of Los Angeles. Here, under smog conditions, ozone concentrations up to 1000 y/meter3 were found [73, 761, which were confined to the layer below the inversion. According to Table VIII these concentrations are far in excess of those observed elsewhere in the troposphere. The maximum at noon between 1100 and 1400 TABLE VIII. Concentrations of tropospheric ozone as given in more recent and extensive studies. ~~

Location, time, and remarks

Observer Gotz and Volz I811 Regener [82]

Arosa, Switzerland, 195051, high valley, daily maxima values Mt. Capillo, and Albuquerque, New Mexico, USA, 1951-52

O’Neil, Nebraska, USA, 1953 Ehmert [86] Weissenau, Bodensee, Germany, 1952 Teichert [84] Lindenberg Obs., Germany, 1953-54 Farnborough, England, Kay [781 Regener I851

1952-53

Brewer [79]

~~

Tromso, Norway, 1954

Altitude 1860 meters

above mean sea level 3100 meters above mean sea level 1600 meters above mean sea level 12.5 meters above ground 20 ma gm at the surface 80 ma gm at the surface 0-12000 meters above mean sea level 0-10000 meters above mean sea level

Oain Tlmetera Range * Average * 19-90

50

18-85

45

3-120

36

30-100

60

0-90 0-70 0-50 0-50 26-50

35 30 30 27 38

60-70

65

~

*As interpreted from the pubIislied data.

hr is obviously related to solar radiation and seems t o indicate photochemical origin [76]. The high ozone values found at some greater distance from LOSAngeles may have the same origin [73]. It is unlikely that other than photochemical sources are important, e.g., the production by electrostatic point discharge at industrial installations and in the electric field of the atmosphere. Experiments in Los Angeles have shown that ozone is formed when air collected on a smoggy day is irradiated with sunlight. Details of the reaction are still unknown. Only Los Angeles and perhaps a few other places exhibit this exceptional behavior. In other industrial atmospheres, especially that of London, a mounting degree of

ATMOSPHERIC CHEMISTRY

57

pollution is usually characterized by its SOZcontent and is linked with a decrease of the ozone content. 3.4. Nitrous Oxide

The following nitrogen oxides are known: NzO (nitrous oxide), NO (nitric oxide), Nz03 (dinitrogen trioxide), NO2 (nitrogen dioxide), Nz04 (dinitrogen tetraoxide), Nz06 (dinitrogen pentoxide), NO3 (nitrogen trioxide), and NzOs (dinitrogen hexoxide). A t normal temperatures and with small partial pressures a s present in the atmosphere, the following oxides are completely dissociated :

+

NzO3-t NO NO2 NsOc -j 2N02 Nz06-+ NzOa 0 2

+

For example, a t room temperatures and with an NO2 concentration of 10 y/meter3, the equilibrium is displaced so far toward the right that only 1 0 P y/meter3 of Nz04 are presentj [87]. Since the rate of dissociation of these three oxides is independent of pressure, the adjustment of the equilibrium occurs fairly rapidly even a t the low partial pressures in the atmosphere. Under normal conditions, NO3 and NzOs are unable to exist in the atmosphere. The presence of NO is assumed. Only N2O and NO2 have been verified by measurements. Nitrous oxide (NZO), which we will discuss first, was discovered in the solar spectrum in 1939 by Adel [88]. It has since been frequently confirmed by the identification of additional absorption bands (e.g., a t 3.9,4.5,7.8, and 8.6p ) , which are quite well suited for quantitative determinations. More recent and reliable measurements give a total amount 4 t o 5 mm STP [89]; this would correspond to a constant mixing ratio of 5.2 X 10-7. Goody and Walshaw [go], making spectroscopic measurements from an airplane, found th at their measurements are compatible 0.8 X 10-7 a t an altitude of from with a constant mixing ratio of 2.7 3 to 10 km. Slobod and Krogh [9l] in Texas found values between 2.5 and 6.5 X 10-7 near the ground by mass spectroscopy. All these observations point t o a fairly constant mixing ratio of about 3.5 X corresponding t o a concentration of 690 y/meter3 a t STP. A nearly constant mixing ratio in the vertical has also been confirmed spectroscopically by ground observations. Having measured the dependency of NzO absorption on the height of the sun, Goldberg and Mueller [92] compared the observed variations with those computed for assumed vertical distributions in which the NzO was concentrated at various heights. The agreement is best in the case of the uniformly mixed atmosphere. There is agreement among investigators that NzO is dissociated in

58

CHRISTIAN E. JUNQE

the upper atmosphere, and that the present concentration corresponds to the equilibrium resulting from this process and from that of formation. Bates and Witherspoon [93] computed the photochemical dissociation of N20at various levels of the atmosphere and obtained the following values for the life time: at a height of 10 km, 4000 days; a t 20 km, 800 days; at 30 km, 50 days; and at 40 km, 20 days. Since chemically N20 is a very stable and inert gas, photochemistry is the only way by which the NzO concentration can be changed. Hence, in view of the known data on the rate of vertical mixing in the atmosphere, we can infer a constant mixing ratio up to an altitude of about 25 km. Using these values Goody and Walshaw computed a total NzO dissociation of 8 X 1O'O molecules per om2 and sec as the mean value for the total atmosphere. The question now is which source can make up this loss. Two views regarding the origin of N20 have been advanced: (1) NzO is produced by soil bacteria upon the decomposition of nitrogen compounds. (2) N2O is not released from soil but is formed photochemically in the lower layers of the atmosphere.

Adel was the first to consider the soil bacteria process [94]. More recent investigations [go] indicate that it is by far the most probable. In detailed experiments Arnold [95] has examined bacterial transformation NH4- or NO8- ions in the soil into NzO and partly into Nz. It becomes evident that the amount of NzO produced increases strongly with poor aeration of the soil, e.g., with high water content. Under average conditions the entire amount of fixed nitrogen in the soil is transformed in about 100 to 1000 days. Using this value and also the best data available for soil area, depth, and average content of fixed nitrogen, Goody and Walshaw obtained an average production of NzO over the entire earth of 1.6 - 16 X 1 O l o molecules per cm2 and sec. These figures are of the same order of magnitude as the NzO dissociation and show that the soil can actually supply the main quantity of N20. As for the photochemical production of NzO, the conditions, according to Bates and Witherspoon [93], are as follows: the reaction Nz03 -+ NzO 02 is the most promising of all the photochemical ones and should be able to balance out the NzO dissociation. However, Goody and Walshaw found by a rough experimental check that this reaction can only account for 2.5% of the loss and is, therefore, of little importance. The scattering of the available NzO values, it should be noted, shows that a time- and space-constant mixing ratio represents a first approximation only. If the soil were actually the chief source of NzO, we might expect differences in concentration in the lower troposphere between

+

ATMOSPHERIC CHEMISTRY

59

mainland and ocean and a slight decrease of the mixing ratio with height. The fact that the soil can play a dominant role in the budget of an atmospheric trace substance of such fairly high concentration is of great significance. More recent rain-water analyses seem to indicate that the soil is of similar importance for the NH, and SOz content in the atmosphere. 3.5. Nitric Oxide, Nitrogen Dioxide, and A m m o n i a

Nitric oxide has not been detected in the atmosphere. Possibly it has been included in those analyses which were generally interpreted as NOz. The existence of NO has been discussed in a number of papers, mostly for high altitudes, however, without any definite conclusions being reached. Since NO2 has been found in the troposphere, the equilibrium 2 N 0 O2 + 2NOZ is of interest. Fortunately, our information on the equilibrium constant and the rate of this reaction is quite good [87]. Given an NO2 concentration of 10 ylrneter3 and the partial pressure of 02 in the troposphere, the equilibrium would be shifted so far to the right that no more than y/meter3 of NO could be present. However, as a second-order reaction its rate decreases rapidly with the partial pressure of NO. Given an initial NO concentration of 10 y/meter3, only 10% would be transformed after lo3 days. No equilibrium can, therefore] be expected; and if sources of NO were present, the gas should be found. NO can be produced by photochemical dissociation of NzO with wavelengths below 4300 A, that is, in all layers of the atmosphere. In the upper atmosphere, in the presence of short-wave radiation and atomic 0 and N, the number of possibilities for formation and dissociation of NO increases rapidly. However, in view of insufficient accurate data, these considerations are all purely speculative. The only concrete statement comes from Migeotte and Neven [96]. Their spectroscopic measurements show that no more than 0.2 mm STP atmospheres can be present. With uniform mixing, this would correspond to a mixing ratio of 2.5 X lo-* (= 33.5 y/meter3 at STP). This limit is still very high, compared to the natural level of various other trace substances (e.g., that of NOz), which we will discuss now. The presence of NOz was indicated with the discovery of nitrate in rain water; however, the data obtained from direct measurements of NOz in the atmosphere is still quite inadequate. Table IX contains the the few values considered to be fairly reliable] including some data for partly polluted atmospheres. Reynolds [97] made parallel measurements for a period of several years at distances of 8 and 20 km from the center of London. Unfortunately] his paper contains only a few figures. Reynolds absorbed the gases in an alkaline solution. Because of this, the retention may not have

+

60

CHRISTIAN E. JUNQE

been complete, and his figures, therefore, represent minimum values. He finds that NOz is predominantly a component of urban air and shows no relation t o lightning discharges, as has frequently been assumed. TABLE IX. Concentration of NOS in air. Observer Reynolds [97]

Edgar and Paneth 1981

Location, time, and remarks

Amount of NO2 -y/meterJ

Plaistow, 8 km from center of London, 1923-27, strongly influenced by polluted air.

max in fog av in summer

Upminster, 23 km from center of London, 1923-27, fairly representative for unpolluted air.

about $4 of the values in Plaistow; no detailed values given -3

South Kensington, London, strongly influenced by polluted air, 23 values, Feb.-June, 1938.

range average

Kew, suburb of London, 2 values, May, 1938, partly unpolluted air. Junge [Ill

60 16

1-40 15

1 and 6

Southeast coast of Florida, 13 values, July-August, 1954, trade winds.

range average

1 . l-3.7 1.8

Hawaii, 14 values, Oct.-Nov., 1954, trade winds.

range average

1.5-3.2 2.6

Mauna Kea, Hawaii, 3200 above range 1.6-2.3 sea level, 4 night values, average 1.9 0ct.-Nov., 1954, representa(values reduced to surface) pressure tive of the air above the trade-wind inversion. Ipswich, Mass., USA, 9 values, Dec.-Jan., 1954-56.

range average

0.6-3.8 2.6

Edgar and Paneth [98] separated NO2 from ozone by adsorption on cooled silica gel and subsequent fractioned dist,illation. Their data, though quite reliable, unfortunately relate almost exclusively to polluted air in London. In order t o obtain data on the level of various trace gases in pure maritime air masses, Junge [ll]made measurements in the trade winds

ATMOSPHERIC CHEMISTRY

61

on the east coasts of Florida and Hawaii. After removing all aerosols by means of filters, the sir was sucked through alkaline absorption solutions and analyzed for Nos-, among others. Due to incomplete retention in the absorption solution and also to some absorption of the gases in the aerosol filters, the true NO2 values may be 30% higher than those obtained. The samples were collected right on the coast in order to eliminate any influence of land. Some additional measurements in northern Massachusetts are also included in Table IX. We see that in unpolluted atmospheres NO2 is present in concentrations of 1 t o 10 y/meter3, whereas in polluted atniospheres much higher concentrations are observed (see also Section 5). The NO2 in unpolluted atmospheres appears to be fairly uniformly distributed. The degree of daily variation in Florida is indicated in Fig. 17. Some values (Table IX) obtained on Mauna Kea (Hawaii) above the trade-wind inversion yield a smaller mixing ratio than below the inversion. Because it is generally assumed today th a t trade-wind inversions represent only an internal boundary layer through which the air masses descend over a wide area, we would have to conclude that the sea represents a t least some source of Nos. The values obtained with chemical methods were generally interpreted and computed in terms of NO2 concentration. They may include small amounts of NO, but as far as the author knows, no attempt has been made t o separate the components. Unfortunately, the much more specific spectroscopic or mass-spectrograph methods fail completely in this concentration range. N H 3 is a constituent of the atmosphere, which was detected very early in rain-water analyses. It is present predominantly a s a gas (see Section 3.9). Until quite recently this was not clear at all; it was believed that ammonia is chiefly fixed on dust particles [58]. The presence of NH, in the atmosphere has not been spectroscopically substantiated with certainty. Mohler and others believed that they had found it [99]; however, Migeotte and Chapman [loo] were able to show, on the basis of better data, that the actual NH3 content must be below the limit of detection (0.132 mm STP), a value that would correspond t o a constant mixing ratio of 1.66 X lo-*, or t o a concentration of 10.6 y/meter3 near the ground. I n a number of investigations the total NH3 concentration was determined by bubbling air through absorption solutions. Since it seems t o be fairly well established that the predominant amount of NH3 is present a s a gas (see Section 3.9), it is possible to list these values with good approximation under gas concentrations. Quite a number of these determinations were made in the second half of the last century. It was in this period th a t the importance of fixed nitrogen compounds for the biological cycle was

62

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recognized, and an interest aroused in the content of nitrogen compounds in the atmosphere (see, e.g., [loll). These old values from various locations in Western Europe are fairly high compared with more recent data. The lowest values a t the ground were around 20 ?/meter3. In some cases local pollution might be suggested; however, values from the Pic du Midi (2877 meters above m.s.1.) for the year 1880 fluctuate between 7 and 30 y/meter3, with a mean value of 13.5 ?/meter3. With the turn of the century the interest in direct measurements of atmospheric ammonia ceased almost completely, and it was not until quite recently that new data became available. In 1953, Egn6r and co-workers [lo21 created a network of sampling stations in Scandinavia. Small amounts of air were continuously sucked through absorption solutions at these stations in order to obtain monthly average values for different trace substances, e.g., NHz. This network has been extended through other parts of Europe, chemically disturbed areas being avoided where possible. Table X gives a survey of the values obtained a t four of the Swedish stations; the listings are from North to South. Despite noticeable fluctuations, the general level for all stations lies in the neighborhood of several ?/meter3. On the whole, this indicates a rather uniform distribution. Most stations seem to indicate an annual variation of the ammonia concentration with the maxima in summer and fall. One may hope that this valuable material will soon be evaluated in greater detail. Simultaneously with his NO2 measurements Junge [ 111 measured NH, in Florida and Hawaii, after removal of aerosols. Due t o gas absorption in the filters of the system, the values may be lower by about 20 %. Table XI gives a survey of these results. The values of Tables X and XI seem to agree fairly well with each other and with the upper limit of Migeotte, but are considerably lower than those of the last century in Western Europe. It is not inconceivable that parts of the European continent showed, or show, higher values than other parts of the world because similar differences are indicated in NH4 analyses of rain water (Section 4.3). Such values can also remain compatible with the above-mentioned spectroscopic limit, as in the case of regional enrichments the NH3 will remain confined essentially to the lower layers of the troposphere. As in the case of NOz, a comparison of the values from Mauna Kea with the ground values from Hawaii (Table XI) seems to point to the ocean as a source of NH3. On the basis of simultaneous measurements of the pH and NH4+ concentration of sea water, the equilibrium concentration of NH3 in the air above the surface of the ocean was computed to be 1 to 2 y/meter3. This value is only about half as large as that actually

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found. It has been suggested that the films of organic substance frequently observed on the surface of the ocean represent an additional NH3 source for maritime air. The relatively small differences between the values in pure sea air and those over land, according to Tables X and XI, point also both to land and sea as sources of NH3. The literature dealing with the formation and role of NH3 in the soil is very extensive. Since the biologically fixed nitrogen is present essentially in the form of amino acids, NHs must originate from the dissociaTABLE X. Monthly average values of the total NH3 from some stations of the Swedish network [102]. Data represent predominantly the gas phase. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 1954 1954 1955 1955 1955 1955 1955 1955 1955 1955 1955 1955 Offer Erken Falsterbobruk Alnarp Average

1.4 0.6 2.2 3.8 2.0

2.0 2.3 1.0 2.2 1.9

2.6 1.1 1.3 3.4 2.1

2.2 2.2 3.8 3.4 2.9

3.0 1.4 1.3 4.0 2.4

4.2 1.2 2.2 4.5 3.0

4.0 1.3 1.8 3.5 2.6

4.1 1.0 1.9 6.0 3.2

5.9 2.2 2.9 9.4 5.1

4.9 2.2 4.0 9.4 5.1

4.2 0.1 2.9 5.0 3.0

2.1 3.6 3.4 4.8 3.5

TABLE XI. Concentration of NH3 in unpolluted atmospheres [ll]. ~

Location

Remarks

Trade winds, southeast coast, 13 values, July-Aug., 1954. Hawaii East coast Island of Hawaii, 14 values, Nov., 1954. Hawaii Mauna Kea, 3200 m, above the trade-wind inversion, 4 night values, Dec.-Jan., 1954. Ipswich, Mass. 9 values, Dec.-Jan., 1954-55. Florida

Concentration y/meter3 2.2-8.0 5.1 1. l-3 .9 2.5 0.7-1.3* 1.1*

range average range average range average

3.3-13.9 6.1

range average

* Reduced t o sea-level pressure. tion of organic substances. This has been confirmed by various investigations (see [loll). However, no absolute values seem to be available for the amount of NH, escaping from the soil under various conditions. This amount appears to be small in cases where the aeration of the soil is poor; i.e., in the case of high water content. Moreover, the pH value of the soil plays an important role in the escape of NH3. Noticeable amounts of NH3 are released from soils rich in CaC03 and low in humus; i.e., where the pH is high. To reduce the NH3 losses of the soil following fertilization, acidification of the soil is recommended. Our discussion on this subject will be continued in Section 4.3.

G4 3.6. Sutphur

CHRISTIAN E. JUNGE

Dioxide, Hydrogen SuZJide

The significant role of SO2in polluted atmospheres is well known and has been the object of numerous investigations. The data for nonpolluted air, however, are very inadequate. Again it becomes evident that spectroscopic methods. are not sensitive enough to discover such trace components in the atmosphere. It is only possible to estimate an upper limit [lo31 of about 0.05 mm STP, corresponding to a constant mixing ratio of 0.6 X lo-* gm/meter3 or to a concentration of 15 y/metera near the ground. As in the case of NO2 and NH3, the predominant amount of oxidized sulphur over land is present in gas phase (see Section 3.9). This may be different over the ocean, because noticeable amounts of sulfate can appear TABLII XII. Monthly average concentration of SO1 (?/meter$) from some stations of the Swedish network, calculated from the total sulphur concentration under the assumption that SO2 is the predominant component [102]. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 1954 1954 1955 1955 1955 1955 1955 1955 1955 1.955 1955 1955 Offer 0.0 3 . 4 Erken 1 . 0 13.4 Falsterbobruk 3 7 . 8 0 . 0 Alnarp 32.0 27.4 Average 17.7 11.1

3 . 6 1 . 6 12.8 14.0 1 4 . 8 1 2 . 0 8 . 4 22.2 13.4 40.4 38.1 42.0 16.6 1 9 . 3 20.1

8.6 7.4 7.8 24.0 11.9

1.0 1.0 0.6 6.8 2.3

5.6 7.2 6.6 14.6 8.5

12.4 1.4 5.6 5 . 2 13.8 3 . 4 0 . 0 6 . 4 6.S 1.4 8.8 0.0 12.4 24.0 22.0 26.0 1 1 . 3 7 . 5 9 . 1 6.0

there in sea-salt nuclei, while the SO2 concentrations are small. Analyses for SO4 over land can, therefore, be listed with good approximation as SO2 values, even though the analyses do not separate aerosol and gas. Egn6r and co-workers [lo21 have obtained rather extensive data for the total sulphur content of the air in Northern Europe. Table XI1 represents the same selection of stations as in the case of NH,. The values of SO2 fluctuate considerably between 0 and 40 y/meter3, with a mean value of about 10 y/meters. The general decrease of the SO2 concentration from south (Alnarp) t o north (Offer) seems to point to the influence of industrialized Central Europe (see Section 5.2). It is probably not until one reaches more northerly locations, such as Offer, that one finds undisturbed conditions, with values between about 0 and 10 y/meter3. It is of interest to compare these data with those obtained in marine locations ([ll] and Fig. 17). The values of SO2 at these places, however, can only be regarded as minimum values. In Florida and Hawaii, mean values of 3 y/meter3 and 1 y/meter3 were found, which are of the same magnitude as those of northern Sweden, indicating that small traces of SO2 are fairly widespread, as in the case of NH3 and NOz.

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65

Occasionally SO3 has been named as an additional gaseous constituent of the air, primarily in a polluted atmosphere. Because of its great reactivity with water, any SO, will react immediately with the humidity of the air t o become HzS04 particles. In other words, oxidized sulphur is present in the atmosphere almost exclusively as ail SOz gas, or as sulfite and sulfate aerosols. Aitken [lo41 assumed that the oxidation of SO2 results in the rapid formation of HzS04 aerosols under the action of short-wave solar radiation; he believed that he could explain certain fog formations following sunrise on the basis of this process. According t o the very careful investigations of Gerhard [24], the oxidation rate of SOZ, up t o concentrations of 30 ppm, is proportional to its concentration and amounts to 0.1% t o 0.2% per hour under conditions of intense natural sunlight. The presence of nitric oxides, NaCl aerosols, and water vapor in amounts u p t o 90% relative humidity had no effect on the rate of oxidation. This rate, though small, may lead to the oxidation of several per cent SOz t o sulfate over a period of a few days in stagnant air masses, but cannot explain the rapid formations of fog. Fog formation, however, may be due to reaction of SOz with other trace gases; as a matter of fact, Aitken’s paper, which continues t o be stimulating even t o this very day, gives experimental evidence that O3 and NH, form large numbers of nuclei in the presence of soz. The chief source of natural SO2 is presumably the HZS which has escaped from the ground or certain portions of the sea and subsequently oxidized. This conclusion is based on the fact that in many rural areas the SOa content of rain water is greater in summer than in winter, in contrast t o industrial regions, where the SO, content is greatest in winter due t o the increased coal consumption [105]. The chemical literature gives very inadequate information as to whether and to what degree H2Sis oxidized in small concentrations [106]. The effect of 0 2 at normal temperatures seems slight and then apparently leads only to the formation of free sulphur. If ozone is present in considerable excess, it seems t o oxidize HZS in concentrations up to 1000 y/meter3 completely in about one hour. However, other observations disagree with this. The most probable assumption is that small concentrations of HzS are oxidized partly t o sulphur and partly to SO*, through the action of natural ozone. Unfortunately, no data are available on the mean H2S content of the atmosphere. It is well known that H2S originates from decomposing organic matter. Several extensive natural source regions have been named, primarily the soil and the shallow regions of the sea. I n Dutch cities, which generally have canals running through them, local concentrations of 100 t o 1000 y/meter3 have been established [106, 1071.

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In addition to the oxidation of H2S, the industrial sources of SO2 are of importance, even on a continental scale (see Section 5.2). 3.7. Halogens

Of all the halogens, only chlorine and iodine have so far been found in the air. Cauer [21] analyzed air at various places in Europe by means of his condensation method. He found that the ratios Cl/Na and Cl/Mg were essentially smaller than in sea water, a result recently confirmed in rain water on a large scale [32]. Cauer concluded that C1 escapes from seasalt droplets through reactions with ozone. In order to pursue this question further, Junge [ll, 371 looked for gaseous C1 components in the atmosphere in Florida, Hawaii, and Ipswich, Massachusetts. All aerosols were carefully filtered out prior to measurement and the gaseous character of the C1 component verified. Table XI11 contains some mean values. The variation of gaseous C1 TABLE XIII. Average C1 concentrations (y/meters) of particulate and gaseous matter at different localities [ll, 371. Figures in parentheses indicate the number of individual mcasurernents. Large and giant nuclei together Florida Hawaii Ipswich, Mass.

all data land breeze sea breeze all data all data

1.54 (13) 0.56 (6) 2.39 (7) 5.09 (10)

-

Gas 1.57 (13) 0.80 (6) 2.23 (7) 1.92 (14) 4.40 (9)

parallels that of the aerosol in Florida (see also Fig. 17); the values for both are of the same order of magnitude. Nothing is known about the composition of this gas; quite probably it is HC1 or Clz. The true values may be higher, due to some absorption in the aerosol filters and also, in the case of Clz, due to the fact that the absorption solutions were analyzed only for C1- ions. The evidence for an apparently widely distributed gaseous chlorine component seems to be quite strong. In addition to this natural C1 Component there are also industrial sources of Cl which are doubtlessly to some degree gaseous; however, no details are known about such components. Investigations of the iodine content of air, in part inspired by the interest in nutritional physiology, have been made in Europe almost exclusively by Fellenberg [lo81 and Cauer [log]. They found a mean value of about 0.5 y/meter3 as representative for Central Europe up t o 1933, with higher values in the western part of Europe and lower ones in

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67

its eastern regions. The fluctuations around this value were high, up to two orders of magnitude, indicating source regions of limited geographical extent. The rapid decrease of this value to about 0.05 y/meter3 after 1933 in Central Europe coincided with a considerable decline of the West European iodine industry, due to increased importing of iodine from Chile. The decrease of the iodine concentration occurred more slowly in Southern Germany than in the North. The iodine industry of Western Europe was located principally in Brittany and Scotland and, to a lesser extent, in Scandinavia and Spain. In Brittany the iodine industry continued after 1934, but on a much reduced scale. Iodine was obtained by the burning of seaweed, releasing a considerable portion of the iodine to the air. This raised the local iodine level by a factor of 1000, according t o Cauer’s observations in Brittany. There is no information about the form of the iodine in the air, but presumably the predominant portion is gaseous. According to these findings, the anthropogenic contamination of the atmosphere with iodine in Europe had reached a continental scale, at least prior to 1934. Because of its low natural level and the coincidental breakdown of its industry, iodine so far is the only chemical component where this could be proven beyond doubt. Very little is known about the natural or other sources of iodine. According to Fellenberg it comes in part from iodides in the soil. Fuel, however, also contains about 5 X lo-‘ per cent of iodine; this, too, may contribute to the iodine content of the air. The transport of iodine back to the earth’s surface is probably primarily due to precipitation. 5.8. Methane, Carbon Monoxide, and Formaldehyde

Methane was discovered spectroscopically by Migeotte in 1948 [llo]. More recent determinations give a reliable value of 12 mm STP [ l l l ] , which corresponds to a mean mixing ratio of 1.5 X low6gm/meter3, or to a concentration of 1070 y/meter3 near the ground. This value is quite high, compared to the other trace gases treated here. It seems that the mixing ratio is constant with height and that methane is distributed very uniformly over the earth [112]. Hutchinson [58] concludes that CH4 can be traced back essentially to animal sources and that the amount originating from lakes and swamps may be disregarded. He estimates that the total CH4 content of the atmosphere could be replaced by the animal sources in approximately 50 to 100 years. The sink for the CH4 may be photochemical decomposition under the influence of very short-wave radiation; however, this would occur only above 90 km. As yet it is not known whether and to what extent oxidation of methane is possible in the troposphere.

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CHRISTIAN E. JUNGE

Carbon monoxide was also discovered spectroscopically by Migeotte [96]. The total concentration found fluctuated between 0.1 and 1.6 mm STP, depending on the method employed in determining it. This corresponds to concentrations of 0.0125 - 0.20 ppm or 16 - 250 y/meter3, if a constant mixing ratio with height is assumed. According to Goldberg [112], the most probable value is 0.6 mm STP (94 ?/meter3). This again is a fairly large concentration compared to other trace substances. The large variations observed appear to be real, indicating that the source regions are at the earth’s surface and are geographically limited. This may point to anthropogenic sources. Dhar and Ram [113] found formaldehyde in rain water and dew in amounts ranging from 0.1 t o 1.0 mg/liter, with a mean concentration of 0.5 mg/liter. These data offer no basis for conclusions concerning the actual concentration present in the air. No relationship with thunderstorms could be established. The concentration in dew was higher than in rain water. Dhar and Ram believe that C H 2 0 is formed through the action of sunlight on water solutions of organic substances. It is not very probable that CHzO originates in higher layers of the atmosphere through the action of photochemical processes [21]. The only data on C H 2 0 concentrations in the air have been obtained in Europe by Cauer [21]. His values vary between 0 and 16 ?/meter3, with a mean value of 0.5 y/meter3. According to Cauer, part of this CHzO may be due to incomplete combustion processes, i.e., anthropogenic sources. 3.9. Ratio of Gaseous to Particulate Matter for Some Chemical Components

In our preceding discussion of NH,, NO2,SOz, and Clz, the question arose as to what fraction of these substances is fixed on particles as NH4+, NO3-, Sod--, and C1-. Although this question has general importance for the chemistry of the trace substances in the atmosphere, it has barely been touched upon in the literature up to now. Besides the soluble salts named, the aerosols will also contain insoluble sulphur and nitrogen compounds of mineral and organic origin. However, so little is known about these, that they have to be disregarded in the following discussion. Table XIV gives a summary of the values available for unpolluted air and, for comparison, also some data for polluted atmospheres. With few exceptions the concentration of the gaseous components is higher by one to two orders of magnitude than that of the aerosols. The exceptions are the SO2/SO4 values from Hawaii and those obtained by Katz in the vicinity of smelter plants. I n the first case almost all of the SO4 comes from the sea salt of giant nuclei (see Fig. 19) and thus has an entirely different origin than the sulfate found in the large nuclei. The sulfate values of Katz comprise numerous other soluble components of

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TABLE XIV. Comparison of the concentration of gaseous and particulate matter for some chemical compounds. If not otherwise indicated, the data consist of simultaneous measurements. Values in r/meter3. Location and remarks Florida, 1954, 13 values [ I1 1 Hawaii, 1954, 14 values Hawaii, Mauna Kea, 3200 meters, 1954, 4 values

NHX-gas (calculated as NH4+)

NHa+ in particles

Ratio

5.05

0.12

42

2.45

0.047

52

1.08

0.003

360

S o t (calculated as S04--)

SOA-- in particles

Ratio

Florida, as above

3.00

about 10

Hawaii, as above

1.10

true value between 0.06 and 0 . 6 true value between 0 . 4 and 0 . 8 values varied between 1 and 20

Coste and Courtier [114], London, 1936

values varied between 440 and 2200 44 998

Suburb of London [114] Ellis, London, 1931 V151 Katz [116] smelter areas, 1952 4700 Concentration high 2000 Concentration medium Concentration mild 880 Cincinnati, no 510, Kettering Lab., simultaneous data 1954 [I171

NOz (calculated as N03-j Florida, as above

2.70

Hawaii, as above

3.90

Cincinnati, no simultaneous data

110, Kettering Lab., 1954 (1171

4 103

about 2 about 100 11 9.5

620 350 140 5.6 Chambers, 1955 [50]

7.5 5.7 6.2 100

NO3- in particles

Ratio

true value between 0.29 and 0.35 true value between 0.046 and 0.09 1.O Chambers, 1955 [501

about 8 about 50 110

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CHRISTIAN E. JUNQE

the aerosol (a result of the analytic method employed) and are thus probably too high. The total sulfate given by Ellis [115] also appears rather high; about 10% of it is represented by free HzS04. Others, e.g., Coste and Courtier [114], found higher ratios of S02/S04 in polluted atmospheres. It appears that the sulfate content of aerosols in polluted air generally amounts to only a few per cent of SOZ.Katz [116], to be sure, points out that the many metal aerosols in the vicinity of smelter plants represent excellent catalysts for the oxidation of SO2, so that it might be possible, under certain circumstances, to find low S02/S04 ratios (see also [118]). For chlorine (see Table XIII) it becomes evident that in maritime air the aerosol and gas phase are of the same order of magnitude. There are no data available for this ratio over land. It is very probable, however that here the gas concentration is much higher than that of the aerosols, The fact that gas concentrations of NHI, SOZ,and NOZare considerably higher than NH4, Sod, and NOs in aerosols over a wide range of conditions (from pure maritime air to highly polluted atmospheres) appears significant. This may suggest that the material present in particulate form stems chiefly from the gas phase. For the formation of SO4 in polluted atmospheres this is generally accepted [114, 1181. The SO4 content in London smog is not the cause but the consequence of the formation of fog droplets; the droplets, as a consequence of SO4 formation, grow even larger and give the smog the appearance of an autocatalytic process. Certain conditions are necessary for this process to take place: (1) Sufficiently high humidity (but not necessarily saturation) for the formation of large droplet volumes; (2) The presence of substances with favorable catalytic properties in the droplets to oxidize the SO2that has gone into solution, and (3) A sufficiently long reaction time.

The direct oxidation of SO2 in the gas phase [24] may also be of importance during periods of smog lasting several days. The formation of sulfate as a function of time in a polluted atmosphere can be well demonstrated by measurements of Katz [116] (Fig. 25). This figure indicates that the process of sulfate formation ceases after a few hours a t a fairly high sO,/s04 ratio. On the basis of Table XIV it might be assumed that something similar also occurs in uncontaminated air, though it is obscured in the presence of sea spray. Although little is known about the chemistry of this process, it is certainly of importance for a better understanding of smog formation and of the origin and growth of natural aerosol particles, especially in the size range of the large particles. Volz found some evidence that a growth of

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aerosol particles occurs after the evaporation of clouds and it might be that this is due to the fixation of SO2 [lo]. The process of the fixation of SOZ, NH3, and probably also of NOz, in connection with the process of water-vapor condensation, has been known for some time and has been used for measurement purposes in atmospheric chemistry; however, its interpretation has not been entirely correct. In extensive studies of atmospheric chemistry, Cauer and Quitman [119,21,22] have concentrated the trace substances of the air in the condensate formed on a cooled metal sphere. The purpose was to obtain

Hours

-

FIG.25. Oxidation of SO2 in a polluted atmosphere as a function of time according to Katz [116].

artificial samples of “rain water” for analysis when natural samples were not available. They assumed the trace substances to be precipitated from the same volume of air as the condensate and computed their concentration in air from the known absolute humidity of the air. Laboratory investigations (unpublished) show that the SO4 and NH4 content of aerosol particles do not contribute very much to the SO4 and NH4 content of the condensate, but that its major part is fixed SO2 and NH3. This is to be expected because of the higher concentrations of gaseous components and the different rates of diffusion by which particles and gases migrate toward the metal sphere. Cauer’s data, therefore, do not represent the condensation nuclei for components like S04, NH4, and NO1. In agreement with this, his values for concentrations obtained by this method are often higher than those expected for aerosols on the basis of Figs. 18 and 19. 4. PRECIPITATION CHEMISTRY 4.1. The Removal of Trace Substances from the Atmosphere

Precipitation, besides supplying the water so necessary for life, is also of great, though less obvious, importance in cleansing the atmosphere. In

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CHRISTIAN E. JUNGE

an age when slight traces of radioactive materials may constitute a menace, increased attention should be paid to this process. It, therefore, appears justifiable to devote a special chapter to the chemistry of precipitation with special emphasis on the physical and chemical processes by which the trace substances enter precipitation. To be sure, precipitation is only one of several processes whereby trace substances are removed from the atmosphere: (1) Removal of aerosols is possible by: (a) Fall-out due to gravity; (b) Impaction of particles on obstacles at the earth’s surface; (c) Wash-out by precipitation. (2) Removal of gases is possible by: (a) Escape into space; (b) Absorption and/or decomposition a t the earth’s surface; (c) Decomposition in the atmosphere by reactions which result in the formation of aerosols or other gases; (d) Wash-out by precipitation. We saw in Section 2.2 that fall-out of aerosols is important only for particles larger than 10 to 20 p radius, i.e., in the vicinity of their sources. For other particles it is of minor importance when compared with the wash-out by precipitation. This becomes evident if we compare analyses of rain-water samples which were collected 20 km west of Boston simultaneously in two identical gauges one of which was opened during rain only and thus did not collect the fall-out of dust between rains. The average ratio of open/closed funnel for various ions in rain water over a period of several months was: N a 1.09; C1 1.12; Ca 1.22; K 1.46; Mg 1.02 Measurements in England [120] of the fall-out of radioactive materials confirm this; only about one-fifth as much material was deposited on a sticky surface as was collected in the rain during the same time interval. These data lead us to assume that the dry fall-out of aerosols, a t least in regions with normal amounts of rainfall, is around 5 % t o 40% of the total, and that this percentage varies with the component. The removal by impaction seems to be a t least locally much more efficient. Eriksson [121] came to this conclusion upon comparing the amount of chloride received at the surface by rain water and that carried away by river water in Sweden. He found that the geographical distribution of both values is approximately the same, but that the runoff is about four times as great. Estimates seem t o indicate that this difference can only be explained by a n additional supply from the atmosphere,

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possibly by the collection of sea-spray particles from the air on the foliage in the extensive wooded areas of Sweden. The observation that rain water collected under trees shows a substantially higher concentration of trace substances than normal rain water, primarily a t the onset of rain, lends support to this view. The decrease in chloride particles observed by Byers in the layer near the ground (Fig. 13) was attributed by him to the same process. However, the world-wide geochemical significance of this effect is hard to estimate and is seriously minimized by the fact that a great portion of the earth’s surface has no vegetation. The removal of gases by escape into space applies only to those with low atomic weight, such as Hz, and not to the components treated in this paper. For gases like CO1, NzO, CHI, CO, and probably CHzO, the removal processes (b) and (c) are certainly the predominant ones. Removal by precipitation is probably the decisive process for the sulphur and nitrogen components (with the exception of NzO); however, very little is known about it. Summarizing, it may be stated that precipitation is probably the most important process whereby active trace substances are continuously removed from the atmosphere. It is by no means the sole process and is of quite variable importance for different components.

4.2. Physical and Chemical Processes of Wash-Out by Precipitation By “wash-out” we mean the over-all process by which trace substances are removed from the atmosphere through precipitation. It comprises the following processes which contribute to the accumulation of trace substances in the precipitation: (1) The consumption of condensation nuclei during the formation of cloud elements. (2) The subsequent attachment of aerosol particles t o the cloud elements as a result of Brownian motion. (3) The subsequent attachment of aerosol particles to cloud elements through the “ Kumai-Facy ” processes. (4) The absorption and fixation of trace gases on cloud elements. (5) The interception of aerosol particles by falling raindrops. We wish t o discuss these processes in somewhat more detail because of their importance for an interpretation of rain-water analyses. For an estimate of the first process it is important to know which aerosol particles, with respect to size and composition, serve as condensation nuclei, and eventually reach the earth through precipitation. More detailed statements about this process are now possible on the basis of

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CHRISTIAN E. JUNGE

investigations by Kuroiwa [47],Yamamoto and Ohtake [48]. These authors took individual cloud and fog drops (mountain and ocean fogs) and studied the size distribution and origin of the evaporation residues under the electron microscope. In Table XV the results are summarized TABLE XV. Comparison of the total number of nuclei in various size ranges and the observed size distribution of nuclei found in clouds and fog. Radius of particles in p 0.1-0.2 0.2-0.4 0.4-0.6 0.6-1.0 1.0-2.0 2 . 0 - 4 . 0 Number of nuclei in Frank- 1200 150 16 5 1.2 0.15 furt (see Figs. 3 and 4) per cmJ. Percentage of observed nu28 18 16 17 7 <1 clei in cloud and fog droplets according to Yamamot0 and Ohtake [48]. 12% with T 5 0.1 p are not included. Total numbers according to 4.8 3 .O 2.8 3 .O 1.2 Yamamoto when percentOrigin of these nuclei: age figures are normalized 26% sea salt, 57% combustion products, 13% soil, for the largest particles 4% unknown, total number 217. between 1-2 p of the 1st line. Percentage of total nuclei 0.4 2 17 60 100 which served as true condensation nuclei in various size ranges (line 3 compared with 1). Percentage of total nuclei 0.2 1:7 15 24 100 which served as true condensation nuclei in various size ranges according to Kuroiwa 1471, calculated in the same way as those of Yamamoto et al. in line 4. Origin of nuclei of Kuroiwa. Total number of Average 7 24 % sea salt 5 1 1 6 11 4 2 52 % 11 16 combustion products 8 0 1 24 % 6 5 soil matter

and compared with Junge’s size distribution of aerosol particles. Both series of observations (lines 3 and 6) show fair agreement as to the very heterogeneous materials that can act as condensation nuclei. There might, of course, still be a preferred selection of certain nuclei (i.e., hygroscopic

ATMOSPHERIC CHEMISTRY

75

v s nonhygroscopic), but this question could only be settled by simulta-

neous measurement of the composition of the original aerosol. However, such a selection with respect to composition seems very unlikely and is also not expected with mixed nuclei. The selection with regard to size, on the other hand, seems to be very pronounced when the observed nuclei distribution is compared with the size distribution of the natural aerosol itself (lines 4 and 5). Such a comparison is, of course, only quite approximate; still the basic result can hardly be questioned. Only a small fraction of the particles of 0.1 p radius and less are apparently used in condensation, unless there is a lack of large or giant nuclei, as may occur over the ocean, though very rarely over land. Kuroiwa [47] found no indication of a correlation between the size of the cloud droplets and the size of the nuclei. However, Woodcock and Blanchard [122] conclude, with respect to the orographic showers in Hawaii, that evidently the largest drops in the clouds form around the largest salt nuclei, and that a one-to-one relationship exists between the number of raindrops and the number of salt nuclei. By coordinating the observed size distribution of raindrops with that of the salt nuclei, they found a characteristic dependence of the chloride concentration upon the size of the droplets, with a minimum around 1 mm diameter. This conclusion conforms well with Turner’s measurements of the chloride concentration of various raindrop sizes, which he obtained a t the cloud base in Hawaii [123]. Hence, Woodcock and Blanchard infer either that the drops in the showers in Hawaii grow only as a result of condensation and not of coagulation, or that, if coagulation is involved, the majority of the small droplets in the clouds do not grow around sea-salt nuclei and therefore do not alter the salt content of the larger droplets. The last conclusion agrees well with our conception that even over the oceans the large nuclei and the Aitken nuclei do not consist predominantly of seasalt. With a cloud droplet concentration of 150 to 300/cm3, not more than 10% of the droplets, according to Table 11, have actually grown around salt nuclei. In cloud formation over land, a considerable part of the large particles and almost all the Aitken nuclei remain unused in the cloud air (see, for example [l], p. 200), but some of them attach themselves subsequently to the cloud elements by Brownian motion. As in Fig. 5, predominantly the smallest Aitken particles participate in this process [15]. The effect of this process on the content of trace substances in cloud droplets is small as may be seen by the following estimation: If, as an extreme example, we assume an aerosol distribution similar to that in Frankfurt (Fig. 3) in a cloud of 100 cloud droplets of 15 p radius, lo4 particles with radii of less than 0.04 p would coagulate with the cloud droplets in four hours.

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CHRISTI.4N E. JUNGE

This corresponds to an increase in substance of about 2 X gm per cloud drop, which is equal to a condensation nucleus of 0.1 p radius. As most original condensation nuclei are larger, we must conclude that under less extreme conditions than those of our example the coagulation of aerosol particles due t o Brownian motion is without significance for the chemistry of cloud waters. Some observations, however, seem t o indicate a much higher rate of attachment. Kumai [124] evaporated snow crystals, collected at an altitude of 1000 meters a t temperatures below freezing, and examined the residue under an electron microscope. Besides the big (‘center nucleus” on which crystal growth started, he found a large number of small particles. The size distribution of these particles shows a maximum a t a radius of 0.025 p , in agreement with natural aerosols. The particles are equally distributed throughout the crystal, with a concentration of 1 per pa. A snow crystal of 1.6 mm diameter and a thickness of 10 p thus contains 107 particles with a total mass of 5 X 10-lo gm. This mass corresponds to an aerosol particle of about 5 p radius and represents an amount of material comparable to the “center nucleus.” Facy [ 1521 observed directly the migration of aerosol particles towards and from the surface of droplets depending on the direction of the water vapor flux (condensation or evaporation). Due to this effect most of the material found in cloud droplets may not be identical with the original condensation nuclei. We now come to the absorption of trace gases in cloud droplets. Here we must distinguish between gases which dissolve according to Henry’s law and those which undergo transformation in water. The first group comprises NzO, NO, HzS, Clz, IS, CO, CH4, and CHzO; the second group includes COz, 03,SOz, NH3, and NOZ. With the observed partial pressures in air of the first group, the calculated concentrations in rain water range from t o lo-‘’ mg/liter, which can be completely ignored when compared with the observed concentrations of other components in rain water. The concentration of these gases in air is not influenced by rain. In the second group, data sufficient for quantitative considerations are available only in the case of C02 and NH,. The components formed by these gases in an aqueous solution are appreciably controlled by the p H value of the solution. We will illustrate this in more detail with respect to COz [125]. The partial pressure P (atmospheres) of COP over a solution is, according t o Henry’s law, proportional to the concentration (mole per liter) of the undissociuted, dissolved COZ:P X (Y = CO1. The undissociated COZ is in equilibrium with C03-- and HC03- ions with the equilibrium constants K 1 and Kz:

ATMOSPHERIC CHEMISTRY

K1

=

77

[H+] X [HCO,]

[cod

If no other ions are present, we also have K,

(4.3)

=

[H+] X [OH--]

and

[H+] = [OH-]

(4.4)

+ 2[COa--] + [HCOX-]

(see [122]),which gives

(4.5) This relates the pH value ([H+]) with the partial pressure of COz in the air. A t 10°C, the constants have the following values: a!

=

5.36 X low2mole per liter/atmosphere

K1 = 3.4 X 10-7 mole per liter

K Z = 3.2 X lo-" mole per liter K,

=

3.6 X 10-l6 (mole per liter)2

Below a pH value of 6.5 there are hardly any carbonate ions present, and all the dissociated carbon dioxide is present as bicarbonate. The expression for P can then be reduced t o

With a COZ concentration in the atmosphere of between 150 and 400 ppm, pH values between 5.5 and 5.7 result. With a pH value of 5.5 and a t 20°C, the carbon dioxide is dissolved in water in the following manner: undissociated CO2 = 1.04 mg/liter HCOa- = 0.13 mg/liter total COZ= 1.17 mg/liter The pH values actually found in rain water vary over a wide range of from 3 t o 7, with averages around 5. According to Barret [126] one can justifiably consider the equilibrium pH value of carbon dioxide as the normal pH value of rain water upon which the other dissolved substances are superimposed. If, for example, 0.30HzSO4,0.20HNo3, and O.11HC1 (expressed in mg/liter) were present in rain water, each corresponding t o a pH value of 5.5, then with the addition of carbon dioxide the pH value

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CHRISTIAN E. JUNOE

would decrease from 5.5 to 5.29. With the presence of 0.17 mg/liter of KOH, for example, the value would rise to 5.65. Similar, though simpler, is the NH3-H20 system [127]. If all concentrations are expressed in moles per liter, the system is described by

“&]air

(4.7)

P[NH3]nster = B[NH4OH]wster

=

and , (4.8) K3 =

“H4+1

[OH-] “HIOH]

2.0

=

x

10-5 moles per liter at IOOC

For the ratio F of the total concentrations in air and solution we obtain (4.9) With [H+] = 10-7, (4.10)

F

s

PKw/K3[H+l

Thus for a pH value of 5.5, (4.11)

F

=

3.2 X

This small F value indicates that almost all of the NH3 gas present in the air goes into solution when a cloud forms. As an example we might assume an NH3concentration of 3 y/meter3, in which a cloud forms with a liquid water content of 1 gm/meter3. The volume ratio of air/water is thus 10+8 and the actual ratio of gaseous NH, to that dissolved in water, 3.2 X 10-2, which value corresponds to 2.90 y NH3 in solution and to only 0.1 y remaining in the air. Due to the presence of COZin the air one should, therefore, expect an NH3 content in rain water of about 3 mg/ liter and a very high wash-out efficiency for ammonia. This NHa content, however, is about ten times higher than the values usually observed, and the high wash-out efficiency is not in accord with the observed fairly uniform distribution of NH8. Further investigations are necessary in order to clarify this problem. Very little is known about the systems S02-Hz0 and N02-H20. The physical and chemical literature hardly goes beyond qualitative data, and these are full of contradictions. It appears that at very small SO2 concentrations a certain amount of SO2 is oxidized to SO4 in the solution. This oxidation process is limited and the so4 formed is irreversibly attached to the droplets. This apparently is not a true equilibrium, but rather a case of negative autocatalysis, in which the pH value might regulate the process of SO4 formation. Besides this direct fixation through oxidation, there are, of course,

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ATMOSPHERIC CHEMISTRY

many more reactions possible between the dissolved gases NHa, SO2, NOz, etc. ; however, their significance for precipitation chemistry is not known. Due to this lack of data, the question as to which fraction of the NH4, Sod, and NO3 content found in rain comes from aerosols and which from the gas phase cannot be answered a t present. Probably the share of both sources is of the same order of magnitude. Raindrops can receive a considerable increase in substance through the collection of aerosol particles under the clouds. This effect can be estimated quantitatively [8]. If N ( r ) is the concentration of aerosol particles (of density 1) underneath the cloud at the beginning of the rain, E(r,R) the collection efficiency, r and R the radii of the particles and raindrops, and H the altitude of the cloud base, then the concentration of trace substances in the precipitation by collection is (4.12)

E is known from Langmuir's investigations [la81 and depends upon the radius of both the raindrop and the aerosol particle. The calculations of E show the important fact that aerosol particles of less than about 2 p TABLEXVI. Calculated concentration K of soluble material collected by falling raindrops of radius R [S].The assumed size distribution of aerosol particles is that of Frankfurt (Fig. 3) and H = 1000 meters.

R

K

= 0.1 = 71

0.4 29

0.2 45

0.8 15

1.6mm 7.5 mg/liter

radius cannot be collected by raindrops of any size. Thus, under the clouds the large nuclei and the Aitken nuclei cannot be reduced by the rain itself. Assuming a normal size distribution of soluble aerosol particles, we obtain the values of K as a function of R listed in Table XVI. These values are of the same order as the observed ones, indicating the importance of this process for rain chemistry. One must also expect this concentration to be inversely proportional to the size of the raindrops, Turner [123] has measured the relationship of the C1 concentration to the size of the raindrops. In addition to his observations in Hawaii at the base of the clouds as well as in them which did not contain this effect, he also made measurements below the clouds in Australia. Figure 26 shows a few results under varying conditions. Even though the concentration in general decreases inversely to the radius, the exponent n in

K

a

R-"

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CHRISTIAN E. JUNGE

can increase to 2.6. Turner attributes this to the combined effect of the collection and evaporation of the droplets on their way to earth. The little droplets thereby decrease in size and gain in concentration more rapidly than the larger ones, a process which can quantitatively account for the high exponents. However, exponents of less than 1 are not explicable in this manner. Turner also calculates the absolute values of R and finds good agreement with the ones observed. This confirms that collection through falling rain plays a significant role in rain chemistry for those particles which are larger than 1 f i and concentrated in the lower layers (as is the case for sea-spray particles over or near the ocean).

-*,---if\,-

3

0.6 1.0

2 3

Raindrop diameter (mm)

FIQ.26. NaCl concentration

(1) 121 as a function of raindrop size according to Turner.

(1) Typical results in Sidney, Australia. (2) Comparison of NaCl concentrations under different conditions, (a) Wind from sea, more than 35 km/hr. (b) Wind from sea, less than 35 km/hr. (c) Wind from inland. (By courtesy of the Royal Meteorological Society.)

Landsberg [129] has measured pH values of individual raindrops. He found values between 3 and 5.5, which are somewhat lower than the values of other observers and may indicate the proximity of Boston. The small droplets have the lowest values. This again seems to indicate that most of the substances which influence the H+ concentration were collected below the cloud. The concentration K of the precipitation as a function of the height h of the fallen precipitation [S] is (4.13)

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ATMOSPHERIC CHEMISTRY

where N o is the initial concentration of particles. The formula reflects the gradual removal of particles from the air through which rain is falling. Assuming that the average size of the collected aerosol particles is 8 p (lower value 2 p, upper value 15 to 21 p), we can calculate the height of precipitation hl a t which the concentration in rain water has been reduced t o one-half, as well as height hz a t which the concentration of 8 p particles below the cloud has been reduced to one-half (Table XVII). It is a t once evident how efficiently giant aerosol particles are washed out by rain. The amount of precipitation h can, of course, be replaced by tp, in which t represents the duration, and cp the intensity of the rain. After a certain amount (or duration) of rain, the term e--3Eh’4R becomes very small, indicating that all aerosol particles are completely washed out. Subsequent rainfall then results only in a further dilution, expressed by the fact that K = h-l. TABLE XVII. Amount of rainfall hl and hz necessary to reduce the initial concentration in the rain and the initial particle number below the cloud to 36 as a function of raindrop size. R hl hz

=

= =

0.1 0.38 0.17

0.2

0.61 0.27

0.4 1.0 0.46

2.5

2.0 5.4

1.1

2.4

1.0

mmradius mmrain mmrain

A decrease of the trace-substance concentration with time during precipitation has been noted by many observers. Careful measurements, for instance, of nitrates were made by Anderson [130]. His values agree with the approximate equation K a: h-l. But such agreement does not necessarily mean that the major part of the trace substances in rain is collected by falling raindrops. Those trace substances from within the cloud will also show a depletion with continuing rainfall and the two effects cannot be distinguished in rain samples a t the ground. 4.3. The Content of Rain Water with Respect to the Predominantly Continental Components NH4+, NOa-, NOz-, SO,--, and C u f f

I n this and the following section we wish t o give a concise survey of of the observations of the trace-substance content in rain. As we saw in the preceding section, it is difficult on the basis of such values to draw conclusions about the concentrations of these substances in the air itself. The natural process of collecting trace substances in rain water is too complex for this. However, with a sufficiently large number of observations one may expect that differences with respect t o cloud topography and precipitation processes will be largely eliminated. Average concentrations in rain water may, therefore, be considered as approximately

82

CHRISTIAN E. JUNGE

proportional to the trace-substance concentrations in the air within the troposphere. Moreover, it may be that rain-water analyses represent the average trace-substance concentrations in the troposphere better than do direct measurements in air at the ground level with its local sources and sinks. A large number of rain-water analyses are thoroughly discussed by Drischel ([131], 189 references) and, more recently, by Eriksson ([132], 317 references). The material reviewed in these two papers will to a large extent form the basis for our treatment. The nitrogen compounds NH4+ and NO3- were among the first t o be studied thoroughly; the reason for this interest was their importance for the problem of nitrogen fixation in soil and plants. TABLE XVIII. Average data on Nos- and NH4+ concentrations (mg/liter) in rain water a t various places [ S ] . Locations Nine locations near the coast * Seven undisturbed locations inland t

Nos-

NH4+

range: 0.15-0.60 average: 0 . 2 9 range: 0.31-0.78 average: 0 . 5 8

range: 0.04-0.29 average: 0 . 1 5 range: 0.10-0.76 average: 0 . 3 7

* The locations near the coast and their respective years of

observation are as follows: Georgetown, British Guinea (25 years); Madras, India (8); Ceylon (2); Mississippi, USA (Gulf of Mexico) ( 1 ) ; Hebrides (6); Trondheim, Norway (1); Lincoln, New Zealand (2); West Coast of England (4); Hsmamatsu, Japan (1). t The seven undisturbed locations inland and their respective years of observation are a8 follows: Cairus, Auetralia (2 years); Debra Dam, India (1); Flahult, Sweden ( 8 ) ; Goodwell, Texas. USA (1); Manhattan, Kansas, USA (1); Reinerz, Czechoslovakia (leas than 1); Oberschreiberhau,Czechoslovakia (less than 1).

Table XVIII gives an idea of the range of the average concentrations of NO3and NH4based on more extended and representative measurement series, which are apparently free of local influence. Values near the ocean are somewhat lower than those at inland stations, though otherwise the concentrations are quite uniform. The table indicates that the main sources of these compounds are to be found over land. According t o Eriksson, neither NO3 nor NH4 show a marked change with geographical latitude. However, this conclusion is based on only a few tropical measurements, and none beyond 60" North and 45" South. Apparently the European values are in general somewhat higher than those for other parts of the world; this may reflect the higher population density on this continent and may have some connection with the high NH3 values in France mentioned in Section 3.5. Angstrom and Hogberg [133] discussed the distribution of NO3 and NH4 concentration in rain water over Sweden. They found that the an-

ATMOSPHERIC CHEMISTRY

83

nual average concentration for both decreases from south-southwest toward north-northeast. The above-mentioned lack of a wide-spread trend with latitude and the higher values over Europe strongly suggest the influence of sources in West and Central Europe, which diminishes with distance due to horizontal and vertical mixing as well as to wash-out. The annual variations of NO3 and NHI concentrations are not very distinct. Most of the uninfluenced inland stations show higher values in summer than in winter in agreement with the Swedish air analyses for

FIG.27. Average NH,+ concentration (mg/liter) in rain water, July 1955. The hatched area indicates no rainfall or insufficient sample.

NH3. Sites along the coast or those near anthropogenic sources show irregular variations, sometimes with maxima in winter, which are apparently due to the annual fluctuation of these sources. Long-time variations on a global scale do not seem to be indicated; however, the observational data are still too inadequate for such conclusions. The longest available measurement series a t Rothamsted (18881916) and at Ottawa (1908-1924) show a systematic increase of NO3 (Rothamsted) and of NHI (Ottawa) [132]. In both cases this is probably the result of human activities. The basic features of the large-scale NHa and NO, distribution with time and space are confirmed by results (not yet published) of a rainwater analysis network, in operation in the United States and parts of the Atlantic since July, 1955 [134]. For example, Fig. 27 gives the average NH4+ concentration for the month of July, 1955, showing lower concen-

84

CHRISTIAN E. JUNGE

trations over the ocean, pronounced local differences over land, and no systematic variation with latitude. The zones of higher and lower concentration change considerably from month t o month with only a slight increase over thickly settled regions, indicating that natural sources predominate by far. Only the southeastern United States always shows very low NH4 content for all months available. We suspect that the low pH value of the yellow-red laterite soil, the boundary of which is outlined in Fig. 27, prevents the escape of NH3 from the soil in this area. The NH3 concentration over the U. S. shows a pronounced annual variation, with a maximum during summer. TABLE XIX. Change in concentration (mgbiter) of various compounds in rain water with increasing distance from Berlin [136]. The average concentrations are given for the year, summer and winter. Location Center of Berlin Berlin-Dahlem, 15 km SW of the center of Berlin Muncheberg, 50 km E of the center of Berlin

Total insoluble matter

Total soluble matter

84 50 46 37 35 41 23 13 37

87 70 110 67 58 85 28 24 34

SO4--

25 12 42 19 6 42 10 7 14

C1-

NHr+

6.0 4.1 9.2 4.4 3.4 6.3 3.5 2.5 5.4

0.60 0.62 0.61 1.0 1.1 0.9 0.4 0.5 0.4

All this points to the soil as the main source of NH3. Russell and Richards [135] as well as Drischel [131] come t o the same conclusion, whereas Eriksson [132] considers fuel consumption t o be the main source of NH,. However, Table XIX indicates that a big city like Berlin is not a very efficient source of NH3, even in winter. If the soil is the major NH, source, one may expect that more intensive agricultural exploitation of the land increases the production of NH3; this might explain the higher NH, content over Europe. Compared with the land the ocean is only a small NH, source (see Section 3.5). The NO, concentration behaves differently : it shows no pronounced annual variation and no anomaly in the Southeast, such as there was with NH4. In summer the concentrations are fairly evenly distributed over the U. S., indicating that probably the basic source of NO3 is the soil. I n winter time higher concentrations in the northeastern parts of the U. S. may be related to human sources. No relation t o thunderstorm activity seems to exist, in agreement with Hutchinson and other observers [58] who regard lightning as an unimportant source of Nos.

ATMOSPHERIC CHEMISTRY

85

In many Nos- analyses, the NOZ- content is included. The infrequent investigations which analysed it separately reveal that it constitutes approximately 10 % of the nitrate content [130-1321. A few observations in the United States, India, and Japan give NOz- concentrations of between 0 and 0.15 mg/liter, with average values of around 0.012 mg/ liter. Since NOz- is never found in aerosols, it must be formed during rain formation by absorption of gases. An important and interesting component in rain water is SO4. The so4 concentrations in rain water [131, 1321 are comparatively high. The lowest concentrations of about 0.5 mg/liter are found in undisturbed areas in the United States and in Russia. The values over the sea due t o spray are usually somewhat higher, about 1 mg/liter, but the difference is in general small. The most frequent values over land are between 1 and 5 mg/liter, but may increase to 20 mg/liter and higher in thickly settled and industrial areas. No relationship seems t o exist between SO, and latitude, but the observational material is too scanty to draw any definite conclusions. In several geographical areas the annual variation shows a winter maximum which is more pronounced over regions with greater industrialization. This clearly points t o the fact that the combustion of coal is an essential source of SO2 and subsequently of so4. However, the greater frequency in winter of stable weather conditions with moderate winds over continental areas favors a greater local accumulation of SO2 in the air, so that the winter maximum is not caused solely by the variation of the source itself. In undisturbed rural areas the annual variation is slight. The long-time variations are quite varied and show an increase when the location falls within the sphere of influence of growing cities or industrial areas. No systematic variation was observed in other localities which maintained their undisturbed character, as e.g., in Stillwater, Oklahoma, with its long series of observations between 1927 and 1942 [137]. This indicates that over large parts of the U. S. the SO2 supplied by man-made sources is still insignificant compared with natural sources. An example (Fig. 28) from the United States network again provides an illustration of the distribution and concentration of sulfate in rain water. A large maximum in the northeastern United States reflects the concentration of industry and population in this part of the country. A second very strong maximum in the West has not yet been explained. The location and strength of these areas of high SO4 content undergo considerable month-to-month variations, due to the general circulation ; however, by and large they occur in the same regions and thus seem to be geographically linked. Of interest is the fairly constant so4 background on this map. It

86

CHRIBTIAN E. JUNGE

points to a quite uniformly distributed natural SOZ source which we believe is the soil. If our interpretation of the areas of high SO4 concentration (due to the activity of man) and of the SO4 background is correct, we can estimate that the total amount of natural SO2 present in the atmosphere over the United States is of about the aame order of magnitude as the amount supplied by man. The main source of anthropogenic sulphur components is the combustion of coal, oil, and other fuels. The significance of this source becomes

FIQ.28. Average SO,-- concentration (mg/Eter) in rain water, July, 1955. The hatched area indicates no rainfall or insufficient sample.

clear when one considers that the sulphur content of these materials can amount to as much as 4%. Another strong source of industrial SOz are the smelters which process sulphur-containing ores. We already mentioned in Section 3 that organic decomposition is a major source of natural sulphur oxides, presumably from oxidation of HzS which escapes from ground, shallow seas and marshy areas, and t o a small degree even from the ocean. The immediate source of SO4 in rain water seems t o be SO2, which readily oxidizes in solution and which can be accumulated in droplets partially neutralized by cations like NH4+ and Caw. Part of the SO4 is certainly contributed by aerosol particles which, as we suggested in Section 3, may in turn be the remnants of former rain and cloud drops. But the large particles cannot contribute very much to the SO4 content in rain water because the NH4/S04 ratio is much

ATMOSPHERIC CHEMISTRY

87

smaller in rain than in the large nuclei, as indicated by Table XIX for Central Europe. Another natural source is the SO4 of sea-salt nuclei. The sulfate content in sea water is 14% of the chloride content. With chloride concentrations in rain water of about 10 to 20 mg/liter near as well as over the ocean, we may expect concentrations of maritime SO4 of 1.5 t o 3 mg/liter, which are observed. As sea spray is not the sole source of SO4 in rain water even over the ocean, the ratio c1/so4is always smaller than in sea water, where it is 7.1. The observed c1/so4 values at the coast are in fact no more than half as large as 7.1 and decrease rapidly with increasing distance from the coast [132]. Very low Cl/SOk ratios were found by Houghton [138] in water samples of sea fog at various places along the northeast coast of the U. S. The maxima of the SO4 concentration were between 13 and 125 mg/liter. Air masses in this area are, of course, basically continental, because of the west wind circulation, even if the air had some over-water trajectory prior to sampling. Larson and Hettick [139] find a relationship between the concentration of SO4-- and the sum of NH4+ and NOS- ions. They explain it by the fact that all three materials come from the same source, namely from the combustion of coal and oil. But even in nature these three materials presumably have the same source, viz. the soil, and the general validity of such a relationship thus becomes understandable. Another important soluble component of rain water is Ca; however, our information [132] is very limited in this case. The Ca content varies considerably with time and place from about 0.1 to 10 mg/liter. A United States network map for July (Fig. 29) shows a large area of high concentrations in the Southwest and some small isolated areas of higher concentration in the East and South. Similar patterns are also observed in other months. From this distribution it becomes evident that the predominant source of the Ca content is the dust blown into the air in the arid regions of the Southwest. Most of the Ca enters the air as carbonate and becomes soluble bicarbonate through the action of atmospheric COZ. Another part is probably converted to CaS04by the oxidation of atmospheric SO2in droplets. Larson and Hettick also found a good relationship between the sum of the HC03- and SO4-- ions, on the one hand, and the sum of the Ca++ and Mg++ ions on the other, in Illinois rainfalls. This supports the view that lime and dolomite particles react with the H2SO4formed in rain. Gorham [33], too, found a relationship between the SO4 and Ca content in North England. Sea water contains only 2.1 yo Ca with respect to chloride, hence seasalt particles represent no significant Ca source over land.

88

CHRISTIAN E. JUNGE

4.4. The Content of Rain Water with Respect to the Predominantly Maritime Components Cl-, Nu+, K+, Mg++and the Role of Precipitation in the Natural Cleansing Process of the Atmosphere By far the largest quantity of the C1 found in rain comes from the ocean. This, for instance, is indicated in Figs. 30 and 31 by the rapid decrease of the C1 content as one goes inland as well as by the lack of influence from industrial areas. Generally the industrial sources of C1 are not important. Eriksson [132], for the industrial area of Leeds (England), reports that the chloride varies only by a factor of two when the sulfate

FIG.29. Average Ca++ concentration (mgfliter) in rain water, July, 1955. The hatched area indicates no rainfall or insufficient sample.

content varies by a factor of ten. Volcanism [132] is another source of C1, but also of local importance only. Of all the trace substances in the air, sea salt (and thus chloride) is the only one whose major source is geographically sharply defined. A study of its horizontal distribution over land, therefore, would give valuable information on the cleansing of air by precipitation processes. Reliable data on the decrease of the C1 content with increasing distance inland were compiled by Leeflang [ 1401, Emanuelsson, Eriksson, and Egn6r [141], as well as by the United States network. Facy’s data [142] from the Breton peninsula are too vague as regards the true distance from the ocean. A comparison of these data is made in Fig. 30. Both United States profiles, one from the Atlantic Coast toward the northwest and one from the Gulf of Mexico toward the north, show a roughly logarithmic

ATMOSPHERIC CHEMISTRY

89

Kilometers FIG.30. C1- concentration in rain water as a function of the distance from the coast. Curve 1 according to Leeflang 11401 for the Netherlands. Curve 2 according to Emanuelsson et al. [141] for Sweden. Curves 3 and 4,cross sections from Cape Hatteras, North Carolina to northwest and from Mobile, Alabama to north (United States). Average July-September, 1955. Curve 5, calculated decrease due to wash-out only, under conditions similar to those for curves 3 and 4. The initial concentration was arbitrarily assumed to be 3 mgbiter.

FIQ.31. Average C1- concentration (mg/liter) in rain water, July-September, 1955. The indices a t the figures indicate the number of months from which this figure was formed. No index means all three months. The hatched area indicates no rainfull or insufficient sample.

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decrease up to 500 km after which the C1 concentration remains practically constant. The values are averages for July t o September. The curve for southern Sweden was derived from a map in [141] along the line of the strongest gradient from southwestern to northeastern Sweden. It agrees approximately with the United States curve up to 300 km. The renewed slight increase from 300 t o 500 km, when the east coast of Sweden is reached, is probably attributable to the influence of the Baltic Sea, with its low salinity. Leeflang’s curve shows a steep drop in the first few kilometers from the coast, similar to the results of Neumann [46]. This decrease soon stops and approaches an apparently constant value of 3.0 mg/liter. It is of interest that similar high values were found in Muencheberg (Table XIX), a location which is fairly representative for Central Europe. Rossby and Egn6r 1321 have drafted a provisional map of chloride concentrations in rain water for Europe which shows values around 3 mg/liter all over West and Central Europe, while the substantially more sparsely settled interior of Scandinavia has values of only 0.5 mg/liter. As with COz and NH3, we again encounter higher levels in Europe, pointing t o the influence of human activity. It would no doubt prove interesting to study more closely the chloride distribution in Europe with respect t o possible anthropogenic sources. Figure 31 and the curves from the Southeast of the U. S. in Fig. 30 show the remarkable phenomenon that a constant value for chloride concentration is reached at about 500 to 600 km from the coast. The attempt t o find a quantitative interpretation for this chloride distribution led t o interesting results. Various considerations and calculations offer evidence that the decrease in the C1 concentration, at least in the U. S., is the result of vertical mixing by convection when the air masses enter the continent rather than the washing out of particles by precipitation. It is the resulting decrease in the salt-particle content of the lower layers of the troposphere that is reflected in the decrease of the chloride concentration in rain water. The following facts support this view: (1) As discussed previously on the basis of Fig. 13, the total amount of sea-salt particles at the center of the continent does not differ very much from that over the Gulf of Mexico. (2) The washing out through precipitation can be estimated. The average volume of tropospheric air out of which precipitation falls can be computed from the average daily rainfall and the liquid water content of raining clouds. Assuming with Woodcock that all sea-salt nuclei will be removed from the cloud air and considering the collection of salt particles by falling raindrops, the

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concentration of the salt particles should decrease to half its value in approximately four days. With an average southerly air flow of 12 km/hr from the region of the Gulf, this corresponds to a half-value distance of 1200 km and is indicated by curve 5 in Fig. 30. Even if we consider that the assumptions made in this calculation are only approximately correct, the wash-out is not efficient enough to explain the observed decrease of C1 content inland. (3) Computation shows that the speed of vertical mixing as maritime air masses cross the coast and move inland during the summer is sufficient to explain the observed decrease in the chloride content. From Fig. 30 one can see that mixing should be completed after a path of 600 km, a distance 60 times the height of the tropopause. This appears to be reasonable. The effect of vertical mixing over land through convection naturally plays a lesser role in winter or over more northerly latitudes, as e.g., in Scandinavia. Correspondingly the wash-out has a more significant influence. Summarizing this discussion we can distinguish the following three zones for chloride decrease inland : (1) Near the coast, within about 10 km, the decrease of sea-salt

particles, especially from the surf area, occurs by fall-out. (2) From about 10 to 600 km, the decrease in the salt content is primarily accounted for by tropospheric mixing. (3) Following this, wash-out becomes efficient. Before we go on to a further consideration of wash-out, we should discuss changes in the chemical composition of the precipitation with increasing distance from the coast. In their very interesting study of the “chemical climate” in Sweden, Rossby and Egn6r [32] demonstrated that the ratio Cl/Na, which amounts to 1.8 in sea water, undergoes large fluctuations over Scandinavia, being obviously dependent to a large degree upon the general circulation. With a general advection of southern air masses they find values which decrease from 3 in southeastern Sweden, to 1.5 or 2 in northern Sweden. With predominantly northerly winds the Cl/Na ratio for all of Sweden lies between 0.00 and 0.30, i.e., lower by one order of magnitude. With westerly winds the values decrease from about 1.30 in southwestern Sweden t o 0.25 in northern Sweden. These observations can be explained in two ways: either the sea-salt particles undergo a chemical decomposition (release of C1 by oxidation) on their way over land, resulting in different removal rates of the released C1 and of the Na-enriched sea-spray particles, or supplementary sources of C1 or Na are present over land.

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Considering all observations together, one must give preference t o the second interpretation, although the final decision of this question must await further investigations. The supplementary Na sources may be mineral dusts, as was the case with Ca. Should the Cl sources prevail over the Na sources, as possibly in industrial areas, then the Cl/Na ratio can exceed 1.8. This is obviously the case when strongly polluted air masses from Central Europe are transported to Sweden with southerly winds. The advection of continental air masses from the north and the east with relatively high mineral-dust and low sea-salt contents will reduce the Cl/Na ratio considerably. Kalle [143] confirmed these ideas by studying the question of mineral dust in more detail. Using the Swedish values [141] he attempts to separate land and sea components in rain water by subtracting from the observed values of Na, Ca, and K those amounts which correspond t o the observed C1 concentrations and the composition of sea water. The difference gives the " hypothetical dust portion." This dust portion is essentially independent of the distance of the coast, and has a relative composition Na :K :Ca = 20 :15 :65, which corresponds satisfactorily with the composition of various types of rock. The values of the United States network show Cl/Na values that vary over a wide range from 0.1 to over 2, with the most frequent values being around 0.6. Only very sporadic values above 1.8 occur inland, particularly in winter. This, too, is compatible with the second interpretation: The lower density of population and industry in the United States as compared to Western Europe the artificial C1 sources result in lower concentration and thus the mineral Na sources nearly always prevail. Similarly to Na, the K, Ca, and Mg over land show higher values with respect to C1 than the corresponding values in sea water. Leeflang [140] found ratios of K/C1, etc., in Holland, which were higher even a t the coast than in sea water (dust from England?) and which increased rapidly farther inland. Emanuelsson and others [141] give maps of the Ca/Na ratio (increase from the coast to the interior: 0.3-1.5; sea water: 0.038), and the K/Na ratio (increase: 0.1-0.5; sea water: 0.036) in Sweden, showing the considerable excess of these ions with respect t o the sea water. From the United States network data, there is no, or only very little, relationship between the additional Ca, Na, K, and Mg sources over land. The continental Na and K is more evenly distributed than the Ca and Mg, This behavior seems to point to independent disintegration processes for the individual components. The problem of the distribution of maritime and continental aerosols over continents and oceans leads directly to the following basic question about the behavior of our atmosphere: After what time interval or after

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what distance does the aerosol content of the troposphere decrease by a definite fraction, say one-half, due to washing out and other processes? As we saw above, sea-salt nuclei have probably a half-value time of 4 days during the summer in the Southeast of the United States. If we relate this value to the annual average rainfall of 600 mm for the north temperate zone, we obtain 8 days. It is interesting t o compare this value with data obtained by Stewart and others [120].For months, these authors followed the radioactive content of the troposphere resulting from atom bomb experiments in Nevada. During this test series practically no material was injected into the stratosphere, so that the radioactive material was limited essentially to the troposphere. The data were obtained on flights over the Atlantic and are fairly representative values for the troposphere. They present the following picture: after the dust clouds had traveled about half-way around the world, they were quite uniformly distributed within the west-wind belt with respect to height and breadth. Mixing with air masses south of the horse latitudes and above the tropopause occurred very slowly, so that the observed decrease in the temperate zone must be ascribed to removal of aerosols by precipitation, etc. The half-value time of this removal was 22 days. The difference between this value and that of 8 days for sea-salt nuclei is in the expected direction when the size of the particles is considered. We must assume that a substantial part of the radioactive particles is smaller than 1 p, so that their over-all wash-out efficiency is less than that of the giant sea-spray particles; according to Table XV we should actually expect a greater difference. Moreover we must bear in mind that the value of 22 days naturally represents a minimum, since the decrease caused by fall-out, collection, and mixing have been included. Particles with a radius of between 0.05 and 0.1 p are probably the most difficult ones to remove from the atmosphere. For smaller particles the higher rates of coagulation with larger aerosol particles and cloud droplets increases the probability of wash-out. Particles of less than 0.1 p will probably be washed out preferably over the ocean, because the total number of nuclei there is so small that even the Aitken particles will become active nuclei. I n Hawaii, for example, in several clouds no Aitken nuclei could be found [37]. It would be important t o study more closely the half-value time of the aerosols as a function of particle size (and possibly of their hygroscopic characteristics as well) in order to be able t o make predictions about the duration of their stay in the atmosphere. Other values of the half-life time of natural aerosols were obtained by Blifford et al. [144] and Haxel and Schumann [145] by comparing the concentrations of the various decay products of radon with the equilibrium decay concentrations. Because of their removal the aerosol particles show

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a lack of the long life products, particularly radium D. The half-life times are Blifford et al. 12 days Haxel et al. 4 days

It is probable, that these times refer to a “short cycle” of removal, because most of the natural radioactive material is concentrated in the lowest layers of the troposphere, as indicated in Figs. 20 and 21, and is easier removed than aerosols, which are uniformly distributed throughout the troposphere to which our calculations referred. However, the order of magnitude agrees well with the data given above. The importance of the wash-out process for the cleansing of the troposphere becomes strikingly evident from the following observation : Stewart and others have found that radioactive material which has been injected into the stratosphere by the much stronger hydrogen bombs can remain there for an exceptionally long time. After the fall-out of coarser material, finer material can be removed from the stratosphere only by way of diffusion into the troposphere through mixing. The absence of any wash-out in the stratosphere brings the half-value time of the stratospheric material up t o an estimated ten years! These figures show at the same time the degree to which the purity of our atmosphere might be endangered by human activity. From these data we want to draw one more conclusion with respect to natural aerosols. With a half-value time of from 8 to 22 days for particles of less than 1 p, it is immediately understandable that even over the center of large oceans a considerable part of the condensation nuclei will be of continental origin, as was indicated by Figs. 18 and 19. Since it takes about 6 days under average conditions for air masses to cross the North Atlantic, maritime air masses which arrive in West Europe will still contain considerable quantities of (‘American” or even “ Asiatic” nuclei. On the basis of this knowledge the old controversy between Simpson and Wright (see Sections 2.5 and 2.6) over the nature of nuclei below 1 p in “pure maritime” air masses appears in a new light. Simpson’s argument that they are not of maritime origin is also supported by these considerations. 5. AIR POLLUTION AND ITS ROLEIN THE CHEMISTRY OF UNPOLLUTED AIR 6.1. The Main Components i n Polluted A ~ T

In view of the present development of industry in large parts of the world there can no longer be any sharp division between polluted and

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unpolluted atmospheres. Nevertheless, the interrelation between air chemistry and air pollution has never been very closely examined since both fields‘were approached by diff erent groups of investigators. For this reason we will close our discussion with a review of these facts and phenomena in air pollution which may have a bearing on air chemistry as defined in this article. The composition of a large number of polluted atmospheres is controlled by the consumption of coal, coke, gas, and other fuels. The classical land of such “coal-atmospheres” is Great Britain ([146], p. 135) where 180 million tons of coal are consumed annually, yielding the following pollutants (with the exclusion of CO and C 0 2 ) in millions of tons: smoke 2.4, ash 0.6, SO2 5.5, and HC1 and other chlorides 0.5. Smoke contains a large amount of carbon black, tarry hydrocarbons, and some ammonium sulfate. Ash is noncombustible solid material and represents a fraction of the 2% t o 10% of mineral matter normally con’ to 4%, is almost tained in coal. The sulphur content of coal, about 1 % wholly converted to SO2 by combustion and released into the air. The HC1 and other minor constituents may be important t o the study of air chemistry, but little information is available on these. A large fraction of the smoke and ash particles are big enough to settle fairly rapidly by gravity. Gases and smaller particles spread by mixing over large parts of the atmosphere and may travel long distances before returning to the earth’s surface. Unfortunately, most of the data in Great Britain are obtained by deposition gauges, which, of course, give no information on the actual concentration of the pollutants in the air. Comprehensive data giving concentrations in the air are available only for smoke (total particulate matter) and SO2. A different type of pollution is encountered in the Los Angeles area of California, where the amount of coal used is small compared with petroleum fuels. The contaminants in this area are introduced by petroleum production, refining and distribution facilities, as well as by the operation of motor vehicles and incinerators and show a large variety of hydrocarbons, comprising methane, ethylene, acetylene, acetone, as well as phenols, organic acids, tars, and a host of related products. The atmosphere of Los Angeles is further characterized by high concentrations of NOz, which reacts under irradiation of sunlight with certain hydrocarbons t o produce considerable concentrations of oxidants. The term oxidant includes ozone and comprises substances which react with potassium iodide. Little is known about the chemistry of the gas reactions involved which yield the characteristic smog. Some values of the concentrations of pollutants are given in Table XX. The levels are only approximations, as wide variations with time

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and location within the polluted area are observed. Maximum values may be higher by a factor of 5. The London and Leicester tabular entries are representative of the coal atmospheres.” The most abundant gas is CO, but as its concentration is far below the level producing toxic effects and as it is apparently not involved in reactions with other components to produce harmful substances, its presence is not considered very important in air pollution. The SO2 is present in significant amounts and attracts special attention through its ability to form aerosols, which according t o their acid TABLE XX. Comparison of various contaminants in polluted atmospheres. The values are only approximate averages in r/meters.

Location Los Angles London Washington, D. C. Leicester, England

Total particulate Oxi- Hydro- Alde- Organic matter CO SOa NO2 dant* carbonst hydest Cl§ NH3§ 400 6000 [76]** [76] 800 6000 [146] [146] 150 7000 [50] [147] 400 ~481

250 400 [76] [76] 500 20 [146] [98] 300 100 [147] [147] 400 [ 1481

* calculated as 01.

t Calculated as C H L

t: Calculated as CHs0. 0 Not very reliable data during smoggy conditions.

** Numbers in brackets are references.

character may be harmful. A few measurements of O3and NO2 in London are reported which indicate low concentrations. Nothing is known about the concentrations of the minor constituents in the coal combustion products, such as HzS, or halogen compounds. The sparse data on free NH3 indicate a fairly low level in Leicester, even lower than that of the surrounding area. The data for Los Angeles are typical for a hydrocarbon-nitrogen dioxide-oxidant atmosphere. The difference between Los Angeles and London and Leicester is small as regards the total particulate matter and CO, becomes more pronounced for SO2 and is significant for NO2 and oxidant and probably for hydrocarbons, too. Washington, D.C., which is smaller than Los Angeles and less industrialized, shows an intermediat,e position. The difference in the character of the smog, however, is caused not

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only by the variable composition of the polluted atmosphere but also by the climate. The cloudy, humid climate of Great Britain favors the production of sulfate smogs, whereas the dry, sunny area of Los Angeles is conducive t o photochemical reactions. It appears that high oxidant and SO2 contents t o a certain degree exclude each other [147]. An example of the composition of the particulate matter present in coal atmospheres is given in Table XXI. Although based on material collected in deposition gauges, it probably adequately reflects the comTABLE XXI. Composition of material (in per cent) collected by deposit gauge ([1461, p. 158). Undissolved matter Ash Combustible matter other than tar “tarry matter”

% 40.0

total Dissolved matter

68.6

so,--

27.0 1.6

15.4

c1-

6.5

Ca+ others

3.6

total

5.9

31.4

position of airborne material. It is assumed that about 10% of the material collected is natural mineral dust and that 50% of the C1 is of maritime origin. The composition of aerosols in other contaminated areas is indicated by Table 111. The differences between the various towns are small and can be accounted for by industrial sources. The high P b concentration probably results from the use of leaded gasolines in automobiles and reflects the density of traffic. The total particulate loading in the air of a n area can be related to the size of the population. A comparison of the data for towns in Great Britain [148]indicates that other conditions being equal the smoke concentration is proportional to the square root of the population. It becomes evident that mixing with the higher layers of air is one of the most important controlling factors with regard to the concentrations in polluted atmospheres. This is well substantiated by the air pollution disasters in the Meuse Valley and in Donora, where vertical distribution was limited by inversion layers and horizontal mixing by the topography. The daily, weekly, and seasonal trends of the degree of pollution

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depend upon the interaction of the production rate of the pollutants and the over-all ventilation as influenced by the local meteorology and topography. The diurnal variation of ventilation shows a sharp increase after sunrise, upon the onset of convection, a maximum in the early afternoon, and a decrease t o low values a t night. The production rates of most contaminants also have a pronounced diurnal variation. The SO2 production in English towns is highest in the morning when coal is consumed simultaneously in most residences for heat. The production rate of CO by automobiles, etc., has maxima in the morning and late afternoon, coinciding with traffic peaks. The concentration of oxidants in the Los Angeles area has a regular and very pronounced maximum a t noon, confirming its photochemical origin. The hydrocarbons show maximum concentrations a t night and in the early morning; on the other hand, NO2 has no appreciable variation [76, 1461. Pollutants of industrial origin exhibit a weekly variation in concentration with the minimum occurring on weekends when there is a considerable reduction of industrial activity. A seasonal variation of the SO2 concentration in coal burning areas exists, with a minimum in summer and a maximum in winter correlating with the use of coal for heating purposes. A similar variation in the extent of vertical mixing probably adds significantly to the annual amplitude. It is evident from Table XX that some of the abundant components of polluted atmospheres such as CO, SOZ, NOz, HC1 (?), as well as the particulate matter are also components of uncontaminated air masses and that their concentrations are 1 to 2 orders of magnitude higher than in unpolluted air. The question as to their part in the chemistry of unpolluted air cannot as yet be answered. An anaIysis of the observations leads t o the conclusion that our civilization has created a permanent level of SO2 pollution in such areas as Great Britain, continental Europe, and the northeastern part of the United States. T o a lesser degree this might also be true of NOz and C1 (Europe ?, see Section 4.4), but the data are still far too inadequate for any definite conclusions a t this time. The fate of CO in the atmosphere is unknown, but it is probably removed much more slowly from the air than the other components. As CO is one of the most abundant industrial contaminants its role in air chemistry may be important not only over large areas but also on a semiglobal scale. The wide ranging influence of industrial particulate matter has already been discussed. 6.6. The Area of Influence around Pollution Centers

O f special interest to us is the question as to just how far around the source the contamination spreads. The excellent three-year study a t

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Leicester is the major source of data in this case [148]. This town in the middle of Great Britain has a closely built-up center of about 3 km diameter surrounded by houses and gardens in a belt about 4 km wide. Anetwork of 13 stations was established in this area to measure the concentration of smoke and SO2 as well as the deposition of particulate matter. The contours of smoke and SOz mean concentrations conform fairly closely t o the shape of the developed area. The asymmetry due to the prevailing westerly winds is very small. The ratios of concentration a t the center t o that of the suburbs was 2.2:l for smoke and 3 . 4 : l for SOz. The mean concentration levels a t the center were 420 y/meter3 and 390 y/meter3, respectively. At a distance of a few kilometers the values dropped t o the level of the surrounding country, which, however, is still strongly influenced by more distant pollution sources. The effect of the wind on the distribution of contaminants is remarkably small. The highest contaminant density for winds up to 15 km/hr is still very close to the center of the town and the other isolines shift only 1 or 2 km downwind. The concentration a t the center is only slightly higher during a calm than with wind. Similar results have been obtained in other studies. Flach [149], for instance, uses the concentration of Aitken nuclei a s a n indication of the pollution of the cities of Halle, Berlin, and Dresden. The isolines parallel the outlines of the population density and are little influenced by winds. The foregoing is valid for the concentrations of pollutants a t ground level. The total amount of smoke in a vertical column is approximately indicated by the attenuation of sunlight, particularly of the UV radiation. This total amount of smoke at Leicester shows a somewhat more pronounced asymmetry with the wind : its maximum shifts 1 t o 2 km from the center and the other isolines are distorted even more, say by 2 t o 5 km. Comparison of this pattern with that for ground level indicates th a t considerable amounts of particulate mat>ter(and gases too, of course) are rapidly borne aloft by turbulent mixing and slowly spread horizontally. These studies give a good representation of the concentration, a t least a t ground level in polluted areas; however, little attention has been given t o the decrease in contaminants over large distances. Some inferences along this line can again be drawn from the Leicester study. At distances of more than 20 km on the west side of Leicester are extensive industrial areas, whereas there is no important commercial development in the sector t o the northeast. Consequently, the background concentration in Leicester varies with wind direction, being 2 to 4 times higher with west than with east winds and in either case being 10% t o 40% of the total concentration a t the center of Leicester. The anthropogenic origin of these background concentrations of smoke and SO2 a t Leicester,

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even with easterly winds, is confirmed by the fact that they show the same annual variation in this “country air” as in the “town air” of Leicester. Meetham’s maps of smoke and SO2 concentrations at ground level in Great Britain [150] offer additional confirmation of this. The average content over Great Britain is about 40 and 60 ?/meter3 for SO2 and smoke, respectively. When compared to the average SO2 concentration of 10 ?/meter3 in Sweden for instance, it is evident that pollution is a permanent feature of the island’s atmosphere and that much material must be carried eastward to the sea. It very likely affects the air chemistry of western continental Europe. The Leicester report contains some interesting, though rough, estimations of the spread around centers of pollution. Some evidence shows that between distances of 50 and 150 km downwind from the source the concentration in y/meter3 can be expressed by

C1= 65700:Np for smoke X

and

where N, is the population in millions and x the distance in km. A city of 2 million, for instance, with British heating habits will raise the concentration at a distance of 100 km by 12 and 5 ?/meter3 for particulate matter and SOZ, respectively. These amounts are comparable to the natural levels of unpolluted air. If the distance is less than 50 km and equal to or smaller than the source diameter, the concentration decrease is slower and varies inversely with the distance. At more than 50-km distance from the origin of contaminants the decrease by the square of the distance, as indicated by the formulas, is to be expected. I n this case the source can be considered as a point source and the simple geometrical square law controls the concentration, provided that vertical and horizontal mixing are unrestricted. At some point not far beyond the 150-km distance it is expected that the pollutants will have reached the top of the mixing layer with further vertical mixing thereby prevented, so that the decrease in contaminant concentration will vary again inversely with the distance. The maximum height of the mixing layer is the height of the tropopause, but the average height in the middle latitudes is often much less, for instance, around 4 km, as indicated by Figs. 20 or 21. It is concluded from this discussion that unpolluted areas in the sense that the contamination level due to human activity is small compared to the natural level no longer exist in regions like West and Central

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Europe and the northeastern part of the United States. This was already vaguely indicated by several independent observations referred to in the previous chapters, especially for Europe, and is an important result. It means that studies in air chemistry, if they are to provide other than local information, have to be made at very carefully selected sites or at a number of stations within a network of continental dimensions. So far this inquiry has dealt with contaminants released at ground level only. In the event that material is forced into higher layers of the troposphere, or even into the stratosphere by some violent process, the material will easily spread over large parts of the earth. For example, we may refer to published data on the Nevada, USA, tests [151], which indicate that the radioactive debris was deposited in a well-defined pattern in the U. s. and was traced through the whole northern hemisphere LISTOF SYMBOLS concentrations collection efficiency’ ratio of concentration in air and solution height of fallen precipitation height of cloud base concentration equilibrium constants exponent total concentration of particles initial concentration of particles population in millions concentration of particles of radius r partial pressure hydrogen ion concentration parts per million parts per hundred million radius of particle radius of raindrop standard temperature and pressure duration of rainfall volume of particles per cms distance from source of pollution solubility constant constant, exponent ly = 10-6 gm l p = 10-3 mm intensity of rain

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3. Israel, H., and SchuIz, L. (1932). Ueber die Groessenverteilung der atmosphaerischen Ionen. Meteorol. Z . 49, 226-233. 4. Junge, C. E. (1955). The size distribution and aging of natural aerosols as determined from electrical and optical data on the atmosphere. J . Meteorol. 12, 13-25. 5. Dessens, HP (1949). The use of spiders’ threads in the study of condensation nuclei. Quart. J. Roy. Meteorol. Soc. 76, 23-27. 6. May, K. R. (1945). The cascade impactor: s n instrument for sampling aerosols. J. Sci. Znstrum. 22, 187-195. 7. Woodcock, A. H. (1952). Atmospheric salt particles and rain drops. J . Meteorol. 9,200-212. 8. Junge, C. E. (1953). Die Rolle der Aerosole und der gasfoermigen Beimengungen der Luft im Spurenstoffhaushalt der Troposphaere. Tellus 6 , 1-26. Investigations on the composition of aerosols by electron diffraction by W. Jacobi and W. Lippert are included. 9. Wempe, J. (1947). Die Wellenlaengenabhaengigkeit der atmosphaerischen Extinktion. Mitt. Astrophys. Obs. Potsdam 21, 1-25. 10. Volz, F. (1954). Die Optik und Meteorologie der atmosphaerischen Truebung. Ber. Deut. Wetterd. U.S.Zone 13(2), 1-47. 11. Junge, C. I?. (1956). Recent investigations in air chemistry. Tellus 8, 127-139. 12. Woodcock, A. H. (1953). Salt nuclei in marine air as a function of altitude and wind force. J . Meteorol. 10, 362-371. 13. Moore, D. J., and Mason, B. J. (1954). The concentration, size distribution and production rate of large salt nuclei over the oceans. Quart. J . Roy. Meteorol. SOC. 80, 583-590. 14. Effenberger, E.l(l940). Kern- und Staubuntersuchungen amlcollmberg. Veroeffentl. Geophys. Inst. Univ. Leipzig 12, 305-359. 16. Junge, C. E. (1955). Remarks about the size distribution of natural aerosols. I n “Artificial Stimulation of Rain.” Pergamon, New York, in press. 16. Kohler, H. (1936). The nucleus in and the growthof hygroscopic droplets. Trans. Faraday SOC.32, 1152-1161. 17. Junge, C. E. (1952). Die Konstitution des atmosphaerischen Aerosols. Ann. Meteorol. Beiheft pp. 1-55. 18. Junge, C. E. (1952). Das Groessenwachstum der Aitkenkerne. Ber. Deut. Wetterdienstes U.S. Zone 38, 264-267. 19. Jacobi, W., Junge, C. E., and Lippert, W. (1952). Reihenuntersuchungen des natuerlichen Aerosols mittels Elektronenmikroskops. Arch. Meteorol. Geophys. Biokl. AS, 166-178. 20. Twomey, S. (1954). The composition of hygroscopic particles in the atmosphere. J. Meteorol. 11, 334-338. 21. Cauer, H. (1951). Some problems of atmospheric chemistry. I n “Compendium of Meteorology,” pp. 1126-1136. Am. Meteorol. SOC.,Boston, Mass. 22. Cauer, H. (1949). Ergebnisse chemisch-meteorologischer Forschung. Arch. Meteorol. Geophys. Biokl. B1, 221-256. 23. Forster, H. (1940). “Studie ueber Kondensationskerne.” E.T.H. Zurich, Promotionsarbeit, pp. 1-163. ABC Druckerei u. Verlags A.-G., Zurich. 24. Gerhard, E. R. (1953). The photochemical oxidation of sulphur dioxide to sulphur trioxide and its effect on fog formation. Tech. Rept. No. 1, pp. 1-101. Contract No. SF-9, Engineering Experiment Station; Univ. Illinois, Urbana, Illinois. 25. Burckhardt, H., and Flohn, H. (1939). Die atmosphaerischen Kondensations-

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91. Slobod, R. L., and Krogh, M. E. (1950). Nitrous oxide as a constituent of the atmosphere. J . Am. Chem. SOC.72, 1175-1177. 92. Goldberg, L., and Mueller, E. A. (1953). The vertical distribution of nitrous oxide and methane in the Earth’s atmosphere. J . O p t . SOC. Am. 43, 1033-1036. 93. Bates, D. R., and Witherspoon, A. E. (1952). The photochemistry of some minor constituents of the Earth’s atmosphere. Monographs Natl. Roy. Ast. SOC.112, 101-124. 94. Adel, A. (1946). A possible source of atmospheric NzO. Science 103, 280. 95. Arnold, P. W. (1954). Losses of nitrous oxide from soil. J . Soil Sci. 6, 116-128. 96. Migeotte, M. V., and Neven, L. (1952). Recent progress in the observation of solar infrared spectrum a t Jungfraujoch (Switzerland). Mlm. SOC. TOY. sci. LiBge 12, 165-178. 97. Reynolds, W. C. (1930). Notes on London and suburban air. J . SOC.Chem. Ind. (London) 49, l68T-172T. 98. Edgar, J. L., and Paneth, F. A. (1941). The determination of ozone and nitrogen dioxide in the atmosphere. J . Chem. SOC.144, 511-519. 99. Mohler, 0. C., Goldberg, L., and McMath, R. R. (1948). Spectroscopic evidence for ammonia in the Earth’s atmosphere. Phys. Rev. 74, 352-353. 100. Migeotte, M. V., and Chapman, R. M. (1949). On the question of atmospheric ammonia. Phys. Rev. 76, 1611. 101. Gmelin, L., ed. (1934-1936). “Handbuch der anorganischen Chemie,” 8th ed., System 4 (Nitrogen), p. 16 ff. Verlag Chemie, Berlin. 102. Egn6r, H., and Eriksson, E. (1955). Current data on the chemical composition of air and precipitation. Tellus 7, 134-139 and subsequent issues. 103. Price, W. C. (1943). Absorption spectra and absorption coefficients of atmospheric gases. Repts. Progr. in Phys. 9, 10-17. 104. Aitken, J. (1911). The sun as a fog producer. Proc. Roy. SOC. (London) 32, 183-2 15. 105. Eaton, S. V., and Eaton, J. 1%. (1926). Sulphur in rain water. Plant Physiol. 1, 77-87. 106. Gmelin, L., ed. (1953). “Handbuch der anorganischen Chemie,” 8th ed., System 9, Section B1 (Sulfur), p. 46 ff. Verlag Chemie, 13erlin. 107. Gmelin, I,., ed. (1934-1936). “Handbuch der anorganischen Chemie,” 8th ed., System 4 (Nitrogen), p. 16 ff. Verlag Chemie, Berlin. 108. Fellenberg, T. v. (1926). Das Vorkommen, der Kreislauf und der Stoffwechsel des Jods. Erg. Physiol. 26, 176-363. 109. Cauer, H. (1939). Schwankungen der Jodmenge der Luft in Mitteleuropa, deren Ursache und deren Bedeutung fuer den Jodgehalt unserer Nahrung. Angew. Chem. 62, 625-628. 110. Migeotte, M. V. (1948). Spectroscopic evidence of methane in the Earth’s atmosphere. Phys. Rev. 73, 519-520. 111. Goldberg, L. (1951). The abundance and vertical distribution of methane in the Earth’s atmosphere. Astrophys. J . 113, 567-582. 112. Goldberg, L. (1953). The absorption spectrum of the atmosphere. I n “The Earth as a Planet” (G. P. Kuiper, ed.), pp. 434-490. Univ. Chicago Press, Chicago, Illinois. 113. Dhar, N. R., and Ram, A. (1939). Formaldehyde in rain and dew. J . Indian Chem. SOC.10, 287-298. 114. Coste, J. H., and Courtier, G. B. (1936). Sulphuric acid as a disperse phase in town air. Trans. Farad. soc. 328, 1198-1202.

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115. Ellis, B. A. (1931). Report on the determination of sulphur gases in air, App. I. I n “The Investigation of Atmospheric Pollution: 17th Report on Observations in the Year Ended 31 March, 1931,” pp. 38-49. H.M.S.O., London. 116. Kate, M. (1952). The photoelectric determination of atmospheric sulphur dioxide by dilute starch-iodine solutions. I n “Air Pollution : Proceedings of the United States Technical Conference on Air Pollution” (L. C. McCabe, ed.), pp. 580-595. McGraw-Hill, New York. 117. Kettering Laboratory (1955). The concentration of oxidizing substances in the atmosphere of Washington, D. C. and Cincinnati, Ohio. Final Rept. Project V I I I , pp. 1-15. Am. Petrol. Inst. Smoke and Fumes Comm. 118. Jacobs, M. B. (1952). Methods for differentiation of sulfur bearing components of air contaminants. I n “Air Pollution: Proceedings of the United States Technical Conference on Air Pollution” (L. C. McCabe, ed.), pp. 201-209. McGrawHill, New York. 119. Quitmann, E., and Cauer, H. (1939). Verfahren zur chemischen Analyse der Nebelkerne der Luft. Z . anal. Chem. 116,81-91. 120. Stewart, N. G., Crooks, R. N., and Fisher, E. M. R. (1955). The radiological dose to persons in the United Kingdom due to debris from nuclear test explosions. Report for the M.R.P. Committee on the Medical Aspects of Nuclear Radiation. Atomic Energy Res. Establishment, Harwell, June 1955, pp. 1-22. 121. Eriksson, E. (1955). Air borne salts and the chemical composition of river waters. Tellus 7 , 243-250. 122. Woodcock, A. H., and Blanchard, D. C. (1955). Tests of the salt-nuclei hypothesis of rain formation. l‘ellus 7 , 435-442. 123. Turner, J. S. (1955). The salinity of rainfall as a function of drop size. Quart. J . Roy. Meteorol. SOC.81,418-429. 124. Kumai, M. (1951). Electron-microscope study of snow-crystal nuclei. J . Meteorol. 8, 151-156. 125. Harvey, H. W. (1955). “The chemistry and fertility of sea water,” Cambridge Univ. Press, London and New York. 126. Barrett, E., and Brodin, G. (1955). The acidity of Scandinavian precipitation. Tellus 7 , 251-257. 127. EgnBr, H. (1932). Losses of nitrogen from manure by evaporation of ammonia. Medd. Centralanstalt. forsoksviisendet jordbruks. 409, 257-291. 128. Langmuir, I. (1948). The production of rain by a chain reaction in cumulus clouds a t temperatures above freezing. J . Meteorol. 6 , 175-192. 129. Landsberg, H. E. (1954). Some observations of the p H of precipitation elements. Arch. Meteorol. Geophys. Biokl. A7, 219-226. 130. Anderson, V. G. (1915). The influence of weather conditions upon the amount of nitric acid and nitrous acid in the rainfall at and near Melbourne, Australia. Quart. J . Roy. Meteorol. SOC.41,99-122. 131. Drischel, H. (1940). Chlorid-Sulfat- und Nitratgehalt der atmosphaerischen Niederschlaege in Bad Reinerz und Oberschreiberhau im Vergleich zu bisher bekannten Werten anderer Orte. Balneologe 7 , 321-334. 132. Eriksson, E. (1952). Composition of atmospheric precipitation. I. Nitrogen compounds. Tetlus 4, 215-232; 11. Sulfur, chloride, iodine compounds. Bibliogr?phy. Ibid. 4, 280-303. 133. Angstrom, A., and Hogberg, L. (1952). On the content of nitrogen in atmospheric precipitation in Sweden. I. Tellus 4, 31-42; 11. Ibid. 4, 271-279. 134. Junge, C., and Gustafson, P. E. (1956). Precipitation sampling for chemical analysis. Bull. A m . Meteorol. SOC.37, 244.

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135. Russell, E. J., and Richards, E. H. (1919). The amounts and composition of rain and snow falling a t Rothamsted. J . Agr. Sci. 9, 309-337. 136. Liesegang, W. (1934). Untersuchungen ueber die Mengen der in Niederschlaegen enthaltenen Verunreinigungen. Kleine Mitt, j . Mitglied. d. Vereins f. Wasser,Boden- u. Luflhyg., Berlin 10, 350-355. 137. Harper, H. J., and College, M. (1943). Sulfur content of Oklahoma rainfall. Proc. Oklahoma Acad. Sci. 23, 73-82. 138. Houghton, H. (1955). On the chemical composition of fog and cloud water. J . Meteorol. 12, 355-357. 139. Larson, T. E., and Hettick, I. (1956). Mineral composition of rainwater. TetZus 8, 191-201. 140. Leeflang, K. W. H. (1938). De chemische Samenstelling van den Neerslag in Nederland. Chem. Weekblad 36, 658-664. 141. Emanuelsson, A., Eriksson, E., and EgnBr, H. (1954). Composition of atmospheric precipitation in Sweden. Tellus 6 , 261-267. 142. Facy, L. (1931). La composition des eaux de pluie de la rdgion de Brest et d u Nord finisthre. Ann. hygiene publ. ind. et sociale 9, 504-518. 143. Kalle, K. (1953-1954). Zur Frage des “cyklischen Salzes.” Ann. Meteorol. 6 , 305-314. 144. Blifford, I. H., Lockhart, L. B., Jr., and Rosenstock H. B. (1952). On the natural radioactivity in the air. J . Geophys. Res. 67, 499-509. 145. Haxel, O., and Schumann, G. (1955). Selbstreinigung der Atmosphaere. 2. Phys. 142, 127-132. 146. Meetham, A. R. (1952). “Atmospheric Pollution: Its Origins and Prevention,” pp. 1-268. Pergamon, London. 147. Kettering Laboratory (1955). The concentration of oxidizing substances in the atmosphere of Washington, D. C. and Cincinnati, Ohio. Final Rept. Project V f l f ,pp. 1-14. Am. Petrol. Inst. Smoke and Fumes Comm. 148. Great Britain, Department of Scientific and Industrial Research (1945). Atmospheric pollution in Leicester: a scientific survey. Tech. Pap. Atm. Pollut. Res. 1, 1-161. 149. Flach, E. (1952). Ueber ortsfeste und bewegliche Messungen mit dem Scho1z’schen Kernzaehler und dem Zeiss’schen Freiluftkonimeter. 2. Meteorol. 6 , 97-112. 150. Meetham, A. R. (1950). Natural removal of pollution from the atmosphere. Quart. J . Roy. Meteorol. Soe. 78, 359-371. 151. Lynch, D. E. (1955). “Radioactive Debris in North America from Operation Teapot,” pp. 1-3. U.S. At.omic Energy Comm., New York. 152. Facy, L. (1955). La capture des noyaux de condensation par chocs moleculaires au cours des processus de condensation, Arch. Meteorol. Geophys. Biokl. A8, 229-236.

THEORIES OF THE AURORA

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Joseph W Chamberlain Yerkes Observatory. University of Chicago. Williams Bay. Wisconsin

Page 1. Introduction . . . . . . . . . .

. . . . . . . . . . . . . . . 110

2.1. Elementary Considerations for Single Particles ... 2.1.2. Uniform Electric and Magnetic Fields . . . . .

2.3. Currents and Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Stormer’s Theory of Aurorae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Motion of a Particle in the Field of a Dipole . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. The Dipole Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Integrals of the Equation of Motion ... . . . . . . . . . . . . . . . . . . . . . 3.1.3. The Equations of Motion for the Meridian Plane . . . . . . . . . . . . . . . 3.1.4. Orbits Lying in the Equatorial Plane . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5. Forbidden Regions in the Three-Dimensional Problem . . . . . . . . . . . 3.1.6. Motion of a Particle in Three Dimensions . . . . . . . . . . . . . . . . . . . . . . 3.1.7. Orbits through the Origin; Families of 0 3.2. Application to the Aurora . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. The Auroral Zone ... ........ ....... 3.2.2. Auroral Forms . . . . . . . . . . . . . . . . . . . . . . . . 4 . Electric Currents between the Sun and Earth . . . . . . . ............ 4.1. Early Criticisms and Modifications of Stormer’ 4.2. Bennett and Hulburt’s Self-Focused Stream . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Qualitative Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. The Hydromagnetic Pinch Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3. Total Current Required for Constriction ............... 4.2.4. The Radial Electric Field . . . . . . . . . . . . . . . . . ............... 4.3. Ferraro’s Criticism . . . . . . . . . . . . . . . . . . . . . . . . . . ............... 5. The Chapman-Ferraro Stream and Ring Current ... ............. 5.1. Theory of a Neutral, Ionized Stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1. Motion of a Plane Slab in a Uniform Magnetic Field . . . . . . . . . . . . 5.1.2. Cylindrical Stream in a Uniform Field . . . . . . . . . . . . . . . . . . . . . . . 5.1.3. Advance of a Stream into a Magnetic Field . . . . . . . . . . . . . . . . . . . 5.1.4. The Cylindrical-Sheet Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Theory of a Ring Current . . . . . . . . . . . . . . . . . . . . . . . . ............. 5.3. Martyn’s Theory of Aurorae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

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Page 173 6. Other Electric-Field Theories of Aurorae.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. AlfvBn’s Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 6.2. Hoyle’s Theory,,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 ......................................... 178 6.3. Lebedinski’s The0 6.4. Discussion of Sola ms . . . . . . . . . . . . ..................... 180 6.4.1. Speculations on Electric Fields in Theory.. . . . . . . . . . . . . . 180 ..................... 181 6.4.2. The Nature of Solar Ion Streams. e . , . . . . . . . . . . . . . . . . . . . 183 7. Additional Mechanisms for the Production of 7.1. Dynamo Theories of Wulf and Vestinr. . . . . . . . . . . . . . . . . . . . . . . . . . . 183 186 7.2. Singer’s Shock-Wave Theory.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Parker’s Theory of Hydromaglietic Displacement of the Lines of Force. . 189 violet-light Theory. . . . . . . . . . . . . . . . . . . . . . . 190 ........................................ 190 7.5. Meteor Theorie 8. Theories of Auroral ......................................... 191 8.1. Electrons in Au ......................................... 191 ........................................ 191 8.1.2. Primary Electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.2. Incident-Proton Theory of Arcs.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 194 8.2.1. Auroral Ionization by Protons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............... 196 8.2.2. Excitation of Hydrogen in Aurorae 8.2.3. Discussion of the Angular Dispersio 8.2.4. The Velocity Dispersion of t 8.3. Electric-Discharge Theory of Rays. . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 List of Symbols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . .................... 210

1. INTRODUCTION 1. I . Historical Summary

Since the time of Aristotle [l],scientists have struggled-so far largely without success-to give a precise explanation to one of the most aweinspiring natural phenomena familiar to man: the aurora. A wide variety of theories, hypotheses, and speculative suggestions have arisen, lived, and passed on. De Mairan [2] conducted extensive statistical investigations and first established the relation between auroral occurrences and sunspot numbers as well as the seasonal variation. He theorized that the aurora is produced when material from the zodiacal light falls into the atmosphere, antedating by two centuries the suggestions by some current authors that aurorae are excited in part by small meteors. Electromagnetic theories of the aurora may be said to have originated with the astronomer E. Halley, who in 1716 suggested rather vaguely that the aurora was due to a luminous magnetic fluid. The concept of electric discharges in aurorae was first introduced independently by Lomonosov [2a] and by Canton [2b] in 1753. Canton also created the first laboratory imitations of aurorae. Franklin [3] made a modification

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to the electric theory of aurorae, suggesting th a t water vapor rises in the tropical regions of the earth and carries electricity to high altitudes, whence it moves to the polar regions and produces the aurora. (This idea is vaguely similar to an ultraviolet-light theory proposed in more recent years.) Lomonosov in Russia, Canton in Great Britain, and Franklin in America, all developed their ideas on aurorae in connection with their studies of lightning discharges. For example, Canton’s paper t o the Royal Society (read less than two weeks after Lomonosov’s paper t o the Academy) , dealt primarily with laboratory experiments designed t o elucidate thunder and lightning. He concluded with the query, “Is not the aurora borealis, the flashing of electrical fire from positive, towards negative clouds a t a great distance, through the upper atmosphere, where the resistance is least?” Dalton in 1793 proposed that aurorae were due to a ferromagnetic dust, which becomes aligned along the geomagnetic lines of force and serves as a conductor for the atmospheric electrical discharges. These ideas were based on long studies of the relations between aurorae and magnetic disturbances. The electrical nature of the aurora was further demonstrated in the next century by the artificial aurorae produced in laboratory experiments by de la Rive and later by Lemstrom [4] and Plant6 [ 5 ] .By the end of the 19th century it was generally agreed (largely because of the success of these experiments in reproducing the forms and appearance of auroral displays) t ha t the aurora was fundamentally an electrical phenomenon. Lemstrom [4]believed the entire phenomenon was due to electric discharges. Edlund [6] developed an auroral theory based on the phenomenon of unipolar induction: thus the auroral energy was pictured as coming from the rotational energy of the earth. Stewart [7] advocated the idea tha t magnetic disturbances were produced by currents in the upper atmosphere arising from tidal and convective forces, and thus laid the foundation for the modern dynamo theories of aurora and of the daily magnetic variation. The sun was suggested as the source of auroral particles by Becquerel (see [S]), who thought hydrogen was ejected from sunspots and carried with i t positively charged electricity. Goldstein [9] adopted a similar view, but considered the solar-terrestrial currents to consist of moving electrons. I n 1896, Birkeland performed some experiments that suggested to him that electrons were “pulled” toward a magnetic pole. He advocated that the earth’s magnetic poles would have the same effect on a stream of electrons from the sun, and began his remarkable series of terrella experiments to illustrate and study the phenomenon more thoroughly [lo].

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These experiments indeed showed that a stream of ionized particles would bombard the sphere around its auroral zones. In the meantime, after Birkeland’s first experiments, Poincar6 [ 111 quickly offered an explanation of these experiments by a mathematical description of the motion of a charged particle in the presence of a single magnetic pole. It appeared from the experiments and the theoretical analysis that a particle, say from the sun, incident on the geomagnetic field, might be guided in by the lines of force and strike the atmosphere, thus inducing the optical display. Stormer at this time became fascinated with the mathematical challenge offered by the electrodynamic problem of the motion of a charged particle in the field of a dipole. This was a far more difficult problem than that treated by Poincar6, but it seemed that the earth’s field approximated that of a dipole sufficiently well and that the interactions between the charged particles might be sufficiently negligible for this hypothetical problem to give a good description of auroral trajectories. Once the simplifying physical assumptions were made, the mathematical theory was developed exactly as far as possible and then solutions were completed by many lengthy and tedious numerical integrations. More recently these solutions, and others carried out on modern high-speed computers, have been applied to the trajectories of cosmic rays near the earth. In this early work electrons were considered almost exclusively as the fundamental auroral particles, both in regard to the orbits of the particles and the excitation of the atmospheric atoms to produce the observed glow. (Occasionally a-particles were considered as well, until Lindemann (Lord Cherwell) [12] showed that the radioactivity thus attributed to the solar atmosphere was incredible, as it implied a lifetime for the sun of only a few thousand years.) Excitation by electrons is a familiar phenomenon in laboratory physics; because they have much greater mobility than heavy particles, electrons are the dominant exciting particles in discharges, for example. Stormer’s solutions, however, can be readily modified to apply to any charged particle. The current recognition of protons as important primary particles grew out of a series of events that may, in retrospect, be said to have originated with Vegard’s [ 131 identification of Balmer lines in auroral spectra. Swings [14] and Warm [15] emphasized the role that heavy ions might play. Later Gartlein [16] confirmed the H lines in a thorough examination of a large series of spectra. The culmination of these observations was the detection by Meinel [17] of the Ha line from an arc near his magnetic zenith with a large Doppler shift toward the violet. It has often been surmised on the basis of these observations that solar protons alone are the cause of all aurorae. But such an extrapolation of the data does not seem justifiable.

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The hypothetical streams of solar particles that have been used as bases for auroral theories may be classified into two categories: those in which charged particles of only one sign are important and those in which particles of both signs move with the same velocity in a stream or cloud that is electrostatically neutral. Perhaps neither of these limiting cases is especially descriptive of real corpuscular st,reams (cf. Sections 4.3 and 5.1) but we shall nevertheless review the major recent work as it has been presented. Stormer’s theory is fundamental when particles of only one sign are important. A ponderous objection to one-sign theories was first voiced by Schuster’ [ 181: electrostatic repulsion between the individual particles would disperse the beam quite rapidly. There have been attempts, most recently by Bennett and Hulburt, to modify and resurrect the Stormer theory so as t o overcome this objection. The attempt to salvage Stormer’s auroral orbits is understandable, since his theory has had some qualitative success in explaining observations; but an evaluation of all this work will be reserved for Section 4. The hypothesis of an electrostatically neutral cloud of ionized matter was first proposed by Lindemann [12] in a criticism of earlier papers by Chapman [19, 201 th at dealt with a stream of particles of only one sign.2 Since then Chapman and Ferraro have developed a theory of magnetic storms and aurorae on the basis of a neutral stream. Like Stormer they have made simplifying physical assumptions and then attempted highly accurate mathematical solutions of these approximate problems. Their theory was unable to demonstrate how the charged particles found their way into the earth’s atmosphere; more recently Martyn has made some extensions of the theory-mostly of a qualitative n a t u r e w i t h an explanation of the auroral phenomenon in view. This work is discussed in Section 5. Other modifications have resulted in “ electric-field ” theories (Section 6). It has not always been widely accepted th a t solar ion streams form the basis of geomagnetic storms and aurorae; even today there are a few 1 Schuster did not himself object to the Birkeland-Stormer hypothesis, but only to theories of magnetic storms that required a sufficient density of particles of one sign in the stream to affect directly the magnetic field of the earth. See Section 4.1. 2 Chapman’s paper [19] was primarily devoted to describing magnetic storms in terms of equivalent currents in the upper atmosphere. The magnetic variations were separated into two parts: (1) a storm-time component that first showed a brief, increased magnetic field (first phase) and then a stronger decrease in the magnetic elements (main phase); and (2) a diurnal variation that depends on local solar time. Chapman’s approach to the theory was to show how these currents could be induced in the atmosphere, and was in this respect similar to modern electric-field and dynamo theories. Conversely, the Chapman-Ferraro approach considers the currents as largely extraterrestrial. The later paper [20] was concerned with problems of energy balance.

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well-informed auroral physicists who favor a dynamo origin of these disturbances. Indeed, perhaps atmospheric origins of magnetic storms should not be discounted too readily. And the belief that all aurorae emanate directly from collisions of extraterrestrial particles with atmospheric atoms is still largely a matter of faith. There are certain observational data that actually seem to demand a dynamo origin. Wulf and Vestine have recently given serious consideration to dynamos, but a quantitative theory which would even approach the elegance of Stormer’s or Chapman and Ferraro’s theories has not been developed. The possibility of a dynamo supplemented by ion streams has not been exploited. Dynamo mechanisms are treated in Section 7.1. Other theories will be mentioned later, but the most fundamental and important ones are listed above. Electrodynamics is a difficult subject, as those who have worked in auroral theory are well aware. For the most part proponents of auroral theories have been cautious in making claims for their theories, other than what seemed to flow quite naturally from their mathematical and physical reasoning. It is generally admitted by workers in this subject that we are far from a satisfactory solution. In Sections 3 to 6 we discuss and evaluate theories that have, as their starting point, streams of solar ions. Section 7 reviews the theories that consider various other mechanisms as the primary or dominant feature of aurorae. Finally, in Section 8, we discuss the problem of auroral excitation. In that section the starting point for theoretical developments will be the observed auroral spectrum. It appears that careful analyses of the spectroscopic and photometric evidence may give invaluable guidance toward the proper theory. 1.2. T h e Observed Phenomena

Geomagnetic storms and aurorae are so closely related that any theory of the one should also be adaptable to the other. Similarly a rise of the F-layer, high-speed drifts of ionization in the upper atmosphere, and even the brightness of the Gegenschein [21] seem to be associated with these phenomena. For the present discussion, however, we will be concerned primarily with the aurora and will list only a few of the dominant characteristics to be explained by theory. (A list of salient features of the aurora, meant to serve as a guide to attempts at theoretical interpretations, was given in a recent review article dealing with the observed data [22].) Until the theories become more successful in describing the highlights, it seems premature to insist on explanations of all the details. Suffice it to say that both solar streams and atmospheric dynamos have the essential features necessary to explain geomagnetic variations; we shall examine their ability to explain aurorae.

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The hypothesis of corpuscular streams assumes that somehow matter is ejected from the sun. That material does leave the sun is supported by optical and radio observations of flares [23]. However, the Milne [24] mechanism of outward acceleration by the pressure of radiation at the wavelengths of the absorption lines is not likely to be important [25], since hydrogen must be completely ionized throughout the corona. Also, the evidence for a solar component of cosmic rays seems overwhelming, although, of course, even the lowest energy cosmic rays are many times as energetic as auroral protons (less than 1 Mev). Still we do not know where, when, why, or how fast the auroral particles are ejected from the sun. The difficulty in devising a method (on the basis of current theory, and with the high conductivity believed to exist in the solar atmosphere) whereby cosmic-ray or auroral particles can be formed has provoked Eugene Parker to make the whimsical remark that “acceleration mechanisms are a theoretical absurdity.” The main features of aurorae are: (1) Auroral zones. Aurorae occur in northern and southern belts roughly 20” to 25” from the geomagnetic axis p01es.~The time and space relationships between northern- and southern-hemisphere aurorae are poorly understood. The auroral zones move toward lower latitudes during strong disturbances. This zone is also characterized by severe magnetic disturbances. (2) Hydrogen lines. Homogeneous auroral arcs at low auroral latitudes invariably show hydrogen lines. On the rare occasions when arcs have been observed near the zenith, the H lines are shifted to the violet indicating incident protons. At higher latitudes the H lines are much weaker. Hydrogen lines seem to be much weaker when the aurora is composed predominantly of rayed forms. However, the great aurora of March 2, 1957, which covered most of the sky a t Yerkes Observatory, showed strong hydrogen lines when only draperies and other active, rayed structures were apparent. The rate at which the hydrogen lines decrease when an arc breaks into rays needs further investigation. (3) Heights. If aurorae are produced by extraterrestrial particles, the height of the lower boundary of auroral arcs (around 100 km) requires protons with energies of the order of W Mev (lo9 cm/sec). Electrons ‘These poles are the axis points of a dipole situated a t the earth’s center and approximately representing the geomagnetic field. They differ considerably from the north and south dip magnetic poles, where the compass points down, because of higher order terms in the Gaussian expansion of the geomagnetic field in spherical harmonics, because of localized irregularities, and the component of the field above the earth’s surface. A better dipole representation is possible if the dipole is not assumed to be a t the earth’s center, but since axial symmetry is then lost, this approximation is not particularly helpful.

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could reach this depth with somewhat less energy (30 kev) but higher speeds (9 X loQcmlsec). (4) T i m e variations. A strong seasonal variation shows a maximum occurrence of aurorae in the spring and the fall. An eleven-year cycle, with a maximum probably a year or two later than sunspot maximum, is prevalent a t least in lower latitudes (several degrees out of the auroral belt). The auroral zone moves south near times of sunspot maximum, which probably explains many of the increased low-latitude occurrences. ( 5 ) Relationship with solar events. There is some association between solar activity and strong auroral displays. If an aurora does follow a solar flare, it is most likely to do so about a day after the flare. This implies a mean sun-to-earth velocity of 108 cm/sec. But aurorae are not rare phenomena: displays are present in the auroral zone almost every night. There is a weak 27-day recurrence tendency for a t least low-latitude aurorae. (6) Typical display. A fully developed, strong display often begins with a homogeneous arc (nearly along a parallel of geomagnetic latitude) which moves southward and then breaks into active rayed structures. The rays are parallel to magnetic lines of force and in lower latitudes show westward motions up to 1 km/sec before local midnight (roughly), after which the motions are less systematic, but probably tend eastward. The display fades out, perhaps leaving a faint, extended, nebulous glow. Later a similar display may begin and repeat the sequence. It is probable that severe local disturbances in the magnetic field always accompany aurorae, especially the active forms.

PARTICLES IN MAGNETIC FIELDS 2. THE MOTIONSOF CHARGED 2.1. Elementary Considerations for Single Particles

For a more general discussion of electrodynamics in magnetic fields, we refer the reader to the discussions in books by Spitzer [26] and Alfv6n [27]. Here we shall merely review and set down for later reference some of the fundamental relations. The basic equation of motion of a charged particle in an electric field E and magnetic field B is (2.1)

dv m z = kq[E+vXB]

where v is the velocity, m the mass, and q the absolute value of the charge on the p a r t i ~ l eThe . ~ plus sign applies to positive ions, the minus sign to electrons. The vector qv X B is the Lorentz force. We shall use electromagnetic units (emu) throughout this chapter. In particular, p = e/c, where e is the electrostatic charge ( = 4.80 X 10-lo esu for an electron). Also

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117

If there is no electric field, the energy of the particle remains constant. To show this we take the scalar product of the velocity times equation (2.1) :

where v = 1 ~ 1 .Thus, ~ as the acceleration is always perpendicular to the velocity, the scalar speed does not change. 2.1.1. Uniform Magnetic Field. In a uniform magnetic field the motion is therefore circular in a plane perpendicular to the field. I n a righthanded system of coordinates (see Fig. 1) with the magnetic field along

FIG.1. Position vectors and angles of the coordinate systems used in this chapter.

the z axis, a positive particle gyrates in the - 4 direction, a negative particle in the opposite direction. That is, a particle tends to circle an external field in the direction such that the small magnetic field produced by the particle is in the direction opposite to the external field. (There may in addition, of course, be uniform motion along the field lines.) Equating centrifugal force to the Lorentz force, we find for the angular velocity, (2.3) the symbol B (strictly, the magnetic induction) is used throughout, rather than H (magnetic field strength). Because we are concerned here with the interactions of charged particles and magnetic fields, the induction is the physical quantity we are usually interested in. However, when we deal with currents we shall agree to consider the magnetization current J’ as incorporated in the (total) current J. Ordinarily V x B = 4*(J J’) and V X H = 4rJ; but with our convention of considering magnetization current as a conventional current, B and H are equivalent, and they may be interchanged as the reader desires. 6 Throughout this article we shall write A for [A], where A is any vector quantity.

+

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JOSEPH W. CHAMBERLAIN

Here v1 is the velocity component perpendicular to the field, oc is the gyrofrequency or cyclotron frequency, and p is the radius of gyration. For a proton in the earth’s field (about 0.5 gauss), wc = 5 X lo3 radians/sec. If v = lo8 cm/sec the radius is p = 2 km. For an electron with a comparable velocity the orbital radius is much smaller. The product Bp ( = m v J q ) is often designated as the magnetic stij’ness. 2.1 .2. U n i f o r m Electric and Magnetic Fields. If a particle is under the influence of crossed electric and magnetic fields, its orbit consists of a circular motion v’ superimposed on a drift velocity (2.4)

+

If we write v = v‘ vd, where vd is given by equation (2.4), it readily follows from equation (2.1) that, when E and B are perpendicular, (2.5)

dv‘

m-

at

=

fqv’ X B

which shows that the component v‘ involves only gyrations about the lines of force and is independent of E. The drift motion is in the direction E X B regardless of the sign of the charge. If E and B are at right angles to one another, the velocity of drift is E/B, and is independent of the mass. As before, v’ may also include uniform motion parallel to B. We may interpret the drift motion in the following way: an observer moving with the X’Y’Z’ axes with velocity vd relative to a coordinate system X Y Z will experience electric and magnetic fields given by the Lorentz transformation (for field components perpendicular to v),

and

The approximate equalities are valid for nonrelativistic velocities and for ionized gases where E is usually small because of the high conductivity. The magnetic field observed in the X’Y’Z’ system is essentially the same as in the “stationary” coordinates. If vd is given by equation (2.4), and if E is perpendicular to B, then from equation (2.6) we have E’ = 0; the electric field thus vanishes in the moving system and only the gyrational motion remains. Thus an observer in the X‘Y‘Z’ system experi-

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ences no electric field perpendicular to the magnetic field, and he consequently observes no drift. (When E and B are not perpendicular, the particle will also be accelerated parallel to B.) 2.1 3. Inhomogeneous Magnetic Field. If the magnetic field is not uniform in space a charged particle may drift for two reasons, which we shall treat separately. First, suppose that the field lines are straight and everywhere parallel to the y axis, but that B increases (that is, the lines crowd closer together) as the z coordinate increases. Then a particle gyrating around the lines of force will experience a stronger magnetic field on parts of its orbit than on other parts, with the result that the orbit is no longer circular but contains a drift as well as gyrational motion. The drift is in the -2 direction in our coordinate system, or, in general, in the direction B x V B for a positive particle. A minus-sign particle drifts on precisely the same path, but in the opposite direction. AlfvBn has shown that the ratio of drift to the gyrational speed is

where VIB is the gradient of the scalar field B in the plane perpendicular to B. Let us now consider the special case where there are no currents in the region considered, the currents producing the magnetic field being external to this region. Then from Maxwell's eyuatioris (cf. equation (2.41), Section 2.3) V X B = 0. In general, the lines of force will not now be straight, as postulated above, but equation ( 2 . 8 ) will be valid so long as the radius of curvature % of the lines of force is large compared with the distance the particle moves along the field during one gyration. For simplicity, we choose a magnetic field with B = B+i+and B, = BE = 0 in cylindrical coordinates. Since the curl of the field vanishes, we have dB,/dz = 0 and B4 % Substituting this into equation (2.8) and eliminating (2.3), we have

p

with equation

(2.10)

+

If B is in the rp direction, then the drift of a positively charged particle is toward +z. Notice that there is no drift if the lines are straight (% + m ) ; this is a consequence of the fact that if there are no currents and the lines of force are straight, they must also be uniformly distributed in space.

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Equation (2.10) gives the drift caused by the divergence or convergence of the field in a direction perpendicular to the field. In addition, a particle moving along a curved line of force with velocity v11 will experience an outward (centrifugal) force mvl12/Rtending to pull the particle off its curved trajectory. As in the case of an electric force perpendicular to the magnetic field, the net effect is not an acceleration in the direction of the centrifugal force but rather a uniform drift at right angles. In general, the drift for a positive particle is in the direction X B and has a magnitude vl12/~,R. If B is in the direction of i+, the total drift in an inhomogeneous field, due to nonuniformity of the lines of force and the centrifugal force on the particle is then (2.11) 2.1.4. Constancy of the Magnetic Moment. Thus far in considering magnetic fields we have restricted ourselves to lines of force that are always parallel to one another, whether they be curved or straight. But a most interesting effect appears when we follow a charged particle in a field where the lines of force converge toward one another. Picture a particle with a spiral path symmetric about a line of force on the z axis. This spiral trajectory is composed of a gyrational velocity v+ and a motion of the guiding center along the field with velocity v.. Off the z axis the magnetic field has a small component BE measured positive away from the z axis. The field is azimuth independent and B+ = 0. Since the lines of force must be continuous, V B = 0 or

(2.12)

The convergence is assumed to be gradual, so that during the time required for the particle to make a single gyration it has experienced little change in the field. Then we may set dB,/dz = dB/dz. Then integrating equation (2.12), we have R 2_ dB R B R -- - _ (2.13) 2

a2

At the position of the particle ( R = p ) , we have B P aB (2.14) R 2 az If we consider the possibility of a uniform electric field E, accelerating the particle along the magnetic field, the equation of motion (2.1) is (2.15)

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Employing equation (2.3) to eliminate p, we have (2.16) where the minus sign is inserted in the second term on the right because the sense of gyration of a positive particle is in the - q5 direction with our convention for the direction of the field. The equation is valid for particles of either sign. Thus if the lines of force are converging in the direction of motion (aB/dz > 0 ) , the magnetic field tends to decelerate the forward motion of the particle. But as we have shown in equation (2.2), the magnetic field alone cannot change the total speed of a particle. Hence, it is clear that the loss of velocity along the field must reappear as an increase in the absolute value of the v+ component. We shall investigate this point further. It is convenient to write the equation of motion (2.16) in terms of the magnetic moment of the particle, p, which is defined as the product of the current produced by the particle times the area encircled by this current. Thus (2.17) where the second equality follows directly from equation (2.3). Multiplying the equation of motion (2.16) by v2 and substituting from equation (2.17), we obtain

p

(2.18) Here d/dt indicates the substantial derivative, which is taken along the path of the particle. (For a stationary observer, we would have aB/at = 0.) Another relation between v, and p (or vd) can be found from energy considerations. Since the total kinetic and potential energy of the system is a constant, (2.19)

=

qE,

dz

=

qE,v,

Using equation (2.17) we then obtain (2.20)

z”(’ t z mvZ2)= qE,v2 - d

(pB)

A comparison of equations (2.18) and (2.20) illustrates that, in the limit of our approximation of a slowly converging field, p is a constant. Let x be the angle between the total velocity vector v and the magnetic field. Then v+ = v sin x. Further, let E = Xrn(uz2 v + ~ )= %mu2, the kinetic energy of the particle.

+

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JOSEPH W. CHAMBERLAIN

The constancy of the magnetic moment may then be expressed as (2.21)

If there is no electric field acting on the particle, so that B = constant, and “initially” the field and angle of pitch are B1 and X I , respectively, then the particle will be magnetically reflected when the field seen by the particle increases to the value B - 1 (2.22) B1 sin2xl At this point all the kinetic energy has been transformed into the gyration of the particle. But it is clear from equation (2.16) that so long as aB/& > 0, there will be a force on the particle in the -2 direction so that the particle recedes, gaining speed parallel to the field as 1 0 + 1 decreases. If there is an electric field involved (which is possibly the case for extraterrestrial auroral particles accelerated into the atmosphere) the last equation in the set (2.21) should be used, rather than the more familiar relation (2.22). Again we must caution that these relations are not exact and do not strictly apply, for example, to the motion of particles over large distances in the field of a dipole. Nevertheless, Alfv6n [27] has successfully applied equation (2.21), along with equation (2.1 1) for the perpendicular drift of the guiding center, to an approximate treatment of the Stormer problem-the motion of a charged particle in the field of a dipole. Also in Section 8.2.3 we shall use equation (2.21) for an approximate calculation on the angular distribution of protons to be expected in the production of a quiet-arc aurora.

2.2. Motion of a Particle in the Field of a Monopole The solution of the problem of a charged particle moving in the field of a single magnetic pole was obtained by Poincar6 [Ill, soon after Birkeland announced his first experiments. Birkeland had suggested auroral particles from the sun were pulled toward the earth by the dipole magnetic field. The monopole problem is, of course, unrealistic, in that single poles are merely a mathematical construction. It was felt, however, that the solution to this problem would give a qualitative description of the auroral trajectories, as the geomagnetic field near one of the poles crudely approximates the monopole field. Since the speed of a particle in a magnetic field remains constant, it is clear that a particle is not strictly “pulled” toward the pole. The trajectory will, however, circle about a line of force and if there is a

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component of motion toward the pole, the guiding center of the orbit will move straight toward the pole along a line of force. There is no drift arising from the inhomogeneity of the field, since the lines of force are straight [cf. equation (2.11)]. In the case of a dipole field, the motion is not so simple; and, indeed, unless a particle coming from an infinite distance is initially on the dipole axis, it must cut across closed lines of force in order to penetrate close to the dipole. Thus the dipole field can be a barrier as well as a trap, depending on the initial conditions for any particular particle. So in this sense, also, the monopole problem is not too descriptive of the dipole phenomena. We shall work through its solution, however, as an introduction to Stormer’s theory, since the problem does illustrate fundamental concepts and is rather basic to an understanding of the more difficult dipole problem. The monopole field follows an inverse square law: B = Zmr/ra, where ill?is the strength of the pole. The lines of force thus radiate in all directions. For zero electric field, the equation of motion (2.1) for a positively charged ion is then dv - = - -qZmvXr (2.23) dt m r3

It is convenient to use ds, the element of length along the trajectory, as the independent variable in place of dt. Since v = ds/dt, we have dv/dt = vdv/ds; and if we choose our unit of length as (q%Jl/mv) cm, equation (2.23) becomes d v-- -v X r ds r3 This unit of length, rather than centimeters, will be used throughout the remainder of this section; since v is constant, the unit of length is a constant for any one particle. Further, we have v = dr/dt = v drlds, and

-=-+ dv vdzr ds

as2

(:;)- :; -

The last term vanishes, however, as the scalar speed remains constant. Thus the equation of motion is written finally as (2.25)

If we take the vector product of r times equation (2.25) and expand the resulting triple vector product on the right, we find (2.26)

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JOSEPH W. CHAMBERLAIN

In deriving equation (2.26) we have used the identity r * dr/ds We may write equation (2.26) as (2.27)

L (r x ds

g)

=

=

r dr/ds.B

4 (I) ds r

which is easily proved by expanding the derivatives in equation (2.27).

This equation may be integrated directly: (2.28)

where h is an integration constant. If we take the scalar product of r times equation (2.28), the left side vanishes, and if we let a be the angle between h z and r we have h COB a = 1 (2.29) Since h is a constant, a is also a constant. Thus all the vectors r that are crossed by the trajectory make a constant angle a with the vector h; that is, the trajectory lies on the surface of a cone and h is along the axis of the cone or along the guiding center of the orbit; h is along the z axis in Fig. 2. To investigate further the nature of the orbit, let x be the angle between the unit vector dr/ds (along the path of the particle) and r. Then taking the absolute value of equation (2.28), we have, since the unit vector r/r is at a constant angle FIQ.2. The mag- with h, netic monopole prob- (2.30) r sin x = \he\ = tan a

lem. Lines of force lie along the vectors r. The orbit of a particle in the neighborhood of the pole is shown.

where he is the component of h perpendicular to the cone. If the cone is unrolled into a plane sheet, the trajectory as given by equation (2.30) is obviously a straight line; hence the orbit is a -geodesic on the cone.' The distance of closest approach to the origin is r = tan a;after passing this point the particle again recedes to infinity. 'The reader should bear in mind that d r l d s indicates dlrllds and not Idrldsl. This point may be demonstrated somewhat more elegantly from equation (2.25). The acceleration given by the left term must be along the principal normal to the trajectory since D remains constant. From the right side it appears that this normal is also normal to the surface (r) on which the trajectory lies. By definition, the path is therefore a geodesic. 7

125

T H E O R I E S OF T H E AURORA

Since the magnetic field follows the inverse square law, equation (2.30) is equivalent to sin2 - x - constant (2.31) B This is the relation (2.21) governing magnetic reflection that was previously shown to hold approximately in the general case of a slowly converging field. Here we have demonstrated that for the particular case of a monopole field, the equation is exact. Figure 2 illustrates the trajectory near its closest approach to the origin. 2.3. Currents and Magnetic Fields

If the number of charged particles moving in a magnetic field is large, it may be necessary to consider the magnetic field arising from the current that is produced by these particles. In this case the equations governing the motion of a single particle in an external magnetic field no longer apply, and we must seek a more general treatment. We now make a distinction between the mean velocity of a set of positive ions and electrons and the current, which is a result of their differential velocity. The mean m a s s velocity is (2.32) where n is the number density of the particles and m is their mass; subscripts i and e refer to positive ions and electrons, respectively. Similarly, when the positive ions are singly charged the current density is

J

(2.33)

=

q(nivi - we)

Neglecting any external gravitational field and assuming that a scalar pressure p (rather than a stress tensor) is appropriate, we have for the equation of motion for singly charged positive ions (cf. Spitzer [26]) (2.34)

dv dt

nimi 2 = niq(E

+

Vi

X B ) - Vpi

+ 'pie

and for electrons, (2.35)

nCme5 dt

=

-n,q(E

4- V ,

X B) - v p s

+ '$hi

Here pie and ' p s i represent the rate of transfer of momentum to protons from electrons and vice versa.

JOSEPH W. CHAMBERLAIN

126

The total derivative on the left sides of these equations is

av---av + v * v v at at

(2.36)

But in order to proceed with the analysis, we neglect the second order term in v and its derivatives in equation (2.36). Actually this term may be appreciable for solar ion streams, but the following equations may be applied where the stream is assumed to be in a steady state. Specifically, the gradient term vanishes if the velocities are axially symmetric (&/a+ = 0) and are constant along the length of the stream (av/az = 0 ) , and if the stream is not rapidly expanding or contracting (VR= 0). We shall neglect m,/mi compared with unity and assume electrical neutrality: Ini - n81/n,<< 1. Also, the use of a scalar pressure puts a limitation on the validity of the equations insofar as interactions between a fast beam and a stationary interplanetary medium are concerned. In this situation the effective pressure in the direction of motion would be considerably different from the lateral pressure. But so long as we consider only the particles within a given stream, and assume that there is no interaction with other masses of gas, the use of a scalar pressure is probably an acceptable approximation. With the foregoing limitations and approximations in mind, then, we add equations (2.34) and (2.35) to find the equation of motion:

av nimi - = J X B - Vp

(2.37)

at

-vei.

since '$is = Similarly, by subtraction and some simplification of terms (see Spitzer [26]), we obtain the generalized Ohm's law: (2.38)

-me -E n,q2 at

1 J x B + -vP, 1 +v x B - 'W n4

-

J

where the electrical resistivity is 7. In a steady state, v and J are constant and these equations reduce t o (2.39)

JXB=Vp

and 1

J = E + v X B - - vpi neq If we can neglect the magnetic field and the diffusion due to a pressure gradient, equation (2.40) reduces to the ordinary Ohm's law. To the above hydromagnetic equations we add Maxwell's equations governing electromagnetic fields. Neglecting rapid oscillations of electric (2.40)

127

THEORIES OF THE AURORA

fietds (i.e., neglecting electromagnetic radiation), we may write Amphre’s law as

V XB

(2.41)

=

47rJ

where we omit the term (l/c2)aE/at on the right. Faraday’s law is

aB V X E = -at

(2.42)

Maxwell’s equations are completed with

V * B= 0

(2.43) and (2.44)

We shall derive from Maxwell’s equations a relation to be used in our later discussion of atmospheric dynamos. If diffusion is negligible, Ohm’s law (2.40) for a steady state may be written (2.45)

J

=

1 (E li

+ v x B)

Substituting this expression for J into equation (2.41) and taking the curl, we find (2.46)

L V XV X B

47r

=

V X E + V X (V X B )

We eliminate E with equation (2.42) : (2.47)

-aB _ at -

-

li 4TV

X (V X B) + V X

(V X

B)

The first term on the right represents the decay of the magnetic field through Ohmic resistance, whereas it may be shown that the second term expresses the change in the field produced by lines of force being dragged about by the fluid. 3. STORMER’S THEORY OF AURORAE

Because of its fundamental nature in the electrodynamics of solar particle streams, we shall discuss Stormer’s theory in some detail. A number of major objections might be raised against the theory in its original form; these we shall discuss in Section 4.1. But the study of the motions of particles in the field of a dipole, which is the main feature of Stormer’s theory, is important, regardless of the ultimate fate of theories based on particle streams that carry a current from the sun t o the eart’h.

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JOSEPH

W.

CHAMBERLAIN

This theory is also of permanent importance to the study of the orbits of cosmic rays near the earth. The theory was published in a large number of papers, some of which are rather inaccessible. Stormer published the most important features of the theory in his so-called “Geneva papers” of 1907 [28] and 1911-1912 [29]. Recently, Stormer published an excellent and very readable book [30],which contains an account of his many observational as well as theoretical researches. For further details on the theory, and for many valuable diagrams, the reader is referred to this book. Here we shall present as concisely as we can the main features of the theory. 3.1. Motion of a Particle in the Field of a Dipole

3.1.1. The Dipole Field. The potential of a dipole field may be readily derived by adding (algebraically) the scalar potentials of the two single poles, each of which has an inverse square field. Thus we find the dipole potential Q p at a point P is

(3.1) where r is the vector from the dipole to P , and where the gradient is taken a t the point P (that is, the dipole is held fixed). Here M is the magnetic moment of the dipole. For the earth’s field M = [MI= 8.1 X loz6gauss cma. The magnetic field is then

The earth’s dipole field is oriented with the “south” pole of the magnet in the northern hemisphere (the axis point is near Thule, Greenland). The situation is a bit confusing, because we usually speak of the Thule pole as the “north magnetic pole.” But according to the convention that has been set up, the “north” pole of, say, a compass magnet, will orient itself to point northward. Hence it points toward the “south” pole of the geomagnetic field. Thus we may picture the lines of force of the geomagnetic field as proceeding from south to north outside the earth and from north to south within the “magnet.” We shall choose the z-axis along the axis of the dipole and positive toward the north. That is, the dipole moment M is oriented along the -2 direction. With our axis so chosen, we have in Cartesian coordinates, from equation (3.2)

THEORIES OF THE AURORA

129

From this equation it is readily seen that (3.4)

B

=

(B,2

+ B,2 + B*2)%= $ (1 + F)”

Thus at the equator ( z = 0) or a t the poles ( z = r ) the field decreases with the inverse cube of the distance. At the surface of the earth the field strength is a little over 0.3 gauss at the equator and nearly 0.7 gauss at the poles. 3.1 .d. Integrals of the Equation of Motion. For the dipole field given by equation (3.3), the equation of motion (2.1) is (3.5)

ds

mv

where we use the path length s, defined by ds = v dt, as the independent variable in place of t. Analogously to our treatment of the single magnetic pole, we adopt as the unit of length the value

This “Stormer unit” will be used through the remainder of this discussion of Stormer’s theory, except where otherwise explicitly stated. The equation of motion is then, for a positive particle,

(3.7)

-dv as_ -vxv(;)

For a negatively charged particle we may use the same solution and merely reverse the direction of motion about the dipole axis; in other words, we might represent the solution for an electron in a left-handed system of coordinates instead of the right-handed system adopted here. The first integral may be obtained by taking the scalar product of v with equation (3.7), as we did with equation (2.2). We thus obtain the condition that the kinetic energy remains constant. In cylindrical coordinates we may write the integral of equation (2.2) as

fg)’ + R 2 (2)’ +

($2

= 1

where the integration constant is unity by virtue of our use of s instead of t as independent variable. To relate s and t we need to use the unit of length in equation (3.6); hence we may consider CSt(or v) as an integration constant to be fixed by the initial conditions.

130

JOSEPH W. CHAMBERLAIN

A second integral is obtained by integrating one of the scalar equations composing the vector equation (3.7). In cylindrical coordinates the v+ component of equation (3.7) is

Multiplying this equation through by R, we obtain an expression equivalent to (3.10)

This relation is immediately integrable, and we have the angular momentum integral, (3.11)

where 27 is the integration constant. 3.1 3. The Equations of Motion for the Meridian Plane. The complete formal solution of the problem requires a third integral. Since this has never been found, it is necessary to carry out integrations numerically. Many properties of the motions in a dipole field may be obtained, however, from a study of the differential equations combined with partial solutions as given by the kinetic-energy and angular-momentum integrals. Let (3.12)

where the second equality is obtained by eliminating d$/ds between equations (3.8) and (3.11). Now we write the R and 2 components of equation (3.7): (3.13)

and (3.14)

If we replace d4/ds in these equations by equation (3.11), and then differentiate equation (3.12) (where we use the first equality sign), we find that these equations of motion may be expressed as (3.15)

and (3.16)

THEORIES OF THE AURORA

131

These two equations describe the motion of the particle in its meridian plane. From equation (3.12) it is apparent that Q is the kinetic energy of motion in this plane. On the other hand, the meridian plane for the particle is itself in motion with a variable angular velocity &/ds given by equation (3.11). 3.1.4. Orbits Lying in the Equatorial Plane. It is instructive to review this two-dimensional problem, which can be solved analytically, before passing to the more general auroral orbits. We assume the particles lie in the equatorial plane and have no z component of velocity. For this problem it is not necessary to use the equations of motion involving Q. For the second equality in (3.12)) remembering that r = R in the equatorial plane, we have (3.17)

dR--

ds

[ (2 )’]’’ 1-

-+-2

Equation (3.11) gives (3.18) Combining these two equations to eliminate ds, we have (3.19) which can be integrated by elliptic functions and thus represents the formal solution to the problem. For our present purposes this solution itself is of little interest; it is more instructive from the standpoint of the so-called “forbidden regions,” to examine the properties of equation (3.19). For a real solution, the square root must obviously be real. That is, we must have

+

R2 > (2yR 1) > - R 2 (3.20) where we consider the possibility of either positive or negative values of y. Hence the allowed values of R, when y is specified, must obey the ineaualities R2 - 1 (3.21) 2R and (3.22) - R 2 + l < y 2R In Fig. 3 are plotted the curves (3.21) and (3.22) with equalities replacing the inequalities. These relations between R and y then imply a particle can exist only to the left of curve (3.21) and to the right of curve (3.22). All other regions on the diagram are forbidden.

132

JOSEPH W. CHAMBERLAIN

In Fig. 3 the orbit of a particle coming from infinity is represented by a straight vertical line, a t some value of y. The particle approaches the R = 0 axis (the dipole) until it reaches one of the boundaries between the permitted and inaccessible regions. At this point it is magnetically reflected back again to infinity along the same value of y. Toward the left of the figure, there is a shaded region bounded on top by curve (3.22) and below by curve (3.21). A particle from infinity cannot penetrate into this region (without some perturbation to its orbit) R

FIG.3. Permitted regions in the equatorial plane versus the integration constant Y for a Stormer particle. Curves plotted from equations (3.21) and (3.22) are indicated and explained in detail in the text. The shaded region contains captive orbits.

and a particle once in this region will remain there. These are the “captive orbits.JJ I n Fig. 3 these particles move up and down, bouncing between the two curves, which act as barriers to inaccessible regions. These captive orbits must have y < - 1. Another interpretation of Fig. 3 is possible. For a given point R in space, y determines uniquely the direction of motion of the particle. If we let w be the angle between the tangent t o the orbit and the R axis, then the “velocity ” I in the c$ direction is (3.23)

R -a4 as

= sin w

since the total velocity is one in our units. Then from equation (3.18) we immediately find R2 sin w - 1 (3.24) ’= 2R

* By “velocity” we shall often mean the derivative of the particle’s position with respect to arc length s rather than time t. In this usage the total velocity is always unity.

THEORIES O F T H E AURORA

133

In Fig. 3, curve (3.21) corresponds to sin o = +1 and (3.22) to sin w = - 1. At large distances R the algebraic sign of sin w is the same as the sign of y. Hence particles with y < - 1 and those with y > 0 move in one sense throughout their trajectories, as seen from the origin. On the Y--I2

FIG.4. Stormer trajectories in the equatorial piane. The circle has a radius of one Stormer unit, C,t. After Stormer [29]; courtesy Oxford University Press.

other hand, when - 1 < y < 0, the sign of sin w reverses at some point on the orbit. For those values of y close to - 1, this reversal takes place quite rapidly and a smal loop appears in the orbit (see Fig. 4). The closest possible approach to the dipole occurs when y = - 1 and

JOSEPH W. CHAMBERLAIN

134

the particle is reflected from curve (3.21). We thus find Rmin= 0.414 in Stormer units Cat. A number of equatorial orbits for various values of y are illustrated in Figs. 4 and 5. 3.1.6. Forbidden Regions in the Three-Dimensional Problem. TOgeneralize the treatment in the preceding section, let w be the angle between the tangent to the orbit and the meridian plane, and let h be the latitude of the particle a t a given instant. In the ,/----...\ meridian plane the particle’s velocity is then /’ 1’--1.2032‘\\, cos w and transverse to this plane it is /‘ x‘, Rd@/ds = sin w . ; / \\ Refer now to the angular momentum 1 equation (3.11)’ which is the basis for I \ ,/ establishing the forbidden regions. Since \\ ,I’ R = r cos X, we have r-----C

\\\

,I’

\

\

,/

‘\

‘\ ‘\

/’

(3.25) r cos X sin w

..-_____--’

=

//’

FIQ. 5. An example of a captive orbit in the equatorial plane. For this particular value of y, the orbit is periodic, in th a t it repeats itself precisely with each revolution about the dipole After St&mer P91; courtesy Oxford University Press.

cos2 h r + 27

If we set k = sin a and solve equation (3.25) quadratically, we obtain (3.26)

r =

y f (y2

+ IC

C O S ~A)%

k cos X

where Ikl 1. This equation corresponds t o equation (3.24) in the two dimensional problem. By setting k = +1 and - 1 we may obtain the points a t which the particles turn around; that is, the boundaries to the forbidden regions. It will be noticed from equation (3.11) or (3.25) that (3.27) where the last equality follows directly from equation (3.12). Hence Q = cos2w, and k = k 1 corresponds to Q = 0. Physically this means simply that when the particle turns around in the meridian plane, all its kinetic energy is in transverse motion. Stormer ([29], pp. 231 ff.) has discussed equation (3.26) in detail and has shown that the case of interest in the auroral problem-viz., when the allowed regions stretch continuously from infinity to the dipole-corresponds to values of y between 0 and - 1. Figures 6 and 7 illustrate the regions of constant Q within the meridian plane for values of y on either side of y = -1. These Q curves are ob-

THEORIES OF T H E AURORA

FIG.6. Regions of constant Q in the meridian plane for y = [29]; courtesy Oxford University Press.

135

- 1.001. After Stormer

FIG.7. Regions of constant Q in the meridian plane for y = -0.999. After Stormer [29]; courtesy Oxford University Press.

tained from equation (3.26), where k is related to Q by equation (3.27). For our present discussion, the important point to notice in the figures is that a Q = 0 curve forms a barrier for a particle. Thus a particle coming from the sun (at large R ) , with y = -1.001, cannot penetrate to the dipole (i.e., to the origin). On the other hand, if y = -0.999, the particle

136

JOSEPH W. CHAMBERLAIN

can just squeeze through the neck around R = 1. It can reach the dipole, if it is projected just right, by sliding toward the polar regions between the two Q = 0 curves. For protons with sufficient energy to penetrate to auroral depths (5 X lo6ev), the Stormer unit of length is 3 X 101O cm, nearly the radius of the moon’s orbit. Hence the earth, with a radius of 6.4 X lo8 cm, would be quite small in Figs. 6 and 7. This explains our earlier statement, that it is necessary to consider only those orbits that actually can penetrate to the origin. As y increases above -0.999 the neck a t R = 1 opens wider and makes it easier for particles t o slip in. But a t the same time the inner Q = 0 region increases in size, so that when y > 0 the dipole is again completely blocked, as illustrated in Fig. 8. 3.1.6. Motion of a Particle in Three Dimensions. We consider separately the motion within the meridian plane and the (nonuniform) rotation of this plane about the z axis. In some respects this method of dividing the problem can be a little confusing, when we try to visualize the orbit as a whole; but it is the most convenient way to attack the mathematical problem. First consider the motion of the meridian plane. We have shown that for auroral practical purposes y < 0. Hence define y1 3 -7, where y1 will always be a positive number. The angular-momentum integral (3.11) is thus (3.28)

since R = T cos A. Hence dcp/ds changes sign and the meridian plane reverses its direction of motion when (3.29)

It may easily be shown from the T and h components of a dipole field, that the equation of a line of force has the same form as equation (3.29). Thus a particle reverses direction when it reaches the surface formed by rotating the line of force (3.29) about the z axis. Referring to Figs. 4 and 5, we see that this situation arises in the equatorial plane when the orbit forms a little loop. On the inside portion of the loop the 4 component of motion is in the opposite direction to that over the main portion of the curve. In the three-dimensional case, as a particle spirals toward the dipole around a line of force (approximately), its meridian plane reverses twice during each loop of the spiral. This phenomenon occurs because near the

THEORIES O F THE AURORA

137

dipole the guiding center of the particle follows closely a line of force. Picture the surface formed by rotating this line of force about the z axis. Then every time the particle crosses this surface the meridian plane reverses. Farther from the dipole, the guiding center diverges from the

r m y=

-0.97

m

0.03

y =

m

y =

0.2

FIQ.8. The diagrams show (in white) allowed regions for different values of y . The figure illustrates why only values of y between -1 and 0 are important to the auroral trajectories. After Stormer [29]; courtesy Oxford University Press.

line of force, but the reversal still occurs precisely when the particle crosses this surface. It is also of interest that whenever the meridian plane reverses direction (d+/ds = 0), we find, by comparing equations (3.11) and (3.12),

138

JOSEPH W. CHAMBERLAIN

that Q = 1. From the second equality of equation (3.12), it is apparent that this Q is consistent with all the kinetic energy being in the meridian plane and none in the + direction. Hence, by the discussion in the previous paragraph, we see that a Q = 1 curve corresponds to a line of force in the (moving) meridian plane. The motion within the meridian plane is governed by equations (3.15) and (3.16). These equations are analogous to the equations of motion in the R,z plane of a free particle of unit mass that rolls over hills and valleys in the third dimension. In this analogy we consider s as representas the potential energy. ing time and From Fig. 7 it becomes clear that as a particle coming from infinity approaches the neck, and again as the particle approaches the dipole, the curves for constant Q crowd closer and closer together. In general, in the neighborhood of small Q, the particle experiences a force tending to deflect it back. Where the Q values crowd closer together this repulsive force increases. The total speed remains constant, so energy lost from motion in the meridian plane goes into angular motion of the plane. As the particle moves back to larger Q values the 4 motion and the repulsive force decrease. Now consider a particle moving toward the dipole and spiraling about a line of force. It will continually interchange energy between its different components of motion. At two points of each loop on the spiral it will have all its motion in the meridian plane (Q = 1) and at two other points (about 90" from the first two) a large portion of the motion is in the transverse direction (small Q). Unless the particle is projected just right to reach the dipole, it will eventually, at some point on its orbit, have all its energy in the transverse direction (& = 0). When this occurs the particle starts to spiral out again. Whereas this discussion for the case of the dipole is necessarily a little complicated, it is merely the particular solution of the problem of magnetic reflection, discussed more generally in Section 2.1.4 with some simplifications. The actual computation of three-dimensional orbits has been carried out numerically by Stormer and others. Our discussion here has merely attempted tos how some of the characteristics of the orbits and clarify the physical meaning of the differential equations involved. 3.1.7. Orbits through the Origin; Families of Orbits. We have seen that the characteristics of an orbit may be studied from the standpoint of the Q value of the particle a t different points on its orbit. Thus the motion of the meridian plane reverses whenever Q = 1, and the particle is magnetically reflected when Q = 0. The curve Q = k is merely a particular line of force (depending on the value of y1 3 -7) in the meridian plane. On the other hand, the Q = 0 curves may be obtained from equation

-sQ

THEORIES OF THE AURORA

139

(3.12). Substituting R = r cos X and solving the resulting equation, quadratic in l / r , we find for Q = 0 that (3.30)

r =

y1

+

cos2 X c0s3 A)%

(y12k

I n obtaining this solution, we chose only the positive sign in front of the square root, since asymptotically near the dipole these curves must merge into the Q = 1 curve (or line of force) given by equation (3.29). The plus-minus sign in equation (3.30) arises from the squared term in equation (3.12) and gives two Q = 0 curves. Figure 9 shows the curves for Q = 0 and 1 near the origin for y1 = 0.5. Notice that the numerical computations of Stormer show that the orbit through the origin is not precisely along a line of force. This is understandable when we recall that a particle moving in an inhomogeneous field will drift (in the 4 direction). Hence, to project a particle so that it will go into the origin asymptotically with a line of force, we should start it with just enough angular motion t o compensate for the drift. This means that initially Q # 1; but this orbit through the origin approaches Q = 1 as the dipole is approached. Let us now visualize a group of orbits all starting from (or passing through) a given point Ro,zol (bo. This point will lie on an orbit through the origin for some particular value of yl. Hence, let us consider only those particles coming from this point that have this value of y1 (or initial angular momentum). (Having determined both meridional coordinates of the point, we cannot independently specify both y1 and the condition that the point is somewhere on the orbit through the origin.) The orbit is completely fixed by five parameters. (The general equation of motion is sixth order, the final integration constant fixing the particle in the orbit a t a particular time.) So far we have specified 71, and fixed z and # as functions of Ro.As a fourth initial condition we specify the total velocity or the unit of length C a t ;these four conditions specify the “family.” As we vary the fifth initial condition (which specifies the velocity component in some direction in the meridian plane) we obtain the various members of the family, three of which are shown in Fig. 9. These various orbits oscillate within the meridian plane until they touch a Q = 0 barrier, then recede back to infinity. One should also visualize the meridian plane as oscillating and drifting in the # direction] with maximal angular velocities for Q = 0 and zero velocity when:the particle is at Q = 1. A family member (labeled “spiral curve” in Fig. 9) just off the orbit through the origin is of interest. It oscillates about the curve through

4

FIG.9. Curves for Q = 0 and Q = 1 near the dipole. The diagram shows a section of the meridian plane: Abscissa and ordinate or the R and z axes, respectively. The orbit through the origin and various spiral orbits are illustrated. After Stormer [29]; courtesy Oxford University Press.

THEORIES OF T H E AURORA

141

the origin, not about the line of force. Hence its 4 motion varies in magnitude but the meridian plane does not reverse. For such a particle the drift motion outweighs the spiraling, and the former merely appears slightly irregular. We shall return to a discussion of this family of orbits in connection with Stormers explanation of aurorae. 3.2. Application to the Aurora

With the fundamentals of Stormer's theory given in the preceding section; we shall sketch rather briefly his application of dipole orbits to auroral theory. 3.2.1. T h e Auroral Zone. For both protons and electrons of auroral energy the unit of length, C,t, is much greater than the radius of the earth. Hence we are concerned only with orbits capable of traveling from the sun (taken as essentially a t infinity) almost all the way to the dipole. Thus we have 0 5 y1 < 1. We wish to find the lowest latitude at which particles can enter the dipole. This boundary corresponds to the intersection of the earth's surface with the inside boundary (& = 0 curve) of the permitted region for the family of orbits in the vicinity of an orbit through the origin. For a given value of yl, this low-latitude extension is given by equation (3.30), where the plus sign is chosen under the square root. (The minus sign would give the boundary nearest the pole.) Also, we see from equation (3.30) that particles with the larger values of y1 will enter a t lower latitudes than those with y1 = 0. Therefore we want the intersection of equation (3.30) for y1 = 1 with the curve r = a, where a is the earth's radius. Thus the maximum polar angle el( = s / 2 - A) a t which auroral particles can hit the earth is given, in cgs units, by

a=

(3.31)

1 The solution of (3.31) is

(3.32)

sin

a2 el = 2C,t 2-

Catsin2 81

+ (1 + sin3 el))*Cm

+

where the approximate solution supposes a << Catand actually is quite good for auroral energies. For auroral protons able to penetrate to a height around 100 km ( B = 500 kev, v = lo9 cm/sec), the radius of the zone is el = 13". For electrons with the same penetrating power (e = 30 kev, v = 9 X lo9 cm/sec), we have B1 c 3". On the other hand, the average auroral zone

142

JOSEPH W. CHAMBERLAIN

at about = 23" requires protons with speeds of about 10'" cm/sec, which would produce aurorae at heights of 40 km or so. Similarly, electrons would have speeds close to that of light and also result in very low aurorae. For the strong auroral displays that frequently reach overhead in central Europe and northern United States, the situation is much worse. Recognizing these difficulties, Stormer postulated EL ring current in the earth's equatorial belt and at several earth radii. This current was assumed to be sufficiently strong that it would exert appreciable magnetic influence on the particles. By making the net field (seen by an incident particle at the distance of the current) considerably less than the dipole field alone, the current would allow particles to enter a t lower latitudes. A ring current was later invoked by other workers to explain the small decrease of the magnetic field in the equatorial regions during a magnetic storm, and we shall later review Chapman and Ferraro's theory for such a ring. Stormer has also attempted an explanation of the more gradual decrease of aurorae on the polar side of the auroral belt. For y 1 = 0 in equation (3.30), 6' is very small, which means that aurorae should be frequent near the magnetic poles. However, Stormer points out that as the particles approach the earth they are bent around it in the cp direction. His numerical integrations show that for values of y 1 between 0 and about 0.5, the particles will not be bent in longitude sufficiently to reach the night side of the earth. Hence auroral particles should penetrate near the poles but only on the day side, where they are unobserved. Another difficulty with this explanation of the auroral zones has been pointed out by Vegard and Stormer. Because of the inclination of the earth's equator to the ecliptic (23%'") and the inclination of the geomagnetic equator to the geographic equator, the geomagnetic latitude of the sun may vary between f35". But none of the orbits through the origin for auroral energies and for 0.5 < y1 < 1.0 can make such a large angle with the geomagnetic equator. Thus it is not clear how aurorae are produced, say, at certain times during winter nights when the sun has a very low geomagnetic latitude. Petukhov [31] has proposed that the difficulty of getting the particles into the auroral zone, and other ohjections to solar currents, might be circumvented by assuming the particles emitted from the sun are neutrons. These particles decay into protons and electrons with a mean lifetime of about 30 min. Only a few of the originaI particles would get well into the geomagnetic field (say, within 100 earth radii) before decay, but these few would be guided (presumably) to the auroral zone. We foresee little promise for this postulate. For example, it is doubtful that the auroral structures can be explained; Stormer's explanations would no longer apply, because the charged particles now ''originate" over a wide region in space.

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To summarize this section, one may state that whereas Stormer’s theory gives a qualitative explanation of the geographic occurrence of aurorae, fundamental modifications appear to be necessary if quantitative agreement with observations is to be achieved. 3.2.2. Auroral Forms. One of the most remarkable features of Stormer’s theory is the explanation it gives to auroral arcs. Before discussing the arcs, however, let us consider in general the limiting size of an auroral form produced by a homogeneous beam. That is, we consider the family of orbits discussed in Section 3.1.7, where all particles had the same total velocity and angular momentum at a specified point. The various particles do not follow the same orbits but have different initial inclinations in the meridian plane to the lines of force. A particle is magnetically reflected before it reaches the earth if it collides with a Q = 0 surface. Hence the limiting north-south extension to an auroral form is given by the intersection of the Q = 0 surfaces with the surface of the earth. From equation (3.12) for Q = 0 we have (3.33) Solving this quadratic and taking the differencebetween the two solutions (which correspond to the high- and low-latitude boundaries), we find in cgs units

(3.34)

a3

R1 - R g = - cm Cat2

In high latitudes the lines of force are at a small angle to the x axis, so that equation (3.34) may be regarded as essentially the limiting northsouth diameter of an auroral form. From equations (3.6) and (2.3), it may be seen that this distance is the same as one obtains from the maximum diameter of gyration in a homogeneous field. For an auroral proton this diameter will be of the order of 3 or 4 km. Bates [32] has pointed out that the real diameter may be appreciably greater than that computed from the spiraling, since a proton, for example, is alternately charged and neutral as it falls through the atmosphere, and its average charge will therefore be less than p. Minimum diameters computed in this fashion have been used by Vegard [33] to demonstrate that protons cannot directly produce the auroral rays. The diameters of rays are frequently less than 0.5 km; hence, one cannot invoke a family of proton orbits, with various amounts of spiraling, to explain the long luminosity curves of the rays. Further elaboration on these luminosity curves will be reserved for Section 8.3. There is no obvious reason for rejecting protons as the particles responsible for homogeneous auroral arcs and much of the evidence actually suggests this primary mechanism for exciting arcs. Consider a family of

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JOSEPH W. CHAMBERLAIN

proton orbits all starting from the same point on the sun. All the particles are ejected with identical total velocities and angular momenta (measured about the earth’s dipole axis) so that C,t and y 1 are the same for all particles, We suppose that the source point on the sun lies on the orbit through the origin for the chosen value of yl; this essentially specifies one of the coordinates, say XO, of this point. We also specify r0(= 00) and t$o( = 0). Thus we have a family of orbits, as discussed in Section 3.1.7. One member of this family will go directly toward the origin; neighboring members will spiral about the orbit through the origin and some of these orbits will strike the atmosphere, although many will be magnetically reflected before getting very close to the dipole. Now let us vary y1 slightly; but as we insist that the source point on the sun be on an orbit through the origin, we shall also have to vary Xo t o compensate for the change in this orbit. The other initial conditions will be assumed to remain the same in all families, and we shall inquire as to the variation in the position of the aurora on earth when y 1 (or what is equivalent, A,) is varied. Both the polar angle O1 and the longitude (measured from the longitude of the sun) of entry on the earth will vary. But Stormer’s calculations demonstrate that 91 will vary much more than 01,so that this spreading of the emitting region on the sun essentially gives a big dispersion in the longitude of the resulting aurora on earth. Stormer associates this spreading with the observed arcs. The situation is illustrated in the rather complicated but informative diagram of Fig. 10, which shows the earth as seen from above the north magnetic pole. The lightly drawn circles are O values for 5, 10, and 15 degrees from the pole. The set of numbers lying on the outside of the figure give y 1 values for corresponding values of the longitude of entry, a1.The latitudes of the emanation points a t infinity, XO, are inserted around the line of precipitation. As y1 is varied monotonously from 0 to 1, A 0 goes through several maxima and minima. At t,hese points in particular a large change in 4il will occur for a small change in Xo. Figure 10 shows the precipitation curve only for y1 values between 0.1 and about 0.93. However, the detailed calculations show that another striking phenomenon occurs for y1 values in the neighborhood of 0.937. If y 1 is varied slightly about this value, it is found that a1goes through a reversal. A similar change in occurs at certain other values of y1 and Stormer relates these bends in the precipitation curves t o the horseshoelike auroral curtains. A displacement of t degrees in longitude t$o on the sun would simply mean a corresponding displacement of E degrees in a1a t the earth. Thus

THEORIES OF T H E AURORA

145

one can estimate the size and shape of the aurora that would be produced by particles originating from a surface of a given size on the sun. For example, if the emitting region is 0.2 degrees square, and the region corresponds to the minimum in Xo values that occurs a t about AD = -16", the (east-west) length of the aurora will be 179 km and the (north-south) width will be 9 meters. These values consider only the dispersion in the To the emanation point

0.9

Fro. 10.Line of precipitation of positive particles. The earth is viewed from above the north magnetic pole. For various points on the curve the appropriate values of y1, @, XO, and e are indicated, along with the points at which XO goes through maxima or minima. After Stormer [29]; courtesy Oxford University Press.

orbits through the origin, so that the north-south extent must also consider the possibility of widening (discussed previously) as a result of a dispersion in the angles of pitch among the members of one family. Stormer points out that rays could be interpreted as due to particles with small values of yl, so that (cf. Fig. 10) an area on the solar surface would give an aurora concentrated in a small region on the earth, with little spread in longitude. He does not prefer this interpretation, however, as it limits the rays to the late morning (from protons) or early evening (from electrons).

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JOSEPH W. CHAMBERLAIN

To summarize, Stormer’s theory for the various auroral forms is as follows : Rayed arcs arise from particles, probably protons, passing through the dipole, with very few or no particles exhibiting spiral orbits about the lines of force as they enter the atmosphere. The size of the aurora is governed entirely by the size of the element of solar surface ejecting the particles. Homogeneous arcs occur when most of the particles enter with a considerable amount of spiraling; that is, the particles enter a t large angles to the lines of force. The size of bhe auroral forms is then governed by the size of the radius of gyration as well as the size of the emitting region on the sun. Thus the structure in a rayed arc is blurred out by the large spirals and the lower border of the homogeneous arc is higher than for the rayed arc. Single rays result from a whole family of particles (probably electrons, according to a private communication from Professor Stormer) from a very small area on the sun. The whole family strikes the atmosphere a t the same point, but the great length of the rays results from the various amounts of pitch in the individual orbits within the family. Other forms that are composed of bundles or sheets of rays have the same expIanation but with a slightly different solar emitting region for each ray. These various explanations would appear to give a qualitative explanation of the auroral structure, but a more quantitative description is desirable. Indeed, by postulating the primary mechanism for auroral excitation and making certain assumptions about the orbits of the particles, one may make fairly accurate calculations on the appearance of various auroral forms. On the basis of these calculations it does not appear likely that Stormer’s explanations can adequately explain arcs and rays. We defer a discussion of these matters to Section 8. I n the next section a review is given of work that criticized and extended Stormer’s theory. Therefore, rather than attempt to evaluate his theory here, we shall proceed to a discussion of some of the important papers on the subject of solar-terrestrial currents.

4. ELECTRIC CURRENTS BETWEEN

THE

SUN AND EARTH

In this section we propose to discuss only ion streams in which a net current flows between the sun and the earth. In these theories the return current is neglected. Currents appear also in other theories but in different connections. For example, we shall later see that currents are induced on the surface of a Chapman-Ferraro stream, although there is no net current between the sun and earth.

THEORIES OF T H E AURORA

147

Stormer’s theory involves a sun-earth current, since it treats the motion of single particles of one sign, without regard to the forces between particles. We should expect this theory to hold in the limit of a very low density of particles and when particles of only one sign are moving. This situation is probably closely approximated in the case of cosmic-ray primaries and there the theory seems to fit admirably. But for the auroral problem, difficulties were soon pointed out. 4.1. Early Criticisms and Modifications of Stormer’s Theory

Many auroral theorists consider the beginning of the end to Stormer’s theory to lie in a paper by Schuster [18]. In 1911 he criticized theories in which magnetic storms were ascribed to the effects of solar ion currents passing in the neighborhood of the earth. From considerations of magnetic energy and electrostatic repulsion, Schuster concluded that a stream of solar particles of one sign could not produce the observed magnetic effects.He did not object to Birkeland’s proposal that such streams caused the visible aurora, and in fact suggested a dynamo mechanism for magnetic storms wherein particles from the sun triggered the release of dynamo energy.1° In 1916, Vegard ([34]; also cf. [33], p. 611) pointed out that these electrostatic difficulties were inherent in a beam of auroral particles of one sign. He suggested that Stormer’s theory of aurorae might be salvaged if the bundle of one-sign particles, when expelled from the sun, drew in charges of opposite sign from all sides. Vegard equated the number of positive and negative charges in his beam, but since they had different velocities, a current was carried, as given by equation (2.33). Although the orbits would then be more complicated than in Stormer’s theory, he suggested that the particle stream would be dominated by the charges having the greater “magnetic stiffness” pB = mv,/q. Chapman [19, 201 proposed that magnetic storms might be interpreted in terms of equivalent current systems in the upper atmosphere. He discarded the possibility of these currents arising from thermal energy or the rotational energy of the earth. Instead he suggested that solar charged particles of one sign penetrated the atmosphere; the imprisoned electric charge, under mutual electrostatic repulsion, produced an upward momentum of the outer atmosphere. This motion across the horizontal component of the geomagnetic field induced an east-west current system. The speed and density of charge required in this theory were less than 10 It would appear that this suggestion has considerable merit even today. An increase in the conductivity in the upper atmosphere by incident particles may well have important effects on an atmospheric dynamo.

148

JOSEPH W. CHAMBERLAIN

would be necessary if the magnetic storm5 were due to the direct magnetic action of solar currents, Hence Schuster’s objections were thought not to apply to this theory. Lindemann [12] pointed out, however, three difficulties with Chapman’s theory: (1) Schuster’s objection based on electrostatic repulsion was shown to be applicable for streams of very low density. The stream with a density of 4.4 X 10-7 Q! particles/cma, as assumed by Chapman, would not proceed as a beam for more than a few solar radii. (2) The particles “could not approach the earth after the first few seconds on account of the charge the earth would rapidly acquire,” (3) Finally, he objected to the then prevalent idea that solar radioactivity was responsible for the ejection of heavy particles, by showing that the necessary rate of decay implied a ridiculously short lifetime for the sun. Lindemann suggested rather that the solar stream was electrostatically neutral but ionized and that it traveled with a velocity of the order of los cm/sec. This velocity estimate was in accord both with observed velocities of material ejected from the sun (for more recent measurements see 1351) and with the average delay time between solar and geomagnetic events. He noted the difficulty in explaining the penetration of these rather slow particles to a height of 100 km in the atmosphere. Several features about this hypothetical ion stream were investigated by Lindemann. He showed that recombination would not occur during passage from the sun to earth and that by expansion the cloud would increase its size sufficiently to account for the duration of magnetic storms. He also proposed that light pressure was the acceleration mechanism, an idea later developed further by Milne [24]. 4.2. Bennett and Hulburt’s Self-Focused Stream

4.2.1, Qualitative Description. Suppose the solar particles originate near the surface of the sun. Then in passing through the solar corona the particles may, if the density is high enough, experience collisions, which tend to slow down and scatter the particles out of the beam. Thomas [36] has made calculations on the rate of deceleration of particles in ionized hydrogen. The whole problem is rather difficult, as one must distinguish between actual loss of energy by a particle in collision and its merely being deflected or scattered out of the beam by a series of (distant) encounters. Spitzer ([26], p. 76) has discussed the problem of computing the time required for an initial velocity distribution to become appreciably altered by these collisions. At any rate it appears quite possible that coronal collisions will be important, and, in particular, much more important for electrons than protons. Bennett and Hulburt [37, 381 maintain that electrons will thus be

THEORIES O F THE AURORA

149

essentially stopped in the corona and the protons will continue on their way.ll This leads to two important considerations. Firstly, in order to preserve electrical neutrality the stream presumably attracts electrons from the interplanetary medium. However, these electrons will not be accelerated to the velocities of the fast protons and the stream is thus composed primarily of slow electrons and fast protons. This neutralization effect is predominantly an electrostatic one, and is the same effect discussed earlier by Vegard (cf. Section 4.1). The formation of the current has not been treated mathematically in their papers and, indeed, this point has been the basis of a rather severe criticism, to be discussed presently, by Ferraro, who maintains that the original electrons will not be left behind in the first place. Secondly, since this electrostatically neutral stream now carries a current, it will have associated with it a magnetic field. Picture a cylindrical stream; the magnetic lines of force will be circles around the axis of the cylinder. This magnetic field, if strong enough, will have the effect of restricting the ionized stream within a definite cross-sectional area. This constriction of a current by its own magnetic field was first discussed in 1934 by Bennett [39, 401, who refers to the stream as being “magnetically self-focused.” The terminology of Tonks [41],who independently investigated this effect, seems to be rather generally accepted, and following him we shall call it the “pinch effect.” What is the importance of the pinch effect in auroral streams? Bennett and Hulburt feel this constriction is necessary to keep the stream from diverging so much that at the earth it has too large a diameter to produce the observed geomagnetic effects. Although these points are not mentioned explicitly by Bennett and Hulburt, arguments in favor of a stream with a small diameter are the following: (1) the duration for strong magnetic storms and auroral displays of a few days a t most; (2) the tendency for active solar regions to have their maximum geomagnetic influence near central-meridian passage; (3) the strong seasonal variation (which possibly is due to the fact that around the equinoxes the earth also happens to be near its maximum distance above and below the equatorial plane of the sun) ; and (4) the eleven-year cycle, in which the geomagnetic and possibly the auroral maxima lag behind the sunspot maximum (which could possibly be due to the fact that early in the sun-spot cycle the active regions are farther from the sun’s equator).I2 11 The numerical values given in the papers by Bennett and Hulburt are computed for velocities of 1010 cm/sec. Bennett [39] later concedes that this velocity is probably too high, but the qualitative results of their theory are unchanged. 12 From similar considerations Gnevyshev and 01’ [42]estimated the diameter of solar streams to be the order of 8 or 9 degrees.

150

JOSEPH W. CHAMBERLAIN

Moreover, the pinch effect has the property of helping the current maintain itself or even grow stronger. As we shall see in the next section, the magnetic field acts in such a way as to constrict fast protons and slow electrons. But any slow protons or fast electrons will be ejected, rather than restrained to the beam. Still the pinch effect itself does not make the basic concept of sunearth currents any more plausible than did Vegard’s [33] suggestion of a neutral beam with a current. It is true, however, that this constriction adds to the physics of the problem and should be considered in a quantitative theory of these currents. It is believed by some theorists that if sun-earth currents exist, one can then explain aurorae in terms of Stornier’s theory. If we grant the possible existence of strong currents, the pinch effect is very likely to be an important physical process governing the behavior of the stream. In this case, how much of Stormer theory can actually be applied to the streams? Because of this constriction effect, individual particles cannot be so easily bent out of the main stream. Qualitatively, this feature appears to be an asset, suggesting the auroral zone is a t lower latitudes than was Stormer’s zone. But quantitatively, rather than remove any difficulties inherent in Stormer’s theory for single particles, these new ideas merely pose new problems, and in the present stage of development of these ideas, it is not at all clear how aurorae are to be produced from the solar particles. Thus, without meaning this as a criticism of their work, we wish to emphasize that this theory is really concerned with certain features of hypothetical solar streams; but as a mechanism for producing aurorae, it is largely conjectural. Needless to say, the same remarks apply to various other theories. If the current were in vacuum, the fast positive charges would run ahead of the electrons and then their mutual electrostatic repulsion would destroy the beam. This self-focusing theory requires, therefore, a finite density for the interplanetary medium. Bennett and Hulburt suggest (without elaborating on the point) that this medium should have a density at least as high as that of the fast stream particles. Then it should be relatively easy for the stream to neutralize itself with interplanetary electrons whenever electrons in the stream are lost. Their estimates would indicate that the density of the stream is low enough for the replenishment to occur and, therefore, a current should be able to exist without blowing itself apart. The theory described here has reawakened interest in Stormer’s theory and Bennett, especially, has been concerned with demonstrating how current streams can produce aurorae. He has built an experimental apparatus that he calls a “Stormertron.” Electrons fired a t a magnetized

sphere give off auroral light i n the “iiiterpla~ic~tary hpaw” ty exc*itiitg mercury vapor; these experiments illustratr the trajectory of w i t aurorttl stream as well as the mtes where it strikes the cwth. k’i’igure 1 1 shows several frames from a motioii picture of these experiments. As the solar stream moves across thtb earth, the sceiie is viewed from above the pole and in the equatorial plane. 4 2 . 2 . The Hydromagnetic Pinch Effert. M‘hcrcas Betiitett [30] has recently giveti a rather elaborate discwsioii of the pinch effe(.t l,y applying the Boltzmaitii equation (microscopic approavh), it is possible to obtaiii essentially the same solution through the ordiitary (macroscopic) approach by hydromag11etic.s. Our treatment is a slight genrralizatio~iof that given by 8pitzer (261. 4.2.3. Total Current Rquirc.tl j’or Constriction. We consider a cyliiidricd ionized stream with a cwrreitt, as discwssed in Sertioii 2.3, and the condition for the piiirh effecst will b~ taken to he dVR

-< 0 (it -

which expresses tjhe cwidition that the radial expaitsion is tle.c*eleratiiig. (Higher derivatives will be neglected.) Froin t)he equation of motion (2.37) we have in cylindrical wordinates, when equatioit (4.1) is valid,I3 (4.2) We shall want to eliminate R, by appeal to Masiwll’s equatioits. Ampere's law, equation (2.41) gives for the c” rompoilelit l a(RR,)

(4.3)

R aR

=

4rJ:

Integrating, we have

(4.4)

KB,

=

2

/d’ 2rJ,RdR = 2 I ( K )

where I ( R ) is the total c w ~ e n within t a cylinder of radius I?. Using equation (4.4) to eliminate B, from equation (4.2),wr find (-4.5) 1 3 Strictly speaking, as wc arc now c.onsicl&ny :I radially expanding stream, we should use the tot,al derivative dv/dt rather tha.n av/ai on thc, right sidc of cyuatian (2.37). However, our pinch condition (4.1) also involvc~sthe total cleriyative, w1iic.h t requires t,he volume element nt,tached to the gas to 1x2 d e w l ~ r aing.

Fro. 11. Frames from a motion picture of Bennett's Stormertron. Various phases of the interaction between a stream of charged particles and the magnetized "earth " are shown in snccessive photographs, taken as the stream sweeps by the earth. (a) Top row and first two frames in bottom row, viewed from above a pole; (b) second row and last two frames in bottom row, corresponding views in the equatorial plane. Note the captive orbits in frames 4 and 6. Official U.S. Xavy photograph; courtesy R. H. Bennett.

THEORIES OF THE AURORA

153

Multiplying by 2nR2 and integrating, one obtains

(4.6) where R1 is the total radius of the stream (at which the number density n goes to zero) and T is the mean ionic and electronic temperature. (For purposes of deducing the magnetic constricting forces we neglect the density of the interplanetary medium.) If we let N o represent the total number of particles in a cross section of the stream, one centimeter in length, equation (4.6) gives

where # = kT is the mean energy in the transverse components of motion. Bennett imposes the condition th at the second time-derivative of the moment of inertia is negative, rather than equation (4.l), and derives the pinch effect through use of the virial theorem. His final result, for the case where there is no net separation of charge, may also be written I 2 = 2No#, where # is now the mean transverse energy per particle, including transverse (radial) mass motions as well as random thermal motions. In applying this equation to solar streams Bennett neglects the random (temperature) motions and considers instead the transverse energy due to the divergence of a conical beam with half-angle a. For a stream velocity of lo9 cm/sec he finds a stream starting with a = 7!5 will be constricted (self-focused), if the total current is I > 10 amp. But if the cone is as wide as a = 12O, the current must be I 2 lo6 amp. All this assumes that mutual electrostatic repulsion of the ions is halted by an influx of interplanetary electrons (see Section 4.2.1). If the current is not strong enough to produce the pinch, the stream merely continues t o accelerate outward (in the R direction), since the magnetic field is not strong enough to overpower the pressure gradient in equation (2.37). But would this really make so much difference as far as an auroral theory is concerned? Perhaps yes, if the solar streams are initially ejected with a wide angle. But in Section 4.3 we shall review Ferraro’s criticism, which maintains that currents of sufficient intensity to focus wide-angle streams cannot exist. 42.4. The Radial Electric Field. To illustrate how the pinch effect operates in constricting fast protons and slow electrons, we shall derive a steady-state expression for ER, the radial electric field that would be necessary t o balance exactly the Lorentz and diffusive forces of the stream. (It should not be concluded th at in a real stream this equilibrium would be achieved; the problem considered here is merely illustrative.)

154

J O S E P H W. CHAMBERLAIN

From equation (2.40), for an infinite conductivity (q

=

O), we have

(4.8)

Since the charge separation must be small, we may substitute in the diffusion term the approximation 1 ap, = -1-ap -(4.9) piaR pan

+

where p is the total pressure ( = p , pi). Also from equation (2.39) we have _ -- -J,B4 (4.10)

zL

Using equations (4.9) and (4.10) to eliminate the pressure gradient from equation (4.8), we find for the electric field measured by a “stationary” observer (4.11)

According to the Lorents transformation (2.6), the apparent field ER’ seen by an observer moving with velocity w Zis (4.12)

ER’ = ER - wZB4

Hence an observer moving with velocity W, = ER/B+will detect no electric field (ER‘ = 0). And a particle traveling with velocity (4.13)

will be affected by an inwardly directed field ( E R ’ < 0). I n the simple case where p , = pi (or T, = Ti)this condition for ER’ < Ois

+

(4.14) wz > v z - S ( V-~v e ) = % ( ~ iv,) where we have used equation (2.33) to eliminate J, and have set vi = v,, the mean mass velocity, according to equation (2.32). The interpretation of equation (4.14) is that a particle traveling with a velocity greater than the mean of the ionic and electronic velocities will see an electric field directed toward the axis. For slower particles the field is directed outward. Hence our previous statement that fast protons and slow electrons are constrained toward the axis. In the above derivation all the simplifying assumptions have been introduced for the purpose of clarifying the basic physics involved. I n a real stream the apparent field seen by a particle is likely to be more complicated than is given in equation (4.14).

155

THEORIES OF THE AURORA

4.8. Ferraro’s Criticism Ferraro [43] discussed the possibility of the emission of electronic currents from the sun. Recently [44] he has republished these same arguments to call attention to difficulties inherent in such modifications t o Stormer’s theory as have been proposed by Vegard and by Bennett and Hulburt. If a current flows along the z axis it will have a magnetic field associated with it, according to AmpBre’s law (2.41), with the lines of force being circles with R = constant. And if the current is increased or decreased there will be a corresponding change in the magnetic field. But this changing magnetic field produces an electric field by Faraday’s law (2.42), which tends to oppose the original current. Ferraro concludes that this induced field is so strong as to make it unlikely that there could be appreciable change in the current. We shall discuss this further after presenting the mathematics. The discussion presented here is a slight modification of that given by Ferraro. The magnetic vector potential A is related to the field by i

B = V X A

(4.15)

Faraday’s law (2.42) may then be written (4.16)

where @ is the electrostatic potential. We shall neglect V@, which is equivalent to postulating no net separation of charge. At any instant the relation between the current and its magnetic field is given by equation (2.41), which may, in terms of A, be written (4.17)

V X (V X A )

=

-V2A

=

4aJ

where the first equality is true since V * A = 0 when there is no space charge. The general solution to equation (4.17) is

A

(4.18)

=

/’& r

where r is the distance from the point where the potential is being evaluated to the volume element dr, and where the integration is over the volume of the stream. Except near the ends of the stream, we obtain approximately (-1.19)

A

=

2nR12JIn

L RI

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JOSEPH W. CHAMBERLAIN

where we take J to be uniform across a cylindrical stream which has a radius R1 and a length L. Near one end of the stream the value of A drops to approximately one-half the value of equation (4.19). Putting equation (4.19) into equation (4.16) we may compute the electric field set up by a change in the current density: (4.20)

L aJ E = -2?rRI2 In R~ a t

We may consider d J l d t to be composed of two parts: The primary change, a1J/6t, arises from some unspecified cause, such as differential slowing of electrons and protons by collisions. The secondary change, 62J/6t arises because of the induced field E. To find &J/St we appeal t o the generalized Ohm’s law (2.38). For negligible resistivity ( r ] = 0)’ a constant pressure in the direction of the current flow, and negligible net motions perpendicular to &J/&t, we have (4.21)

Combining (4.20) and (4.21), we find (4.22)

where (4.23)

neq2 me

I, RI

A = 27rR12__ ln-

Equation (4.22) may be written (4.24)

For A >> 1 we see that the induced current is practically equal and opposite to the primary component of the current; in this case the net change in current density will be very small, because of the large self-inductance of the stream. Alternatively, we may express equation (4.22) in the form (4.25)

which gives the final current in terms of the initial displacement of charges. Suppose that initially the electrons and protons have equa.1 ) . accordance with Bennett and Hulvelocities: v(0) = v i ( 0 ) = ~ ~ ( 0In burt’s assumptions, suppose further that the primary change in current results from the electrons being completely stopped by collisions but the protons suffer no change in velocity. The electrons are then re-accelerated

THEORIES OF THE AURORA

157

by the induced electric field and from equation (4.25) we may obtain the final net difference in proton and electron velocities: (4.26) (We neglect the presence of coronal or interplanetary electrons, which might be accelerated by the electric field at the expense of some of the original stream electrons.) Rough estimates suggest that A is indeed much greater than unity (-loll) and therefore the differential velocities of protons and electrons must remain a small fraction of the mean velocity. Ferraro makes an estimate of the maximum total current likely to flow in the solar stream, with differential velocities given by equation (4.26). Using equation (2.33) we have (4.27) Inserting the expression for A given by equation (4.23), with the logarithmic factor set equal to unity, we find approximately (4.28) For ~ ( 0 = ) lo9 cm/sec, which is probably an upper limit for auroral ion streams, I = 30 emu = 300 amp, which would have negligible importance as a current interacting with the geomagnetic field. On the basis of Bennett's calculations with similar parameters, it appears that a stream with this current would have to be ejected with a half-angle of less than one degree for the pinch effect to be appreciable. But with such narrow cones, magnetic constriction is not necessary to make the beams sufficiently small to satisfy the various criteria listed in Section 4.2.1. However, Ferraro's criticism as outlined above is not strictly valid when the stream moves through an ionized medium. First of all, when the electrons tend to lag behind, the induction process will act on all electrons in the region, not just on the original stream electrons. Even if the total current density J remained negligible in the stream, as in equation (4.25), Ferraro's conclusion that the protons in the stream have the same velocity as the electrons is not necessarily true. Also, Bennett, in a paper now in press, justly points out that the vector potential A immediately outside the stream decreases very gradually (as log LIR). Hence, the induced return current is not confined to the outward moving stream, but is distributed over a much larger volume of space, The solar stream itself may thus possess a finite current density,

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JOSEPH W. CHAMBERLAIN

although the total net current vanishes when integrated over a very large surface. An ionized interplanetary medium from the sun to the earth requires a complete revision of several concepts and ideas that have been cherished for many years. Needless to add, however, it has not yet been convincingly demonstrated that sun-earth currents do exist or that they could cause aurorae if they did. 5. THE CHAPMAN-FERRARO STREAM AND RING CURRENT

Chapman and Ferraro have adopted, in their theories of a neutral, ionized stream and a ring current, certain simplifying assumptions. But then, like Stormer, they have attempted to develop their theory along precise analytical grounds. I n order to accomplish this mathematical development, it was necessary occasionally to make assumptions of a physical nature that depart significantly from real conditions. They have maintained, however, that the precise treatment of certain idealized problems would give added insight to the real problem. Hence an extrapolation of the Chapman-Ferraro theory to an explanation of aurora, for example, involves considerable speculation and cannot be said to rest on a very firm foundation. Nevertheless, the mathematics has suggested one or two ways in which aurorae could be produced by solar particles, and it is not likely that these ideas would have originated from purely speculative and qualitative reasoning alone. The division of the theory of Chapman and Ferraro into two parts, the solar stream and the ring current, is a natural one for several reasons. According to their ideas, the stream itself is responsible for the initial phase of a magnetic storm, whereas the ring current is associated with main phase. Also the theoretical developments are quite distinct: Both the ring current and the stream are hypothesized to exist; it has not been demonstrated, for example, how the ring would be formed from the stream. And, finally, it seems that an aurora might appear either directly from the stream particles or through the intermediary of the ring, but these two methods of auroral formation are quite distinct. 6.1. Theory of a Neutral, Ionized Stream

The basic assumptions of Chapman’and Ferraro’8[45-50b]-theory’ofa solar corpuscular stream are that the stream is composed of an equal number of electrons and singly charged, positive ions, all of which are moving with the same velocity toward the earth. Before arriving in the neighborhood of the earth, the stream is unaffected by any magnetic or electric fields and moves through a vacuum. We may wish to question the validity of some of these basic assump-

THEORIES OF THE AURORA

159

tions. As we pointed out at the end of Section 4.3, the assumption of equal electron and proton velocities is questionable, even if we accept the conditions of zero current and electrostatic neutrality. Further, the recent work of Behr, Siedentopf, and Elsasser [51-531 and of Blackwell [53a] on the zodiacal light indicates an electron density of the order of 600 cm-a at the earth’s distance from the sun. If this continually increases toward the corona, as the observations indicate, then the interplanetary density of ionized matter is probably considerably greater than that of the solar stream throughout its journey from the sun to the earth. Also the research of Storey [54] and others on radio whistlers seems to confirm the high electron density around the earth. Alfven [27] has also objected to the neglect of the general magnetic field of the sun, which he feels would have an important effect on the stream even at one astronomical unit. But we shall defer discussion of this matter to a later section. A somewhat different objection was first raised by Hoyle [55], who points out that a cloud of ionized material that breaks away from the sun would have to carry some of the solar magnetic field with it. The electrical conductivity is so high that the lines of force would move with the gas. The importance of these considerations cannot be decided until more is known about the sun’s field, both in the neighborhood of the region where matter is ejected and the general (dipole) magnetic field. More recently Hoyle [56] has suggested that the interstellar medium gauss, accompanied by an interstellar magnetic field of the order of penetrates the solar system. At a distance of about 10 earth radii, the terrestrial field is closed and beyond that distance the interstellar field prevails. These considerations could certainly make a profound difference in the behavior of a stream near the earth. Discussion of this matter will be deferred to Section 6.4. Various assumptions are made by Chapman and Ferraro on the form of the stream and in some cases simplifying assumptions are made for the magnetic field of the earth. We shall mention these approximations in the subsections below, as they differ for the different problems. Their several idealized problems proceed from simple to the more difficult; as we progress through these cases, different aspects of a gas stream are illustrated. At the end of each subsection we shall attempt to summarize the “moral” of that particular problem. Here we shall only sketch the fundamental aspects of the problems; but Chapman and Ferraro have in some cases carried the discussion of the pressures, temperatures, and other characteristics of the stream to an astounding degree of completeness. Additional investigations of the physics of an ionized stream have been published by Landseer-Jones [57, 611.

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JOSEPH W. CHAMBERLAIN

The basic idea of a neutral, ionized stream without a current was proposed first by Lindemann 1121, in a criticism of an earlier theory of Chapman’s (see Section 4.1). At first, Chapman [58] insisted that the conveyance of a current was an essential feature of the solar stream, but he has since rejected this idea and adopted Lindemann’s hypothesis. 5.1.1. Motion of a Plane Slab in a Uniform Magnetic Field. Chapman and Ferraro [45, p. 831 first consider an infinite slab with faces parallel (away from the to the 2, z plane. The slab is moving with velocity origin) and the field is in the + x direction. If the magnetic field were applied all of a sudden, the particles would be deflected in the direction pv X B; hence positive particles would go in the -y direction and electrons would go toward +y. This drift would continue until the electrostatic polarization field balanced the Lorentz force. From equation (2,1), when there is no acceleration, we have (5.1)

EU(O)= V,(O)&

inside the slab. On the periphery, however, where a charged layer exists, the net relativistic field will not be zero. If the thickness of a charged layer is d, then at a distance 8 d (where 0 < 8 < 1) measured from the inside edge of a charged layer, the electric field will be (5.2)

E ( e J = E(o)(1- 8)

where E(O)is given by equation (5.1). By equation (2.1) the equation of motion of a particle at position 8 d is then

From the discussion in Section (2.1). we see that the motion may be represented as a drift velocity (5.3)

and a circular velocity (5.4)

y’

= OV,(O)

The radius of the gyration would be (5.5)

And from the known expression for the field EU(O)inside an infinite condensor of surface charge uo, we find, for the thickness of the charged

THEORIES OF THE AURORA

161

layer (or displacement of the charges from their neutral position), (5.6)

These equations show the following properties of the stream: If the magnetic field is suddenly impressed on the stream so that all particles start moving in phase, the surface layers will pulsate with a frequency w/2a = qB,/2~mand with an amplitude depending on position and given by equation (5.5). There will also be a shear between layers of different 8. Outside the slab (0 = 1) the electric field and drift velocity are zero; inside the slab (e = 0) the electric field is balanced exactly by the Lorentz force and all the motion is a uniform drift. The importance of these pulsations in a real stream might be questioned. Putting numerical values in equations (5.5) and (5.6) (e.g., B, = 100 gammas, u , ( O ) = lo8 cm/sec, we) find p >> d. In . , n, = lo2 ~ m - ~ this case, any divergence of the stream 2 from plane-parallel motion as well as the random thermal motions would tend to smear out the systematic pulsations. These deviations from the ideal situation would cause a single particle to move through varying values of 8 ;its radius of gyration would change over a single revolution. At the surfaces of the slab there are currents resulting from the motion of charges of only FIG. 12. Cylindrical stream one sign and the magnetic field associated in a uniform magnetic field. with these currents has been neglected in The diagram shows the polarcomparison with the external field. ization of the stream and the Thus an accurate discussion of even a direction of the electric field outsimple problem becomes an exceedingly side the cylinder. complicated task, except when quite idealized conditions are postulated. 5.1.2. Cylindrical Stream in a Uniform Field. Consider the cylindrical stream of radius Rl illustrated in Fig. 12. The displacement is now twice as much as in equation (5.6) (for the plane slab) : (5.7)

where (TO is the surface charge per unit area perpendicular to the y axis. At a point on the periphery ( y = R1cos 4; z = R1sin b), the “algebraic” surface charge per unit area perpendicular to the radius vector is (5.8)

u = -uo cos

4

162

JOSEPH W. CHAMBERLAIN

where the minus sign enters because negative charges tend toward the y direction. Outside the cylinder the field does not vanish, as in the case of the plane-parallel condenser, and the potential will be

+

=

- ~ T u ~ c ~ ( Rcos ~ ~4/ R )

The potential inside the cylinder is Gin = -2moc2R cos 4. It may readily be shown that the displacement quoted in equation (5.7) is consistent with this internal potential when the Lorentz force balances the electrostatic field. Outside the cylinder the field E = -V@ is (5.9)

and

(5.10) The component Ev is crossed with B, and merely gives rise to oscillations and shearing motions as in the plane slab. The component E, causes an acceleration of particles away from the plane z = 0, as shown in Fig. 12. Hence, in the general problem of an ionized stream in a magnetic field, the surface charges are not stable (as they are in the special case of a plane slab), but are accelerated away from the stream. The electrons escape with higher velocities than do the heavier particles, and the electric potential and resulting distribution of surface charge become horribly complicated. I n any event the field inside must remain E, = v , ( ~ ) B , . Chapman and Ferraro ([45], p. 91) estimated that protons accelerated by this mechanism along the lines of force might reach terminal velocities of the order of los cm/sec. However, precise calculations in the field of a dipole are rather difficult, so they were reluctant to claim too much importance for this mechanism of accelerating auroral particles until a more detailed analysis became possible. 5.13. Advance of a Stream into a Magnetic Field. To illustrate some of the phenomena accompanying the advance into a region of increasing field strength, Chapman and Ferraro [46] considered an infinite plane sheet moving perpendicular to itself and to the magnetic field. The sheet is assumed to be rigid (so that distortions in the surface that would be produced by the interaction of the sheet with the field can be neglected) and perfectly conducting. Let the ionized sheet be centered at the origin; the velocity of the sheet is +v, (toward the dipole), the lines of force in

163

THEORIES O F T H E AURORA

the equatorial plane extend toward +z, and the dipole moment M oextends toward - 2 (see Fig. 13). (Alternatively, we can think of the sheet at rest in the dipole moving toward it with velocity -uz.) This problem was considered by Maxwell [59] in terms of the magnetic scalar potential. We suppose that outside the sheet there is no ionized matter, so that V X B = 0. Then the scalar potential il can be defined for every point except in the sheet so that B = - V Q . Let Oo be the potential due to the permanent dipole with moment Mo. Maxwell showed that the field as modified by the induced currents in the sheet can be described by the superposition of the permanent-dipole field and an image-dipole field, but we must use different image dipoles for the field in front of and behind the sheet. 2

REGION II

n, + n;

t

REGION I

FIG.13. The magnetic field produced by an infinite sheet of ionized matter, which moves toward a permanent dipole, Mo.The induced dipoles are M Iand MI';actually MI'is coincident with MO, and is separated in the figure only for clarity. The scalar magnetic potential for the regions in front of and behind the sheet are given in terms of the potentials of the permanent and induced dipoles.

The situation is illustrated in Fig. 13. For region I (on the same side of the sheet as the permanent dipole) the image is MI, which is located behind the sheet. In region I the total scalar potential is Q O %. For region I1 the image dipole is M1', which is superimposed on Mo (in the figure they are separated slightly for clarity) and is in the opposite direction to Mo. Let the electrical resistance of the currents in the sheet be 2nb. Maxwell showed that -MI' = M i = Mo- 02 (5.11)

+

b

+

02.

For infinite conductivity we have b = 0; the field behind the sheet vanishes, whereas that in front of the sheet is increased in the equatorial

164

JOSEPH W. CHAMBERLAIN

plane.130 I n the terminology ofihydromagnetics we may alternatively think of this change in the magnetic field as resulting from a compression of the lines of force by the ionized gas. For the ideal case of infinite conductivity, it may be shown that the lines of force move with the fluid and cannot therefore penetrate the sheet. The currents induced in the sheet are illustrated in Fig. 14. The current lines are intersections with the sheet of the equipotential surfaces of the dipole. These currents move in the eastward direction in the equatorial plane (counterclockwise as viewed from the north) , which, of course, is the proper direction to increase the magnetic field a t the earth. This increase of the terrestrial magnetic field has been identified by Chapman and Ferraro with the Jirst or initial phase of a magnetic storm. It will be noted in Fig. 14 that there are two foci where the currents vanish. These points are of some further interest in the following discussion of the deformation of the stream. Although we are considering a rigid sheet, let us examine the interaction of the current in this sheet with the magnetic field and the resulting retardation in the sheet’s advance toward the dipole. If the pressure (which would have a physically implausible discontinuity in the sheet) is neglected, the acceleration on the gas is, by equation (2.37) av, 1 (5.12) - = __ (J,B, - J,B,) 5 0 at nmi The deceleration vanishes a t the foci (where both the current is zero and the field lines are perpendicular to the sheet). Whereas an accurate discussion of the deformation of such a sheet would be exceedingly difficult and has not been done, a qualitative picture of the profile of the stream is shown in Fig. 15. The so-called horns of material that protrude toward the earth seem to be a possible route of entry into the atmosphere for auroral particles. Chapman [GO] has discarded this possibility, on the grounds that the particles are not likely to gain energy and speed and should therefore not have the penetrating power of auroral protons. To summarize, the rigid, plane sheet acquires a current system over its surface as it moves toward the dipole. These currents modify the magnetic field, and through interactions between the field and the currents, the stream is distorted. 185 I n some regions off the equatorial plane the field lines from the image dipole will be in the opposite direction to those from the permanent dipole. Hence the field is in some places decreased rather than increased. However, the total magnetic energy of the field in region I is increased. The deceleration of the stream is essentially a result of the conversion of kinetic energy into magnetic energy.

165

THEORIES OF THE AURORA

This analysis, however, postulates a scalar magnetic potential everywhere except in the current-bearing sheet itself. Suppose, as we have good reason to believe, that the interplanetary medium has a density of ionized matter that is a t least comparable to that in the stream. The N I

\

W

S FIG. 14. Currents induced in an infinite, plane, rigid sheet by the motion of the sheet into a dipole magnetic field. The points A and B are null points, where the current vanishes. The stream is viewed from the magnetic equator of the earth as the stream approaches the observer. After Chapman [50a]; courtesy Geophysics Research Directorate, A. F. Cambridge Research Center.

changing magnetic field will induce currents in this medium so that the condition V X B = 0 will no longer be strictly true and the scalar potential is no longer defined. Although this idealized problem may be descriptive of real streams to some extent, the adoption of such an approximation to discuss fine

166

JOSEPH W. CHAMBERLAIN

details, such as the formation of horns and the penetration of auroral particles to the earth, would seem to require some further demonstration of applicability. 6.1.4. The Cylindrical-Sheet Problem. The shape of the stream of ionized material treated in this problem differs radically from any real solar stream, but the geometrical simplification is necessary if an analytical solution is to be obtained. Chapman and Ferraro [50] wished to consider in detail a current system, such as that described in the previous

OF f ’/, <

IONIZED PARTlCLES

-b

DIPOLE

I

Fro. 15. Profile of the stream shown in Fig. 14. Points A and B correspond to the null points in Fig. 14 and are the regions where “horns” are formed on the stream. The figure gives only a qualitative p i c h e of the distorted sheet. After Chapman [50a]; courtesy Geophysics Research Directorate, A. F. Cambridge Research Center.

section, when a stream advances toward the earth. The problem considered may have some analogy with what actually occurs in the equatorial plane. We postulate an infinitely long cylindrical sheet that is contracting uniformly toward its axis (the z axis). The magnetic field is taken to be B, = Bo(a/R)a,which decreases from the axis at the same rate as the earth’s field, and which has lines of force everywhere parallel to the z axis. At t = 0 the sheet starts moving toward the axis with velocity VR. The motion of charges across the magnetic field cause a Lorentz deflection, in opposite directions for particles of opposite signs. Hence a current is set up in the sheet. The current modifies the magnetic field and, in turn, the field interacts with the current to decelerate the radial (inward)

167

THEORIES OF THE AURORA

motion of the particles. If the plus and minus particles separate radially, there will be an electric polarization field; otherwise the field E arises only from the changing magnetic field. The electric and magnetic fields are expressed in terms of the potentials Aand CP by equations (4.15) and (4.16), to which we add the condition (5.13)

to complete the definition of A. The deflection in the 4 direction and the retardation of the stream are governed by the equation of motion (2.1). I n this axially symmetric problem, then, (5.14) (5.15)

with the other components of E and B vanishing. We also write the magnetic potential as Ad = A,, A J , the sum of the potentials due to the permanent field and due to the induced currents. It is clear that - Boa3 (5.16) A, = R2

+

If we let Qo be the amount of charge of either sign on a strip one centimeter high around the whole circumference of the cylinder, then the potential A J at a point R inside the sheet is (5.17)

where R1 is the radius of the sheet and vd,; and vd,e represent velocity components in the 4 direction for ions and electrons, respectively. If there is any radial separation of charge, the field between the electron and proton sheets will be E R = 2Qoc2/R.Hence there will be no separation as long as the differential radial force on protons and electrons is less than QER.That is, separation of charges will occur when and only when (5.18)

Iv4.i

+

vg,alBs

2 2Qoc2/Ri

Before separation the electrons are essentially carried toward the axis by the more massive protons. After the separation point is reached, the protons advance closer to the axis, with the electrons being left farther behind.

168

JOSEPH W. CHAMBERLAIN

The problem is thus solved in two parts: Before and after separation of the charges. The important feature of the analysis is that the electrons will be able to progress much closer toward the axis by following the protons, than if electrons were treated alone, as in Stormer’s theory. We shall not work through the rather lengthy solution of the equations of motion, but the essential features of the physics have been sketched above. At the current sheet the magnetic and electric fields are discontinuous, so Chapman and Ferraro adopt average values of those quantities inside and outside the sheet, for purposes of discussing their effects on the particles in the sheet. The solution gives the following description of the motion, when the charges do not separate. Originally all the motion is directed inward. As the Lorentz force begins to operate, protons and electrons are accelerated in opposite directions so that the current is eastward and the field is increased. Eventually the field reaches a maximum, with all motion in the 9 direction, and the current sheet begins t o recede. At the radius where the inward motion stops, only a small part of the initial kinetic energy remains in the form of angular motion round the cylinder; the rest has been converted into magnetic energy. The angular velocities will be the same at corresponding times during contraction and expansion of the sheet. Finally, the sheet will recede t o the distance a t which it started and continue on to infinity. When separation occurs the solution is somewhat more complicated, but basically the same type of motions occur. 6.2. Theory of a Ring Current

The ring current was originally proposed by Stormer (see Section 3.2.1) in 1911 to modify the polar distance of the auroral zone. Later Schmidt [62] postulated a current to explain magnetic variations. In more recent years Chapman and Ferraro [49,63] have developed a theory for a ring current and its bearing on the main phase of a magnetic storm ~341. The actual existence of a ring current is still somewhat doubtful. Cosmic rays give a potential means of detecting the ring, but so far no definite evidence one way or the other has been obtained [65]. Also it has never been demonstrated just how a ring current could be set up. The direction of the current, to lower the field at the surface of the earth, would be westward, but the direction of flow of the ions and electrons could be either eastward or westward, depending on which flows faster. For a ring current to exist and be stable it is necessary that the centrifugal force of the (heavy) ions moving about the earth be balanced by a Lorentz force deflecting the stream inward. If we neglect the electronic

THEORIES O F THE AURORA

169

mass in comparison with the ionic, we have as the condition of balance, Vi2

(5.19)

mi-

R

= -q(vi

- vJBZ

Here B,, the equatorial field, is the sum of the permanent field and that due to the current: (5.20)

For a cylindrical sheet, as we discussed in Section 5.1.4, (5.21)

BJ

=

2Qo(vi - v e ) / R l

for R < R1,where Qo is the total charge in the strip around the sheet and one centimeter wide (in the z direction), and R1 is the radius of the ring. The field B J outside the cylindrical sheet is zero, so for the effective value of BJ we choose one-half the value quoted. Then since QO = niq2rRlAR1, where ni is the density of ions and AR, is the thickness of the ring or sheet, we have (5.22)

Vi2

miR

=

(i)3 -

-q(ui - v,)B0

q2(vi - vJ22~niAR1

Since the left side of this equation is greater than zero, we must have, algebraically, vi < v,; hence the current must flow westward, as already stated. This is the same direction that the hypothetical earth currents must flow in, t o produce the permanent dipole field. (Everywhere inside the cylindrical sheet the field due to the current is given by (5.21). For a ring the field would be

Bj

(5.23)

=

2aqn'i(vi - v,)h

R

where b is the cross-sectional area of the ring.) During a magnetic storm, the decrease in B at the equator might be about 100 gammas gauss). Chapman [60] supposes that at the distance of the ring the dipole field still predominates; otherwise variations in the cosmic-ray intensity should follow closely the geomagnetic disturbances, and they do not. For a value of BJ of 100 gamma, the ring would have to be closer than about 4 earth radii for this condition to be true. If the disturbance field is small compared with the dipole field, even a t the assumed distance of the ring (3.5a), we may neglect the second term on the right side of equation (5.22). Putting in numerical values, one finds lo8 cm/sec, then v, - vi lo4 or lo6 cm/sec. Hence the that if lvil

-

-

170

JOSEPH W. CHAMBERLAIN

differential motion is quite small compared with the mass motion. (As we have adopted our coordinate system, a positive value of velocity is taken in the eastward direction.) Alfven (661 has objected to the Chapman-Ferraro idea of a ring current on the grounds that it would not be truly stable. For example, he states that a single particle would not be stable if the field decreases outward more rapidly than -l/R. The dipole field varies as l / R 3 so should not support a stable ring current. The problem, however, does not yet seem to have been completely investigated. Single-particle considerations are not valid for a stream of gas that interacts with the magnetic field. The ring current will have associated with i t a certain tendency to constrict through the mechanism of the pinch effect, and this constriction may be adequate to give the ring the necessary amount of stability. Of course, it is not necessary nor even desirable to insist on a perfectly stable ring, since the main phase of magnetic storms decays with a lifetime of a few days. A more important objection to the concept of a ring current stems from recent observations, through whistlers and the zodiacal light, of a n ionized gag around the earth. These data suggest that the conductivity of this medium is very high, insofar as the decay of induced currents is concerned. I n this regard see Section 7.3 and the discussion of Section 6.4.2.

6.5. Martyn's Theory of Aurorae The starting point for Martyn's [67]theory is a ring current of the type envisioned by Chapman and Ferraro. It is assumed without proof that such a current would be formed from a solar stream of ionized matter, although Martyn does give a plausibility argument (discussed below) for its formation. The theory of Chapman and Ferraro on the first phase of the magnetic storm is also accepted by Martyn. He calculates that the ionized sheet should be stopped at a distance of 5.5 a, where a is the earth's radius, if the first-phase increase in the field is 25 gammas at the earth's ~urface.1~ Hence 5.5 a is adopted, still rather arbitrarily it would seem, as the radius of the ring. But this radius is a critical point in the theory; the dipole lines of force that cut the equatorial plane at this distance intersect the 25". earth at a polar angle 0 The plausibility argument on the formation of a ring current is based on analogy with a purely hydrodynamic stream flowing around a submerged obstacle. Martyn contends that a gap would not be formed on

-

14 This calculation may be readily verified through the use of the image dipole, as explained in Section 5.1.3 and Fig. 13.

171

THEORIES OF THE AURORA

the side of the earth away from the sun. The analogy appears to be a little weak. In an ordinary fluid the pressure is of dominating importance, whereas for a hydromagnetic stream moving at high velocity, the scalar pressure is physically meaningless for an observer “ a t rest.” Rather, one should use a stress tensor in which the effective pressure along the direction of motion will be much greater than the transverse pressure. But accepting Martyn’s analogy, we still find the argument questionable. He states essentially that these hydrodynamic properties of the stream show that the gap is closed, but on the other hand he invokes the Lorentz force J X B to counteract the centrifugal force (see equation 5.19) and actually close the gap. One wonders why the electromagnetic forces are necessary if the phenomenon is accomplished by hydrodynamics alone! Certainly a more rigorous treatment is called for. To obtain an estimate of the density in the stream, Martyn equates the energy density of the particles in the stream to the magnetic pressure: (5.24)

1 2

-nimp2 =

Ba 87r

Or when the effective “pressure” of the incident solar stream is balanced by the pressure of the magnetic lines of force, the stream will be stopped. Let us examine this condition in more detail. A single (Chapman-Ferraro) sheet would probably be repelled away from the earth, after reaching the minimum distance (see Section 5.1.4). But a succession of such sheets or a continuous stream of matter would keep the effective gas pressure in the direction of motion of the stream at about the value given in equation (5.24), and we might expect this equation to be fairly reliable. The velocity v is taken as the stream velocity (lo8 cm/sec), and equation (5.24) does thus not apply strictly on the morning or afternoon sides of the earth and it does not apply a t all on the night side. (That is, the left side of the equation is not an isotropic pressure.) Evaluating B a t a distance of 5.5 a, Martyn ascertains a density ni = n, 10 cm-s. According to the most recent studies of the zodiacal light [51-531 and radio whistlers [54], the interplanetarymedium hasadensity closer t o ns = 600 cm-8. In general, we might presume that any attempt to discuss a terrestrial ring current that moves in otherwise empty space will be abortive. Thus one may quarrel with Martyn’s particular formulation of the problem, but some of the qualitative ideas involved may be worth further consideration. In Section 5.1.2 we discussed the instability of particles in a cylindrical stream moving in a magnetic field. The induced electric field will not vanish outside the stream and particles on the surface will be accelerated outward. Martyn has applied this idea to the acceleration of auroral particles

-

172

JOSEPH W. CHAMBERLAIN

from the ring, along the lines of force, to the auroral zone. The scheme is illustrated in Fig. 16. Suppose the ring, centered at distance R1 = 5 . 5 ~produces ~ a perturbation BJ = 50 gammas a t the equator ( R = a). From equation (5.23) we may evaluate the cross-sectional area b of the stream, since the density ni has already been estimated and vi - v, is obtained from equation (5.19) with v i = lo8 cm/sec. Martyn postulates a circular cross section, and he thus concludes the ring has a diameter of 4a. Extending the dipole lines of force from the boundaries of the ring back to the earth, he finds a (north-south) width for the auroral zone of 681 = 6". The electric-polarization field produces a current system that is

FIG. 16. Schematic picture of Martyn's theory of aurorae. The ring current becomes polarized, with negative particles escaping off the far side and positive particles off the near side (as seen from the earth). The particles are accelerated along lines of force to the ionosphere,

closed through the ionosphere. An order of magnitude calculation suggests that the potential difference between the ring and the ionosphere is as high as 1 MeV, which would provide adequate acceleration to explain the penetration of auroral particles to the observed heights. Martyn also suggests that this mechanism of transferring much of the electric-polarization field to the ionosphere results in the auroralzone current system associated with magnetic storms. To ascertain the direction of this field consider how the particles are deflected a5 they progress from the sun into the earth's magnetic field. On the evening side positive particles are deflected to the outside of the ring, electrons to the inside. Just the reverse happens on the morning side. (The separation of charge is limited, of course, by the polarization field.) Hence on the evening side protons go to the higher latitudes of the auroral

THEORIES OF THE AURORA

173

zone, electrons strike the atmosphere in lower latitudes, and E is directed southward. On the morning side the field points northward. In the northern auroral zone B is almost vertical downward; the drift is in the direction E X B (regardless of the sign of the charge) and the magnitude of the drift is approximately (5.25)

where v, is the collision frequency. Equation (5.23) is the generalization of equation (2.4) when collisions are allowed for. The conductivity of the ionosphere is probably much lower than t h a t of the interplanetary medium. The total potential drop across the ring is of the order of lo6 volts, according t o Martyn, and we would expect most of this drop to be in the ionosphere. Without presenting detailed calculations in his note, Martyn concludes that the Hall current thus induced in the ionosphere may be adequate to explain the auroral-zone current systems. It is merely necessary to postulate that positive ions will drift slightly faster than negative ions. Then the morning and evening current's are directed toward the midnight meridian and the currents are closed over the polar cap and a t lower latitudes. l6 One rather severe difficulty with the theory is that the direction of drift of visible auroral structures and ionization detected by radar is usually toward the sunlit hemisphere-opposite to that of Vestine's current systems. The auroral ionization drifts and the currents could be interpreted as a single phenomenon if electrons (or negative ions) should drift faster than protons. For the ionization to drift toward the noon meridian because of the ring current, however, the polarization of the ring would have to be opposite to that predicted by the theory; and it is not clear how one might patch things up without a complete revision of the basic ideas. 6. OTHERELECTRIC-FIELD THEORIES OF AURORAE .

Electric fields have occupied an important place in some of the work we have already reviewed. For example, a neutral, ionized stream in a magnetic field develops an electric polarization as a result of the Lorentz deflecting force. Moreover, we have seen that Martyn has made use of an electric polarization across the ring current to accelerate particles into the auroral zone. When material ceases to enter the neighborhood of the earth, the entire flow in the ring will, according to Martyn, go in the westward direction. The ionospheric currents would then also be westward, all around the auroral zone.

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I n this section we shall be concerned with additional theories in which an electric field is utilized to accelerate auroral primaries. 6.1. Alfvdn’s Theory Although it was originally published in 1939 and 1940, this theory is most readily accessible in AlfvBn’s [27] book, where a complete chapter is devoted to it. Some of the ideas have been extended in a more recent paper [66]. The basic idea is that the solar stream must move in a magnetic field, even before it reaches the earth. Either the general magnetic field of the sun or the localized magnetic field in the region where the particles were emitted could contribute. Alfvh [27] originally maintained that the sun’s general field should be important. This matter has been the cause of some dispute, since solar physicists have not been able to detect an appreciable general field in recent years. The marvelous observational work on the Zeeman effect by the Babcock’s [68] suggests a field of less than 1 gauss. But Alfvh [69] has replied that because of the sun’s turbulent and highly conducting atmosphere, the ordinary theory of the Zeeman effect cannot be used to measure the field. With a theory of hydromagnetic turbulence, one might estimate the magnetic field from the amount of turbulence, on the assumption that energy is contantly reshuffled between the magnetic and kinetic states. The whole problem is one of considerable discussion a t present. More recently Alfvh [66]has emphasized the point, suggested also by Hoyle [55], that a cloud of ionized gas emitted from the sun must carry some of the solar field with it. In a highly conducting gas, the lines of force are “frozen in,” to use AlfvBn’s descriptive terminology, and one might expect some sort of magnetic field to accompany the cloud to the earth. Just what the form of such a field would be is anyone’s guess. But Alfvdn assumes that the field is parallel to the z axis-i.e., parallel to the earth’s dipole moment. I n any event, an observer moving with the stream, before it is distorted ahd slowed down near the earth, sees no electric field. But a “stationary” observer will experience an electric field in the cloud, since a polarization E( = -v X B) will be set up.l6 Thus the basic assumption of the theory is that the earth is imbedded in an electric field; this field could be produced by a wide (compared with the earth) solar stream and an extraterrestrial magnetic field. Alfv6n has given consideration to the motion of charged particles 16 If we consider the magnetic field as frozen to the cloud, then the “stationary observer,” who is in motion relative to the cloud, will “see” a -v X B field, which is entirely equivalent to an electric polarization field.

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under the influence of this electric field superimposed on the dipole field. As we showed in Sections 2.1.2 and 2.1.3, a particle will drift when it is (1) under the influence of crossed electric and magnetic fields and (2) when it moves in an inhomogeneous magnetic field. Similarly, a drift will result from any external force crossed with a magnetic field, and AlfvBn has considered the drift due to (3) deceleration of the forward motion as the particle moves toward the dipole. (Actually, the only decelerating force considered is that produced by E X B.) Now let us consider again the electric field. To a “stationary” observer (say, on the earth) an individual particle in the stream may be thought of as drifting under the action of the electric and extraterrestrial magnetic fields. As the particle approaches the earth, B increases and the particle slows down (equation (2.4)). The deceleration causes a drift sideways (parallel to the electric field). In addition, as the particle begins to move in the inhomogeneous dipole field, additional drifts occur. An idea of the type of motion resulting can be gained from Fig. 17, which was computed with item (3) above (the drift due to the deceleration) ignored. In AlfvBn’s theory the motion is treated for single particles and not for a stream as a whole as in the case of Chapman and Ferraro’s theory. The magnetic field produced by stream currents would also affect the orbits, but this effect is neglected. If positive ions are considered, their orbits are, in AlfvBn’s theory, mirror images of the curves in Fig. 17, except that the scale of the figure may be changed, depending on the mean energy of the particles. AlfvBn postulates that the electronic temperature is much greater than the ionic temperature. Consequently, he suggests that positive ions will tend to penetrate closer to the dipole (i.e., the hollow or forbidden region for ions will be smaller). The positive ions will not actually penetrate into this hollow, however, because as soon as they cross the boundary they will encounter a positive space charge that accelerates them toward the auroral zone along the magnetic lines of force. Thus protons will flow around the dipole in almost straight lines, the more complicated orbits being prohibited by the fact that they lie on the inside of the electron forbidden region. On the night side of the hollow, then, there will be a deficiency of protons and a negative space charge will exist, since electrons but not protons will be deflected around to the rear boundary of the hollow. 17 The drift due to the inhomogeneity of the field gives a westward current, related by Alfven to the main phase of a magnetic storm. When the deceleration drift ( ff X B, where the inertial force is f = --m dvldt) is considered, an eastward current appears first (initial phase of the storm) and then gives way to the westward current.

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A discharge, between these regions of opposite space charge, along the magnetic lines of force and through the polar atmosphere, gives rise to the aurora. Rather severe objections have been advanced regarding the existence of the space charge around the hollow. (It should be noted that there are

FIG. 17. AlfvBn’s theory of aurorae. The solid lines are orbits of electrons under the combined influence of the terrestrial dipole field and the homogeneous electric field in the stream. After AlfvBn [26]; courtesy Oxford University Press.

really two types of electric field in this theory: One results directly from the solar magnetic field crossed with the stream velocity; the other is a by-product of the electron and ion drifts. It is the latter that presumably accelerates particles to the atmosphere and is the most questionable feature of the theory.) Cowling [70] has pointed out that most of the positive ions would be magnetically reflected from the auroral zone and that a net positive charge would continue to build up until it leaked away in some other fashion. Also, the electronic space charge will not accumulate on the night side,

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since it would discharge as soon as it leaves the region where positive ions can also exist. Chapman [60] has also objected to the neglect in AlfvBn’s theory of the electrostatic forces, when charge separation is presumed to occur. Chapman and Ferraro’s (see Section 5.1.4) cylindrical-sheet problem has illustrated t ha t the positive ions would have a great effect on carrying the electrons closer to the dipole than they would otherwise penetrate. But Alfvhn treates the separation of charge in a qualitative fashion and neglects the interaction of proton and electron sheets. AlfvBn concedes that some of these effects might reduce the amount of space charge, depending on the densities involved in the solar stream. It would seem that the neglect of these forces, likely to be of dominating importance, is a serious deficiency in the theory. Whereas Alfvdn discusses a number of other aspects of the auroral theory and the magnetic effects of the stream, we shall have to refer the reader to the original papers for further details. We should mention, however, that Alfvdn puts considerable emphasis on terrella experiments performed in his laboratory by Malmfors [71] and Block [72], which suggest that aurorae might be explained by an electric field acting on the earth and that the individual particles in the stream itself do not have important roles in the production of the aurorae. Presumably the main function of the solar stream is to provide the electric field; interplanetary ions, and not the ions in the stream, may be the observed auroral particles. These ideas are merely suggestions; the detailed theory applies to stream, not interplanetary, particles. 6.2. Hoyb’s Theory

Hoyle [SS] has emphasized th at the magnetic field carried away from the sun by a n ionized cloud is likely to be important in the cloud’s interaction with the terrestrial field. If B, represents this solar field carried to the neighborhood of the earth by the stream, then inside the stream the electric field will be -v X B,. If by some means this magnetic field should suddenly vanish a t some point, particles a t that point would experience an acceleration owing to the electric field. At certain “neutral” points near the earth, the terrestrial and solar fields might just cancel one another. Hoyle suggests that in the neighborhood of these points particles will be accelerated to auroral energies. Some of these particles presumably find their way to the auroral zone along the lines of force. Hoyle’s suggestion differs somewhat from Alfvdn’s in th a t the former would have the auroral particles accelerated directly by the electric field of the stream. Alfvdn, as we have seen, used the electric field to produce a space charge, which in turn discharged the particles.

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Needless t o add, there are many questions still to be answered regarding the feasibility of this accelerating mechanism. Hoyle makes the observation that this process is essentially a conversion of solar magnetic energy into kinetic energy. At present we cannot regard it as anything more than an interesting speculation. Recently, Hoyle [56] has suggested that the interstellar magnetic field penetrates to within a few earth radii of the earth. But no discussion of aurorae on the basis of these ideas has been published (cf. Section 6.4). 6.3. Lebedinski’s Theory

The electric field in Lebedinski’s [73] theory also arises from a large ion cloud (or plasma) passing by and enveloping the earth. He neglects the solar magnetic field, however, and considers only the effect of the terrestrial dipole field. The electric field in the plasma is then E = -v X B. As the stream moves around the earth a hollow is formed in the stream by action of the earth’s field. Outside this hollow let us approximate the trajectories of the individual particles as straight lines from the sun. Particles that leak into the hollow actually will follow complicated orbits governed by the crossed electric and magnetic fields and will also drift by virtue of the inhomogeneous magnetic field. However, let us approximate these orbits as spirals along the magnetic lines of force. Lebedinski calculates the potential difference between the opposite sides of the hollow by assuming that the electric field in the hollow is given approximately by v X B, where v is the stream velocity and B is the magnetic field at the edge of the hollow. Actually this assumption is an oversimplification. Chapman and Ferraro have pointed out (see Section 5.1.2) that a stream (other than a plane-parallel sheet) will have an electric field outside the gas. Indeed, this is the source of the electric field used in Martyn’s theory. But a precise calculation of the field inside the hollow would be quite complicated; whereas particles might be assumed to leak off the inside of the hollow along lines of force, Lebedinski’s calculation of the potential involved cannot claim much rigor. At any rate Lebedinski’s calculation assumes the field is of the order of vB. Then the maximum potential difference between two points on a sphere of radius T would be @

2vM = 2Er = 2vBr = -

r2

where M is the magnetic moment of the dipole. At the surface of the hollow, chosen at T = 8.5 a, and with v = lo8 cm/sec, @ = 5.6 X l o 6 volts. The space around the earth is presumed to be more highly conducting

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than the ionosphere, so that this potential is of the order of the potential difference that will be applied to the atmosphere. Lebedinski concludes that particles can be accelerated along the lines of force, from the inside surface of the hollow to the polar regions, with a potential difference of the order of 10’ volts, which is actually more than the proper energy to explain auroral heights. The discharge current is visualized as flowing downward in the atmosphere (along lines of force), producing auroral ray structure. Then the current flows in the east-west direction exciting auroral arcs. These currents also give rise to magnetic effects. Lebedinski considers the auroral luminosity to result from electrical breakdown of the gas, and accordingly estimates the breakdown potential necessary to start the discharge. However, the laboratory concept of electrical breakdown would seem to be beside the point, insofar as auroral discharges are concerned. In the upper atmosphere an appreciable electron density is always present, and to produce excitation by an electric field it is merely necessary to accelerate these electrons so that they produce excitation. Of course, some atoms will become ionized and the electron density will increase until the rate of ionization equals that of recombination. But detailed calculations (cf. Section 8.3) indicate that to produce the luminosity observed in rays, the electric field need be only of the order of volts/cm or a total potential of, say, lo2 volts over a ray. The electron density is around lo6 ~ m - ~ . On the other hand, the breakdown potential calculated by Lebedinski is about 104 volts. This potential would be required to start a discharge in a neutral gas in the laboratory, where only an occasional electron (liberated by cosmic rays, for example) is available to start an avalanche of ionization. The potential applicable to an auroral discharge would probably be more analogous to the sustaining voltage of a glow discharge, which is considerably less than the ignition or breakdown voltage.‘* The paper contains a number of new and bold ideas, not the least of which is the explanation of auroral arcs! In the present form, however, the theory ignores a number of observational data: Auroral arcs are apparently associated with hydrogen emission ; and although there are difficulties encountered when one attempts a quantitative explanation of arcs as produced by incident particles (Section 8.2), the hydrogen lines should not be entirely ignored in the theory. Also, it is not clear how the semiempirical system of currents in the auroral zone can be reconciled with the strictly east-west currents of the theory. 18 However, in the laboratory discharge the cathode is bombarded by ions, which thereby liberate new electrons. As the atmosphere contains no electrodes, one must be cautious in applying laboratory concepts and results.

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6.4. Discussion of Solar Streams 6.4.1. Speculations on Electric Fields in Auroral Theory. The great virtue of an electric field in auroral theory seems to be its role in accelerating particles to the auroral zone. Without such a mechanism, its proponents claim, it is difficult to reconcile the velocity of lo8 cm/sec believed to apply to solar streams with the lo9cm/sec necessary for protons to reach auroral heights. Besides the theories discussed in this section, Martyn’s theory also makes use of a n electric field, but a t present none of these seems entirely satisfactory. It is not clear how important the solar magnetic field will be; but it does seem possible that electric fields could be important even without the benefit of a solar or interplanetary field. Chapman and Ferraro have shown that a stream of arbitrary crosssectional shape will not have all its electric field confined to the inside of the stream. As we pointed out in discussing Lebedinski’s theory, it would seem that particles could leak off the inside surface of the hollow carved out of a Chapman-Ferraro stream and these particles would receive sufficient electrical acceleration to produce the aurora. Many details need to be developed before these ideas can properly assume the aspect of a true theory. For example, one difficulty inherent in all the electric-field theories so far proposed is that protons should enter in one part of the auroral zone while electrons penetrate another region. There does not seem to be any such selective region in longitude (i.e., relative t o the midnight meridian) in the observed distribution of hydrogen lines. A latitude effect may exist, but none of the theories predicts, say, that protons will always be a t lower latitudes than electrons. l9 Therefore, it would appear that if an electric-field theory is to survive, i t must include effects of drift (around parallels of latitude) to explain the appearance of protons at all (nighttime) longitudes. Moreover, more attention might be directed toward the use of the electric-field to explain auroral forms. As protons are accelerated toward the earth, many of these may enter the atmosphere to produce arcs. On the other hand, if the electric field is strong enough to accelerate electrons in the atmosphere, electrons may start upward, producing rayed forms of aurorae (see Section 8.3). I n this case the direction of the current would not change as the arc breaks into rays, but the particles carrying the current would change from protons to electrons. When both protons and electrons are active, we would observe the familiar form of a rayed arc. 18 A latitude effect of this type appears in the main phase i n Martyn’s theory. But in the initial phase protons enter at higher latitudes than electrons during the cvcning hours.

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It also seems possible (but certainly not proved) that during the electrical discharge that produces rays, it is not necessary for many protons to actually enter the atmosphere. A large number of protons must approach the earth and be prohibited from entering by magnetic reflection. These particles could still serve the purpose of helping to bring the electric potential from the stream to a (localized) region of the atmosphere. Of course, the current must be closed somewhere, perhaps at higher latitudes, or even on the day side of the earth. It is not necessary that electrons enter the atmosphere with the same energy as protons. If they did, they should produce aurorae considerably lower than a proton arc. With an ionized interplanetary medium surrounding the earth, it seems likely that sufficient electrons can be pulled into the atmosphere to neutralize the influx of protons or loss of electrons or both, produced in a display. It is perhaps not necessary that the current systems responsible for magnetic storms be explained by the emf set up by auroral particles entering in different localities. This approach was used by Martyn, AlfvCn, and Lebedinski with only qualitative success. Rather, consideration should perhaps be given to the dynamo mechanism for the currents. This point is discussed in its proper place in Section 7.1, but we would mention here that given an increase in the conductivity in the auroral zone, the currents may naturally proceed from dynamo action. 6.4.2. The Nature of Solar Ion Streams. Just what sort of particle stream should one expect from the sun? The answer depends on a number of factors about which we have only a meager amount of information: e.g., the mechanism of ejection from the sun, the density of the interplanetary medium, and the character of the magnetic field near the earth. At present the concept of strong currents between the sun and the earth seems an unjustifiable postulate on which to build a theory (Section 4.3). The Chapman-Ferraro stream is also an idealized hypothesis and, as we have pointed out previously, does not seem adequate to cope with the details of auroral production. One has the feeling that something quite fundamental is being omitted from auroral theories, through the understandable tendency to simplify the problem. Let us first of all ask what happens to a solar stream at the sun. If the material escapes in the neighborhood of a sunspot region, the ionized gas most likely has a strong magnetic field imbedded in it. Thus Hoyle’s [55] advice that this field be considered would seem to merit further consideration, as the decay time for a magnetic field in such a stream is likely to be very long.

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Moreover, is there a time delay in the escape of the ionized matter from ,the sun after a flare? The recent analysis by Meyer et al. [74] of the solar cosmic rays associated with a large flare indicates that these cosmic rays are stored for several hours near the sun. If auroral particles are similarly delayed, their travel time to the earth may actually be only a few hours, and the often-quoted velocity of lo8 cm/sec should be abandoned. Secondly, what is the nature of the interplanetary medium? The density of several hundred electrons/cma obtained from the zodiacal light [51-53a] might be questioned on the grounds that the investigators attribute all the observed polarization to electron scattering (albeit, with some justification). And the radio whistlers [54] could perhaps be propagating in a halo to the earth’s atmosphere. Thus, the evidence for an appreciable amount of ionized material at one astronomical unit from the sun is fair, but not overwhelming. Simpson et al. [75] have suggested that a highly ionized interplanetary medium is responsible for the westward shift of the “cosmic-ray dipole” (compared with the dipole deduced from geomagnetic measurements). But the matter has not yet been fully investigated theoretically. Finally, we should like t o know the character of the magnetic field in the neighborhood of the earth. At several earth radii the westward shift mentioned above will appear. But since auroral particles enter with much slower velocities than cosmic radiation, they will be able to adapt more readily to the magnetic field. Hence the auroral zone will not necessarily deviate from a symmetrical belt around the geomagnetic dipole. Probably what is more important to the auroral problem is whether the magnetic field still approximates a dipole at all, at several earth radii, where an ionized medium could seriously modify the dipole lines of force. Further, there is the question of whether an interstellar magnetic field exists within one astronomical unit of the sun. Hoyle [56] has proposed that such a field, quite near the earth, is required to explain the cosmic-ray cutoff at low energies during sunspot minimum. Davis [76] first drew attention to interstellar fields insofar as cosmic rays from the sun are concerned. Davis points out that the detection of solar cosmic rays indicates that the region earth-sun is free of significant magnetic fields. Meyer et al. [74] concluded that this region was free of magnetic fields greater than lo-‘‘ gauss at the outbreak of the great flare of February, 1956. Hoyle’s main argument for the interstellar field near the earth is that cosmic rays cannot escape from the interstellar field; therefore, for cosmic rays to strike the earth, the interstellar field and medium must penetrate close to the earth. This argument seems to be based on the assumption of a uniform interstellar field, although if the solar sys-

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tem carves a hollow out of the interstellar gas, as Davis suggests, this postulate may be seriously in error. The analysis of solar cosmic rays do suggest that a magnetic field exists beyond the earth's orbit and that it diffusely reflects solar cosmic rays back toward the earth and sun.

7. ADDITIONAL MECHANISMS FOR

THE

PRODUCTION OF AURORAE

The majority of this review has been concerned with the theories of Stormer and Chapman and Ferraro and with variations on their theories. No apology is offered for this emphasis, because their work is of fundamental importance to the whole subject and today forms the basis for most of the speculation on and interpretation of auroral observations. Indeed, for these very reasons I have thought it desirable to emphasize the weak as well as the strong points in these theories and to spend a considerable amount of space on, for example, the controversial question of sun-earth electric currents. On the other hand, there is a growing belief among researchers in this field that the primary mechanism for auroral production must involve some phenomenon not considered in these theories. Consequently, recent years have witnessed the proposal of several stimulating new ideas and revisions of old ideas. In this section we shall review some of this work. Some of these theories are still in the process of being developed; certainly none of them can claim the thoroughness or rigor of the Stormer and Chapman-Ferraro theories. Hence we shall be primarily interested here in discussing the physical ideas involved, the mathematical developments still being of secondary interest in these theories. 7.1. Dynamo Theories of Wulf and Vestine

Dynamo mechanisms, which involve transforming kinetic energy of convection, winds, or other mass motion of air into magnetic energy, have been seriously considered for several years as the probable source of the solar (S,) and lunar (L) components of the quiet-day magnetic variations [64]. The theory of atmospheric dynamos has been developed and applied to these quiet-day variations by Schuster [77] and Chapman [78]. In more recent years there have been some suggestions that magnetic storms as well are due entirely to currents concentrated in the upper atmosphere and generated by winds. Vestine [79], for example, has called attention to the fact that the main phase, initial phase, and even sudden commencements seem to be associated with currents directly overhead, since there are important magnetic variations over short distances on the surface of the earth. Moreover, if the interplanetary medium immediately surrounding the earth is actually a highly conducting plasma, rather than a near vacuum,

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the earth would be shielded from the magnetization associated with currents outside the atmosphere. Wulf [80, 811 has considered the possibility that the winds that generate currents might also be responsible for aurorae. Consider a zonal (east-west) wind of 50 meters/sec in the partially ionized region around 90 km and suppose this wind is a few thousand km wide (in north-south extent): Since the wind moves across the vertical component of the lines of force, an electric field is generated of the order of vB = 5 X lo3 X 0.5 = 3 X los emu = 3 X 10W volts/cm. The potential difference between the southern and northern edges of the stream could thus be several thousand volts. If a similar wind system were a t higher altitudes but in the opposite direction, there could be a large vertical potential difference. Wulf pictures the Lorentz force as providing electrostatic separation and discharges as completing the circuit; indeed, without a nearly vertical discharge there will be no current flow and the slight displacement of charge (about 10-8 cm for each ion in the above example) will be of no importance in exciting atomic and molecular emissions. Vestine [82,83] has extended this work and suggested another mechanism whereby aurorae might be created as a result of dynamo action. Suppose the ordinary Ohm’s law (equation (2.45)) is valid. Then from Amphe’s and Faraday ’s laws we previously derived an expression (2.47) for the change in the magnetic field due t o a velocity field (or wind system). Let us divide the magnetic field into toroidal (BT) and poloidal (Bp) components and the winds into zonal (2111) and rneridional ( u p ) components. Then (7.1)

B

=

BT

+ Bp

and

+

v = VT vp (7.2) Substituting these equations into equation (2.47) we obtain separate equations for the increase in the two components of the magnetic field: aBT 11 (7.3) -at= - - 4r vXVXBT+VX ( v T X B P + V P X BTI and -aBp - - - v X v X Bp v X (vp X BP) (7.4) at 47r

+

The term in 7 represents the decay of the magnetic field through ohmic resistance. Neglecting this term, we see that a toroidal field can result from zonal winds moving through the poloidal (e.g., the dipole) field. On the other hand, the poloidal field can be increased by meridional winds

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in the dipole field. Physically, these field increases result from the lines of force being carried along and lengthened by motion of the conducting medium (see [84]). Vestine [82] makes a rough estimate that a toroidal field (in the upper atmosphere in the auroral zone) of the order of a gauss might arise if the conductivity is sufficiently high. This toroidal field would not only have important geomagnetic implications, but may exert a strong local influence on the incoming auroral particles. Auroral protons would then presumably have a pronounced east-west asymmetry and would not emanate precisely from the (dipole) magnetic zenith as is usually assumed. Spectroscopic investigations should demonstrate if this prognostication is correct. A second possibility suggested by Vestine would abolish the need for getting auroral protons from the sun; the toroidal field would produce these fast protons by the betatron effect: The zonal winds are likely to be highly variable; if the conductivity is quite high, then a change in the wind speed would be immediately accompanied by a change in the magnetic field strength. Then from equation (2.42)

(7.5) where Ep is a n electric field in the meridional plane. Thus the electricfield lines are loops around the toroid that carries the winds. One component of EP will lie along the dipole (poloidal) magnetic lines of force and some acceleration of particles along these lines might be expected. Again with rough calculations, Vestine estimates that protons could be driven downward (and electrons upward) from around the 150-km level with energies of the order of 5000 ev, which corresponds to a velocity of 1000 km/sec for protons. This velocity is at least the right order of magnitude for the observed Doppler shift in the hydrogen lines (see Section 8.2). Vestine himself has offered one serious objection to the theory: There is no observational evidence that any element but hydrogen shows Doppler-shifted lines in the auroral spectrum and hydrogen is presumably of relatively low abundance in the upper atmosphere. Another difficulty with the theory is that actually i t is necessary to provide far more energy to the protons than what is deduced from the spectroscopic Doppler shift. Vestine neglects the important energy losses due t o collisions with atmospheric atoms. It is more likely th a t the observed Doppler shift depends solely on the velocities at which protons are capable of capturing electrons, rather than on their “initial” energy at great altitudes. The energy supplied to the protons will determine the

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amount of matter that they can penetrate before being stopped. Therefore, unless large amounts of acceleration can be supplied over a distance of the order of a scale height, the vertical height of hydrogen emission should give a precise measure of the initial velocities of the protons (see Section 8.2). It would seem more plausible that even if dynamo mechanisms are truly important for the production of magnetic storms, we must still depend on extraterrestrial ions to initiate aurorae. But if this is the case, the influx of ions may have an important bearing (through increases in the conductivity in the ionosphere) on an enhancement of the dynamo effect during aurorae and magnetic storms.

7.8’. Singer’s Shock-Wave Theory Gold [85] has suggested that to explain the sudden commencement in magnetic storms, one should abandon the idea of solar ion streams interacting directly with the magnetic field of the earth as with Chapman and Ferraro’s theory. He states that the thermal dispersion in velocities would alone cause a buildup time of half an hour for the magnetic storm. A shock wave, on the other hand, would be generated by the expulsion of gas from the sun, and this shock would have a sharp boundary, unlike the stream itself. The suggestion has been adopted by Singer [86], who has developed a theory on the basis of the shock wave followed by a stream of particles. While some mathematical support is given for various conclusions reached, the theory is still largely intuitive. We shall summarize its main aspects rather briefly. The shock wave is estimated to travel with 50 times the speed of sound in the interplanetary medium. The mean free path (based on deflecting “collisions” between ions and electrons) for interplanetary ionthe sun-earth distance. ized material is much less than (about Hence it appears that a shock wave, if once initiated, will exist in the medium and will exhibit a sharp front. (The thickness of the shock front is usually taken to be about 4 mean free paths.) From a known relation (from the elementary theory of strong shock waves) between the velocity of the gas and that of the shock, Singer estimates that the original gas cloud itself should arrive a t the earth about 8 hr after the shock front. We now wish to inquire as to what happens when the shock front enters the dipole field in the equatorial plane. We know, first of all, from Chapman and Ferraro’s papers, that an ionized gas cloud in a vacuum is stopped by the magnetic field and, in turn, compresses the lines of force so as to increase the field.

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Singer supposes that a shock front will be stopped by the magnetic field in roughly the same fashion as an ionized cloud, and he accordingly equates nimp2 - B 2 (7.6) 2 8T where v is the velocity of the shock. He uses this expression to deduce B , and hence the distance from the earth, a t which the equatorial shock wave is stopped. (Martyn used the same relation, equation (5.24), to deduce nil with B obtained from other conditions.) Singer’s use of this equation evidently supposes that the width of the shock front is much greater than the earth’s radius a. Indeed, his numerical estimates indicate that the mean free path near the earth is about 200a. If this is the case, then the shock front itself would take about a half-hour to pass the earth, and the big advantage of the shock in producing sudden commencements would be lost. In a note added in proof, Singer maintains that the shock front is much sharper in the earth’s upper atmosphere, presumably disposing of the above objection. But this argument seems questionable. Let us suppose that the velocity of the shock front remained constant and the thickness decreased as the front moved into a region of gradually increasing density; even then, there would be a negligible change in the duration of shock passage in the ionosphere, since an appreciable rise in density occurs over a distance which is small compared with the original shock thickness. I n any case, it is not clear that the duration time (between passage of the first and last part of the front) could be appreciably affected by even a gradual change in density. Thus, if a shock wave is t o explain the sudden commencement it must somehow be much more narrow than has been supposed. But if this were the case, equation (7.6) would no longer be admissible. A hydromagnetic shock wave is not t o be regarded as an unmagnetized gas cloud that will penetrate into a magnetic field until the gas-kinetic and magnetic pressures are equal. Rather in the shock wave each volume element of gas moves only the order of a mean free path and each element has associated with it a magnetic field. Hence, in general, the incident wave of gas has magnetic as well as kinetic energy and equation (7.6) is an oversimplification. Singer goes on to state that with a conducting medium around the earth, an increase in the magnetic field will not occur as in the ChapmanFerraro model. An ionized gas will tend to resist changes in the magnetic field through induced currents, so that one must wait for these currents to decay (the lifetime depending on the conductivity l/q) before alterations in the magnetic field manifest themselves.

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JOSEPH W. CHAMBERLAIN

According to the theory, shock waves will be able to propagate into the auroral zone. At higher latitudes there is, supposedly, less resistance from the component of the magnetic field perpendicular to the direction of propagation ; moreover, Singer suggests that the field will guide the wave like the walls of an elastic shock tube. The shock wave is considered to generate magnetic disturbances by (a) pushing the lines of force directly, and (b) producing a separation of charge (because the shock is moving in an inhomogeneous field), which in turn gives an emf to the lower ionosphere. This same separation of charge accelerates ions and electrons, thereby exciting the aurora. An entirely different aspect of the theory is its explanation of the main phase of magnetic storms. The shock wave serves the purpose of modifying the field so that it is no longer strictly a dipole at several earth radii from the earth. When the ion cloud itself arrives, particles leak into the inside forbidden region for Stormer orbits (inside the inner Q = 0 curve of Fig. 9). Particles will be trapped in this region as the field recovers its dipole form. These trapped particles drift in captive Stormer orbits; one of the main features of the drift is that protons and electrons drift in opposite directions, with a westward current being set up. This ring current is responsible for the main phase. Although the theory involves some stimulating ideas, there are several items requiring clarification. The propagation of a shock wave through a dipole magnetic field is a most difficult problem, and one wonders if it will actually be stopped in the equatorial regions rather than decay gradually as i t generates transverse hydromagnetic waves. Singer mentions that expansion waves set up behind the shock will eventually overtake and destroy the shock wave; but the mechanism considered in his numerical computation seems to be based simply on an energy balance, as discussed above. Also questions raised by the theory on the refraction of shock fronts by lines of force in higher latitudes need to be investigated further. Since a shock wave is transmitted with greater velocity perpendicular to the field, the refraction of the front might be in the opposite direction to that assumed by Singer. The problem thus involves complicated features of both the decay of shocks and their velocity of propagation, and we suggest that an extension of theoretical analyses [87, 88) of hydromagnetic shock waves would be desirable. Finally, we might inquire as to just how important will be the energy received a t the earth in the form of a shock wave. If the initiating disturbance is a solar event, we would anticipate that the energy would dissipate itself in all directions. Not only would the amount of energy reaching the earth be negligible, but the theory would seem to lose one of the main advantages usually held dear by proponents of solar-stream

THEORIES OF THE AURORA

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theories; oiz., the small angular extent of the beam a t the earth (Section 4.2.1). 7.3. Parker’s Theory of Hydromagnetic Displacement of the Lines of Force

Parker’s [89] theory is concerned primarily with magnetic storms, not with aurorae directly. We shall merely mention his ideas. It is well known that a magnetic increase or decrease can be visualized in terms of a displacement of the lines of force. And if the magnetic field exists in a perfect conductor, this description of magnetic disturbances is quite convenient) since the ionized matter is “frozen” to the field lines. Parker notes, then, that an increase in the field, as in the initial phase of a storm, can be represented by the lines being crowded closer together (say, by an ion stream from the sun). The theory concerns itself with an explanation of the main phase of a storm by an upward displacement or expansion of the lines of force-or, rather, a displacement of the conducting gas in which the lines are imbedded. Two cases are discussed which might lift the lines of force at the earth. The first is atmospheric heating. Should a large amount of heating occur as the result of solar corpuscular emission, the gas would expand and raise the lines of force. A second possibility is that the earth captures an interplanetary cloud of ionized hydrogen. (The cloud must be moving slowly relative to the earth; otherwise induced currents will appear on its surface and decelerate it.) The cloud has no internal magnetic field and diffuses into the magnetic field of the earth. As gravity pulls the gas downward, the lines of force are pushed aside; they do not penetrate the highly conducting gas. The pressure of the gas continually adjusts itself to balance the magnetic pressure B2/8na t every point. Since the magnetic pressure is lowest a t the equator (for a given distance from the center of the earth) most of the hydrogen will tend toward the equatorial plane. A sufficiently large cloud will settle to the top of the atmosphere. It will not readily diffuse into the denser air below and it will, by displacing upward the material carrying the lines of force, effectively decrease the field, especially near the equator. Much detailed discussion is given to these two processes by Parker, who offers them only as speculative suggestions. But the suggestions were inspired by the observational data [51-54, 751 suggesting a high conductivity in the medium just above the atmosphere. An approximate calculation given by Parker indicates that the magnetic field of a ring current would require about 3 months before it could penetrate to the earth.

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JOSEPH W. CHAMBERLAIN

7.4.Maris and Hulburt’s Ultraviolet-fight Theory A number of years ago the theory of Maris and Hulburt [go, 911 attracted considerable attention. Its main feature was that solar ultraviolet light excited atoms in the region of the equatorial plane. Other, neutral atoms colliding with the excited (or with recombining) atoms, received enough energy to allow them to almost escape from the earth. These high-velocity atoms attained heights of around 50,000 km (8 earth radii). At such high equatorial altitudes the atoms are ionized, attach themselves to lines of force, and slide down to the auroral belt, producing the aurora and magnetic storms. Chapman (see summary in [64]) has offered numerous objections to the theory. The main ones are: (1) no satisfactory account of the 27-day recurrence tendency in magnetic storms is given, and (2) the energy acquired by the primary ions in falling by gravitational attraction is insignificant compared with that required to penetrate to auroral heights and produce atomic excitation. 7.6. Meteor Theories It has been argued by V’iunov 1921 and Dubin [93] that meteors may be the cause of magnetic storms and aurorae. The idea that interplanetary particles produce the aurora is over 200 years old [27], but in that time it has failed to acquire many supporters. The arguments in favor of meteors are mostly indirect and speculative. The authors feel that solar ion streams do not satisfactorily explain enough features. Some correlations between aurora and noctilucent clouds, coupled with the theory that the latter are due to cosmic dust, is offered as supporting evidence. The meteor theory claims to offer an explanation of the seasonal variation, the equinoxes apparently coinciding approximately with the time the earth crosses numerous meteor orbits. Although these meteoric arguments are not particularly compelling, it may be well to point out explicitly one or two rather important deficiencies in the theory. If the meteors become electrically charged by solar radiation and the photoelectric effect, as Dubin suggests (and it is not clear why else they would favor the auroral belt), the theory encounters the difficulty of any ultraviolet-light theory in failing to explain the 27-day variations. The particles must have a very small charge to mass ratio; hence the radius of gyration should be enormous (equation (2.3)). No attempt has been made to reconcile this fact with the narrow (north-south) width of arcs. (Dubin ascribes rays to electrical discharges; while I will not quarrel with his conclusion, his computation of the accelerating potential is invalid, as shown in Section 8.3.)

THEORIES OF THE AURORA

191

And finally there is the embarrassing evidence of the spectra: the aurora does not show characteristic meteor spectra but does indicate incident hydrogen atoms. To summarize, the evidence of a correlation between aurorae and meteor showers is feeble; and even if there is such a correlation, the hypothesis that a cause and effect relationship exists between the two types of phenomena encounters severe difficulties.

8. THEORIES OF AURORAL EXCITATION Most of the work described heretofore has been concerned with what we might call ((theories of auroral morphology,” or explanations of the main features of the occurrence (in time and space) of aurorae. It is often taken more or less for granted that if we can only get the solar particles, say, into the atmosphere, surely they will produce the aurora. I n recent years some effort has been devoted t o quantitative theories of auroral excitation. This research is actually more comprehensive than we shall be concerned with here. For example, some work has been devoted to questions of collisional de-excitation and to determinations of the precise atomic mechanisms whereby certain radiations are excited. For the present, however, we shall deal only with problems of the primary source of auroral radiation, and shall not be concerned with special problems, such as sunlit aurorae, red aurorae, etc. 8.1. Electrons in Aurorae

Before dealing with specific mechanisms for the production of auroral forms, it is necessary to consider the role played by electrons in exciting auroral spectra. In particular, there are two items of specific interest for our purposes: (1) the electron density in aurorae of different types, and (2) the effect of primary (that is, extraterrestrial) electrons. 8.1 .l. Electron Densities. Determinations of the electron density from radar reflections have been hampered by uncertainties in the method of interpretation. A number of authors have interpreted their radar reflections as due to critical reflections by volumes of intense ionization. Some of the radar has operated at frequencies around 100 Mc/sec, which re~ signal is returned quire electron densities of the order of lo8 ~ m if- the by this mechanism. On the other hand, if the results are interpreted as backscatter (partial reflection) by small columns of ionization, the densities are much less. Recently a characteristic of auroral reflections known as “aspect sensitivity” (the reflections seem to occur only when the signal is directed nearly perpendicular to a magnetic line of force) has been rather definitely established. Booker [94] has presented a theory for the auroral reflections that

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JOSEPH W. CHAMBERLAIN

considers them to be scattered from small volumes of ionization. To obtain satisfactory fits with observations, he concludes that the electrons must be oriented in columns about 40 meters in length and one meter in diameter. Although reflections are usually associated with rayed structure in aurorae, it is not clear how these columns of ionization are to be interpreted in terms of the visible features. Booker would interpret the small volumes of irregular ionization as due to turbulence; until the formation of rayed structures is better understood, we are unlikely to arrive at a decision on the matter. Seaton [95] made the first serious estimates of electron densities from visual observations. His adopted values of the brightness, dimensions of the radiating volumes, and the recombination coefficient (10-8 cm3sec-') were uncertain; he obtained n, 2 2 X lo7 electrons ~ m - ~ . Omholt [96] rediscussed the problem with the same recombination coefficient but with improved data and obtained densities between loe and lo7 ~ m - ~ Later . work by Omholt [97], in which the critical frequency of the apparent sporadic E layer and the intensity of the N2+bands of overhead aurorae were measured simultaneously, suggests that the recombination coefficient is actually somewhat higher than expected in the aurora (probably greater than lo-? cm3 sec-I). This result leads to densities between 2 X lo6 and lo6 electrons cm-S. This variation in n, is most probably real, with a linear logarithmic plot being obtained for N2+ intensity versus electron density, as derived from the spectra and critical frequency, respectively. All electron densities quoted here refer to the altitude of the E layer. These densities undoubtedly represent ionization of the upper atmosphere and are not to be confused with primary electrons. There are still some uncertainties involved in these data, One factor that is not known with sufficient accuracy is the ratio of photons emitted in the A3914 Nz+ band, say, to the total number of ionizations, when nitrogen is bombarded with protons. This quantity, which could be derived from careful laboratory experiments, is required to deduce the ionization rate from spectral observations. 8.1.2. Primary Electrons. The extent of primary electrons in the aurora is difficult to assess. At low auroral latitudes homogeneous arcs invariably show hydrogen lines and the natural tendency is to try to explain arcs on the basis of proton excitation alone. Meredith et al. [98] have fired rockets into the upper atmosphere in the auroral zone. They detected a low energy radiation above 50 km that they first interpreted as auroral electrons. If primary electrons, they must have initially had energies of 3 MeV. More recently, Van Allen and Kasper [99] have stated that this soft radiation is instead x-rays of energy 10

THEORIES OF THE AURORA

193

to 100 kev; the data from the rocket flights may be simulated by exposing the equipment to laboratory x-rays. The flux detected is then lo6 photons/cm2 sec and possibly arises from bremsstrahlung from auroral electrons. Singer [lOO], on the other hand, has supposed that this radiation is actually soft y-radiation and fast eIectrons. He has suggested that auroral protons induce nuclear reactions that in turn produce y-rays. These y-rays undergo Compton scattering and thereby give energy to electrons as the y-rays become softer and resemble x-rays. However, the proton flux required to explain the observations is much higher than that deduced spectroscopically. So far, it is not yet known just what this radiation has to do with the visible aurora and with incident protons. Vegard and Harang [loll have developed a theory for auroral luminosity produced by incident electrons. As pointed out, however, by Bates and Griffing [102], the theory is inapplicable as it considers merely the absorption of electrons by air (i.e., the loss of electrons from the beam). Therefore, an electron is neglected in the theory after if undergoes only a very few scattering collisions. In fact, the electron will undergo many scatterings and, if projected along the magnetic field, may be restrained to the original beam throughout. A proper solution of this problem would be most difficult but valuable to have. 8.6. Incident-Proton Theory of Arcs

In 1921, Vegard [lo31 made the first calculations of an auroral luminosity curve on the basis of incident heavy particles. He used experimental ionization (Bragg) curves obtained for a-particles to compute the probable appearance of an aurora produced by these particles. Interpretations were hindered somewhat by uncertainties in the model atmosphere. More recently, Bates and Griffing [lo21 re-opened the problem by computing ionization curves for protons in a model atmosphere based on more modern data. The interpretation of aurorae observed in the light of hydrogen should be particularly instructive, so long as the hydrogen is of extraterrestrial origin. There should be no ambiguity in the interpretations (as there might be in the case of observations in the emitted light of ionized atmospheric constituents, if sufficiently energetic electrons were incident simultaneously with protons). The theory for hydrogen emission in aurorae has been developed by Chamberlain [104, 1051. Below we shall outline briefly the theory for auroral ionization and hydrogen excitation and then present some calculations and compare them with observational data.

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JOSEPH W. CHAMBERLAIN

8.2.i. Auroral Ionization by Protons. The electron density is governed by the rate a t which electrons are created and destroyed: (8.1)

Here ne is electron density; n is the density of neutral atoms at the height in question and no is this density under conditions of standard temperature and pressure (S.T.P) ;8 is the flux of incident protons in particles/cm2 sec; p is the number of ionization pairs created by a proton in one centimeter of air at S.T.P. (from the Bragg curve); and are=is the effective recombination coefficient. Under equilibrium conditions, dn,/dt = 0 and we obtain

The values we choose are necessarily uncertain. But for a height of 110 km, we have n/no = 1.6 X from the Bragg curve we adopt an average value of p = 1.6 X lo4 ionizations/cm; from our discussion in Section 8.1 we choose area = 2.5 X 10-7 cm8/sec and n, = lo6 electrons/ cm8. Then 8 = lo* protons/cm2 sec, which should thus be at least a rough order of magnitude for the proton flux required to produce a bright auroral arc. A somewhat more powerful means of investigating auroral excitation lies in the luminosity curves (the variation of brightness with height). Harang [loll has made many such measurements on auroral arcs by photographic means. For more precise interpretations, however, we need similar data in the light of particular emission lines and bands, such as A3914 of Nzf. The use of photoelectric techniques and interference filters offers perhaps the best means of obtaining and intercomparing these curves. In the computation of luminosity curves it is convenient to express the model atmosphere in terms of equivalent depth (measured in centimeters of air at S.T.P.). This quantity gives us the amount of air lying above a particular height. The model atmosphere adopted for the computations given in this chapter is based on the Rocket Panel (cf. [106]) data and is essentially the same as given by Bates ([32], Fig. 1). We have also adopted the same range-vs-energy data for protons in air that Bates [32] represents in his Fig. 2. The work of Bates and Griffing [lo21 and Chamberlain [lo41 showed that protons entering directly along the lines of force (essentially vertically in auroral latitudes) could explain neither Harang’s luminosity curves nor Meinel’s [17] Ha-profile for an arc in the magnetic zenith. Chamberlain [104, 1051 proposed, accordingly, that a large angular

THEORIES O F THE AURORA

195

dispersion in the incident orbits might explain both types of data and that it would not be necessary to invoke a spread in energies of these particles. (More recently, Omholt [ 1071 has carried out additional computations and extended the work to include the horizon profile.) This hypothesis will be critically examined in Section 8.2.3; for the present we shall outline the theory for arcs based on monoenergetic particles with a certain angular dispersion. We assume throughout that the orbits are independent of the azimuth angle 4. If the particles are indeed extraterrestrial in origin, and the dipole field is not seriously modified during an aurora, their spiraling about the lines of force should insure the validity of this approximation. Let N ( 0 ) be the number of particles per second per unit solid angle incident on one square centimeter of surface normal to the lines of force from a given polar angle 0 (measured from the zenith). Then by definition the total flux is (8.3) 3 = ZT N ( e ) sin ede

+

If Lo(f)df is the luminosity produced between height f and f dE by a single particle from angle 0, then the luminosity resulting from a particle from angle 0 with the same initial energy is

Le(,$)dt= LO([sec 0 ) sec OdE since the path length is proportional to sec 8. If we let ho be the total range (total length of air a t S.T.P. that can be traversed by the incident protons), then the range of a particle a t any point in the atmosphere is ho - f sec e. For the luminosity of the aurora in the light of the atmospheric atoms and molecules (say Nz+),we suppose that the emission is proportional to the rate of ionization. The Bragg (rate of ionization) curves [lo81 are expressed in terms of range; hence, the function Lo for air can be readily obtained for any value of f sec 0. The total luminosity in air at depth 5 is then

(8.4)

e.,,(f) =

/o'm*x

~ ~ sec( e)5 sec elv(e) sin edo

where Cjwill represent proportionality constants and O,nsx = sec-l ( h o / f ) is the maximum angle from which a proton can reach depth f . The Loand N ( 0 ) in equation (8.4) can be represented by approximate functions and integrated analytically [ 1051; however, all the luminosity curves reported here have been computed by numerical integrations.20 30 These computations, previously unpublished, have been performed by Miss Carol Edwards and the writer. I am indebted to Miss Edwards for her diligent assistance.

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JOSEPH W. CHAMBERLAIN

The integrations have been performed for two assumed angular dispersions : N ( 0 ) = const (8.5) N ( 0 ) = const cos2 e The significance of these functions will be discussed in Section 8.2.3. Figure 18 gives the results for S'&), where (8.6)

&(x)

= const

&(t)n(z)

Here z is the linear height in the atmosphere corresponding to depth and the constant has been chosen so as to make Cf equal to unity at its maximum value. All calculations are for protons with an initial range of ho = 0.141 cm, which corresponds to a minimum height of penetration of z = 109.5 km. 8.d.W. Excitation of Hydrogen in Aurorae. The excitation of the Balmer lines is of particular interest, since it can lead directly to information on the incident protons. In place of the Bragg curves used for the luminosity in air, it is necessary to compute the amount of Balmer emission for an incident particle at any given velocity. This rate of emission depends on known transition probabilities and the populations of the excited configurations of the hydrogen atom. The latter are obtained from considerations of statistical equilibrium for a particle passing through air and undergoing collisions with air molecules and atoms. A hydrogen atom may reach an excited state either through an inelastic collision of a hydrogen atom in the ground state or by a proton capturing an electron into an excited state. It is also necessary to include effects of cascading of electrons from higher configurations. The theory for these processes has been developed [104], and we shall not enter into the details. However, it is essential to remark that there are some uncertainties in the cross sections adopted. Although it currently appears unlikely that these parameters could be in error to the extent required to reconcile theory and observations, this possibility should be borne in mind. As the protons pass through the atmosphere they are continuously losing and recapturing electrons. The calculations suggest that each proton undergoes about 700 captures and re-ionizations and emits a total of 50 quanta of H a (or 11 quanta of HP) on its way through the atmosphere. The figures quoted refer to protons initially possessing energies greater than about 90 kev (4000 km/sec), since at higher energies the cross sections are too low to make any appreciable difference in the total Balmer emission. On the other hand, a faster proton can still ionize other atoms

197

THEORIES OF THE AURORA

and cause them to produce radiation. Omholt [lo71 has computed the ratio of ionization (produced by a proton) over the H a emission versus the initial energy (i.e., the altitude of the lower border of the arc). For higher aurorae, Ha should be considerably more intense, relative to other 150-

I

0

140

-

130

-

120

-

110

-

100

:

0

__---

LUMINOSITY OF AIR -

-

1

-

I

1

-

1

w

I

-

-

9

I

FIG.18. Luminosity curves for aurorae seen in the light of atmospheric constituents. Theoretical curves for excitation by monoenergetic protons are compared with a n observed arc. I50

140

I30 t

-r

(1

W

I20

I

110 LUMINOSITY IN !4/3 .I00 0

I

.5

I.o

RELATIVE LUMINOSITY

FIG. 19. Luminosity curves for aurorae seen in the light of incident hydrogen. Theoretical curves are compared with an uncertain luminosity curve, observed spectroscopically.

emissions, than in the lower ones. More data on relative intensities versus height of the arc are required; but with the available data as collected by Omholt, it appears that the N2+/Ha intensities a t low latitudes are consistent with protons being the dominant or only cause of ionization. At

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JOSEPH W. CHAMBERLAIN

higher latitudes the hydrogen lines become much weaker, and it seems quite possible that some other mechanism contributes to the ionization. From the theory of excitation of hydrogen, one may calculate the fraction of neutral hydrogen atoms in any given excited orbit. Considering only protons from the zenith for the moment, and letting n,([) be the number density of protons and nl([)the density of neutral hydrogen atoms, we have for the total flux of particles

+

8 = in,([) n1Mlv(t) (8.7) Here v is the velocity (along the line of force). A relation between n, and nlmay be obtained from the condition of ionization equilibrium. Hence we may relate the intensity of a hydrogen line at any depth to the total flux and obtain the function L o ( [ )applicable to Balmer emission. For a dispersion in directions we simply integrate, as in equation (8.4). Figure 19 gives the results for the luminosity in HP. The observational curve shown in the figure is quite uncertain. It is obtained from Meinel’s [log] ratio of Ha/NZ+, and Harang’s luminosity curves were used to put Meinel’s Nz+ curves on a proper height scale. Meinel’s exposure extended over a considerable period, during which the arc may well have moved, so that his relative heights have not been used at all. Any movement of the arc would nevertheless widen the apparent luminosity curve, since H lines give narrower curves than most atmospheric emissions. We would not expect much difference in the curves for H a and HP; but the calculations here refer to HD, since that line is more easily observable for various reasons. The function Lo([)dt gives the luminosity from protons at a given height. On the other hand, t o investigate the zenith profile, we want the dv, where v emission when the particle was between velocity v and v is the velocity component along the line of force. This quantity is readily obtained from LOby the relation

+

where the derivative is simply the slope of the range-velocity curve for protons. The profile observed for a dispersion of incident angles is then (8.9)

3(v)

=

CZ

/o*” l 0 ( v see e> sec eiv(o) sin ede

For the integration of these profiles an analytic function was chosen that represents ZO fairly well. (This expression is given in reference [105], equation (l),where /3 = 2270 km/sec. For H a one should use /3 = 2000, which is slightly better than the value used in the earlier paper.)

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THEORIES O F THE AURORA

The zenith profiles for HP are shown in Fig. 20. Again the exact shape is not known for the observed curve, and simply for purposes of rough comparisons, Meinel’s observed Ha-profile is shown. Actually, the observed HP-curve should be slightly broader and shifted more toward short wavelengths than is the Ha-curve, since the Ha/HP-ratio is smaller a t higher velocities than it is near the maxima of the profiles. A derivation of the horizon profile is slightly more complicated. The formulas presented here may be shown to be identical to the expressions, derived in a somewhat different manner, by Omholt [107].

2.

L

4000

3000

2000

I000

0

VELOCITY OF APPROACH v (km/sec)

FIG.20. Zenith profiles for HP. The theoretical curves (dashed and dotted) are compared with an approximate observed profile.

Consider the azimuth-independent protons at a particular height and with the same value of 8. The profile from these particles will be propordw, tional to the number of protons in each velocity range w to w where w is the horizontal component of velocity directed toward the observer. Let the maximum horizontal velocity for these particles be w o = V sin 8, where V is the total velocity in the atmosphere. Then the horizontal velocity toward the observer will be w = wg cos 4. The profile from these particles follows from the condition that equal numbers of particles are between all equal intervals to 4 d4. The profile is

+

(8.10)

dW

J.g,c(w)dw = const w osin 4

=

+

const

dw

dw02 - w2;

~~

5 wQ

The total velocity V a t a given height depends on the path length it has already traversed and hence on 8; thus (8.11)

zoo(@ = V ( h o- f sec 8) sin 0

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JOSEPH W. CHAMBERLAIN

To find the total intensity at a given velocity w and depth i we weight the profile (8.10) by the luminosity function L O ( { and ) the angular dispersion N(t9). Hence the profile is (8.12)

&(w) = Ca

/Bzr

Je,t(w)Lo(t sec 0 ) sec eN(0) sin 0dO

The limits eminand emsxare determined from equation (8.11): We integrate essentially over a value of w o such that wo 2 W . When 5 is fixed, then w ois given as a function of e in equation (8.11), where there will in general be two values of 0 for which w o = w. The function wo(e) thus always goes through a maximum value, w - ~ . And at w = wmax1 we have OmiD = emaxin equation (8.12);hence the profile vanishes at wmX. I n Fig. 21 is given a graph of wm,, versus height z for an aurora having its lower border a t 109.5 km. This sharp cutoff of the horizon profiles a t a particular velocity depends only on the range-velocity curves, and is completely different from the gradual decline of the zenith profile at high velocities. Also in the figure are given values of dr, the intensity of the profile, at w = Analogously to equation (8.6), Jz is defined by &(w) = const n(z)$t(w). There are no available data on the variation of the horizon profile with height. A profile of HP, obtained by the author with a dispersion of 35 A/mm, has an apparent semiwidth of about k400 km/sec. This profile was obtained from a long exposure and probably does not pertain to any particular height. A comparison with the intensities and widths shown in Fig. 21, however, suggests that the angular dispersion is less than N ( 0 ) = cos2 0; otherwise we should expect Doppler displacements of around 1000 km/sec to have an observable intensity. 8.2.3. Discussion of the Angular Dispersion of the Incident Protons. The observational data and theoretical computations that must somehow be reconciled with one another are (1) the zenith hydrogen-line profile, (2) the horizon profile, (3) the hydrogen-line luminosity curve, and (4) the luminosity curve in air emissions. We might try to explain the .C’,i, curve on the grounds that other forms of excitation, such as primary electrons or discharges, are active. But if incident protons accompany homogeneous arcs, the hydrogen data should give a self-consistent picture. There are reasons for doubting my earlier suggestion that a dispersion in directions for monoenergetic protons might be sufficient to explain the observations. We note in Figs. 18 to 20 that a very wide spread in angles, characterized by N ( 0 ) = constant, could give a fair representation of the luminosity curves and the zenith profile (if we allow for theoretical

xwmax.

201

THEORIES OF THE AURORA

and observational uncertainties). But as Omholt [lo71 has shown, such a wide dispersion also predicts a wide horizon profile, which certainly is not observed. Indeed, the function N ( 8 ) = constant would give an integrated (in height) profile just twice as wide as that in the zenith (because the horizon profile extends to positive as well as negative velocities). This PROFILE INTENSITY

fL

10 I

(3W,)(RELATIVE

UNITS)

20

30

1

I

I

I

E

t N c

3

w

I

F.

.

1000

2000

INTENSITY

3000

4000

WIDTH OF PROFILE w,,,(krnhec)

FIG.21. Solid line (lower abscissa) : Semiwidth of horizon Hp profile versus height (intensity of profile falls to zero a t w = +wmsx). Dashed and dotted lines (upper abscissa): Relative intensity of the Hp-horizon profile a t w = +4.iwmnx versus height. These curves illustrate, for example, that the intensity of Hp observed only in the line center will decrease with height more rapidly than will the luminosity curve of Fig. 19, since the line is distributed over a wider wavelength interval a t greater altitudes.

point has been demonstrated from symmetry considerations by Omholt. Thus to explain the narrow horizon profile, we must use a more narrow angular dispersion; but the diagrams shown here demonstrate that the narrow distribution N(8) = cos2 8 gives a very poor fit in the other data. We note, also, that for N ( 8 ) = cog28, the zenith profile and luminosity

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JOSEPH W. CHAMBERLAIN

curve are in error in the opposite directions. For the profile, we should increase the theoretical intensities a t low velocities, but it is the highvelocity (i.e., the high-altitude) side of the luminosity curve that should be increased. Hence errors in the cross sections alone cannot explain the discrepancies. Also, it is worth noting that a very wide dispersion in directions for the primary particles is not consistent with the entry of extraterrestrial protons. We shall elaborate on this point. In the computations of Section 8.2.2 we have considered the function N ( 8 ) , which is the number of particles striking a square centimeter of atmosphere per unit solid angle per second. If we let v ( 8 ) be the number of particles in space crossing one square centimeter normal to direction 8 , per unit solid angle per second, then

N(e>=

(8.13)

cos

e

Let us now consider a point in space where the auroral particles are propelled toward the earth. Suppose all particles have the same total velocity and have only a small spread in directions. Assume that those directions are distributed approximately in a Gaussian distribution about a line of force; then for small 9, we have (8.14)

s(e)

=

tr exp

(- s) = c exp (- F sin2 ) 8

where C and a. are constants for a given position in space. As the beam moves toward increasing field strength the ratio sin2 BIB will remain constant, to a first approximation (equation (2.21)), if the particle is not accelerated. Hence as the magnetic field increases, the “ constants” C and a will also change, giving a different angular distribution of particles. By normalizing equation (8.14) so that sin2 BIB does not change, we find (8.15)

c4

where now Cq and Cg are constant all along the path. The widest angular distribution possible, then, is when the exponential is nearly unity for all 8; then v ( 8 ) is proportional to cos 8 and N ( 8 ) = cos2 9. Thus the cos2 8 distribution used in Figs. 18 to 20 would seem to be the widest dispersion consistent with a Gaussian distribution about the line of force. 8.2.4. The Velocity Dispersion of the Incident Protons. Two questions arise regarding auroral arcs: (1) How are the observations of hydrogen lines to be explained consistently? (2) Are protons the dominant or only cause of homogeneous arcs?

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203

Let us consider the second question first. For low-latitude aurorae, at least, the proton flux deduced from hydrogen-line intensities seems adequate to explain ionization (Section 8.2.1). The available data are rather crude, however, and the weak hydrogen seen in the auroral zone causes one t o have some reservations about accepting the incidentproton theory enthusiastically. However, the latitude variations may possibly be a result of different proton velocities a t high and low latitudes. Our order-of-magnitude calculation from equation (8.2), of the proton flux required to produce auroral ionization, assumed a recombination coefficient, which in turn was derived from the rate of ionization as deduced from photometry of N2+bands. A more direct calculation may be made when the brightness of Nz+ and a hydrogen line are measured simultaneously. One may estimate the N2+ brightness t o be expected from a given proton flux, and use the hydrogen line as an indicator of this flux. Preliminary measurements [ 109a] and calculation [lo71 of this type by Omholt, suggest that even low-latitude arcs (as seen from Yerkes Observatory) cannot be produced entirely by protons. The calculations depend rather critically on the adopted cross sections, however, and too much emphasis can not now be placed on this tentative result. Question (2) above might be investigated more fully in the following manner. From the hydrogen emissions we should be able to deduce information about the flux, velocities, and angular dispersion of the incident protons. These same protons should explain the luminosity curves seen in the light of air emissions. Unfortunately, we cannot give a definite answer to the question yet, as sufficient spectroscopic and photometric data from various latitudes are still lacking. To obtain a consistent explanation of the hydrogen-line observations it appears necessary to invoke a spread in velocities of the incident ions. Shklovski [110] was the first to propose that such a velocity dispersion might be the explanation of Meinel’s zenith Ha-profile. And Bates and Griffing [lo21 suggested that this might explain the broad luminosity curves of arcs. The failure of an angular dispersion to explain the horizon profile, however, is the crowning argument. If the angular dispersion is no broader than N ( 0 ) = cos2 8, the maximum intensity for fast protons observed in the zenith should be a t a velocity greater than 1500 km/sec (Fig. 20). A proton entering the atmosphere with a velocity parallel to the lines of force less than v = 1500 km/sec would have its maximum emission at its initial velocity. The observed maximum in the neighborhood of 500 km/sec thus implies that a considerable portion of the protons have velocities around this value and do not penetrate below 150 km. Thus these protons do not contribute to the brightest part of the arc. Detailed comparisons of luminosity curves

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JOSEPH W. CHAMBERLAIN

and profiles have been made by Chamberlain [110a] for various assumed velocity distributions to see whether a consistent explanation of the available data might be obtained on this basis. When a reasonable angular dispersion, N ( e ) = const Cosze, is included to explain the broadened horizon profile, the same velocity dispersion fits both the luminosity curve and the zenith Ha profile. The incident flux is distributed approximately as V-2; if the particles enter in a continuous stream, the distribution function for particles in a unit volume outside the atmosphere would then be proportional t o V-kos 8. At low velocities the distribution function must decrease, of course, although a t present the complete curve cannot be derived from spectral observations. But at present we can state that the dispersion in velocities extends from below 500 km/sec to about 10,000 km/sec, the latter velocity being established by the heights of auroral arcs. This dispersion might be observable in another way : Spectrometer observations by Hunten suggest that there are considerable fluctuations in the intensity of hydrogen emission. If these time variations are due to fluctuations in the flux of incident particles, there may be a time lag in the fluctuations for high altitudes compared with the lower part of the arc. The implications of a velocity dispersion of this magnitude are of fundamental importance. An acceleration mechanism near the earth becomes necessary to account for all the data. Such a spread in velocities for a solar stream would be accompanied by a long time difference in the arrival of fast and slow particles. Therefore, the electric-field type of theory assumes a new importance. As we pointed out in discussing the existing theories, none of them is without severe and fundamental objections. Nevertheless, the basic idea of electric-field acceleration near the earth seems sound (Section 6.4) and more effort might well be devoted toward a theoretical description of how such a field might arise. As we shall show in the next section, there is some reason to believe rayed structures are atmospheric discharges and thus depend on the existence of an electric field. If these explanations are correct, some of the luminosity in arcs might also arise from electric-field acceleration of atmospheric electrons. Indeed, the difference between high- and lowlatitude arcs may be due in part to a different relative importance in excitation by primary protons and atmospheric electrons. 8.3. Electric-Discharge Theory of Rays

Lemstrom [4] discussed in his book, published in 1886, a discharge theory of aurorae, and in 1917 Thomson [lll],after reviewing a number of observational facts, gave arguments for supposing discharges to be responsible for rays.

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205

I n more recent years, several observational workers have suggested, for quite a variety of reasons, that rayed structures might be produced by electrical discharges, and Chamberlain [112, 1131 has recently developed the discharge hypothesis in a more quantitative way. First of all, we should mention that it is not legitimate to consider the upper atmosphere as a large condenser and then compute the electric field resulting from an accumulation of charge a t some layer in the atmosphere. Using this “approximation,” Dubin [93] obtained field strengths of the order of 1volt/cm, which is extremely high. The difficulty with the condenser treatment is that the ionosphere contains an appreciable electron density and is therefore too highly conducting to be approximated as a dielectric. Briefly, my theory starts with the distribution of electron velocities to be encountered in an electric field then applies these computations to the ionosphere. An attempt was made to explain the nearly uniform luminosity of rays over a large range of heights by considering the amount of excitation produced at each height by inelastic electron collisions. At the greater heights fewer atoms are present than near the lower border, but because of the longer mean free path available, more fast electrons are created. We may compute how the electric field must vary over the length of a ray if these two effects are to compensate one another. The computations of energy-distribution curves for various electricfield strengths give immediately the approximate required field a t the base of a ray. If the bottom of the ray is at 120 km, the field must be roughly 5 X 10V volts/cm. For fields smaller than this value by a factor of 3 or more, the amount of excitation of the [OI] green line at this height is vanishingly small for any reasonable electron density. For appreciably larger fields at 120 km, one would expect the electric field a t lower heights to still be sufficiently strong to produce visible excitation, which contradicts the postulate that the lower boundary is at 120 km. The above-quoted field will produce the observed luminosity a t the base of a ray if the electron density is of the order of lo6 cm-8, which seems a reasonable value (Section 8.1.1). If the electron density is different from this value, only a slight change in the electric field will be necessary to produce the same brightness. The variation of the field and electron density with height are ascertained from the conditions that (1) the luminosity in the green line and (2) the current density are constant with height.21To relate the current 81 The current density may actually vary with height. But if the ray has a constant cross section and the current is closed through the E layer, say, then this assumption is probably valid. A consideration of the variations of current density with height requires some additional assumption regarding the source of the electric field.

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density to the electric field, detailed computations of electron driftvelocities were necessary; Ohm’s law is not valid in a discharge, since the random electron velocities (which determine the conductivity) are themselves governed by the electric field. The field decreases with height while the electron density decreases slightly, These computations simply give the field and ionization implied by the observations, without any consideration as to how they arise. However, a discussion of the ionization equilibrium in such a discharge suggests that the required field strengths would produce electron densities of about lo8 cm-a. A number of calculations were also given on the ratio of the oxygen red to green lines. In general, the theory seems to give a rather consistent explanation of the rays, but it should be possible, by observations of a particular nature, to check the theory further. Thus far, there seems to be no other quantitative theory that might explain the long rays. The possibility of incident electrons with dispersion in velocities has not been fully developed. The question arises as to how an electric field might be produced. In Section 6.4 I have discussed one possibility; another, perhaps, lies in the dynamo mechanism of Wulf and Vestine. These matters are necessarily speculative, but if an electric field is what is required to produce the rays, we should by all means examine the possibilities. The discussion in Section 8.2.4 suggests that electric fields are also required to produce arcs. I n an earlier paper [113], I suggested that the penetration of protons deep into the ionosphere, with the electrons left behind, might set up an electric field. Such a field would disappear immediately once proton influx ceased. The mechanism appeared possible, providing the downward electron flow became entirely constricted in the rays, while protons penetrated over larger areas. Still, the total electron current did not agree with the total proton current (deduced from the theory of arcs) as well ae one might wish. In addition, there is a serious difficulty to this hypothesis: Even if large negative currents flow down the rays, there should still be an appreciable amount of current outside the rays, where the electron density and conductivity are not negligible. In view of this high conductivity of the ionosphere, it seems probable that very localized electric fields are responsible for the discharge. ACKNOWLEDGMENTS This review has been based on a series of lectures presented at Yerkes Observatory during the summer of 1956. I am greatly indebted to my colleagues Dr. George Backus, Dr. C. Y. Fan, Mr. Anders Omholt, and Dr. Kevin H. Prendergast for their helpful

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interest in these problems and for numerous stimulating discussions. Thanks are also due Mrs. Beverly J. Negaard and Mrs. Vidya Pesch for their kind assistance in various phases of the preparation of this article. The Air Force Cambridge Research Center, Air Research and Development Command, has supported some of the research reported here under contract AF 19(122)-480; this financial assistance is gratefully acknowledged.

LIST OF SYMBOLS* magnetic vector potential radius of the earth 6 component of A arising from induced currents @ component of A arising from a permanent magnetic field magnetic induction (or field) cross-sectional area of the ring current z component of magnetic field produced by induced currents equatorial magnetic field at the earth’s surface poloidal component of magnetic induction (or field) solar magnetic field carried to the neighborhood of the earth by a particle stream toroidal component of magnetic induction (or field) speed of light .) proportionality constants (i = 1, 2, 3 Stormer unit of length, equal to (MQ/wzu)%cm thickness of a charged surface layer of an ionized stream electric field charge on the electron in electrostatic units (esu) poloidal component of the electric field electric field inside an ionized stream electric field a t position 8 in a surface layer of an ionized stream flux of incident protons in units of particles/cma sec magnetic field strength integration constant in t h e monopole problem total range of air at standard temperature and pressure tha t can be traversed by incident protons unit vector total current within a cylinder of radius R hydrogen-line profile, observed in the magnetic zenith, produced by protons incident from direction 0 hydrogen-line profile, observed in the magnetic zenith, produced by protons incident from various directions current density magnetization current density hydrogen-line profile, observed a t depth E on the magnetic horizon, produced by protons incident from direction 0 hydrogen-line profile, observed a t depth E on the magnetic horizon, produced by protons incident from various directions

..

*Electromagnetic units (emu) are uscd throughout this chapter. Note that if A is a vectur quantity, its absolute value is written as A = IAl. Subscripts z,y, 2 , R, e, and 4 denote components in a particular direction. Subscripts e and i refer to electrons and positive ions, respectively.

208

JOSEPH W. CHAMBERLAIN

P \pi. 'psi

Q 4

Qo

S

s* T

t V

V Vd

hydrogen-line profile, observed at height z on the magnetic horizon, produced by protons incident from various directions lunar component of the quiet-day magnetic variations length of cylindrical stream luminosity distribution versus equivalent depth for an aurora produced by protons incident from direction B luminosity distribution versus equivalent depth for an aurora produced by protons incident from various directions luminosity distribution versus height in the atmosphere magnetic moment of a dipole dipole moment of the permanent field moments of induced dipoles strength of the monopole mass of a particle number density of particles number density of atoms a t sea level the density of neutral hydrogen atoms total number of particles in a cross section of a stream, one cm in length angular distribution of particles per second per unit solid angle incident on one cm2 of surface normal to the magnetic lines of force scalar pressure rate of transfer of momentum to protons from electrons rate of transfer of momentum to electrons from protons kinetic energy of motion of a particle in its meridian plane (in Stormer theory) absolute value of the charge on a particle amount of charge of either sign on a strip one cm high and integrated all around the cylindrical sheet radial coordinate in the equatorial plane radius of curvature of the lines of force radial coordinate radial distance of the sun radius of a cylindrical sheet or ring current; radius of a stream of particles minimum distance from the dipole that a Stormer particle can penetrate in the equatorial plane path length solar component of the quiet-day magnetic variations mean ionic (Ti) and electronic ( T s )temperature time velocity (component of velocity along the magnetic lines of force, when applied to protons in the earth's atmosphere) velocity drift velocity of a particle in crossed electric and magnetic fields or in a nonuniform magnetic field meridional (poloidal) velocity component zonal (toroidal) velocity component initial velocity of particles leaving the sun velocity of a particle at position 8 in a stream circular (gyrational) component of velocity of a particle velocity component perpendicular to the magnetic field velocity component parallel to the magnetic field

THEORIES OF THE AURORA

209

v

total velocity of a proton in the atmosphere 1 / 2 ~times the electrical resistance in an ionized sheet W component of velocity (of protons in the atmosphere) directed toward observer and in a plane perpendicular to the magnetic lines of force wo component of velocity (of protons in the atmosphere) in a plane perpendicular to the magnetic lines of force Wmar maximum value of w oversus 8, for a fixed 5: W* velocity of a hypothetical observer measuring the electric field in a n ion stream Cartesian coordinates angle between h and r in the monopole problem effective recombination coefficient parameter in Stormer theory, related to angular momentum about the z axis by equation (3.11) B

E

e

el

e A

x A0

P Va

E P uo T

a1 40

4 X

-y

thickness of a ring or sheet vector operator gradient in the plane perpendicular to B increment (of current density) produced by differential slowing of electrons and protons by collisions with interplanetary or coronal particles increment (of current density) produced by a n induced electric field kinetic energy of a particle number of ionization pairs created in one cm air (S.T.P.) by a n ionizing particle electrical resistivity, 1/8 E electrical conductivity the number of particles in space crossing one om2 normal to direction 0 per unit solid angle per second polar angle in spherical coordinates ( = colatitude when applied to geomagnetic position; or zenith distance when applied to excitation problems in the atmosphere) colatitude at which auroral particles strike the earth position in a charged layer, measured from the interior boundary in units of d parameter defined by equation (4.23) latitude coordinate (in spherical coordinates) geomagnetic latitude coordinate of point on the sun emitting auroral particles magnetic moment of a single particle collision frequency equivalent depth (amount of air, expressed in cm of air at S.T.P., lying above a particular height) radius of gyration surface charge per unit area volume electrostatic potential longitude of entry of particles onto the earth (measured from the longitude of the sun) longitude of point on the sun emitting auroral particles azimuth angle angle between the total velocity vector v of a single particle and the magnetic field

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JOSEPH W. CHAMBERLAIN

# mean energy in the transverse components of motion w angle between the tangent to the orbit and the meridian plane. (For orbits in the equatorial plane, the angle between the tangent to the orbit and the R axis) W. gyrofrequency (or cyclotron frequency) st scalar magnetic potential for a dipole field a, dipole potential a t a point P Qo potential due to the permanent dipole with moment M O stl, al’ potentials due to induced dipoles REFERENCES 1. Aristotle (ca. 340 B.C.). “Meteorologica,” Book I, Chapter 5. English translation by H. D. P. Lee, Harvard Univ. Press, Cambridge, Mass., 1952. 2. De Mairan, J. J. D. (1733). “Trait6 Physique et Historique de 1’Aurore Borbale.”

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58. Chapman, S. (1920). A note on magnetic storms. PhiZ. Mag. 40, 665-669. 59. Maxwell, J. C. (1881). “A Treatise on Electricity and Magnetism,” 2nd ed. Vol. 2, Chapter 12, pp. 263-275. Oxford Univ. Press, London and New York. 60. Chapman, S. (1952). Theories of the aurora polaris. Ann. ghophys. 8, 205-225. 61. Landseer-Jones, B. C. (1955). The significance of a nonterrestrial magnetic field in neutral stream theories of the aurora. J . Atm. Terr. Phys. 6, 215-226. 62. Schmidt, A. (1924). Das erdmagnetische Aussenfeld. 2. Geophys. 1, 1-13, 63. Chapman, S., and Ferraro, V. C. A. (1941). The geomagnetic ring current. I. Its radial stability. Terr. Mag. 46, 1-6. 64. Chapman, S., and Bartels, J. (1940). “Geomagnetism.” Oxford Univ. Press, London and New York. 65. Ray, E. C. (1956). Effects of a ring current on cosmic radiation. Phys. Rev. 101, 1142-1148. 66. AlfvBn, H. (1955). On the electric field theory of magnetic storms and aurora. Tellus 7, 50-64. 67. Martyn, D. F. (1951). The theory of magnetic storms and auroras. Nalure 167, 92-94. 68. Babcock, H. W., and Babcock, H. D. (1955). The sun’s magnetic field 1952-54. Astrophys. J . 121, 349-366. 69. AlfvBn, H. (1956). The sun’s general magnetic field. Tellus 8, 1-12. 70. Cowling, T. G. (1942). AlfvBn’s theory of magnetic storms and aurora. Terr. Magn. 47, 209-214. 71. Malmfors, K. G . (1946). Experiments on the aurorae. Ark. Mat. Ast. Fysilc 34B, No. 1. 72. Block, L. (1955). Model experiments on aurorae and magnetic storms. Tellus 7, 65-86. 73. Lebedinski, A. I. (1952). The ray and arc forms of the aurora. Doklady Akad. Naulc S.S.S.R. 86, 913-916. 74. Meyer, P., Parker, E. N., and Simpson, J. A. (1956). Solar cosmic rays of February, 1956 and their propagation through interplanetary space. Phys. Rev. 104, 768-783. 75. Simpson, J. A., Fenton, K. B., Katzman, J., and Rose, D. C. (1956). Effective geomagnetic equator for cosmic radiation. Phys. Rev. 102, 1648-1653. 76. Davis, L. (1955). Interplanetary magnetic fields and cosmic rays. Phys. Rev. 100, 1440-1444. 77. Schuster, A. (1907). The diurnal variations of terrestrial magnetism. Phil. Trans. Roy. Soc. (London) A208, 163-204. 78. Chapman, S. (1919). The solar and lunar diurnal variation of the earth’s magnetism. Phil. Trans. Roy. SOC.(London) A218, 1-118. 79. Vestine, E. H. (1953). The immediate source of the field of magnetic storms. J . Geophys. Res. 68, 560-562. 80. Wulf, 0. R. (1945). On the relation between geomagnetism and the circulatory motions of the air in the atmosphere. Terr. Magn. 60, 185-197. 81. Wulf, 0. R. (1953). On the production of glow discharges in the ionosphere by winds. J . Geophys. Res. 68, 531-538. 82. Vestine, E. H. (1953). Note on geomagnetic disturbance as an atmospheric phenomenon. J . Geophys. Res. 68, 539-541. 83. Vestine, E. H. (1954). Winds in the upper atmosphere deduced from the dynamo theory of geomagnetic disturbance. J . Geophys. Res. 69, 93-128. 84. Elsasser, W. M. (1955). Hydromagnetism. I. A review. Am. J . Phys. 23,590-609.

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85. Gold, T. (1955). In an informal discussion on shock waves and rarefied gases. I n “Gas Dynamics of Cosmic Clouds” (J. M. BurKers and H. C. van de Kulst, eds.), pp. 103-104. Interscience, New York. 86. Singer, S. F. (1956). A new model of magnetic storms and aurorae. Trans. Am. Geophys. Un. 38, 175-190. 87. Lust, R. (1953). Magneto-hydrodynamische Stosswellen in einem Plasma unendlicher Leitfahigkeit. Z . Naturforsch. 8a, 277-284. 88. Lust, R. (1955). Stationare magneto-hydrodynamische Stosswellen beliebiger Starke. Z. Naturforsch. 10a, 125-135. 89. Parker, E. N. (1956). On the geomagnetic storm effect. J. Geophys. Res. 62,625638. 90. Hulburt, E. 0. (1928). On thc origin of the aurora polaris. Terr. Magn. 33, 11-13. 91. Maris, H. B., and Hulburt, E. 0. (1929). A theory of aurorae and magnetic storms. Phys. Rev. 33, 412-431. 92. V’iunov, €3. F. (1945). The r81e of meteor streams in the production of magnetic storms and polar aurorae. Izves. Akad. Nauk. S.S.S.R. Ser. Geograf. i Geo$a. 9, 294-3 15. 93. Dubin, M. (1955). Meteor ionization, magnetic storms, and the aurora. Proc. Mized Comm. Zonosphere, 4th Meeting, Brussels (Un. Radio-Sci. Intern.), pp. 2 19-229. 94. Booker, H. B. (1956). A theory of scattering by nonisotropic irregularities with application to radar reflections from the aurora. J. Atm. Terr. Phys. 8, 204-221. 95. Seaton, M. J. (1954). Excitation processes in the Burora and airglow. 1. Absolute intensities, relative ultra-violet intensities and electron densities in high latitude aurorae. J . Atm. Terr. Phys. 4, 285-294. 96. Omholt, A. (1954). Electron density in the E-layer during auroral displays deduced from measurements of absolute brightness of the auroral luminosity. J. Atm. Terr. Phys. 6, 243-244. 97. Omholt, A. (1955). The auroral E-layer ionization and the auroral luminosity. J. Atm. Terr. Phys. 7 , 73-79. 98. Meredith, L. H., Gottlieb, M. B., and Van Allen, J. A. (1955). Direct detection of soft radiation above 50 kilometers in the auroral zone. Phys. Rev. 97, 201-205. 99. Van Allen, J. A., and Kasper, J. E. (1956). Nature of the high-altitude soft radiation. Bull. Am. Phys. Sac. [11]1, 230. 100. Singer, S. F. (1956). Thermonuclear processes in the aurora. Univ. Maryland Phys. Dept. Tech. Rept. No. 62. 101. Harang, L. (1951). “The Aurorae,” Chapter 7 . Wiley, New York. Also see Vegard [33]. 102. Bates, D. R., and Griffing, G. (1953). Scale height determinations and auroras. J . Atm. Terr. Phys. 3, 212-216. 103. Vegard, L. (1921). Recent results of northlight investigations and the nature of the cosmic electric rays. Phil. Mag. 42, 47-87. 104. Chamberlain, J. W. (1954). The excitation of hydrogen in aurorae. Astrophys. J. 120,360-366. 105. Chamberlain, J. W. (1954). On the production of auroral arcs by incident protons. Astrophys. J. 120, 566-571. 106. Whipple, F. L. (1954). Density, pressure, and temperature data above 30 kilometers. Zn “The Earth as a Planet” (G. P. Kuiper, ed.), Chapter X, pp. 491-513. Univ. Chicago Press, Chicago, Illinois. 107. Omholt, A. (1956). Characteristics of auroras caused by angular dispersed protons. J. Atm. Terr. Phys. 9, 18-27.

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108. Landolt (H. H.)-Bornstein (R.) (1952). “Zahlenwerte und Funktionen,” Vol. I (Atom- und Molekular-Physik), Part 5 (Atomkerne und Elementarteilchen), p. 320. Springer-Verlag, Berlin. 109. Meinel, A. B. (1951). Protons and the aurora. Proc. Conf. Auroral Phys. Geophys. Res. Pap. U S A F 30,41-60. 109a. Omholt, A. (1957). Photometric observations of rayed and pulsating aurorae. Astrophys. J. 126,461-463. 110. Shklovski, I. S. (1951). The radiation of hydrogen lines in the auroral spectrum. Doklady Akad. N a u k S.S.S.R. 81, 367-370. 110a. Chamberlain, J. W. (1957). On a possible velocity dispersion of auroral protons. Astrophys. J. 126, 245-252. 111. Thomson, E. (1917). Inference concerning auroras. Proc. Null. Acad. Sci.3, 1-7. 112. Chamberlain, J. W. (1955). Auroral rays as electric-discharge phenomena. Astrophys. J . 122,349-350. 113. Chamberlain, J. W. (1956). Discharge theory of auroral rays. “The Airglow and Aurora” (A. Dalgarno and E. Armstrong, eds.), pp. 206-221. Pergamon, London.

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THE EFFECTS OF METEORITES U P O N THE EARTH (INCLUDING ITS INHABITANTS. ATMOSPHERE. AND SATELLITES) Lincoln LaPaz Director. Institute of Meteoritics. University of New Mexico. Albuquerque. New Mexico

Page 218 219 1.1. Effects Produced by an Infalling Meteorite . . . . . . . . . . . . . . . . . . . . . . . . . 225 1.2. Damage and Injury from Falling Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1. The Probability of Meteorite Hits on the HTA . . . . . . . . . . . . . . . . . 228 1.2.2. The Probability of Meteorite Hits on BTA’s . . . . . . . . . . . . . . . . . . 230 1.2.3. The Probability of Meteorite Hits on VTA’s . . . . . . . . . . . . . . . . . . . 234 2 . Number, Classification, and Weights of Recovered Meteorites . . . . . . . . . . . . . . 235 3. Meteoritic Abundances and Terrestrial Meteoritic Accretion . . . . . . . . . . . . . . . 240 3.1. Elemental Abundances in Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 242 3.2. Observed Meteoritic Contributions to the E a r t h . , . . . . . . . . . . . . . . . . . . . . 3.3. Criteria for Estimating the Population of Meteoritic Showers . . . . . . . . . . 247 3.4. The Detection and Recovery of Meteoritic Material . . . . . . . . . . . . . . . . . 252 3.4.1. The Search for Superficially Buried Meteorites . . . . . . . . . . . . . . . . . 253 3.4.2. The Vertical Distribution of Meteoritic Iron in the Earth . . . . . . . . 255 3.4.3. Meteorite Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 3.5. The Rate of Accretion of Meteoritic Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 3.6. Phenomena Related to the Infall of Meteoritic Dust . . . . . . . . . . . . . . . . . . 269 3.6.1. Anomalous Light Streaks and Noctilucent Clouds . . . . . . . . . . . . . . . 269 3.6.2. The Relation between Rainfall Peaks and Meteor Showers . . . . . . . 272 3.6.3. The Meteoric Ionospheric Layer of Kaiser . . . . . . . . . . . . . . . . . . . . . 273 273 4. The Hyperbolic Meteorite Velocity Problem . I . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. The Ballistic Potential of Meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 4.2. A Photographed Meteor of Strongly Hyperbolic Velocity . . . . . . . . . . . . . . . 274 4.3. Radar-Meteor Velocities and Their Limitations . . . . . . . . . . . . . . . . . . . . . . . 278 4.3.1. Limitations Due to Selectivity Effects in Instrumentation and in Reduction Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 4.3.2. The M-Zone Limitation and Its Implications . . . . . . . . . . . . . . . . . . . 281 4.4. The Hyperbolic Comet Question and Its Relation to the Problem of Meteoritic Velocities . . . . . . ............ . . . . . . . . . . . . . . . . . . . 283 4.5. Nonvisual Methods of Met 4.5.1. The Inverse Acceler 4.5.2. The Coma Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 cable to High-speed Carbon4.5.3. A Method Which May Be ........................... 290 Bearing Meteorites . 5 . The Hyperbolic Meteorite Velocity Problem . I1. . . . . . . . . . . . . . . . . . . . . . . . . . 292 5.1. The Frequency Distribution of Meteorite Falls as a Function of the Right Ascension of the Moon a t the Time of Fall . . . . . . . . . . . . . . . . . . . . . . . . . 294 5.2. B-Processes and the Hyperbolic Velocity Problem. . . . . . . . . . . . . . . . . . . . 306 217

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1 The Effects of Typical Meteorite Falls., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Page . . . . . . . . . 307 6. Crater-Producing Meteorite Falls. ...................... 6.1. The Barringer Meteorite Crater. ..... 6.2. The Odessa Meteorite Crater. . . . . . . . . . . . . . . . . . . . . . . . 319 6.3. Determinations of the Mass of Crater-Producing Meteorites and of the . . . . . . . . . 323 Age of the Craters.. ................................ 6.4. The Diffusion of NiO in the Soil and the Age of the Craters. ........................................ Appendix I. Meteoritical Pictographs and the Veneration Meteorites.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Appendix 11. Basic Meteoritic Data and Classificational Criteria Employed in Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 List of Symbols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 References .................... ......................... . . . . 341

1. THEEFFECTS OF TYPICAL METEORITE FALLS

Meteoriticists have surmised for generations that the apparently fragile objects producing ordinary shooting stars differed significantly in composition and structure from the exceptionally tenacious masses responsible for meteorite falls. It was early observed that, although luminous phenomena of great brilliance might be exhibited by the larger objects falling during so-called meteor showers, the extraordinarily violent sound eff ects-so pre-eminently the characteristic of the lower-descending fireballs that actually produce meteorite falls-were absent. Furthermore, the luminous fireball accompanying a n actual meteorite fall, while often of superlative brightness, might be rather inconspicuous and, in fact, occasionally was altogether lacking [l].Again, as has been emphasized by Meunier [2], not only is coincidence in time singularly absent between the great showers of meteorites and those of shooting stars, but, with the single exception of the Mazapil meteorite fall-an exception certainly chargeable t o coincidence-no tangible meteoritic mass whatever has been seen to fall to earth during even the greatest of the meteor showers. On the basis of such observational evidence as the above, it was natural to make a preliminary twofold classification of the material objects responsible for observed meteoric phenomena into a subclass of ‘(soft ” low-density meteoroids, quite incompetent to survive the rigors of atmospheric transit, and a subclass of “hard l 1 high-density meteorites, capable of penetrating completely through the protective air mantle of the earth. The totality of bodies of cosmic origin falling from the skies has been classified by Lacroix [3] into meteorites, or objects of extra-atmospheric origin, and tektites, or silica-glasses of intra-atmospheric origin which arise from the oxidation of invading “meteorites holometallites microsideriques.” Although majority opinion unquestionably concurs with

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Lacroix in regarding the tektites as essentially meteoritic in nature, it must not be overlooked that no authentic case of a tektite actually witnessed t o fall has yet come to notice. Several instances of tektites observed to fall were reported from 50 to 100 yr ago [4];however, after thorough investigation, each of these “falls” was discredited. Recently, what appeared to be two entirely authentic cases of Australian tektites ( = australites) of witnessed fall were reported by the late E. S. Simpson [5]. On the basis of the extraordinary penetration (30 cm) claimed for one of these tiny objects (a mass weighing only 31 gm), the writer was led to doubt the accounts of eyewitnesses. Correspondence with Simpson and Bowley led to a critical re-examination of the supposed falls, and in each case they were discredited [6], It therefore seems established that tektites of observed fall are unknown. Consequently, we are in no position to discuss the effects they produce, no matter how probable the fact of their actual infall is adjudged to be on the basis of indirect evidence. In the sequel, we shall therefore restrict attention to Lacroix’s ordinary meteorites. 1.i. E$eets Produced by an Infalling Meteorite

The first visible evidence of the infalling of a meteorite to the earth is the appearance of what seems to be an ordinary shooting star. If the fall occurs during daylight hours, this first and extremely high-altitude luminous phase may pass wholly unobserved, the meteoritic fireball first attracting attention only when its brilliance begins to rival that of the sun. In the case of nocturnal falls, where the entire sequence of light variation is clearly visible, the observer cannot fail to be impressed by the very great range in magnitude exhibited by a meteoritic fireball in contrast t o the limited range observed in the case of ordinary meteors, many of which preserve almost the same light intensity from one end to the other of their visible courses. In the lower, brighter portion of its trajectory, a falling meteorite frequently produces a curious whistling or whining sound, sometimes of variable pitch. Such sounds are anomalous in the sense that they are heard by the observer at the same time the fireball is seen in the sky, a simultaneity that could not possibly arise if the noises in question were transmitted at the same velocity as ordinary sounds. According t o RBmusat 171, at Ho-nan in the year 817 of our era, a great fireball was observed which made a noise like a flock of cranes in flight. This curious sound, which was heard at the same time the fireball was seen, is, as far as the writer has been able to determine, the first recorded observation of an anomalous meteoritic sound. As regards the objective reality of these anomalous sounds, the pen-

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dulum of scientific opinion has performed more than one oscillation in the course of meteoritical history. Even as careful an authority as A. Wegener was inclined to regard the sounds as subjective, in spite of the wealth of observational evidence regarding their occurrence that he accumulated during his personal investigation of the Treysa meteorite fall [8]. On the contrary, Udden’s nearly concurrent, and in many respects equally exhaustive, study of the great Texas meteor of October 1, 1917 [9], led him to the conviction of the reality of the anomalous sound reported by eyewitnesses. Recently (possibly as a result of the everincreasing amount of prompt, first-hand interrogation of numerous witnesses of large fireball falls) opinion has turned very strongly in the direction of accepting with Udden the objective reality of anomalous meteoritic sounds, and several attempts have been made to give a rational explanation of their cause. Udden himself, in 1917, suggested the possibility that electromagnetic waves from a falling meteorite “on meeting the earth or objects attached to the earth, such as plants or artificial structures, are in part dissipated by being transformed into waves of sound in the air.” I n 1949, after a brief historical review of instances in which anomalous sounds were unquestionably heard, Barringer and Hart [lo] examined in succession several hypotheses evolved to explain such sounds. Since a luminous meteorite, like any other incandescent body, emits a spectrum of electromagnetic radiations, there are no conceptual difficulties in a theory of radiofrequency radiation emanating from the falling meteorite and transformed in part into audible sound waves by any suitable “receiver”dental gold fillings, stoves, automobile bodies, barbed wire fences, and sheet-metal garages have all either been reported as actual, or suggested as possible, “receivers.” An appeal to Planck’s equation, however, convinced Barringer and Hart that this explanation of the anomalous sounds encounters insuperable quantitative difficulties; and they then considered, in succession, the possibilities that the sounds in question have their origin either in audiofrequency-modulated light waves, or in radiation of the intragalactic type emanating from the relatively large volume of ionized particles created by the falling meteorite. The first of these hypotheses was appraised as untenable, but the second was regarded by Barringer and Hart as, qualitatively, the most likely explanation of the anomalous sounds. The intensity and extent of meteoritically-produced ionization, particularly in the restricted M-zone centering at an altitude of about 95 km, described by Millman and McKinley [ll], is strikingly borne out by the serious disturbances of both radio and television reception noticed throughout a wide area extending on either side of the trace (projection)

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of the path of the falling meteorite on the earth’s surface. Instances have been investigated by the writer in which a total blackout of radio reception, on both normal and shortwave channels, and also of television developed a t the instant of passage of a fireball and continued for from one to several minutes. In one such case, associated with the fall and explosion of an “exceedingly bright” fireball near the U.S. Weather Bureau Station at Charleston Municipal Airport, Charleston, South Carolina, at about 10:45 P.M. on the evening of the same day (November 30, 1954) as the now famous woman-injuring Sylacauga, Alabama, meteorite fall, the “blackout” was permanent. According to an official report made to the Institute of Meteoritics by the radiosonde operator on duty at the time of this fireball fall: My radiosonde signal began to scatter slightly and the operator went up to the roof to try to tune in the signal better on the directional finder. Before he reached the SCR-658, the signal went out entirely. I turned up the volume on the receiver. There was a high pitched noise which may have been caused by the instrument’s being shorted. I listened for possibly five seconds; then turned the volume down. Just about this time, the tower reported the explosion in the northeast and the report of the jet pilot. They fixed the time of the explosion a t the moment at which the 658 operator reached the head of the stairs, approximately the time when the radiosonde signal cut out entirely. At the time we believed the light flash to be caused by an expIoding jet. The radiosonde-from the data secured from the wind direction and velocity aloft-was probably in a position to be struck by a fragment from the exploding meteorite. It was a t about an altitude of 35,000 feet.

Through the courtesy of the National Weather Records Center at Asheville, North Carolina, the writer has been able to examine the radiosonde record referred to in the above report. This record is almost destitute of “paint” until less than one minute before the sharp signal cutoff noted by the radiosonde operator at the time of the fireball explosion. Thereafter, until the recording device was voluntarily shut off in accordance with Weather Bureau regulations, the No. 696 recorder chart was profusely “painted.” Since no evidence that meteorites actually fell at Charleston has been uncovered, it is probable that the permanent blackout of the radiosonde resulted from an internal breakdown rather than from impact damage due to an external body. Occasional reports of powerful sulfur-like smells briefly noticed up to considerable distances on either side of the earth-trace, within a few minutes after the fall of fireballs which rival or exceed the sun in brightness, may be related to the ionization phenomena described above. The writer is inclined to attribute the reports in question to ozone produced by the dissociation of oxygen as a result of the extremely intense ultraviolet radiation emitted at short range by the fireballs. The transient

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odors in question are not to be confused with the pungent sulfur dioxide odors not noticed until some time after the passage of a sulfur-bearing meteorite but, in exceptional cases, like that of the Pasamonte, New Mexico meteorite, enduring for a day or more in the region contiguous to the earth-trace of the meteorite’s path. Toward the end of its visible path, the air resistance encountered by the invading meteorite mounts exponentially in magnitude, as is shown by two frequently observed effects: (1) a notable curvature of its trajectory in such a manner that the tangent thereto is shifted toward a vertical position, and (2) a visible deceleration so striking in character that the region in which it occurs was long ago termed the point or interval of retardation (Hemmungspunlctin German). The velocity reduction effected in this region of retardation often is accompanied by pronounced changes in the color of the fireball, the light from which shifts rapidly toward the deep red end of the spectrum. In the case of all but the most tenacious metallic masses, the region of retardation is further characterized by a disintegration, commonly described as an “explosion,” of the retarded meteorite into a few or many fragments [12]. In the case of the quite friable achondrites, several such “explosions” may occur. This region of violent disaggregation, in many cases, corresponds to a transition from the narrow transient trail of luminous vapor resulting from high-level ablation to development of much longer-enduring-and often quite voluminous-meteoritic dust clouds, produced not alone by superficial fusion and vaporization of the meteorite, but also by its bulk disintegration. From such clouds, tiny meteoritic particles may fall in sleet-like showers, as in the case of the Pantar, Philippine Islands, shower of June 16, 1938, when thousands of objects of the size of rice and corn grains fell on galvanized iron roofs with a pattering that sounded like hail. The sequence of developments briefly outlined above culminates, after the lapse of an interval ranging in duration from a few seconds to several minutesdepending on the position of the observer relative to the meteoritic trajectory-in arrival at his position of a brief, but often surprisingly violent, ballistic headwave. (The terminology here is that of Esclangon [13].) Indeed, this airwave may be so powerful that observers attribute its effects on dwellings and their contents to the incidence of an earthquake. While, in general, actual seismic activity may not be involved, examples are not lacking in which there is indubitable evidence of earth tremors initiated by the ballistic headwave generated by a falling meteorite. The most recent and definite example of this sort was brought to the writer’s attention by H. E. Landsberg. On April 21, 1955, shortly after 2 A.M., E.S.T., an extremely large and brilliant fireball passed across the southeastern states, its flight extending

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from Gordonsville, Virginia, to Jacksonville, Florida. Over Piedmont, North Carolina, the fireball is reported to have burst with a blindingly bright blue-white flash of light. After an interval of from 4 to 5 min, a loud “explosion” was heard over a roughly circular area 200 miles in diameter. This L‘explosion”was instrumentally recorded at Chapel Hill, North Carolina on the vertical Wilson-Lamison seismograph operated by the Department of Geology and Geography of the University of North Carolina. According to MacCarthy [141, the seismographic disturbance showed a clear-cut and sudden commencement at 07:08:45 G.C.T. The maximum (half) amplitude on the trace was about 5 mm and the frequency about 1 to 1% cps. The instrumental record of the disturbance lasted 8% sec. Inquiries made at Columbia, South Carolina, and at Morgantown, West Virginia-the seismological stations nearest to Chapel Hill-show that seismic disturbance was not picked up at either of these two places. Furthermore, no meteorite fall is known to have resulted from the passage of the fireball. MacCarthy concludes that “ . . . the earth tremor must have been caused by the atmospheric shock-wave rather than by any impact of solid material striking the earth.” (The references on the Podkamennaya Tunguska fall to be given in a later section on meteorite craters will make clear that full-scale earthquakes may be generated by the impact of large meteorites on the earth.) Eventually, a time-sequence of instrumental recordings analogous to the one carefully described by MacCarthy will permit precise determination of the speed of propagation of the ballistic headwaves produced by falling meteorites. At present, we must rely on elapsed time-distance data fortuitously obtained by the visual observer under such exceptionally favorable conditions as to justify placing confidence in the resulting values of the speed in question. The best example known to the writer of such a noninstrumentally determined speed is that of the Cumberland Falls, Kentucky aerolite [15], which moved from approximately south-southeast to north-northwest near and roughly parallel to the track of the Cincinnati Southern Railroad. A continuous record of the progress above the railway line of this strange “special” from outer space became possible because the telegraph and telephone operators in the railroad stations and signal towers announced to operators “down the line” with respect to the speeding meteorite the violent disturbance accompanying the passage of its ballistic headwave through each point of observation. A telephone operator at Tatesville, Kentucky, felt this headwave rock his tower at 12:27 P.M., as read on an accurately maintained railroad clock. The Danville, Kentucky operator, who had been forewarned of the mysterious disturbance, announced its arrival at Danville at 12:30 P.M. on another rail-

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way clock synchronized with the first. The airline distance between the two points of observation being 48 mi, the average speed of the meteoritically induced disturbance over this interval was very close to 429 meters per second, a value markedly in excess of the speed of ordinary sound under the same conditions of temperature and pressure. Considerably larger speeds were found for the ballistic headwave of the meteorite fall of February 18, 1948, on the basis of, unfortunately, less dependable elapsed time-distance data secured during the numerous field surveys carried out by the Institute of Meteoritics of the University of New Mexico in the region violently disturbed by passage of this giant many-ton achondrite, the main mass of which is the largest aerolite ever recovered [ 161. The results just cited will better enable the reader to understand how the ballistic headwave of a sizeable meteorite can damage the chimneys and roofs of dwellings and break the branches of trees, as happened, for example, in the case of the Kashin fall of February 27, 1918 [17]. In general, subsequent to the ballistic headwave, but often inextricably intermixed with it (at least in the observers’ minds), a confused body of noises-likened to that produced by an empty wagon bouncing over frozen ground, to long-continued cannonading, to the roar of a railway train, or to ‘(thewheels of the thunder wagon”-beats down from the sky. The intensity of these sounds, initially, may be so great as completely to demoralize not only fowl and animals, but human beings as well. E. A. Fath, who carefully observed the Richardton, North Dakota, meteorite fall of June 30, 1918 from the considerable airline distance of 27 mi, testified that even the general background of noise “was of such intensity that it would have been necessary to shout directly into the ear of another if one had tried to speak intelligibly” [HI. Occasionally, much louder reports rose above the general noise level. To listen to the sound effects produced by a large meteorite fall is a unique and awe-inspiring experience. Neither a hedge-hopping jet nor a keyholing rocket gives rise to the sky-filling reverberations set up by a falling meteorite. In contrast to the swiftest man-made missiles, which produce essentially one-dimensional sound sources in the sky, the meteorite’s hyper-velocity and its continual shedding of high-speed spalled-off fragments set up almost instantaneously a three-dimensional sound source filling a considerable fraction of the bowl of the listener’s sky. The so-called meteoritic detonations just described may endure for from one to several minutes, gradually diminishing in volume and receding in the direction whence the meteorite approached the observer’s position. The direction of recession is easily explained by the fact that the sound waves from the meteorite first reach the observer from the point

EFFECTS O F METEORITES ON THE EARTH

225

on the trajectory nearest to him, thereafter coming in from more and more distant portions of the path traversed by the falling mass. The explanation just given rarely occurs to actual eyewitnesses of meteorite falls, however; and, as a consequence, confusing reversals of direction of motion, based on what was heard rather than on what was seen, all too frequently distort observational reports. In the last stage of its motion through the atmosphere, a meteorite, or the fragments thereof if the initial mass has disintegrated, generally will be invisible, although in rare cases the invading masses have been mistaken for swiftly flying black birds [19]. Nevertheless, the presence of these invisible, rapidly-moving masses is evidenced in a most disturbing manner to the nearby observer by the startling hissing (“it sounded like the sky was full of mad snakes”) or sizzling (“like bacon frying”) noises which they make as they speed through the air. At the instant of impact, these swiftly-moving pieces of meteoritic “shrapnel” may cut off as cleanly as an axe not only small twigs, but also large branches from trees [20]; they may penetrate with greater or less destructive effect through the roofs of human habitations [21]; or, in very rare cases, they may strike and injure both animals [22] and human beings [23]. 1.2. Damage and Injury from Falling Meteorites

The possibility of structural damage or of human injury from falling meteorites has been a subject of perennial concern. At the present time, the topic is definitely not one of purely academic interest for the following reasons: (a) The population of the earth is now increasing very rapidly and hence the human target area (HTA) exposed to meteoritic impact is swiftly expanding; (b) concurrently, the built-over target area (BTA) also is very rapidly increasing in size; and (c) man is preparing to abandon in the very near future the protection normally afforded him and his constructions by the atmosphere against all but the most gigantic cosmic missiles, and to expose both unmanned and inhabited vehicular target areas (VTA) to the hazards of unimpeded meteoroidal and meteoritic bombardment. As Table I will show, the historical record contains numerous allusions to injuries and deaths resulting from meteorite falls. Some of the incidents tabulated (those rated as “doubtful” in the table), while cited by reputable authorities, must now be regarded as questionable because of lack of proof either that a genuine meteorite was involved or that the injury specified occurred. In fact, until the Sylacauga incident of November 30, 1954, a modern critic could contend with much justice that no really well-authenticated instance of death or injury from a meteorite fall was known. Such an assertion can no longer be countenanced. It is

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TABLE I. List of injuries reportedly caused by falling meteorites. Year

Mo.

Day

Prehistoric

Doubtful

C.

ca 1500 B.

Provisional rating

Doubtful

616

Jan.

14

Doubtful

1511

Sept.

14

Doubtful

1647-1654

Doubtful

1790

July

24

Doubtful

1794

June

16

Probable

1803

April

26

Probable

1825

Jan.

16

Possible

1827

Feb.

16

Probable

Account and authority The Lujan, Argentina, stony-iron meteorite was found 6 meters deep in a Quaternary formation, below the remains of a megatherium, which may have been killed by the meteorite. (M. Kantor ) “ . . as they fled from before Israel, and were in the going down to Bcthhoron, that the Lord cast down great stones from heaven upon them unto Azekah, and they died: . . , ” (Book of Joshua 10: 11) “ , . a stone fell in China, shattering chariots and killing 10 men.” (E. Biot) Birds and sheep and one Franciscan friar were killed during the fall of more than 1000 stones a t Crema, near Milan, Italy. (T. F. Phipson) No specimen was recovered and preserved. Sometime in this interval a mass weighing 4 kgm fell upon the bridge of a ship sailing a t full speed between Japa,n and Sicily and killed 2 sailors. (Captain Olaus-Ericson Willmann) No specimen was recovered and preserved. A stone of the recognized Barbotan, France, fall killed a herdsman and a bullock. (G. P. Merrill) One of the meteorites of the recognized howarditic-chondrite shower at Siena, Italy, pierced the hat of a child, who was merely frightened. (S. Meunier) A Atone of the famous L’Aigle meteorite shower grazed the arm of a wire manufacturer working in the open with his men, and fell to his feet. (J. B. Biot; Thomas Dick) A meteorite that fell a t Oriang (Malwate) in British India killed a man and seriously injured a woman. (S. Meunier) No specimen was recovered and preserved. A fragment of the recognized Mhow, India, meteorite “ . . . wounded a man severely in the arm.” (N. StoryMaskel yne)

.

.

227

EFFECTS OF METEORITES O N THE EARTH

TABLE I. List of injuries reportedly caused by falling meteorites. (Confinzied) ~~

~

~~~

Mo.

Year

~

Provisional Day rating

1836

Nov.

11

Possible

1847

July

14

Certain

1860

May

1

Certain

1870

Jan.

23

Certain

1878

Aug. or Sept.

-

Doubtful

1908

June

30

Probable

1911

June

28

Probable

1927

April

28

Probable

1938

June

24

Certain

Account and authority Stones from the recognized Macao, Brazil, meteoritic shower battered several cattle to death. (8. Meunier) The 17-kgm mass of the recognized Braunau, Bohemia, meteorites penetrated the ceiling of a bedroom where three children were sleeping. Their bed was covered with debris and pieces pierced the blanket under which they were sleeping, but the children were not seriously injured. (F. Heide) A stone of the recognized New Concord, Ohio, shower killed a colt. (J. C. Steele) The recognized Nedagolla, India, meteorite struck so close to a man that he was stunned. (G. H. Saxton) The recognized Haraiya, India, meteorite fell near three people weeding in a field, two of whom were knocked insensible and the third was found “charred and dead.” (L. L. Fcrmor) Several families of Tungusrs and many reindeer perished in the central area of the Podkamennaya Tunguska fall. (I>.Kulik) A meteorite of the recognized Nakhla, Egypt, showrr killed a dog. (F. Heide) The recognized Aba, ,Japan, meteorite hit and injured a girl. (I. Yamamoto) (S. Murayama’s recent examination of the missile that strurk the girl has not convinced him of its meteoritic nature.) Immediately after the recognized Chicorn, Pennsylvania, meteorites fell, a cow in a field neighboring the area where finds were made ‘‘ . was discovrred to have its hide torn downward as if struck a glancing blow by a falling stone . ’’ (F. W. Preston) The recognized Sylacauga, Alabama, meteorite fell through the roof of a house, struck a radio, bounced, and injured a woman lying on a couch. (G. W. Swindel, Jr. and W. B. Jones)

. .

..

1954

Nov.

30

Certain

228

LINCOLN LAPAZ

absolutely beyond question that the larger of the two stones recovered from the Sylacauga fall not only damaged property, but also actually injured a human being. This incident was reported by Swindel and Jones [24] as follows: Mrs. E. Hulitt Hodges, a housewife and resident of the Oak Grove community northwest of Sylacauga, was taking an after-lunch nap on a couch in her living room. Suddenly she heard a violent “explosion” and jumped up. At &st she thought the gas heater had exploded or that the chimney had fallen down. It was then that she felt a pain in her left hip and arm and observed the “rock” on the floor . . . The meteorite struck the roof on the south side of the Hodges’ home near the southwest corner of the main part of the house. It penetrated the composition roofing material and the %-inch wooden decking, grazed the rafter and ceiling joist, and then penetrated the %-inch wooden ceiling and the interior wall board . . . Mrs. Hodges’ injuries were caused by the meteorite’s bouncing off the radio with a flight arc having a maximum altitude of less than 6 feet. The impact was transmitted thru two heavy quilts, and the victim suffered painful bruises about the left hip and on her left arm and hand. She was hospitalized the day after the meteorite fell, in order to recover from the bruises and the shock.

The relevancy of the reasons previously enumerated in (a), (b), and (c) is emphasized by the Sylacauga incident. We therefore propose to treat in some detail the probability of hits on the HTA, on the BTA, and on VTA’s of the sort whose realization seems most immediately in prospect. It is natural to begin with: 1.2.1. The Probability of Meteorite Hits on the H T A . The human targets of opportunity exposed to hits from infalling meteorites, either natural or artificial (as, for example, the discarded portions of or debris from satellite vehicles and space rockets) present attackable areas ranging from a minimum near zero to the maximum, horizontal projection of the recumbent adult. The problem is further complicated by the pronounced tendency of all but the largest and fastest meteorites to lose, during their interaction with the terrestrial atmosphere, the randomness of direction which very probably characterized their paths in empty space. Nevertheless, on the basis of both intuitive and analytical arguments, it seems that the approximate value of the target area exposed to meteoritic impact by the average human being leading a normal life is 2.75 sq f t [25]. In order to calculate the areal extent of the HTA presented during any century by a specific group of human beings, e.g., the Europeans, it is necessary to rely on estimates giving the average population of such groups at mid-century. For dates earlier than 1600, no reliable data are available; but for dates later than 2150, excellent reasons have been advanced for expecting the population of the world, as a whole, and of its

229

EFFECTS OF METEORITES ON THE EARTH

various civilized subregions to remain nearly constant at the values attained in 2150, unless nuclear-biological warfare intervenes. Table I1 contains under each designated region, first, a column of population estimates (where derived by extrapolation, these estimates are enclosed in parentheses) ;second, a column of group target areas in square miles computed on the basis of 2.75 sq ft as the target-area presented by the representative human being; and, third, a column of hit-probabilities, P , computed on the basis of the following argument: Data relating to the number of meteorite falls witnessed in the most densely populated subregions of the earth indicate that at least N = 350,000 individual meteorTABLE 11. Populational data and probability results-Europe, and t.he World. Europe Population HTA Year in millions in s q mi 1500 1550 I600 1650 1700 1750 1800 1850 1900 1950 2000 2050 2100 2150

100 100 100 110 120 153 187 294 401 549 (697) (720) (744) (750)

United States

P

Population HTA in millions in sq mi

World

P

-

9.863 0.017 10.85 15.10 28.99 54.16 71.01 73.98

-

-

the United States,

-

(0.05) 0.018 (0.14) 0.0138 0.000 (0.23) 0.2170 0.000 0.026 2.2 5.3 4.043 0.007 0.050 41. 76. 0.091 131. 12.92 0.023 (186.) 0.117 (192.) 18.93 0.033 (198.) 0.122 (200.) 19.72 0.035

Population HTA in millions in sq mi 400 426 (452) (544) (637) 771 906 1257 1608 2197 (2787) (2881) (2975) (3000)

P

42.02 0.072 53.65 0.090 76.05 0.125 124.0 0.196 126.7 0.316 284.2 0.392 295.9 0.405

~

ites reach the surface of our globe each century [26]. In the writer’s opinion, this figure is only a conservative lower bound for N . As these cosmic missiles fall at random, the probability that any one of them will strike a specified HTA is simply the value p , obtained by dividing the HTA by 2 X 108, the area of the earth in square miles; hence, the probability that at least one of the N meteorites falling per century will strike the specified HTA is given by P = 1 - (1 - P ) ~ consequently, ; since p is very small and N is very large, P is given closely by the approximation p = 1 - e-Np (1.1) from which the P values given in Table I1 were computed. A number of interesting conclusions may be drawn from a consideration of the P values thus tabulated. First, the chance that during any

230

LINCOLN LAPAZ

particular one of the centuries listed in the table, a t least one meteorite will hit in the HTA’s of Europe or the United States is exceedingly small, negligibly so in the latter case. If we consider the entire world, there are about 316 chances out of 1000 that at least one meteorite will strike in its HTA during the 20th century. On the basis of the data tabulated in Table 11, the average HTA for the entire world during the three centuries from 1700 to 2000 approximates 139 sq mi. If the value of P corresponding to this HTA is computed, it is found that there is very nearly a 50-50 chance for at least one meteorite to hit this HTA during the three centuries in question. There is another way of looking at the question of meteoritic hits on HTA’s that may appeal to those who like to bet on a “sure thing.” As noted previously, there are cogent reasons for expecting the world’s HTA t o remain nearly constant from about 2100 A.D. onward. Since N may be regarded as constant, it follows that the probability P should remain substantially constant at about 0.4 from century to century after 2100 A.D. Accordingly, the probability P* that in a t least one of the n centuries after 2100 at least one meteorite will hit in the HTA of the world, is given by

p* = 1 - e-nP = 1 - &I.4n

(1.2)

If we assign the value 0.99 to P* and determine the corresponding value of n, we find n = 11.5; hence, it is practically certain that in a t least one of the centuries between 2100 A.D. and 3300 A.D., a t least one meteorite will strike the HTA in question. Inhabitants of the formidable world of the future, however, may regard this meteoritic danger as the least of the hazards to which they are subject! 1.2.2. The Probability of Meteorite Hits on BTA’s. The probability, P, that at least one meteorite will score a hit during an extended period of time, say a century, on a specified built-over target area (BTA), can, of course, be deduced from the formula (1.1) derived in the previous section. For example, since the average area of New York City in the period 1900 to 2000 may be taken as approximately 500 sq mi, the probability P that at least one meteorite will hit in this area during the 20th century is (1.3)

p

= 1

- e-Np

=

1

- e--0.816

= 0.58

That is, there exists somewhat more than a 50-50 chance that such a hit will be registered on the great American metropolis, Unlike the HTA situation, where no certain hits were scored by meteorites until A.D. 1954 (in fact, even the Sylacauga meteorite did not score a direct hit on Mrs. Hodges, but rather clobbered her on the first

EFFECTS O F METEORITES ON THE EARTH

231

bounce!), Table I11 shows that numerous direct hits on buildings have been registered by meteorites during the last 166 years. This fact suggests that it will be of more interest in the BTA case to consider the inverse problem of determining the probable value of N from the number of meteorite hits actually observed on a specified BTA. This inverse problem will be worked out only in the case of hits on buildings in the USA during the interval 1855 to 1955, for it is only for this country during this period that the data necessary for the calculation have been obtainable with any pretense a t accuracy. From U.S. census reports and other official housing data, it may be inferred that, on the average, not more than 2000 sq mi of roofed-over area existed in the continental U.S. during the century in question. The probability p of Section (1.2.1) consequently now has a value < 2 X 103/2 X lo8 = Therefore, if, as before, we denote by N the total number of meteorites striking the earth during the century under consideration, the expected number of hits on our particular BTA will be < N * 10-6. Taken in conjunction with the number of hits actually observed in this BTA, this last result implies that N > 500,000. Results of this size have been obtained from the number of hits actually observed on several specific BTA’s’ and furnish grounds for regarding the value N = 350,000 used in connection with HTA’s as probably no more than a lower bound for N , the more so because one can scarcely agree that 100% recovery occurs even in the case of building-striking meteorites. We shall use the value N = 500,000 to estimate the percentage of meteorites seen to fall that are actually retrieved under the conditions most favorable for recovery. The United Provinces of India, because it is a level, compact, highly-cultivated block of territory with an exceedingly large population density (438 per square mile), may be regarded as providing such optimum conditions for recovery. India, as a whole, while under British rule, showed an extraordinarily large number of meteorite recoveries from witnessed falls per 1000 sq mi per century; and yet Silberrad has recently concluded that the corresponding recovery rate for the United Provinces may be as much as seven times that for the rest of India [26]. According to Silberrad, the recovery rate in the United Provinces averages one meteorite per 4000 sq mi per century. But for an area of 4000 sq mi, the expected number of meteorite falls per century with N = 500,000 would be 10. Hence, one may infer that even in the densely populated United Provinces, recoveries are made from only about 10% of the witnessed meteorite falls. The implications of this result for 1 The writer has found concordant values for N by a more sophisticated argument based on W. Burnside’s theory of the comparative regularity of random distributions of points.

TABLE 111. Meteorites that damaged buildings. Name

Type

Wt

Place

Year

Mo. Day

h3

W

Hour

Remarks

~

Assum Barbotan Barnaul

Stone Stone Stone

25 gm

Baxter

Stone

Beddgelert

France France Siberia

1858 Dec. 1790 July 1904 May

9 7:30 A 24 9:oo P 22 11:30 P

611 gm

Missouri

1916 Jan.

18

9:00 A

Stone 794.05 gm

N. Wales

1949 Sept.

21

1:45 A

Penetrated building, no particulars Struck building, no particulars Struck the roof of a hut. (The figure 25gm represents the total weight of the fall) Penetrated roof and struck a log joist which checked the fall, the meteorite lodging in the attic Made clean hole through 4 thicknesses of slate roof shattered underlying wood (235 x 5 cm in section) +made tiny dent in bottom edge of H-section iron girder broke through plaster ceiling into hotel room below Passed through roof of hut Penetrated garage roof, top of car, and seat cushion. Struck and put 1-in. dent in muffler; then bounded back up and was entangled in seat cushion springs Struck side of wagon house, bounded off, hit log upon ground, bounded again and rolled into grass Fell through roof of hut Penetrated into room where 3 children were sleeping and covered them with plaster and debris. (The figure 19,000 gm is an average of wt published: Watson gives 21 kgm; Prior-Hey gives 17 kgm) Penetrated 2 thicknesses of corrugated iron roofing and smashed ceiling. About >$ broke off and was swept away. The remainder-about 2 Ib-was recovered uninjured

+

+

Benares Benld

Stone Stone

Bethlehem

Stone

Beyrout Stone Braunau (Broumov) Iron

Constantia

Stone

1798 Dec. 19 1938 Sept. 29

8:OO P 9:05 A

1859 Aug.

11

7:30 A

1921 Dee. 1100 gm Syria 1847 J d Y 19,000 gm Bohemia (Czechoslovakia)

31 14

3:45 P 3:45 A

4

4:30 P

999 gm India 1770 gm Illinois

11 gm New York

999 g m

S. Africa

1906 Nov.

N

Kasamatsu

Stone

721gm Japan

1938 Mar.

31

3:OO P

Penetrated roof of house and stopped on floor. Penetrated roof tile >&in. wooden roof-panel layer of clay 1 in. thick between them Two stones hit roofs Passed through 3 thicknesses of shingles a 1-in. hemlock roof board a 5Q-in. hemlock floor board; then glanced in turn against the side of a manger and the stone foundation of the barn and finally penetrated 235 in. into t,he clay floor of the barn Penetrated roof of house Struck building, no particulars Fell through the roof of a shed Struck cottage roof One of the stones fell through a granary Sixteen st.ones were recovered; thousands “as big as corn and rice grains” fell on roofs Penetrated tile roof and floor of building Pierced tile roof Collided with a lighthouse Pierced roof of game-keeper’s lodge Penetrated composition roof material N-in. wooden decking %-in. wooden ceiling interior wallboard, hit radio punching 1-in. hole in plywood top, bounced 90” toward east, struck woman lying on couch Smashed hole in roof of house Fell through roof of house

+

+

Khanpur Kilbourn

Stone Shower 772 gm Stone

Kunashak Kurumi Madhipura MLsing Orgueil Pantar

Stone 200gm Stone Shower Stone Stone 1600gm Stone Shower Stone Shower

Pillistfer Pulsora Shiriya Strathmore Sylacauga

Stone Stone Stone Stone Stone

India Wisconsin

Russia Japan India Bavaria France Philippine Islands

5400gm Latvia 680gm India Japan Scotland 3863gm Alabama

1932 July 1911 June

8 16

12-1 P 5:Oo P

1949 1930 1950 1803 1864 1938

June May May Dec. May June

11 8:14 A 27 Noon 23 2:oo P 13 10:30 A 14 8:OO P 16 8:45 A

1863 1863 1883 1917 1954

Aug. Mar. Oct. Dec. Nov.

8 12:30 P 16 24 3 30

P.M.

1:15 P

l:oo P

+

+

+

Yurtuk Zabrodje

Stone Stone

2000gm Ukraine 3000 gm White Russia

1936 Apr . 1893 Sept.

2 22

1:00 A 4:OO P +

+

+

H

q

r

3 w

Ee M 0

3 M

rn 0

Z

Y

E l M

i CQ W

W

234

LINCOLN LAPAZ

such sparsely populated regions as the southwestern U.S. can hardly fail t o depress the meteoriticist! 1.2.3. T h e Probability of Meteorite Hits on V T A s . As soon as the fundamental researches of the American rocket pioneer, Robert H. Goddard, made clear that space flight was possible, the question as to the magnitude of the threat posed to rockets outside the earth’s atmosphere by meteorite impact became of concern. As early as 1919, Goddard himself made an estimate of the seriousness of this meteoritic hazard in a special but important case, viz., that of impacts by visual meteors upon a MOUSE-like, small, spherical rocket of diameter d traversing a path of length equal to the minimum distance of the moon from the earth at a cruising speed v [27]. Goddard adopted the model of the system of visual meteors which was widely accepted a t the time he wrote, i.e., he took as a basis for his calculations a group of small bodies having a space density q independent of time and position and moving with velocities V directed a t random but constant in magnitude. By the artifice of treating separately the subcases (v = 0, V > 0) and (v > 0, V = 0) and then combining theresults, Goddard reached the conclusion that a spherical rocket with a diameter d = 1 ft and a velocity v = 1 mi/sec would be hit once during 81,300,000 trips to the moon if the constant velocity V of the visual meteors amounted to 30 mi/sec and the space density q of these bodies was such that each cube 250 mi on an edge contained one meteor. While the meteoric model Goddard used in 1919 would not command wide acceptance today, his assumptions are more reasonable than many proposed 30 years later when the success of high altitude firings of the V-2 reawakened interest in space flight.2 Furthermore, his numerical result is close t o the mark. Nevertheless, the case t o which Goddard restricted attention is highly specialized ; and current ideas not only with respect to q for the system of small bodies, but also with respect to the distribution in direction and, above all, in magnitude of the velocities V of these bodies, are in such a state of flux [28] that a t present the chief merit of Goddard’s work resides in its having called attention t o the fundamental role played by the V distribution in those collisional problems of importance in space flight. The importance of settling the vexed 7 and V issues is shown also by other considerations: In any attempt to appraise the ballistic potential of meteoritic missiles, one requires not only information concerning hit In 1948, the writer refereed a manuscript in which the following assumption was taken as basic: “It is assumed that the meteorites travel through the atmosphere along the vertical and that the plan-form area of the body attacked is normal to the vertical.”

EFFECTS OF METEORITES ON THE EARTH

235

probabilities but also relevant kinetic energy estimates. These latter in turn, necessitate data with respect to the mass and velocity of the missiles. Inasmuch as the latter of these quantities enters quadratically into the kinetic energy formula, whereas the mass enters only linearly, the great significance of evidence that meteorites may possess strongly hyperbolic velocities is at once apparent [29]. This is one of the reasons justifying the critical review of the meteorite velocity problem presented later in this chapter. Up to this point, attention has been restricted to meteorites of conventional (terrene) matter. In the sequel, in connection with the atypical Podkamennaya Tunguska fall, references will be given to cogent evidence that can be advanced to support the hypothesis that meteorites composed of unconventional (contraterrene) matter may exist. Theoretical considerations long ago led to the conjecture that such reversed matter was possible, and within the last year the final step in experimental verification of this interesting conjecture has been taken in the laboratory at the University of California. It follows that in any thoroughgoing discussion of the ballistic potential of meteorites, one must take into consideration the quite fantastic energy release possible in annihilation processes involving contraterrene space missiles and terrene vehicles. We shall return to this question in a later section. The problem of calculating the probable number of meteorite hits on a space satellite (like the IGY test objects which have been launched) constrained to move in an orbit only a few hundred miles above the earth’s surface involves considerations so closely analogous to those earlier encountered in Sections 1.2.1 and 1.2.2 that we shall omit its consideration here. 2. NUMBER, CLASSIFICATION, AND WEIGHTS OF RECOVERED METEORITES Although evidence to be presented in Appendix I will make amply clear that meteorite falls have occurred throughout the entire period of man’s habitation of the earth, and that at least as early as the Classical Age, considerable numbers of these interesting objects were carefully preserved and, indeed venerated ; nevertheIess, almost without exception, all meteorites currently recognized as such have been recovered and preserved during the last century and a half. At the present time, the museums of the entire world contain specimens of barely 1600 distinct meteorite recoveries [30], of which 683 were collected from meteorites actually seen to fall. On the basis of the relatively small number of meteoritic specimens SO far available for chemical and mineralogical investigation, it may be said

236

LINCOLN LAPAZ

TABLE IV. Principal meteoritic minerals. (Modified from similar tables given by Leonard [321 and by ZavaritskiI and Kvasha [33]. Minerals marked by an asterisk are not found in the earth’s crust.) Elements

Nickel-iron Kamacite* 93.1% Fe; 6.7Ni; 0.2Co Taenite* 75.3% Fe; 24.4Ni; 0.3c0 Plessite* Kamacite 1- taenite in various proportions Diamond C Graphite C Carbides Cohenite (Fe,Ni,Co)aC Moissanite* Sic Nitrides

Osbornite* TiN Suljdes

Troilite FeS Oldhamite* CaS Daubreelite* CrZFeSror FeSCrzSs Phosphides

Schreibersite* (Fe,Ni,Co)aP Chlorides

Lawrencite (Fe,Ni,Co)Clz Ozides

Quartz SiOa Tridymite Si02 Magnetite FeaO, Chromite Fe(Fe,Cr)*04 Simple Silicates

Chrysolite (Olivine) (Mg,Fe) &3iOl Forsterite MgzSi04 Fayalite FetSi04 Enstatite and clinoenstatite Mg2(SiOa)z Bronzite and clinobronzite (Mg,Fe)z(SiOa)a Pigeonite m(Mg,Fe)z(SiOs)z nCar(Si0t)e (m n = 100%) Hypersthene (Fe,Mg),(SiOl) 2 Diopside CaMg (SiOs)o Hedenbergite CaFe (SiO& Augite (Ti-bearing) Ca(Mg,Fe)(SiO& (Ca,Mg,Fe) (Al,Fe) (AISiOs)

+

+

+

A luminum-Silicales

+

Plagioclase mNaAlSiaOs nCaAlzSizOa (m Maskelynite * .Weinbergerite NaAlSi04 3FeSiOa

+

+ n = 100%)

237

EFFECTS O F METEORITES ON THE EARTH

TABLE IV. Principal meteoritic minerals. (Modified from similar tables given by Leonard I321 and by Zavaritskil and Kvasha [33]. Minerals marked by an asterisk are not found in the earth’s crust.) (Continued) Hydrous Silicates Chlorite-Serpentine

Phosphates Apatite CaaF(PO,)3 Merrillite CrtrNaz(PO4)2O

Carbonales Bruennerite (Mg,Fe)COs Calcite CaC03

Hydrocarbons and Amorphous Carbonaceous Matter

that all meteorites, exclusive of the tektites, are included in one of the following main divisions: AE (the aerolites), SO (the siderolites), and SI (the siderites) [31]. On the one hand, we may regard the totality of meteorites as mineral aggregates. Considered from this point of view, their principal constituents permit classification as in Table IV. On the other hand, the constituents entering into meteorites may be classified on the basis of their genesis and quantitative importance, in much the same way that rock-forming minerals have been subdivided. From this point of view, the meteoritic minerals may be classified as in Table V. Finally, on the basis of chemical composition, internal structure, and the genesis, quantitative importance, and characteristics of the component minerals, more detailed classifications of meteorites have been effected in various ways by several generations of meteoriticists [34]. For our present purposes, it is only necessary to note here that, while opinions vary widely in regard to the bases for and the limits of the more refined subgroupings, all authorities agree on a preliminary breakdown of the three main divisions of meteorites into seven basic classes, in the following manner: AE

=

(A

+ C);

SO

=

(S + L ) ;

SI

=

(H+O

+ D)

where A = achondrite, C = chondrite, S = sideraerolite, L = lithosiderite, H = hexahedrite, 0 = octahedrite, and D = ataxite [31]. A study of the classificational distribution by weight of those meteoritic falls of the world for which the necessary data were available has been made recently by Leonard and Finnegan (see [31], pp. 173-178). The

238

LINCOLN LAPAZ

TABLE V. The essential, primary accessory, and secondary accessory meteoritic minerals. (Modified from Leonard [32], pp. 162-164.) Name

Formula

Crystal system and class

A. The Essential Meteoritic Minerals The Nickel-Zrons Kamacite FelsNi to Fel4Ni I:1 Taenite Fe7Ni to FeNi r:i Plessite Kamacite taenite in various I: 1 proportions Olivine 0:25 Olivine (not differentiated) (Mg,Fe)&iO4 The Pyroxenes (a) The Orthopyroxenes (Enstenite) Enstatite 0:25 MgdSiOd z Broneite 0:25 (Mg,Fe)dSiOdn Hyperathene (Fe,Mg)z(SiO3)a 0:25 (b) The Clinopyroxenes (Clinoenstenite and Polyaugite) Clinoenstatite MgdSiOa)a 1C:28 Clinobronzite (Mg,Feh (SiOa)z 1C:28 Clinohy persthene (Fe,Mg)2 (SiOdz 1C:28 Pigeonite 1C :28 m (Mg,Fe) z(SiOs)2 nCaz (SiOa) I Diopside CaMg(SiOy)2 1C:28 Hedenbergite CaFe(SiOa)z 1C:28 Augite Ca(Mg,Fe) (Si0a)z (Ca,Mg,Fe) 1C:28 (A1,Fe) (A1Si06) 3C:31 The Plaagioclase Feldspars The Silica(s) a-tridymite ( = “asmanite”) SiO, 0:25

+

+

+

B. The Primary Accessory Meteoritic Minerals Carbide Cohenite (Fe,Ni,Co)aC Chloride Lawrencite (Fe,Ni,Co)Cla

0:25 H:13

Element

Graphite (including clif tonite) Amorphous carbon Chromite Magnetite Schreibersite Troilite = pyrrhotite Daubreelite Oldhamite

C C

Oxides Fe (Fe,Cr) 2 0 4 Fe304 Phosphide (Fe,Ni, Co) aP SulJides

FeS

Cr2FeScor FeSCrtSa CaS

H:6 Amorphous z:l z:l

T:24 H:6 z:l z: 1

239

EFFECTS OF METEORITES ON THE EARTH

TABLE V. The essential, primary accessory, and secondary accessory meteoritic minerals. (Modified from Leonard [32], pp. 162-164.) (Continued) Name

Crystal system and class

Formula

C. The Secondary Accessory Meteoritic Minerals Carbide Moissanite Sic Carbonate Breunnerite (Mg,Fe)COo Elements Copper cu C Diamond Phosphorus P I Nitride TIN Osbornite Oxides Ilmenite (trace) FeTiO, Hematite (doubtful) Fez08 Limonite (trace and FezOa-nHzO doubtful) Water (doubtful) H20 Phosphates Apatite (including C a J W O ds francolite) Merrillite Ca~NadPOd20 Silica a-quartz SiOa Silicates Forsterite Mg,Si04 Weinbergerite NaAISiOl 3FeSiOs Kosmochlor A1eFe4Cr 8Sil8 0 7 8 KAlSiaOs Orthoclase

H:8 H:13

z:l Z:3 or Z:l(?) z: l ( ? ) Z:l(?) H:16 H:13 Crystalline (syst. 0) to amorphous H: 15 (as ice) H:10 H:6(?) H:14 0:25 0:25 lC(?):28(?) 1C:28

+

TABLE VI. Classificational distribution by weight of the meteoritical falls of the world. -

A. By division Total number of falls Total weight (metric tons) Average weight (kilograms)

B. By class Total number of falls Total weight (metric tons) Average weight (kilograms)

A

C

AE

so

895 18.2 20.3

56 21.3 380.5

S

L

H

SI 542 427.8 789.3 O

42 18 35 400 756 62 1 . 7 15.9 0 . 9 20.4 3.6 305.0 27.3 21.0 5 0 . 1 581.9 8 4 . 5 762.7

D 62 118.6 1912.4

240

LINCOLN LAPAZ

results of this study are presented in Table VI for the three main divisions of meteorites and also for the seven classes defined above. It is of interest to compare these 1954 results with the earlier weight summary of Merrill [35], which showed that as of 1929, the total known weights of all irons, stony-irons, and stones were 195.6, 13.9, and 9.6 metric tons, respectively.

3. METEORITIC ABUNDANCES AND TERRESTRIAL METEORITIC ACCRETION One aspect of the general problem considered in this section is concerned with the extent to which valid inferences regarding both qualitative and quantitative similarities or dissimilarities between the composition of our planet as a whole and that of extraterrestrial matter in general can be based on direct chemical and mineralogical study of the tangible recovered meteorites in contrast to placing reliance on strictly geochemical data or on the indirect evidence afforded by the spectroscope and other devices for the analysis of radiation. A closely connected question-of particular importance t o those who adhere to the planetesimal hypothesis, or to one of its modifications-is concerned with the chemical and mineralogical contributions accruing to the earth body itself from the infall of meteorites, not only in the past, but also at the present time. 3.1. Elemental Abundances in Meteorites

For nearly half a century, the abundances of the elements in the iron, iron-stone, and stony meteorites have been regarded as giving by far the most reliable evidence concerning the composition of cosmic matter in general. The first person to stress this point of view in contrast to placing complete dependence on geochemical data derived solely from study of the thin skin of the earth which alone is accessible to investigation-a localized sample unquestionably strongly influenced by the processes of magmatic differentiation, weathering, solution, and redeposition-was W. D. Harkins. In 1917, in a fundamentally important contribution from the Kent Chemical Laboratory of the University of Chicago [36], Harkins not only formulated his now famous rule concerning the striking relationship between the atomic weights of the elements and their abundances in the meteorites, as well as in other matter accessible to direct analysis; but also championed reliance on the meteoritically-derived abundances as best representing the average composition of cosmic material. Twelve years later, H. N. Russell first attempted to estimate from spectrograms the relative abundances of the elements in the sun and in the stars [37]. Russell’s conclusion that the relative abundances were very nearly the same in the stars and the meteorites in general and in the earth in particu-

EFFECTS OF METEORITES ON THE EARTH

24 1

lar is almost universally accepted as valid today, although employment of both his indirect spectral method and of the direct method of Harkins has not escaped criticism on various grounds. As regards the abundance methods based on the study of spectra, the main objections relate, first, t o the difficulty of translating observed spectral intensities into atomic abundances; and, second, to the uncertainty that observations necessarily confined t o a quite thin peripheral shell of the incandescent atmospheres of the sun and the other stars accurately reflect the over-all composition of these enormous bodies. On the other hand, attempts t o circumvent these objections by relying on direct analytical determinations of the composition of the meteorites also have encountered dificulties. Not only has the basic assumption that meteoritic matter is truly representative of all cosmic matter been questioned but, as will become apparent in the sequel, in arriving a t the average composition of meteoritic matter, extraordinary divergences of opinion exist in regard t o the proper manner in which to weight not only the three main divisions of the meteorites, but also the various phases-metal, sulfide, and silicate -present in varying proportions in the individual meteorites themselves. For example, in 1930, Noddack and Noddack [38] regarded the average composition of meteoritic matter as represented by { 100:9.8:68) , where the numbers in the triad are parts by weight of the silicate phase, the sulfide phase, and the metal phase, respectively. I n 1934, the Noddacks [39] revised the triad t o read { 100: 6.7 :14.6). I n Goldschmidt’s classic paper of 1937 [40], the triad is chosen as { 100:10:20); in 1949, Brown [41] took it as { 100:0:67) ;while in 1952, Urey [42], limiting attention to a carefully selected subgroup of chondritic meteorites “instead of averages of the chondrites, achondrites, and irons . . . ,” adopted f 100:7: 10.6). This latter triad is fairly close to the second choice of the Noddacks, a choice also based on the assumption that the chondrites best represent the average composition of cosmic matter. Urey’s 1952 paper contains a much-needed critical discussion of earlier abundance estimates, including several valid criticisms of Brown’s procedures. These latter criticisms can be supplemented by the following objection: To give zero weight t o the sulfide phase, as Brown did, overlooks not only the well-known fact that troilite is one of the first components of a meteorite to be lost as a result of weathering once it arrives on earth; but also the strongly marked tendency of siderites to disrupt along surfaces of weakness marked out in the solid metal by large troilite segregations. Such disruptions must lead to loss, before the falling mass has even reached the earth’s surface, of a very considerable proportion of the troilite initially present in the meteorite. On both counts, the amount of troilite actually observed in recovered meteorites must rep-

242

LINCOLN LAPAZ

resent only a lower bound for the sulfide phase in extraterrestrial meteorites. Since this lower bound considerably exceeds zero, there can be no justification whatever for assigning a null value to the sulfide component. As Urey’s detailed critical re-examination in his 1952 paper of earlier abundance determinations, and of his own results, is supplemented by similar meticulous discussions in a later paper [43], published jointly with Suess in 1956, Table VII, based on the tabulations of elemental abundances given in the two papers just cited probably is as nearly definitive as the present state of analysis permits. Intercomparison of the various values assigned to the individual elements not only by different workers employing the same (direct) method, but also-at least in the case of the lighter elements-by different methods, will enable the reader to judge t o what extent modern research has validated the earlier conclusions of Harkins and Russell. Certain of the more outstanding discrepancies may, of course, reflect weaknesses in the method used to determine the abundances; but evidence to be presented in the next secttion suggests that lack of representative character in that limited sample so far collected from the meteoritic universe is a more significant source of error. 3.2. Observed Meteoritic Contributions to the Earth

From tabulations given in Section 2, it is clear that the greater part of the minerals occurring in meteorites are not immediately recognizable as of cosmic origin, but are found also in terrestrial rocks. Only a very few minerals are distinctively meteoritic and, with the exception of the nickelcobalt-iron alloys of the siderites, these characteristic meteoritic minerals occur in relatively insignificant amounts. As will become clear in connection with our later investigation of the vertical distribution of meteoritic iron in the earth, the great majority of these nickel-cobalt-iron masses have penetrated too deeply to be detected or recovered without instrumental aid. It will be pointed out in a later subsection on meteorite detectors that such instrumentation has been developed in sensitive, stable, portable form only recently, and used in but few meteorite-bearing areas. Consequently, up to the present, meteoriticists have been able to secure information relating only to the most superficially situated additions t o the earth body made by that division of meteorites most easily recognized as such, not only through its unusual chemical composition, but also through its unique structural peculiarities, as reflected in the so-called Widmanstatten pattern (see Farrington [l], p. 92). Because of its complete absence in nature and its extraordinary durability, the meteoritic mineral, moissanite, long ago discovered by Moissan in the Canyon Diablo iron, may appear to be ideally suited not only for

243

EFFECTS OF METEORITES ON THE EARTH

TABLE VII. Atomic abundance5 of the elements. (Calculated on the basis of an abundance of 1 X 108 for silicon.) Goldschmidt (as modiUrey fied by (selected Suess and H. Brown chondrites Urey 1956) 1949 1952) 1H 2 He 3 Li 4 Be 5B 6C 7N 8 0 9F 10 Ne 1lNa 12 Mg 13 Al 14Si 15P 16s 17 C1 18 A 19 K 20 Ca 21 s c 22Ti 23 V 24Cr 25 Mn 26 Fe 27 Co 28Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 37 Rb 38 Sr

-

100 20 24

3.5 3.5

x 10'0 x 100 -

-

100 16 20

8.0 X 106 1 . 6 X 107 2.2 x 107 1500 9000 300 9.0 x 106 to 2 . 4 x 107 4.42 X 1044.62x 104 5 . 1 X l o 4 8.7 X IW8.87 x 106 8.7 x lo6 8.8 X 10'8.82 X lo4 8.2 X lo4 1 . 0 X 1061.0 x 106 1.0 X l o 6 5 . 8 X 1031.3 X l o 4 7.5 X los 1.14 X 1063.5 X lo 6 9 . 8 X lo4 4000-6000 17,000 2100 1.3 x 104t0 2.2 x 105 6900 6930 3500 5.71 X 1046.7 x lo4 5.6 x lo4 15 18 17 4700 2600 1800 130 250 150 1.13 X 1049.5 X lo8 8200 6600 7700 6800 8 . 9 X lo6 1.83 X lo8 6 . 7 X lo6 3500 9900 2900 4 . 6 X 1041.34 x 1 0 6 3 . 9 X 1 0 4 460 460 420 360 160 180 19 65 10 190 250 110 18 480 38 15 25 13 43 42 49 6.8 7.1 15 40 41 41

-

Urey (revised 1956)

100 16 20

L

300

-

Suess and Urey 1956

Aller (astronomica 1953-1954) *

4.00 X 1O1O 3.08 X log 100 20 24 3 . 5 X 10" 6.6 X lo6 2.15 x 107 1600 8.6 X lo6

2.94 X 1010 4.05 X lo9 0.6 1 .o 1580 2.7 X lo6 4 . 9 X 106 1.58 x 107

-

1.73 X lo7

4.38 X lo4 4.38 x l o 4 7.7 x 104 9.12 x lo6 9.12 x lo6 1.78 x 108 9.48 X lo4 9.48 X lo4 7.4 X lo4 1 . 0 X lo6 1.00 x lo6 1.0 x 10' 5.0 X lo3 1.00 X lo4 1 . 9 X l o 4 9 . 8 X l o 4 3.75 X lo6 5 . 2 X l o s 2100 8850 300,000 1 . 5 X lo6 1 . 0 X 10' 3160 4.90 x lo4 28 2440 220 7800 6850 6.00 X l o 6 1800 2.74 X 1 0 4 212 180 11.4 65 4.0 24 491

6.5 18.9

3160 4.90 x lo4 28 2440 220 7800 6850 6.00 X lo6 1800 2.74 x 1 0 4 212 486 11.4 50.5 4.0 67.6 13.4 51.3 6.5 18.9

3900 8.3

x lo4

42 1800 300 1 . 9 x 103 5600 4.8 X lo* 2200 4.4 x lo4 932 2880 2.5 25

-

-

1

244

LINCOLN LAPAZ

TABLE VII. Atomic abundances of the elements, (Calculated on the basis of an abundance of 1 x 108 for silicon.) (Continued) Goldschmidt (as modified by Suess and H. Brown 1949 Urey 1956) 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 55 c s 56 Ba 57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 T b 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 w 75 Re 76 0 s 77 Ir 78 Pt

9.7 140 6.9 9.5 3.6 1.3 1.8 3.2 2.6 0.23 29 0.72 0.2 1.4

-

10 150 0.9 19

-

9.3 3.5 3.2 2.7 2.6 1.o 62 1.7 1.8

-

Urey (selected chondrites 1952)

Urey (revised 1956)

Suess and Urey 1956

9.7 140 0.7 5.9 ? 2.1 0.71 1.3 1.9 2.2 0.27 18 0.79 0.16 1.5

8.9 54.5 0.8 2.42

8.9 54.5 1.oo 2.42 1.49 0.214 0.675 0.26 0.89 0.11 1.33 0.246 4.67 0.80 4.0 0.456 3.66 2 .oo 2.26 0.40 1.44

-

2.1 0.71 1.3 0.35 1.9 0.26 1.33 0.12 0.16 1.5

-

-

0.1 8.3 2.1 5.2 0.96 3.3

0.1 3.9 2.1 2.3 0.96 3.3

1.3 3.3 2.1 2.3 0.96 3.3

1.3 8.8 2.1 2.3 0.96 3.3

1.15 0.28 1.65 0.52 2.0 0.57 1.6 0.29 1.5 0.48 1.5 0.40 14.5 0.12 1.7 0.58 2.9

1.2 0.28 1.7 0.52 2.0 0.57 1.6 0.29 1.5 0.48 0.7 0.31 17 .O 0.41 3.5 1.4 8.7

1.1 0.28 1.6 0.52 2.0 0.57 1.6 0.29 1.5 0.48 1.4 0.26 13.O? 0.07 0.97 0.31 1.5

1.1 0.28 1.6 0.52 2.0 0.57 1.6 0.29 1.5 0.48 0.55 0.32 13.07 0.05 0.97 0.31 1.5

0.664 0.187 0.684 0.0956 0.556 0.118 0.316 0.0318 0.220 0.050 0.438 0.065 0.49 0.135 1.oo 0.821 1.625

Aller (astronomical 1953-1954)

245

EFFECTS OF METEORITES ON THE EARTH

TABLE VII. Atomic abundances of the elements. (Calculated on the basis of an abundance of 1 X 108 for silicon.) (Continued)

Goldschmidt (as modiUrey fied by (selected Suess and H. Brown chondrites Urey 1956) 1949 1952) 79 Au 80 Hg 81 T1 82 Pb 83 Bi 90 Th 92 U

0.27 0.33 0.17 9.1 0.11 0.59 0.23

0.82

-

<2.0

0.21 0.02

0.21 <0.006 0.11 <2.0 0.014

-

Urey (revised 1956) 0.140 <0.006 0.11 0.47 0.144

-

Suess and Urey 1956 0.145 0.284 0.108 0.47 0.144

-

Aller (astronomical 1953-1954)

-

-

-

recognition as a meteoritic addition to the earth, but also as an indicator of sideritic additions to our planet. Unfortunately, as the writer recently has emphasized [44], the existence of a widely disseminated commercial product, carborundum, militates against the usefulness of silicon carbide in this connection. In short, one may fairly say that at the present time it is impossible to appraise the quantitative importance from the chemical and mineralogical point of view of sideritic and dderolitic additions to the earth. On the basis of extensive series of meteorite analyses which he had compiled, Farrington long ago suggested [45] that the composition of the earth as a whole might be the same as the average composition of all recovered meteorites. Washington [46] pointed out that for the purpose of obtaining an average proper for such a comparison, iron and stone meteorites should be taken not in the proportions in which they have been found but, rather, in the proportions in which they have been seen to fall. When such a weighting procedure, based on the assumption that 35 stones are seen to descend for each iron of witnessed fall, was adopted by Washington, the general average for “all meteorites’’ was found to differ but little from the average that would be obtained by limiting consideration to the division of aerolites alone. With such limitation, however, much of the rough general concordance on which Farrington rested his thesis disappears. Indeed, as Merrill has emphasized (see [35], p. 68) close similarities in composition are found only if the terrestrial sample compared with the stony meteorites is limited to peridotites of deepseated origin [47]. Of course, as Merrill himself clearly indicated, one must not overlook the possibility that the character of meteoritic accretion at

246

LINCOLN LAPAZ

the present time is quite different from that of the earth’s geological yesterday. As regards the crust of the earth, gross dissimilarities of composition are encountered which are reduced somewhat only if, in making our comparison, we include in the group of all recovered meteorites Lacroix’s intra-atmospheric meteorites, the tektites, none of which actually have been seen to fall. If we seek to obtain a more accurate appraisal of the purely aerolitic contribution now being made to the earth’s crust by still further limiting consideration to stony meteorites exclusively of witnessed fall, then we encounter a sampling difficulty quite distinct from that occasioned by the deep penetration of the bulk of the metallic meteorites, to which reference has earlier been made. The fragile structural characteristics of the stony meteorites almost invariably lead to the more or less complete disintegration of these bodies as they pass through the region of retardation. Consequently, the aerolites, with very few exceptions, fall as showers, the fragments of which spread out over so-called strewn fields. These fields are elliptical in shape, the major axis of the boundary ellipse usually agreeing fairly well in direction with that of the trace of the meteorite’s path on the earth. As regards dimensions, the major axes generally fall in the range from 2 mi to 20 mi, the minor from 0.5 mi to 5 mi; however, Henderson [48] has advised the writer that he has under investigation a strewn field, the axes of which are of an altogether greater order of magnitude than the maximum dimensions listed above. It may be regarded as most probable that areas of hundreds, if not thousands, of square miles are strewn with fragments falling from a single aerolite shower. This typically wide-spread distribution of the aerolites results, on the one hand, in the greater ease with which one or a few of the members of each such shower can be found; but, on the other hand, it also precludes exhaustive recovery of the large number of fragments that fall in such a shower. I n this manner, the problem of the probable population of meteoritic strewn fields has arisen [49]. The difficulty of this problem can be adjudged from such controversies as the one between Stem [50], Paneth [51], and Spencer [52], over the total population N of the strewn field of the Pultusk aerolite shower. Although the Pultusk field was certainly one of the most intensively searched of all fall-areas, and although no shower has been reported on in greater detail in the literature of meteoritics, nevertheless, Stena evaluated N as only 3000, while Paneth and most other authorities assigned to N a value of the order of 100,000. Spencer, in attacking Paneth’s conclusions, called attention to the lack of any mathematical criteria permitting a quantitative appraisal of the magnitude of N . As this type of population problem is of basic importance

EFFECTS O F METEORITES ON THE EARTH

247

not only in meteoritics but also in many other fields-and yet is susceptible to attack by a quite elementary probability argument-the question will here be treated in some detail. 3.3. Criteria for Estimating the Population of Meteoritic Showers

First, it should be pointed out that, as is implied by the occurrence of such controversies as the one mentioned above, the value of N, which for practical reasons obviously cannot be exactly determined by counting, heretofore has been arrived a t on the basis of personal judgments based on tallies derived from partial and often unsystematic searches of the strewn field. While the incomplete character of such counts has been recognized, the only attempts to remedy this defect are easily perceived to amount to no more than educated guesses as to whether one should double or triple or multiply tenfold the tabulated number of recoveries in order to approximate the true value of N. It is the purpose of the argument which follows to derive algorithms permitting the objective calculation of the probable value of N-or a t least of a lower bound for this quantity-on the basis of observed data. I n the following, we shall restrict attention to a meteorite-sprinkled region R, within which the fallen meteorites constitute an essentially homogeneous group insofar as the probability of discovery is concerned. Often the entire strewn field of a shower comprises such a region, for on reasonably level and uniform prairie or desert terrain, the more complete burial of the larger, heavier masses which travel farthest in the direction of the meteorite’s motion tends to offset the disadvantage imposed by smaller size on the multitude of fragments falling in the other end of the shower ellipse. Where such uniformity does not characterize the entire strewn field, it may be necessary to divide it into subregions, within each of which our basic hypothesis is more or less exactly fulfilled. Such a necessity would somewhat increase the computational burden, but in no wise would require a departure from the reasoning applied in the simpler case to which attention is limited below. If the (unknown) number of meteorites actually in R be denoted by N , then the probable value of this quantity can be calculated on the basis of data derived from two wholly independent, equally intensive searches, S1and S2,of R, conducted as follows: The meteorites, nlin number, found during the first search are marked in a manner not altering their visibility, but otherwise are left undisturbed. The meteorites, n2in number, found during the second search are collected as found. Suppose that c of the n2meteorites thus collected are found already to have been marked during the first search. Under our assumptions, the empirical probability that a particular one of the N meteorites actually present in R will be found by

248

LINCOLN LAPAZ

S1 is simply pl = n l / N . Similarly, p2 = n z / N . 3 Consequently, the expected number of meteorites found during the first search which are also found during the second is e1,2 = p z X nl = (n2 n l ) / N . In the same manner, the expected number of meteorites found during 8 2 which also were found by S1is e2,1 = p l X n2 = ( n l . n2)/N. The value of N which best satisfies the condition imposed by equating the common value of e1,2 = ez,l to the observed number c of common discoveries is

[TI nl X n2

N =

where [f] denotes the integer nearest to the fraction, f. It is interesting t o note that a more elaborate argument directed toward minimization of the Pearson X2-function relevant t o the present problem leads to precisely the result (3.1). It may be inferred that where our basic assumption that the individual meteorites in the strewn field are equally likely to be found is fulfilled, the formula (3.1) correctly predicts the probable total population N of the meteorite shower. Repeated tests of this formula on artificial meteorite showers of known population, N , however, have shown that in practice, it tends to give not N , but about 80% of N . A moment’s reflection will explain this tendency. Our assumption that all N of the meteorites are equally likely (and therefore equally unlikely) to be found is never exactly fulfilled in actuality. As a result, a few of the meteorites are more easily found than their fellows, and therefore are more likely to be found by both S1and S2. Consequently, the number c of common discoveries in practice is larger than it would be in the ideal case and the value computed for N from (3.1) is correspondingly too small. As an example of this tendency, it may be noted that in one artificial meteorite shower with N = 100, the following results were obtained: N 1= 21, n2 = 26, c = 7 , n1 X n,/c = 78. On the basis of such results, it appears that formula (3.1) generally gives a lower bound for N , a quantity whose true value may be as large as 5 [ ( n 1X n2/c)/4]. Although the observational data needed for application of this formula are of the simplest sort, nevertheless, with the exception of one of the subregions of the strewn field of the great achondritic shower of February 18, 1948, for none of the very considerable number of fall-areas heretofore searched have the data necessary for the application of (3.1) been obtained. The universal practice has been t o pick up and carry away the meteorites as they are found. Consequently, meteorite hunts subsequent to the first have always been conducted on depleted strewn *Such ratios have been called discovery coeficients by 6pik in his paper on the diecovery of proper motions by means of the blink microscope [53].

EFFECTS OF METEORITES ON THE EARTH

249

fields. Our next problem is to derive an analog of (3.1), applicable t o the population data which actually have been collected and published. First, let us define two independent searches, S1 and Sz, of a strewn field as of equal merit if the only essential difference between them is that the number of meteorites present in the strewn field a t the beginning of S2 is smaller than it was at the beginning of S1. Suppose that our typical region R is subjected to consecutive searches of equal merit, S1 and Sz, during the first of which a considerable number, nl, of meteorites is discovered and removed from R. Then it is almost certain that the number, nz, of meteorite discoveries made during SZwill be less than nl. Henceforth, we shall restrict attention to cases for which

0

< n2 < n1

The empirical probability that one of the N meteorites present in R prior to the first search will be found during S1 is p1 = n I / N . Similarly, the emprical probability that one of the N - nl meteorites remaining in R after S1 is completed will be found during SZ is PZ = n,/(N - nl). Since the passage of time makes more and more difficult the discovery of meteorites, it is reasonable to restrict attention to cases in which (3.2)

0

< p2

= 6p1

(0

<6 5

1)

From (3.2), the unknown N is found to have the value (3.3)

N = 6n12/(6nl- n2)

Consequently, the parameter 0 must satisfy the inequality 6 > nz/nl, for N is necessarily positive. Regarded as a function of 6 on the range n2/nl < 6 5 1, the quantity N in (3.3) is easily shown to be a decreasing function of its argument. Therefore, N assumes its smallest value on this range for the choice 6 = 1. The resulting value of N (3.4)

N

=

ni2/(n1 - n,)

is again precisely that to which we should have been led by use of Pearson’s X2-criterion for the special (and improbable) case, p2 = pl. It may be inferred that in practice, formula (3.4) will give a very conservative lower bound for the actual total population of a meteoritic strewn-field, and this inference is borne out by tests of (3.4) on artificial meteorite showers conducted by the staff of the Meteorite Bureau at The Ohio State University in 1939-1941. The literature contains a few cases providing the values of nl and n2 obtained in what were approximately two searches of equal merit of the same strewn field, R. The best example is that of the tektite-sprinkled

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LINCOLN LAPAZ

Sherbrook River region, R, twice searched with equal care by the same individuals, Baker [54]. During Baker’s first search, nl = 83 australites were found on the surface in R and carried away; during the second search of this same region, only n2 = 52 australites were thus found. Use of these values of nl and n2 in (3.4) led to the prediction that the probable number of australites present on the surface in R at the beginning of Baker’s first search was N = 222 (see 1491, p. 242). Subsequent searches of R resulted in additional recoveries, bringing the cumulative total t o 250. A similar application of (3.4) to the less satisfactory recovery data so far published for the Holbrook, Arizona aerolite of July 19, 1912, leads, with what the writer regards as the most reasonable values for nt and 722 in the case of the quite homogeneous subgroup of “Holbrook peas” (specimens “as like as two peas,” whence the name [55]), to a total population N = 80,000, a value ten times the sum (nl n2 = 8000) of all recorded recoveries of these so-called “peas” made up to 1956 in this strewn field. The ratio of number of actual recoveries to probable population N in the Sherbrook River and Holbrook cases suggests that one meticulous scientist will carry out a far more exhaustive search of a strewn field than is effected by large but heterogeneous groups of paid meteorite hunters, such as were employed to work over the Holbrook area. Finnegan 1561 has proposed that a recovery index, I , be introduced to give an indication of the relative exhaustiveness with which different strewn fields have been searched. He defines the index I by the relation I = 100D/N, where D represents the actual number of individuals recovered in a strewn field of which the (probable) population is the N of formula (3.4), or, preferably, if data are available for its calculation, the N of formula (3.1). For the Holbrook rtpeas,” I = 10%; for the Sherbrook australites, I = 61%. The concordances between computed and observed values of N not only in the case of exhaustively searched natural strewn fields like Sherbrook River, but also in the case of numerous artificial strewn fields of lesser extent resulting from man-made meteorite showers, justify the view that, in general, formula (3.4) provides a fair but ultra-conservative lower bound for N . Furthermore, similar tests have definitely established that where controlled systematic searches, S1, SZ, of a strewn field are carried out in such a way as to give a dependable value of the number of common discoveries c as well as of n1 and n ~formula , (3.1) leads to a satisfactory but almost invariably quite conservative determination of the total population N . Nevertheless, the above discussion will clearly point up the undesirability of relying solely on visual searches supplemented

+

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by calculation in attempting to appraise the contribution to the earth accruing from a meteorite shower. On the one hand, in a sideritic strewn field, it is only too certain that the visual recovery index I will crowd zero, not 100%. On the other hand, the practical difficulties of insuring really scientific meteorite collection procedures seem insuperable. One’s own party may be rigidly subject t o proper rules, but this offers no guarantee that commercially minded meteorite collectors or souvenir-hunting natives of the area will not intrude upon the discovery region and upset all calculations, as occurred in the case of the achondrite shower of February 18, 1948, in Kansas and Nebraska. Such considerations as the above, reinforced by a mathematical investigation of the vertical distribution of iron meteorites in the earth provided the impetus for the developmeiit a t The Ohio State University in the early 1930’s of meteorite detectors of several types which permit a really exhaustive pickup of sizeable meteorites, not only on the surface of a strewn field, but also throughout a three-dimensional volume beneath this surface. These temperamental but highly effective instruments will be considered in the next subsection; and an attempt a t a quantitative appraisal of the accretion resulting from infallirig meteorites will purposely be deferred until the surprising results obtained by use of meteorite detectors have been presented. Before concluding the present subsection, however, it seems desirable to call attention to another factor which may materially affect the accuracy of estimates of meteoritic accretion, namely, uncertainties entering into the determination of meteorite densities. A measure of the importance of accurately determining meteorite densities is provided by a calculation carried out by Foster [57] on the basis of the writer’s preliminary estimates of the annual sideritic accretion to the earth’s mass [58]. Foster showed that an error of only 0.01 gm/cc in the determination of the average density of the iron meteorites would result in an error of the order of 106 gm per year in the calculated annual sideritic accretion. He then pointed out several ways in which errors of from 0.01 gm/cc t o 0.04 gm/cc could arise in routine density determinations. In the case of comminuted meteoritic material, such as the powdered eristatite (magnesium silicate) that descended to earth in enormous quantities soon after the fall of the Norton County, Kansas-Furnas County, Nebraska achondrite (see [12], Plate IX), still larger errors may be encountered if-in the attempt to avoid dissolution and loss of valuable meteoritic material-liquids other than the standard immersion fluid, water, are employed in the process of density determination. Culbertson and Dunbar, for example, cite a silica powder which gave a density of 2.246 gm/cc in water but only 2.149 gm/cc when immersed in benzene [59].

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3.4. The Detection and Recovery of Meteoritic Material

This section is devoted t o a discussion of the various methods which have been and are being used to locate and recover meteoritic material. Such methods range from purely visual search for surface fragments to the utilization of complex electroiiic meteorite detectors designed for the

FIG.1. A. Electromagnetic cane.

location of deeply buried meteoritic masses. The impetus leading t o the development of such meteorite detectors was the writer’s discovery, on the basis of a mathematical investigation, that as far as sideritic material is concerned, something of the order of 100,000 times as much meteoritic materia.1 lies buried below maximum plow depth as above this depth. Since the major role played by the plowman in the recovery of meteoritic

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material is well known, the result just cited made quite clear the urgent need for devices capable of detecting deeply buried meteorites (see [58], p. 112). 3.41. The Search for Superjicially Buried Meteorites. Visual search has been employed successfully in the recovery of small surface meteorites at the Barringer and Odessa meteorite craters. Furthermore, in these areas, location by visual means of a restricted area of ground marked by the “outcrop ” of paper-thin laminae of meteoritic shale frequently was an excellent indication that a solid iron met,eorite of considerable size lay at a shallow depth below the surface. The success of visual field investigation is necessarily limited, however, and it has been essent,ial to supplement such search in various ways. The

FIG. 1. B. A 5000-gauss Alnico magnet mounted for field search.

first auxiliary to be used took the form of a steam plow which tore up meteorite-enriched soil to considerable depths. In another direction, crude magnetic collecting devices were employed tQpick up meteoritic materials, oxidized and otherwise, on or near the surface of the ground. At both the Barringer and Odessa meteorite craters, ordinary horseshoe magnets mounted on the end of a stick were often utilized in searches for surface meteorites. However, the very shape of the horseshoe magnets and the difficulty of attaching them firmly to the handle precluded use of these devices as prods to be pushed vertically downward several inches into the meteorite-bearing top soil. In addition, prior to the development of Alnico alloys, the most powerful horseshoe magnets available could not match the powerful magnetic fields developed about small but properly designed and energized electromagnets.

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An electromagnetic I' cane '' therefore was constructed as a valuable field adjunct in the search for meteorites a t shallow depth [60]. This cane, shown in Fig. lA, consisted of a small coil (1) of No. 20 enameled wire wound on a brass tube (2) of diameter 3.5 cm and length 4.0 cm, which could be slid up and down on a light, but strong, iron rod (3) of diameter 1 cm and length 50 cm, provided with a comfortably shaped wooden handle. In the photograph, the coil is shown in the position proper for picking u p surface meteorites; that is, the base of the coil is about 4 cm above the end of the iron rod. For deep test probing in soil or sand, the coil could be set much higher up on the iron rod. The electromagnet was connected by leads ( 5 ) to a power source carried in the knapsack (6). When using a Burgess uniplex, light-weight, heavy-duty, 6-volt battery, the electromagnetic cane would readily pick up an Odessa iron weighing more than one pound, and would cause smaller meteoritic fragments t o make surprisingly long leaps to the collecting tip (7). I n order t o avoid overheating caused by the strong batteries, a toggle switch (8) was mounted on the wooden handle, and the circuit through the coil was kept closed only for the very brief periods necessary to pick up surface meteorites or to identify subsurface objects. As a result of wartime developments, exceedingly powerful Alnico magnets, designed for use with magnetrons, have recently become available t o the field meteoriticist. These new-type permanent magnets not only rival all but the most powerful portable electromagnets, but also enable the meteoriticist to dispense with such bulky battery power supplies as that carried in the pack sack shown in Fig. 1A. I n use, these magnets may be simply dragged behind the operator, as was done by V. B. Meen in the search he conducted of the environs of the Chubb Crater with a magnetron magnet loaned to him by the Institute of Meteoritics [61]. Preferably, however, these magnets should be mounted on a light wooden sled in such a position that the pole pieces are tilted downward against the ground, as shown in Fig. 1B. The type of meteoritic material collected by weak permanent magnets or by small electromagnets is quite different from th a t collected with the powerful Alnico drag magnets. With the former, unless search is confined t o the greatly enriched terrain about a meteorite crater, one picks up-except by accident-only visible specimens, the weaker magnet serving simply as a lengthened arm. On the contrary, a three-dimensional volume is swept quite clean by the drag magnets. An examination of the collections made also shows that, as might be expected, the eye picks up only the relatively large meteorites. The ground a t Canyon Diablo, which is richly impregnated with tiny particles of meteorites and meteoritic shale ranging down t o those of microscopic size, yields a full harvest of meteoritic material

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only t o the powerful Alnico magnets or their electromagnetic equivalents. The fact that such meteoritic impregnation of the soil a t the Arizona crater occurs has, of course, been known since the earliest days of the Barringer-Tilghman explorations of this topographic feature half a century ago. Nevertheless, recently scientific j ouriials [62] uncritically have given publicity t o baseless assertions that meteoritic granules in the topsoil a t and around the Barringer meteorite crater “were first identified early in 1948 . . . after . . . they had eluded all investigators during the past half century.” The record has been set straight in a brief historical note by the writer [63]. The techniques described up t o this point obviously relate chiefly to the search for surface meteorites or, a t most, meteorite deposits buried at shallow depths. However, the penetration data secured from studies of observed falls, together with the well-known fact that many old meteorites have been plowed u p or found during well digging or other excavation, show that meteorites do not merely fall upon the earth, but that they often actually penetrate into it, sometimes t o considerable depths. I n instances where several meteorites of widely differing masses have struck equally resistant earth-targets-as has occurred in certain of the great meteoritic showers-the measured depths of penetration of the various pieces suggest that, other factors being equal, meteoritic penetration is proportional t o the cube root of the striking mass, i.e., for spherical shape and an assigned density, to the radius of the meteorite. An immediate inference is that, in general, the really large meteorites and, particularly, the dense siderites, bury themselves deeply a t impact. On the other hand, it is recognized that the number of large meteorites which fall is small in comparison t o the total number of meteorites of all sizes reaching the earth. Since it is not immediately apparent which of these influences will predominate in determining the vertical distribution of sideritic material in the earth, a mathematical investigation is necessary t o decide whether the average meteoritic iron mass in a stratum situat,ed at considerable depth is greater than or less than the average meteoritic iron mass in a layer of the same thickness near the surface of the earth. 3.42. The Vertical Distribution of Meteoritic Iron in the Earth. Consider a spherical cap on the surface of the earth, of inradius a so small that the cap may be regarded as essentially a circle of area A (in terms of the surface area of the earth taken as unity), lying in a plane P’, tangent to the earth in the point, 0. Choose 0 as the origin of a n xyz-coordinate system with the y and z axes in the plane P’, and with the positive x axis directed‘downward along that radius of the earth terminating in 0. As noted above, the total penetration of a spherical iron meteorite into a n

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earth target is a function of the radius of the meteorite. Consequently, the same is true of the depth to which the center of such a meteorite is carried beneath the plane P'. Consider a spherical iron meteorite of radius r imbedded in the earth near 0 with its center at a distance (3.5)

d = d(r)

beneath the plane P', Evidently, the entire meteorite is contained between the planes x = d ( r ) - r and x = d ( r ) + r. The given meteorite will therefore have an element of volume lying between the planes, x = x and x = x dx, if, and only if, its radius r satisfies the relations

+

+

d(r) - T < z < d(r) T (3.6) which implicitly determine the range of values within which r must lie. To obtain this range explicitly, we shall suppose that for a given x, the function rl(x) denotes the radius of the smallest meteorite which just attains a penetration to the depth x = x. With this definition, rl(x) can be evaluated by solving for r the equation

+

d(r) r = x (3.7) for the left member of (3.7) is the depth of the lowest point on a spherical meteorite of radius r. Similarly, if we denote by r2(x) the radius of the largest meteorite which does not penetrate too far into the earth to touch the plane z = x,then r2(x) can be determined by solving for r the equation

d(r) - T = z (3.8) Since both of the functions fl(r) = d ( r ) r and ~ Z ( T ) = d ( r ) - r are monotonic increasing functions of r, the values of T satisfying the condition

+

rI(x) < r < ~ 4 x 1 (3.9) and only such values also satisfy the earlier relation (3.6). In view of the equivalence of (3.6) and (3.9), it follows that a given meteorite has an element of volume lying between the planes x = x and z = x dx if, and only if, its radius r satisfies (3.9). Suppose that this equality is satisfied for the particular meteorite under consideration; then the plane x = x actually intersects the meteorite in a small circle of radius (3.10) p ( r ) = ( T 2 - [d(r) - 5]2]$* Thus, the element of mass contributed by the siderite to the total amount of meteoritic material lying between the planes specified above is

+

dM = h[p(r)12 dx where 6 is the density of meteoritic nickel-iron.

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It has been conjectured that the number of meteorites, and, in particular of iron meteorites, falling annually on the earth was larger in remote times than it is a t present [64]. However, if, as seems probable, the siderites are of interstellar origin, this view may be questioned. In the sequel, we shall suppose that the number of iron meteorites with radii between r and r dr striking the entire earth annually is given by No(r)dr and, hence, is independent of the time. It should be noted, however, that if Paneth’s view is correct, then the results we shall obtain on the basis of our supposition will give underestimates of the amount of meteoritic iron buried in the earth. At the end of t years of sideritic infall, the element of the total meteoritic mass lying between the planes x = x and x = x dx contributed by all iron meteorites with radii between r and r dr falling within the dr dx. Hence, the total meteoritic iron circle of area A is AGrrtNo(r)[p(r)]2 mass lying between the planes x = a and x = b > a is

+

+

+

(3.11) Consequently, if a < b 6 A < B , then the ratio q of the total amount of meteoritic iron lying in the strata between depths of B and A , and b and a, respectively, is given by the formula

(3.12) On the basis of the observed penetration of iron meteorites for which the radius of the meteorite, or of its spherical-equivalent, was r cm, we are led to take d(r) = 5r. It is then found that the inner limits of integration of the double integrals in (3.12) have the values x / 6 , x / 4 , respectively. On computing the value of q with A = b = 25.4 and with values of No(r) consonant with observational data, the writer found (see [58], pp. 111112) that something of the order of 100,000 times as much sideritic material lies buried below maximum plow depth (25.4 cm) as occurs above this depth. Even though the per cent of the total number of meteorites found by the plowman is large, the actual number of meteorites found in this manner is surprisingly small if account is taken of the vast tracts of land which are under cultivation. Since the areal extent of systematic excavations carried to depths exceeding 25.4 cm is, and probably will long remain, vanishingly small in comparison with the extensive acreages plowed up, it becomes clear that there is most urgent need for instruments designed to detect the presence of deeply buried masses of meteoritic iron.

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3.4.3. Meteorite Detectors. An iron meteorite buried in the ground is a n example of a n object hidden in an opaque medium. Clearly, detection of such a n object is dependent on the condition that some of its physical properties differ from those of the medium in which it is embedded. In the case of a buried siderite, the magnetic permeability of this body is one such property. I n comparison with that of rock or soil, the magnetic permeability of a n iron meteorite is quite large. For example, unoxidized meteoritic material from the Canyon Diablo, Arizona, area has been found to have a magnetic permeability over a million times greater than that of the sedimentary rocks in which the Barringer meteorite crater was formed [65]. The unusually large magnetic permeability of a buried iron meteorite produces changes in the natural magnetic field of the earth in the vicinity of the meteorite. These changes, if sufficiently pronounced a t the surface of the earth, can be measured by means of devices known as “magnetic balances,” of the type employed in Sweden and Norway in prospecting for buried iron ores. The ordinary dip-needle is the oldest and simplest such balance [SS]. I n meteorite hunting, this relatively crude device seems t o have been the first instrument used in field investigations; and, as late as 1932-1933, in spite of unsatisfactory performance, ordinary dip-needles were still employed at Canyon Diablo [67]. Long before this date, however, such refined equipment as the Hotchkiss Superdip [68] and various forms of stable, portable magnetometer had become available. Results of field search employing these more modern instruments have been quite satisfactory, and the devices in question would seem well adapted for such definitely localized investigations as the search for subsidiary meteorite craters surmised to lie buried in the immediate neighborhood of known meteorite craters. Buried iron meteorites, in addition to magnetic effects, may, under suitable conditions, produce measurable electric effects a t points on the earth’s surface above them. It is easy to enumerate such possible electric effects in terms of the following fundamental electric phenomena:

(1) The field of dielectric force set u p b y an electric charge. (2) The current (and associated magnetic field) set up by such a charge in motion. (3) The electromotive force (and associated notion of potential) appearing when a current passes through a resistance, as it must in any physical situation. 4 In 1940, a small buried crater, approximately circular in outline with a diameter of 70 f t and a depth of 17 ft, was located near the main Odessa crater by such a magnetometric survey conducted by the Humble Oil and Refining Company, in collaboration with the University of Texas.

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(4) The electric-cell effect, arising when two dissimilar conductors are so arranged as t o produce an electromotive force by electrochemical or thermoelectric action. The first and fourth of these effects offer little promise in connection with the detection of meteorites; and the potential-drop-distribution method based on the third effect is applicable only to objects of considerable size (and even for such objects only in case the specific resistance of the object differs greatly from that of the surrounding medium). Consequently, the effects in the second category remain as the only source of practical meteorite detection methods. Such so-called electromagnetic methods may be subdivided into those which are concerned with the differential of flux density and those which depend on magnetic field distortion. The flux-density method rests on the fundamental fact that if the flux originating from a coil is caused to change slightly, then the coil will show a n increment of inductance directly proportional t o the change in flux. One of the modifications of the Wheatstone bridge may be employed to measure this increment of inductance. This scheme was utilized in certain of the “dud-detectors” designed in Europe to locate unexploded shells buried in fields slated for recultivation following World War I. Since i t is impossible to build a search-coil with pure inductance, the performance of these devices was not satisfactory. The search-coils used on these instruments always have associated with them an internal resistance and a distributed capacity. Consequently, the bridge employed can be balanced with a given setting for one frequency only. For all other frequencies, the bridge is out of balance, and the instrument will react in the same manner as if a metallic object had been brought near it. A more promising flux-density method would seem to be the beatfrequency-oscillator system. I n this method, the inductance of the searchcoil is used t o control the frequency of a vacuum-tube oscillator. Unfortunately, many and serious difficulties are encountered in the development of instruments of this type which possess the stability essential for satisfactory performance under the conditions enountered in a field search for meteorites. Finally, we come to instruments designed to measure the magneticfield distortion produced by proximity to metallic masses. It is a wellknown fact that when a ferromagnetic mass is brought into the magnetic field surrounding an energized coil, the flux from the coil is attracted and reinforced by the mass in question. Consequently, the coil giving rise t o the field will exhibit a positive increment of inductance. Foucault currents will be induced in the meteorite if the field intensity oscillates, and the

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existence of these currents will set up a counter-magnetomotive force in such a direction as to oppose the impressed field and, hence, to neutralize a portion of it. This “eddy-current effect,” as it is called, repels and diminishes the impressed field. As a result, among other things, the coil exhibits a negative increment of inductance. The positive effect is independent of the frequency of the energizing current, but the negative effect is proportional to this frequency. For a meteorite of given size, therefore, a frequency of operation exists at which the net distortion and, with it, all possibilities of detection vanish. This is only one of a number of facts which must be considered in deciding at what frequency a magnetic-fielddistortion instrument should be driven. Under the assumption that a frequency of operation is employed at which the net distortion does not vanish, we proceed to an examination of the two chief methods by means of which this distortion can be measured. For the most part, commercial instrument-makers have specialized in the construction of what may be designated as perpendicular-coil detectors. Such instruments consist of a horizontal (vertical) “power” coil or transmitter rigidly joined to a vertical (horizontal) pickup coil by handles having a length of several coil diameters. In the absence of meteoritic material, these instruments may be brought into a condition of balance in which a vanishingly small portion of the flux emanating from the power coil is linked by the pickup coil. The mutual inductance is zero in this condition, and no signal is induced in the pickup system. If the instrument so adjusted is carried over a meteorite, the resultant field distortion results in linkage of power-coil flux by the pickup coil. A voltage is thus induced in the pickup system and, boosted by suitable amplification, this voltage reveals itself either as a signal tone or as the deflection of an indicator needle, or both. The following difficulties were encountered in the use of perpendicularcoil instruments as meteorite detectors on the First and Second Ohio State University Meteorite Expeditions in 1939 and 1941: A weight excessive in view of the long hours required to search extensive meteoritestrewn areas; sizes and shapes precluding convenient use on steep, brushed slopes like those on which the lost Port Orford, Oregon, meteorite is probably located; the necessity of frequent awkward adjustments; excessive battery drain; sacrifice of rigidity for the sake of portability; spurious signals, for example, from lightning; and loss of effectiveness over moist ground or over soil irregularly impregnated with comminuted ferromagnetic material, Some of these difficulties have since been eliminated by the trend toward miniaturization and, particularly, by the introduction of transistorized equipment; but certain difficulties, e.g., the last one mentioned, seem inherent in the perpendicular-coil type of instrument.

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Instruments of quite different design from the perpendicular-coil detectors have been used with considerable success in several investigations where search has been made primarily for ferromagnetic masses such as unexploded airplane bombs and iron meteorites. The forerunner of all such instruments appears to be the “N.A.C.A. Bomb Detector,’’ designed in 1930 by Theodorsen [69], “For the immediate purpose of locating unexploded bombs which were known to have been dropped from airplanes a t targets in close proximity to the site of the new Seaplane Towing Channel at Langley Field, Virginia.” I n the original Theodorsen bomb-detector, three coils were wound symmetrically on a hollow, cylindrical, wooden frame three inches thick, three feet in diameter, and 1% ft high (Fig. 2). A special 110-volt, 6-amp \ \ \ I /I,’ generator, furnishing 500 cps current, ener\ I 1 1 1 \ \ gized the central or power coil, the strong \ \ 1 1 l ’ / \.\ I I I / alternating field supplied by the power coil :’ 1\ I I( II ’l I’ // : inducing electromotive forces in the nearby pickup coils, which were so connected th at \II ‘ only the difference of the emf’s appeared I+$\\ across a telephone receiver connected in i/ I I 1 I I \. /+I1 series with the pickup coils. When the / / ’ 1 1 \ \ instrument was in balance, one pickup coil I \\ \ \ was an “image” of the other with respect FIG. 2. Theodorsen coil. to the central power coil, and no current flowed through the receiver. If the device were carried over a buried bomb, the resulting distortion of the magnetic field destroyed this condition of balance and a signal was heard in the phones. Because of the weight of the cylinder on which the coils were wound, two men were required t o carry the instrument, which was suspended from a ladder-like frame by means of ropes in order to minimize flexure. A large powersupply truck was necessary in field work in view of the great weight of the generator used. A consideration of the cost and the weight of the Theodorsen apparatus will lead t o the conclusion th at no matter how satisfactorily it performed, this type of device would not be suitable for use by the meteorite hunter. I n this age of electronic gadgeteering, however, many possible modifications of the N.A.C.A. instrument speedily suggested themselves; and several of these were developed into first-rate meteorite detectors by the staff of the Meteorite Bureau at The Ohio State University in the 1930’s. Firstly, large scale, three-coil instruments were constructed which could be energized by standard, portable, gas-engine-driven 110-volt generators, of a size suitable for mounting in the luggage compartment of an automobile. Secondly, portable, three-coil instruments energized by

+-+ i$

\‘;

;/q;\

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vacuum-tube oscillators and small enough to be carried in a knapsack were built. Finally, a variation of the vacuum-tube meteorite detector, employing only one pickup coil and one power coil, was designed and constructed by Wisman and the writer in 1940 [70]. Even before miniaturization, this two-coil instrument had an exceedingly small battery drain and could be used anywhere a man was able t o walk or climb. With a search-coil only 10 in. in diameter, the two-coil instrument had a performance comparable to that of Theodorsen’s bulky, three-coil detector and, furthermore, would clearly pick up a 15-lb Odessa iron buried a t a depth of 12 in. in a water-filled hole in muddy ground-a crucial test none of the many perpendicular-coil instruments studied a t The Ohio State University would pass satisfactorily. Since World War 11, numerous attempts have been made t o employ land-mine detectors in the search for meteorites. Many instruments in this category have become available as war-surplus items. All were designed for a specific purpose, namely, the detection of military mines buried a t shallow depth. If this design limitation is kept in mind by the user, late model land-mine detectors like the SCR-625, in perfect adjustment, give satisfactory performance. Theodore Johnson, formerly custodian of the Barringer Meteorite Crater Museum, once informed the writer that more than 10,000 small Canyon Diablo meteorites-none buried t o depths in excess of a few inches-had been recovered by use of landmine detectors in the years between 1946 and 1950. W. A. Cassidy and H. L. Baldwin, Research Assistants of the Institute of Meteoritics, have had equal success with such instruments in shallow searches conducted about the Odessa, Texas meteorite crater. To the writer’s knowledge, however, no large meteorites buried at great depth, like the 130 kg “accordion meteorite’’ found near the Odessa meteorite crater, embedded in limestone a t a depth of over a meter, by the First Ohio State University (OSU) Meteorite Expedition in 1939 [71] have been recovered by the use of land-mine detectors. Before concluding this subsection, evidence must be presented testifying a t once to the large proportion of the iron meteorites buried at considerable depth and t o the efficiency of well-designed meteorite detectors in locating such deeply buried masses. Understandably, such evidence has been collected almost exclusively about meteorite craters, for almost all really systematic instrumental search has been confined to the meteorite-enriched areas surrounding such craters. It should be noted that the sample secured by search of these areas is biased in favor of shallow burial, for most of the meteorites recovered in such regions are “fragments” thrown out at the instant of the crater-forming explosion. These fragments strike the earth a t speeds very low in comparison with

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those possessed by the “outriders,” i.e., smaller, companion meteorites that accompanied the main crater-forming mass in its orbital motion. The “outriders” show a depth of burial which increases roughly as the cube root of the mass, and hence for large meteorites may amount to several feet. Equally heavy “fragments” may be buried only slightly below plow depth.5 Although more meteorite hunts have been carried out around t,he Barringer meteorite crater than in any other locality, nevertheless, the data t o be presented below do not relate t o finds made at the Arizona crater. The reasons for this are as follows: On the one hand, recoveries made during systematic steam-plowings t o depths far in excess of normal plow-depth had depleted large areas about the Barringer meteorite crater years before meteorite detectors appeared on the scene at all. On the other hand, prior t o the Ohio State University Meteorite Expeditions of 1939 and 1941 t o the Barringer crater, a great many commercial meteorite hunters and curiosity seekers had worked and reworked (often surreptitiously) the entire environs of the crater with meteorite detectors of one kind or another, without publishing any information concerning either the capabilities of the instruments used or the weights of the finds made a t depth. Consequently, no amount of care on the part of OSU personnel could guarantee collection of dependable observational datla with respect t o the amount of Canyon Diablo meteorites originally buried in strata a t various depths. In contrast t o the confused situation just described, the field work carried out by the First Ohio State Meteorite Expedition a t the Odessa meteorite crater between September 15 and 17, 1939, was conducted on what, a t least from the viewpoint of instrumental search, was essentially virgin ground. Prior to August, 1939, occasional brief visual searches for meteorites had been carried out-chiefly a t the Odessa crater itself-and a number of small surface finds had been made, the largest specimen recovered having a reported weight of about 8 lb. During the three weeks prior t o arrival of The Ohio State University party a t the crater, a group of approximately thirty WP.4 workers, employed on the recently initiated WPA-University of Texas Odessa Crater Project, had searched for meteorites diligently, but without instruments, not only a t the crater, but over a region of several square miles surrounding it. This search was an intensive one since the very continuance of the WPA-University of Texas Project depended on discovery of enough meteoritic material t o prove tha t the Odessa crater had originated in large-scale meteoritic impact, 6 The terminology employed and results stated stem from observations made during instrumental surveys of the Odessa and Canyon Diablo meteorite craters in 1939 and 1941 [72].

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thereby justifying proposed elaborate and expensive excavations in and about the crater. In spite of this compulsion, the widespread visual search had resulted in the discovery of a single meteorite weighing less than a pound at a distance of over half a mile from the crater rim. Because of high winds, it was possible t o employ the meteorite detectors effectively only during the early morning and the late afternoon. In spite of this fact, in less than 12 hr work during the interval September 15-17 over 400 lb of Odessa octahedrites were recovered from depths between 8 and 40 in. This instrumental search was not confined to areas contiguous to the crater, but rather covered a number of small subregions distributed in various directions and at various distances from the crater. Since the area swept over by the instruments was certainly much less than one-thousandth of that covered by the earlier WPA search, the ratio, q, of deeply buried iron to superficially embedded iron may conservatively be set at 400,000. It is of interest to note that a value of Q of the same astonishing magnitude is clearly indicated by the weight-depth of burial data now becoming available as a result of the exhaustive explorations carried out by several successive meteorite expeditions sent by the Meteorite Committee of the U.S.S.R. to investigate the strewn field of the massive granular-hexahedrite shower of February 12, 1947-a witnessed crater-producing fall in contrast to the Odessa fall, which occurred in remote prehistoric times. 3.5. The Rate of Accretion of Meteoritic Dust

I n earlier sections of this review, it has been-pointed out that no dependable appraisal of the rate of accretion of sideritic materials is possible until exhaustive instrumental surveys have made trustworthy information available concerning the distribution of meteoritic iron in that considerable three-dimensional volume accessible to deeply-penetrating siderites of high sectional density. Again, dependable appraisal of the rate of aerolitic accretion will become possible only when meteoritic strewn fields are subjected to such systematic searches as those basic to application of population criteria of the sort described earlier in this chapter. Although the determination of what might be termed “ordinary” meteoritic accretion thus seems to be a problem for future investigation, the opinion has been widely held for some time that reasonably dependable estimates of the rate of accretion of meteoritic or, as it is commonly called, “ cosmic ” dust are possible. The excellent historical review presented by Buddhue [73], together with the comprehensive annotated bibliography on meteoritic dust later published by Hoffleit [74], will serve to give the reader a complete picture of the exceedingly diverse

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collection techniques employed prior to 1951 at stations scattered all over the globe, and of the manner in which the crude data of observation have been used to obtain rate-of-accretion estimates. Among the investigations in this field carried out since 1951, special mention should be made of the systematic and carefully controlled research on the abundance and rate of infall of meteoritic dust carried out under an ONR-supported Airborne Particle Study by the group at New Mexico Institute of Mining and Technology supervised by W. D. Crozier. Many interesting conclusions have been reached by the NMIMT group, three of which merit special emphasis: first, that a global rate of infall of magnetic spherules of 230,000-265,000 metric tons per year is indicated by NMIMT data; second, that the maximum contribution to this total is made by spherules with diameters in the neighborhood of 15 microns; and third, that magnetic spherules like those obtained from the atmosphere have been found not only in lake sediments in New Mexico but also in clay from Georgia and in water-deposited shale of upper Cretaceous or lower Tertiary age collected near Datil, New Mexico. Because, whatever their particular origin, cosmic dust particles are quite small (ranging in size from a few microns to a maximum of at most 250 p ) , their rate of descent through the atmosphere is always very slow. Having regard to the diverse motions of the medium through which the dust particles fall, their long-continued interaction with it apparently has been considered to guarantee widespread uniformity in the distribution of meteoritic dust, from whatever source, over the face of the earth. Therefore, the simplest, single-station collection techniques and identification procedures seem to have been regarded as adequate for determination of the world-wide rate of accretion of such dust. This view receives no support, however, from such extremely divergent estimates of the accretion rate in question as those to be presented later in this section. In place of the penetration and population difficulties earlier encountered in connection with appraisal of the contribution of the siderites and aerolites, respectively, a new difficulty-that of identification as cosmic dusl-arises to prevent realization of the optimistic forecast given above. Because of the complexity of the identification problem, a controversy dating back a t least to the contributions of Nordenskiold [75] and von Lasaulx [76] has remained unresolved for nearly a century; and even today it calls forth such flatly contradictory opinions as those held by Buddhue [73] and Krinov [77]. Vincent J. Schaefer’s development in 1946 of an etching technique applicable to minute particles under inspection through the electron microscope may eventually provide a thoroughly dependable criterion

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which will permit the investigator t o distinguish between the various cosmic and terrestrial magnetic dusts. Since the equipment necessary for application of Schaefer’s tests is at once expensive and quite difficult t o obtain, there is need for an inexpensive alternative test. Because of the past history of dusts of extra-terrestrial origin, arriving as these do from lengthy sojourns in space and in the higher layers of the earth’s atmosphere, i t would seem certain that meteoritic dusts would exhibit cosmic radiation effects not present in earth-bound terrestrial dusts. Conceivably, well-known and economical nuclear-emulsion techniques would permit detection of the anticipated differences in cosmic radiation effects. The writer suggested such a n autoradiographic test t o V. H. Regener in 1948. TABLE VIII. Estimates of the rate of accretion of meteoritic dust. (Based on tables earlier prepared by J. D. Buddhue and P. M. Millman.) Annual deposit (in metric tons) 8

26 56 100 332-3320 810-129,600 332,000-3,320,000

Source Black spheres from abyssal red clay deposits only From meteors only From meteors only From meteors only From fireballs; visual meteors; faint radio meteors; telescopic meteors Meteoritic dust brought down in rainfall From faintest telescopic meteors; micrometeorites; zodiacal dust

References Buddhue [73], p. 50 Watson [80] Watson-Buddhue [all, p. 115, Table 19 Watson [Sl] Millman [82] Buddhue [73], p. 54 Millman [82],p. 81

Pending development of dependable identification criteria based on electroumicrography, autoradiography, or on some or all of the tests employing chemical, microchemical, and physical means well summarized by Buddhue in 1950 (see [73], pp. 44-49), there would seem to be no alternative but t o present all of the recently published estimates of the rate of accretion, grossly discordant as these estimates may be. The decision to keep a n open mind in this question finds support in the fact th a t recent accretion estimates of the order of several thousand tons per day for the whole earth have won strong approval from Opik [78], but have been criticized by Whipple [79]. Inspection of the trend in Table VIII will bring conviction of the need t o set a n upper bound on the annual increment of cosmic dust received by the earth, preferably by an argument divorced as completely

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as possible from dust collection and identification difficulties. We shall conclude this section with a calculation directed toward this end. Accumulation of meteoritic dust on the surface of the earth, by increasing the moment of inertia of our globe, must decrease the speed of its rotation and hence increase the length of the day. Since an incomparably more potent agency, that of tidal friction, also acts in the same direction, the total observed increase in the length of the day, say AT, must greatly exceed that attributable solely to the accretion of cosmic dust. To calculate the amount of dust that would be necessary to account for the whole of AT would, of course, give an upper bound on the annual meteoritic increment to the earth, but a bound of such magnitude as to be without interest. We therefore shall suppose that only a minute fraction, e * AT(0 < 0 << 1) of the observed secular increase in the length of the day can be assigned to a meteoritic source; and shall then carry through the calculation suggested above with AT replaced by 0 AT. Later, by assigning a numerical value to 0 on the basis of a remark of W. D. MacMillan, we shall be led to a reasonable upper bound on the total amount of meteoritic accretion. Those unwilling to accept MacMillan’s est,imate of e, may substitute values of 0 more to their liking in the general formula derived below and determine the corresponding upper bounds. The problem of calculating the increment, A I , in the earth’s moment of inertia, I , due to the infall of meteoritic material has been considered by Woodward [83] and Stoney [84].Each of these writers limited attention to the effects produced by the gradual accumulation of meteoritic material on the surface of the earth; although, as Stoney pointed out, there are at least two other ways in which invading meteoritic material conceivably may affect the rate of rotation of the earth. By taking into account the decrement in the moment of inertia of the earth-body surrounded by the shell of accumulated meteoritic dust due to compression effects, Stoney was led to the following formula for a l l a t : (3.13)

ar/at

8

=3 - rpr4 (1

-

6) Ar

In (3.13), T is the radius of the earth-body, of mean density pol underlying the shell of cosmic dust of thickness Ar and of density p , while p’ is the density of a fictitious auxiliary deposit, D, which, if spread uniformly over the whole earth, would depress the former surface of the earth-body by an amount numerically equal to the thickness of the D layer. Since Stoney’s investigations indicated that the quantity pf was somewhat less than 2, the parenthetical quantity in (3.13) is a small fraction. Woodward, who ignored earth compressibility effects in his development, was

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led to the same formula (3.13), but with the small quantity (1 - po/3pt) replaced by unity. The law of conservation of angular momentum implies the relation

2?rI - - - constant

(3.14)

T

where I is the moment of inertia of the earth at any time t , and where T is the corresponding time of diurnal rotation. From (3.14)) one immediately deduces (3.15)

wherein I 0 and T O are the values of I and T at the beginning of the year for which we seek to calculate the meteoritic accretion. If we denote by N the number of meteoritic particles which fall to the earth in the course of a year’s time and by f i the average mass of these particles, then (3.16) 4?rpr2Ar= N f i for both sides of this relation give the mass of the shell of meteoritic material accreted in the course of a year. In view of (3.16), formula (3.13) may be written (3.17)

Furthermore, if M is the mass of the earth at the beginning of the year in question, l ois given with sufficient accuracy for our purposes by

%Mr2 Thus, if t is measured in years, (3.15) may be solved to give for AT a t the end of a single year’s time (3.18)

(3.19)

I0 =

AT

=

TO

[TI $) (1 -

Whence the annual meteoritic accretion, N f i , is given by (3.20)

If we recall that (1 - p0/3pt) << 1, then, under our assumption that the meteoritic contribution AT to the observed increase AT in the length of the day has the value AT = 0 * AT, (3.20) supplies the following upper bound for the meteoritic accretion in a year’s time: (3.21)

In (3.21), M has the value 6 X

loz1 metric tons,

T~ =

86,164 sec;

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and, according to the recent investigations of Brouwer [85], AT does not exceed 0.0000164 sec per year. As to the value to be assigned to 8, MacMillan, who did pioneer work on the competency of tidal friction to produce the observed secular increase in the length of the day, once remarked to the writer that he doubted if as much as one ten-thousandth of this increase could be attributed to the gradual accumulation of cosmic dust on the surface of the earth. If we accept the estimate e = 0.0001 and Brouwer’s bound on AT, then (3.21) gives 5.7 X 10’ metric tons as an upper bound on N f i . In view of the magnitude of this bound, even the largest entry in the table above cannot be excluded solely on the basis of size; however, if the neglected effects of meteoritic collisions with the earth, to which Stoney long ago directed attention, were found to contribute significantly to AT, this might no longer be the case. 3.6. Phenomena Related to the Infall of Meteoritic Dust

Whatever the ultimate outcome of attempts to appraise quantitatively the contribution to the earth resulting from the infall of meteoritic dust, there is now at hand cogent qualitative evidence that the infall of this dust produces definite effects on terrestrial atmospheric processes. On the one hand, the important role played by meteoritic dust in producing or triggering the production of certain remarkable luminous phenomena peculiar to the twilight or nocturnal sky now seems almost beyond dispute. On the other hand, the hypothesis that rainfall peaks which have supposedly occurred approximately thirty days after the appearance of prominent meteor showers are due to the nucleating effect of meteoritic dust from the showers falling into cloud systems in the lower atmosphere (the time lag resulting from the slow descent of the dust through the atmosphere) recently has acquired support from the analyses of rainfall records that entitles it to receive consideration. 3.6.1. Anomalous Light Streaks and Noctilucent Clouds. For more than a century, sporadic references to curious faint brightenings of the night sky, of an entirely different nature than the familiar auroral displays and the noctilucent clouds, have been appearing in the literature of astronomy. The first systematic observations of these light streaks and diffuse luminous clouds were made by Hoffmeister [86] who was led to conclude from his studies that the light phenomena in question were caused by the intrusion of clouds of cosmic dust into the upper atmosphere. The most important result of Hoffmeister’s systematic observations was proof that the frequency and intensity of the light streaks and clouds go through a yearly cycle; and that successive individual maxima in this cycle show a surprisingly close relationship to the successive maxima of well-known

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cometary meteor streams. The annual cycle, as disclosed by Hoffmeister’s observations, is characterized by a deep minimum in April, by a maximum of frequency and intensity in the months from August to December, and by relatively weak activity in the other months of the year, probably with a secondary minimum in October. The correlation between light maxima and visible meteor shower maxima, as revealed by Hoffmeister’s observations, is clearly shown in Table IX. As Hoffmeister himself has emphasized, however, the times of maxima, in several cases do not agree exactly; and in one case (that of the Perseids), the light maximum precedes the maximum frequency of visual meteors. Moreover, Hoff meister noted that even when visual meteor frequency was low, very strong repeated disturbances of the ionosphere, as continuously recorded by Goubau and Zenneck [87] using a development based on the echo method of Breit and Tuve, coincided with the appearance of the anomalous light streaks and diffuse luminous clouds. Hoffmeister was therefore led to ascribe both the observed anomalous light effects and the ionospheric disturbances to meteoritic dust invasions rather than to visual meteors. As early as 1934, Vestine [88] and, later, Hoffmeister, in his work, Die Meteore, t o which reference already has been made, seriously considered the possibility that noctilucent clouds-the delicate, glittering, silver-colored, cirrus-like forms long the subject of systematic study by Middle European observers-might be meteoric phenomena. It seems clear that Hoffmeister, as well as Vestine, favored belief in the cosmic origin of the noctilucent clouds; but after a careful review of the literature, Hoffmeister felt constrained to state that the question of their origin “i5 still completely open.” Recently, the question of the cause of noctilucent clouds has been reopened by Bowen [89], who points out that the sudden stoppage in the region 80 to 100 km above sea level of the smaller particles of cosmic dust and the corresponding local increase in the concentration of this dust would lead one to expect a connection between the zone of dust concentration and the noctilucent clouds, which are occasionally seen in the same height interval. Bowen is led to the conclusion that the probability of a relation between meteoritic dust and noctilucent clouds becomes almost a certainty if a comparison is made of the incidence of such clouds and the time of occurrence of certain meteor streams tabulated by Lovell. Such a comparison, based on data published by Bowen, is included in Table IX. On the basis of the data presented in this table, it seems quite probable that both the light streaks of Hoffmeister and the noctilucent clouds are closely related to invasions of the upper atmosphere by clouds of meteoritic dust of cometary origin, for it is well known that such clouds of finely

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TABLE IX. Comparison between dates of appearance of light streaks (L),noctilucent clouds (N), and meteor showers. Based on tabulations published by Hoffmeister (see [86], Part 111, D(3)) and Bowen (see [89], p. 496). Dates of observation of light streaks (L) and noctilucent clouds

(N) Dec. 28-Jan. 11 (L) Jan. 23-Jan. 30 (L) Feb. 6-Feb. 7 (L) Mar. 11-Mar. 16 (L)

-

May 17-May 22 (L)

Date of maximum of associated meteor shower Jan. 1-3

-

Name of meteor shower Quadrantids

-

Apr. 21

-

Lyrids

-

June 3 ( N ) June 3 June 8 June 8 (N) June 18-June30 (L) -

Zeta Perseids Arietids

June 23 (N) June 30 (N) July 7 ( N ) July 12 ( N ) July 24 (N) July 27 ( N ) July 30-Aug. 13 (L)

June 25 July 2

5PPerseids Beta Taurids

July 12 July 25 July 28 Aug. 10-14

Sept. 7-Sept. 15 (L)

-

Nu-Geminids Theta Aurigids Delta Aquarids Perseids (Comet 1862 111)

Oct. 8-Oct. 16 (L)

NOV.?’-NOT‘. 24 (L) Dec. 7-Dec. 14 (L) Dee. 17-Dec. 25 (L)

-

Oct. 10 Oct. 20-23 NOV.16-17 Dec. 12-13

-

-

-

Remarks High maximum Secondary maximum of unknown cause A rise of unknown cause A slight rise of unknown cause

-

Weak maximum, possibly caused by Halley’s comet Daylight stream Daylight stream Noticeable rise, possibly caused by Pons-Winnecke’s comet Daylight stream Daylight stream Daylight stream Daylight stream Daylight stream Light streak maximum apparently on August 4 An interval of frequent brightenings with rise a t the end; possibly caused by Comet 1907(d) Secondary rise

Giacobinids (Giacobini-Zinner comet) Orionids Very high maximum on Leonids NOV.15-16 (Comet 1866 I) High maximum Geminids High maximum. Cause unknown; possibly due to Geminids or to Quadrantids (Jan. 1 max); or to both

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comminuted material are distributed along the paths of the comets responsible for the occurrence of such meteor showers as those included in Table IX. 3.6.2. The Relation between Rainfall Peaks and Meteor Showers. The possibility that meteoritic dust-whether it consists of micrometeorites having diameters no greater than 4 p or has its origin in the relatively large fragments and droplets of material torn or distilled off of meteorforming meteorites-might provide rain-forming nuclei [go] when it descends into the cloud systems of the lower atmosphere must now be given consideration in view of E. G. Bowen’s discovery that “ a t certain stations and at certain times of the year there is a probability of a peak of rainfall appearing some 29 or 30 days after the earth enters a major meteor stream” (see [89], p. 493). Bowen points out that measurements of the concentration of freezing nuclei in the free atmosphere obtained by means of a cloud chamber transported in an aircraft showed extraordinarily large fluctuations from day to day. For example, the number which became active a t a temperature of - 15°C might change in the ratio 1000: 1 from one day to the next [91]. Observations made during the course of the above cloud chamber measurements suggested that, whatever the origin of the freezing nuclei, they might be falling into the air mass from above, As rainfall is the meteorological variable most likely to be influenced by changes in the freezing nuclei concentration, Bowen was led to make a detailed examination of rainfall records covering long intervals of time, with the interesting results quoted at the end of the previous paragraph. In evaluating the validity of Bowen’s quoted conclusion, attention must be given to the results obtained by Crozier [92] on the basis of systematic collection of magnetic spherules from the atmosphere at several localities in New Mexico. Crozier found that on eliminating peaks of short duration apparently attributable to terrestrial matter derived from sources near the observing stations, the rate of deposit of magnetic spherules seemed to vary only slowly. Although indications of correlation with meteor shower maxima were found, it was Crozier’s opinion that several years’ data would need to be analyzed before such correlation could be firmly established; and he concluded that “The apparent absence of rapid changes in rate of deposit argues against the existence of short-period meteorological effects of the spherules or of other meteoritic dust that may be associated with the spherules.” Bowen adduces as further evidence of the reality of the connection between rainfall peaks and meteor showers an effect of the Bielid meteor stream in producing notable rainfall peaks not only in the United States, but also, with less definiteness, in New Zealand and New South Wales at

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intervals of approximately 6 yr, especially during the last half century. I n support of the periodicity mentioned, Bowen presents [93] not only graphs of rainfall totalled for the three days December 29, December 30, December 31 (based on observations made in the United States, New Zealand, and New South Wales), but also tables of serial correlation coefficients computed from these graphs which, at least in the case of the United States, definitely “show a 6-yr recurrence tendency and support the hypothesis that the rainfall about this period is connected with the Bielid meteor system.” MeteoroIogical arguments against Bowen’s hypothesis have been cited by Mason, Whipple, and Hawkins [94], and are implicit in the relatively low frequency E. J. opik [94a] has recently assigned to the larger particles of meteoritic dust in contrast t o the micrometeorites which, as he has strongly emphasized, in his opinion provide most of the extraterrestrial matter entering the earth’s atmosphere. 3.6.3. The Meteoric Ionospheric Lager of Kaiser. I n 1953, Kaiser [95] considered the possibility that a continuous layer of ionization might be produced by meteoric activity in the atmosphere between 115 to 130 km. At the lower level (90 t o 100 km) of the central M-region of Millman and McKinley (see Section l . l ) , except during continuance of the heaviest meteoric showers, no significant departure from the observed regime of discrete ionization trails is to be expected; but, a t the greater altitudes considered by Kaiser, while the ionization per meteor would be less, both the number of meteoric particles stopped and the diffusion rate would be greater. In a later publication [96], Kaiser has re-examined this question. Using what he designates as the M distribution of interplanetary particles, namely (3.22) n(r) = lo-”+ with a = 27.7 k 0.5 and t = 4.0 & 0.1 for 0.5 2 r >= 4 X lop3 cm and the normal E-layer recombination coefficient, he estimates the electron density in the layer between 115 to 130 km as n, = lo2 CM-~. Since, for the nocturnal E-layer, the value of neis customarily set a t = lo4~ r n - ~ , Kaiser concludes that the numerical results can only be reconciled by adopting a recombination coefficient of order 10-l2 cm3 sec-’. The formation of negative ions is regarded as rendering a recombination coefficient as small as this unlikely. 4. THEHYPERBOLIC METEORITE VELOCITY PROBLEM. I 4.1. The Ballistic Potential of Meteorites

The interactions between the earth (including not only its atmosphere but also its satellites, natural and artificial) and extra-terrestrial matter

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are of great complexity and of the widest range in intensity. At one extreme, the impacting matter, minimal in size, through collision with air molecules, attains an equilibrium condition of motion while high in the atmosphere, the interaction of interest ceasing as soon as the particles commence to fall toward the earth with small and essentially constant terminal velocity. At the other extreme, bodies so massive as to be but slightly decelerated by atmospheric resistance strike the earth a t speeds but little less than those possessed extra-atmospherically, and produce as a result of their extraordinarily violent impact with the earth-target those topographic features that have received the name “meteorite craters.” Fortunately, meteorites of such excessively great mass are so rare that, except for targets of planetary size, one may treat the threat their impact poses as negligible. Between the extremes just described lies the province of what may be called “ordinary” meteoritic impacts with the earth. If one excludes the meteorite-crater producing impacts for which, as has only lately been recognized, a hyper-velocity, jet-penetration regime usually develops, then in all of the other cases considered above, one deals with impulsive transformation of the kinetic energy E of the infalling body; and, hence, one is more concerned with the body’s velocity, which enters quadratically into E, than with its mass. Quite apart from dynamical considerations, those of ballistic and probabilistic nature also serve to enhance the critical importance of the speeds a t which meteoritic masses are encountered. One need only recall how very rapidly the difficulty of taking effective evasive action against missiles attacking a t higher and higher speeds increases; and the results given in Section 1.2.3 relating to Goddard’s investigation of the seriousness of the meteoritic hazard to space flight. The singular importance of meteoritic speeds to those responsible for the long-continued operation of satellite vehicles at extreme altitude consequently is at once apparent. Unfortunately, it is precisely in connection with meteoritic velocity determination that an as yet unresolved controversy has arisen in meteoritics. The present section therefore first critically reviews the meteorite-velocity question. Attention is then directed to various nonvisual methods of meteoritic velocity determination and to the results secured by their use.

4.2. A Photographed Meteor of Strongly Hyperbolic Velocity The statement often made that the very first application of the exact photographic method for the determination of meteor velocities has led in every case to an orbit of elliptical character is fallacious. Actually, the methods for reducing meteor photographs, universally accepted as

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proving that all but one of the first group of meteors recorded by the pioneer Harvard Meteor Program (hereafter designated as H. M.P.) belonged t o the Solar System, showed with equal certainty that the remaining meteor, No. 663, came from outside this System. Since not only geophysicists, but radar specialists and astronomers as well, frequently evince unfamiliarity with this highly significant fact, a documented account of the singular treatment accorded to meteor No. 663 will be given in this section. Such an account is a necessary preface t o any presentation of hyperbolic velocities derived by nonphotographic methods, for the phrase, “photographically determined,” a t present commands such respect that velocity evidence believed by nonmeteoriticists to contradict all photographic results is not even accorded a hearing. Our deliberate choice of one of the earlier meteors photographed in the H.M.P. program as an example for discussion is conditioned by the following considerations: The photograph of meteor No. 663 was taken with essentially the same equipment and reduced by essentially the same methods a s the more than 143 other meteors in the so-called Massachusetts and New Mexico groups, an extensive series of meteors photographed in the H.M.P. during the interval 1936 to 1951. The results obtained for the meteors other than No. 663 in the first subgroup of Massachusetts meteors reduced by Whipple, appear essentially unchanged in his most recent (1954) tabulation [97]. Irrespective of other considerations, our choice of a meteor for discussion is necessarily limited to No. 663, for as both opik [98] and the writer (see [29], p. 359) have earlier pointed out, certain data vital to an investigation of the hyperbolicvelocity problem are no longer given for sporadic meteors like No. 663 in the H.M.P. publications. Thus, t o quote o p ik [98], “for the later observations, no radiants, heliocentric velocities or other data relevant to the problem of hyperbolic velocities are published for the sporadic meteors . . . 1 1 The facts relating to H.M.P. meteor No. 663 presented here are, for the most part, taken either from Whipple’s monograph [97] on the first group of meteors recorded and analyzed by the H.M.P. or from later H. M. P. publications. The path of meteor No. 663, which had a length of over 43”, was the longest, and the number of shutter breaks available for measurement on this path, viz., 18, was the next-to-the-highest encountered in the cases treated in Whipple’s 1938 paper. Consequently, the criterion employed to assign weights to photographically determined velocities [loo] would assign high weight t o a velocity deduced from the trail of No. 663 by the usual H.M.P. procedures; and, in fact, the probable error (p.e.) ( = & 0.11 km/sec) of the velocity of No. 663 first determined in this way

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by Whipple was very small in comparison with the average p.e. resulting from his velocity determinations for the group of meteors under consideration. Furthermore, as the extraordinarily high angular velocity of No. 663 (W (663) = 95.”5/sec)-more than double the average angular velocity determined from the A.I. series of H.M.P. photographs-immediately drew Whipple’s attention t o the unusual nature of this swift meteor, exceptional care was taken from the beginning in its reduction. Two different matching techniques were employed in order to determine the time of apparition T , of No. 663, and when both techniques, to quote Whipple, “gave the same identification of breaks, it seemed that the sidereal time of 10* 20” was essentially correct.’’ By using T = loh 20m,there resulted an observed velocity Vo, of 79.69 km/sec, which led t o a strongly hyperbolic orbit with eccentricity, e(663) = 1.8423. The observed hyperbolic velocity of No. 663 was by no means “due to planetary perturbations,” as so often has been asserted in similar cases by those who seek to “outlaw” interstellar comets and meteorites. (The only planet in the same general region of the sky as that from which No. 663 approached was Mars, and the writer has found that No. 663 missed Mars by more than 40 million miles!) The cosmic point of departure of the hyperbolic meteor, No. 663, as well as the very large eccentricity and other features of the orbit first calculated for this meteor by Whipple, will at once be recognized by meteoriticists as conforming to the wide interstellar stream of Scorpionids, first systematically studied by von Niessl [loll. Consequently, routine reduction of the fourth meteor photographed in the H.M.P., in accordance with the procedures habitually employed by Whipple, served to confirm results obtained in Europe by decades of meticulous visual observation and theoretical research on a hyperbolic meteor stream whose very existence too often has been called into question by those unfamiliar with the conscientious nature of the work of von Niessl and his collaborators. In spite of the concordances just referred to, and the fact that the procedures used in his treatment of meteor No. 663 were those he and his associates had followed without exception in the reduction of the other H.M.P. photographs, Whipple rejected the hyperbolic orbit he had found for this meteor; and, indeed, in recent publications relating to the H.M.P. work, no reference is found to the open orbit first determined for meteor No. 663. In this connection, the data on No. 663 (first solution) in Table I11 on pp. 513 to 514 of Whipple’s 1938 paper [99] should be compared with data (exclusively elliptical) given for No. 663 in the last column of Table 1 on p. 204 of Whipple’s 1954 paper [97]. Whipple’s stated reason for rejecting the hyperbolic orbit found initially was that “the hyperbolic solution requires too high a density” to

EFFECTS O F METEORITES ON THE EARTH

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conform satisfactorily to the atmospheric density profile adopted in H.M.P. work in 1936 to 1938. Whatever validity this reason may have had at that time, it no longer provides valid grounds for continuing to reject mention of the hyperbolic solution first found for No. 663, inasmuch as density values determined from this hyperbolic solution agree quite satisfactorily with such modern density profiles as that of the National Advisory Committee for Aeronautics [102]. The rejection of the hyperbolic orbit initially found for No. 663 is, in the writer’s opinion, unacceptable particularly in view of the fact that, in place of the discarded hyperbolic orbit, Whipple elected to assign an elliptic orbit to No. 663 by taking advantage of such considerations as those given in the following quotation from his 1938 monograph: “The eccentricity of the orbit, unfortunately, is very sensitive to changes in the apparent velocity arising from a change in the apparition time, and may vary from its minimum value of 0.9 (at sidereal time lohOm) to values much exceeding unity for later times.” In fact, if the behavior of the eccentricity, e(663), is scrutinized more closely, it is found that the monotonically increasing variable, e(663), takes on unit value at about loh4m and thereafter exceeds the parabolic value. Since, by Whipple’s rejection of the evidence afforded by the standard matching procedure (although twice repeated with concordant results), the position of the time of apparition T within the hour long exposure becomes unknown, it is of interest to consider the value of T from the viewpoint of probability. Evidently, the odds are strongly against a T value giving an elliptic orbit a t all, i.e., against T for No. 663 falling within the first 4 minutes of the hour long exposure. Furthermore, there is, of course, a strictly null probability, under these circumstances, that T for No. 663 should exactly equal that particular instant, lohOm, for which e takes on its “minimum” value. Nevertheless, Whipple chose T(663) = loh Om in obtaining his second solution for the*orbit of the meteor in question. This most improbable value for T led him to an observed velocity, V Oof, 68.43 km/sec -corresponding to a heliocentric velocity just below the parabolic limit.6 6 I n this connection, the following quotation from a form letter sent out by Whipple and Jacchia in 1954 is of significance: “You may notice as paper No. 70 of the program for the AAS meeting a t Ann Arbor this June the title ‘An Interstellar Meteor,’ by L. G. Jacchia and F. L. Whipple. We tried to withdraw this title but were too late. We had investigated the case carefully before sending in the title but continued the investigation afterwards. If the fast meteor is identified as a meteor visually observed during the 12-minute exposures, i t is definiteIy hyperbolic. After more careful study, however, we find that the description of the visual meteor disagrees very badly with the one photographed. Whereas the photographed meteor is some 18” long, the visual was reported as only 3” long with a corresponding error in the position. If we select the instant [of apparition] within the first minute or two of exposure time, the clear-cut 1 km/sec excess over the parabolic velocity is cut down within the parabolic limit.”

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LINCOLN LAPAZ

This “elliptic” value of V othen led to a density value regarded as conforming satisfactorily to the density profile that was a t the time (19361938) accepted as a control in H.M.P. work. The lower density value that was thus obtained by constraining No. 663 to move on an elliptic rather than a hyperbolic orbit does not, however, conform as well to the density profile adopted by the N.A.C.A. in 1949, referred to previously, as does the density value corresponding to the hyperbolic orbit initially calculated by Whipple. Most significant in connection with the above is the fact that in 1948 L. G. Jacchia (H.M.P. Tech. Report No. 2, 1948,14), retaining the apparition time T = loh0” earlier selected by Whipple, redetermined the observed velocity, V,, for No. 663, finding a value Vo(663) = 71.03 km/sec, considerably larger than that earlier reported by Whipple for the same meteor. The writer has found that even when T = loh Om, the orbit of No. 663, corresponding to Jacchia’s value of Vo(663) is hyperbolic! Consequently, it has turned out to be impossible to exclude one-sixth (17%) of the first group of meteors photographed and reduced by the H.M.P. from the hyperbolic category. With this highly significant result, the case for photographically determined hyperbolic meteor velocities must rest a t present until either the old photographic evidence can be re-examined or new photographs become available for study. 4.3. Radar-Meteor Velocities and Their Limitations

The radio astronomers are accustomed to assert that all photographic meteor velocities lead to elliptic orbits; and to conclude that all of the photographic evidence supports the asserted failure of radar to detect any appreciable number of hyperbolic meteors. The case history of H.M.P. meteor No. 663 (Section 4.2) is a t variance with this opinion. On the other hand, exponents of the photographic method of meteor velocity determination usually cite the nonexistence of radar meteors with hyperbolic velocities as supporting the absence of hyperbolic meteors. Evidently, there is need for a documented account paralleling that in Section 4.1 of the many and varied objections which opik and others have raised against radar velocity techniques and/or the reduction and rejection procedures employed by the radar experts in working up meteor-echo data. The purpose of this section is to present such an account. 4.3.1. Limitations Due to Selectivity E$ects in Instrumentation and in Reduction Processes. In 1950, Lovell et aZ. [lo31 announced that results obtained by his Jodrell Bank team did not confirm the existence of any considerable proportion of hyperbolic velocities among the sporadic meteors. In 1954, Lovell [104], after a lengthy review of all radar velocity

279

EFFECTS O F METEORITES ON T H E EARTH

determinations for meteors, wrote ‘‘ . . . the fact cannot be excluded that about 1 per cent of the meteors observed in the apex experiments may have had velocities in excess of the parabolic limit. It is possible, of course, that a result of this nature may be due to planetary perturbations.” While Lovell leaves the reader in no doubt that the conclusions announced are strongly a t variance with the results published by opik and other proponents of the view that a substantial interstellar component is present among the meteors, no hint is given of the fact that the conclusions in question stand in equal contradiction to results earlier obtained on the basis of radar observations by Lovell himself. opik (see [98], pp. 93-94) has quoted the following highly significant statement from a letter written by Lovell on January 12, 1949: You will no doubt remember that we were fairly convinced tha t all the meteors we observed here had less than parabolic velocites, and we regarded the experiment, which Whipple and yourself urged us to do, as in the nature of a “negative results” experiment. However, it has turned out far from being in this category, since we have measured many hyperbolic velocities. so far I have only managed to work out about one-eighth of our total results which have yielded about 30 velocity values. The distribution of these velocities is given in the following table.

...

[Lll Velocity 30 35 40 45 50 between and . . . . . . . . . . . . 35 40 45 50 55 Number 3 1 1 1 2

55

60

65

70

75

80

85

90

95

........................... 60 4

65 2

70 4

75 2

80 1

85 2

90 1

95 100 1 2

C)pik, who had calculated that under the observing arrangements employed 65 km/sec represented the effective statistical upper limit to velocities of elliptic type, found that the probable number of hyperbolic meteors in Lovell’s tabulation (L1above) of the 27 velocities obtained by reduction of one-eighth of the total of 1500 meteor echoes was fortysix per cent. The results of this preliminary work indicated that more than 200 velocity determinations would become available when all of the 1500 echoes were reduced. Actually, reduction of the 1500 values provided only the 83 velocities in the following tabulation: [LZI Velocity

Number

Below Between 35 35 40 45 50 and . . . . . . . . . 40 45 50 55 11 7 10 6 9

55

60

65

70

75

80

..................... 60 12

65 8

70 8

75 7

80 2

85 1

85

Over 90

90 2

0

Consequently, opik concluded that Lovell had instituted a restrictive procedure involving the arbitrary rejection of the higher velocities (i.e.,

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LINCOLN LAPAZ

those exceeding approximately 65 km/sec) derived from reduction of the radar data. This conclusion was and remains inescapable. Nevertheless, the probable number of hyperbolic meteors in Lovell’s table (L) still amounted to twenty-four per cent (see [98], p. 94). Attempts have been made to justify application of a restrictive procedure of selection to radar records on the grounds that to avoid spurious fluctuations in echo intensity that may distort the diffraction pattern, only those meteors should be retained for which the relative spacing between diffraction pattern max and min agrees to a greater or lesser extent with the theoretical spacing. opik [lo51 has stressed, however, that [lo51 “the higher the velocity and shorter the time-scale, the fewer are the pulses upon which the intensity-curve of the diffraction pattern is based, and the greater the distortion by accidental fluctuations of equal amplitude. Therefore, although ‘objective’ from the worker’s point of view, the selection method was unfavourable for high velocities and must have produced a distortion of the frequency curve, in depressing and displacing its maximum towards lower velocities, exactly as observed in Lovell’s apex experiments.’’ In 1949, another series of observations directed toward solution of the hyperbolic velocity question was instituted at Jodrell Bank. In all, 3000 meteor echoes were obtained. On the basis of the output of meteor velocities from the series (L1, L2)earlier reduced, upik conservatively anticipated that about 200 meteor velocities would be found on vorking up the 3000 echoes. Actually, only the following 120 velocities, regarded as t‘good” by the radar experts were forthcoming: [Ld Velocity

Number

Below Between 35 35 40 and . . . 40 45 8 9 9

...

...

...

... .. .

85

90

...

50 55 60 65 70 75 1 5 2 5 2 2 3 2 2 0 1 1

80 5

85 0

90 1

95 1

100 0

45

50

55

60

65

.. . . . . .. . . . . . . .

70

75

80

95

I n spite of the obvious evidence of incompleteness in this velocity sample, the probable number of interstellar meteors it contained still amounted t o thirty-two per cent. Since the Jodrell Bank results and opik’s inferences from them only served to intensify the hyperbolic meteor velocity controversy, the need for a crucial test utilizing radar methods became imperative. Early in 1950, it was pointed out to Love11 that the best arrangements for such a crucial test would be to observe with the radar beam in the apex in the mornings during the interval February to April, or in the antapex in the evenings during the period August to October. The reader of Lovell’s

EFFECTS OF METEORITES ON THE EARTH

281

account of the so-called crucial tests actually instituted would conclude that optimum arrangements for their success were adopted. Upik’s own highly pertinent opinion on this point is the following (see [98],pp. 95-96) : However, in spite of warnings, Dr. Lovell started the spring observations in the antapex and had, of course, to abandon them on account of insignificant yield. Then Dr. Lovell, instead of directing the beam to the apex, switched over to the old arrangement, except that the circle of radiation now passed through the antapex. Dr. Lovell says this was done in order to meet certain objections “in a decisive manner” . . . Here, apparently, words have a different meaning from what is commonly agreed. The heterogeneity of the “parabolic velocity limit” in this “decisive” experiment was not less than in the apex experiment, the limit varying from 16 to 50-60 km/sec (with a strong favouring of small vaIues, on account of zenith distance), and the advantage of a safe, sharp margin at 72 km/sec was lost, too. How could more clarity be expected from such a n obscured case?

T o the writer’s knowledge, no rebuttal has been published either to Upik’s cogent criticism of the circumstances under which “crucial” radar tests so far have been conducted, or to his recently published conclusion [lo61 that, on the basis of his calculations of the selectivity of radar, “ I t is no wonder that the radar lists are not only devoid of ‘hyperbolic’ velocities but also are rather poor in ‘parabolic’ velocities, as revealed by Lovell’s ‘apex experiments’ . . . For this reason radar observations are statistically unfit to deal with the problem of hyperbolic meteors, or the general distribution of meteor velocities.” Until such rebuttal appears, the published evidence strongly supports the view that the percentage of hyperbolic radar meteor velocities much exceeds the 1 per cent level earlier quoted from Lovell. There remains Lovell’s suggestion that the very substantial number of hyperbolic meteor velocities thus revealed by radar observations has its origin in planetary perturbations. Similar suggestions have been made repeatedly by those who seek to outlaw hyperbolic comets and meteors. It is to be hoped that opik’s proof [lo51 of the nonexistence of “Lovell’s interplanetary hyperbolic meteors” will set an end to this argument. g.3.S. The M-Zone Limitation and Its Implications. In addition to the various objections that 6pik has raised against placing implicit confidence either in instrumentation as selective as radar or in conclusions based on radar data to which a restrictive procedure of selection has been applied, the writer has called attention to certain limitations of the radarmeteor velocity technique which must be kept in mind if a proper appraisal of radar velocity results is to be obtained. The radar methods-unlike visual and, to a lesser extent, photographic methods-do not record meteoric phenomena occurring at all atmospheric levels. Actually, radar detection of meteors is limited to what Millman and McKinley [ll, 1071 have termed the M-region, a relatively

282

LINCOLN LAPAZ

thin stratum of the atmosphere described as extending 7.5 to 10 km on either side of the 95 km level in the atmosphere.’ This M-zone limitation quite naturally implies a smaller spread in mean radar heights for meteors than would be found from visual observations of the same meteors. Consequently, the greater spread of mean visual heights reported in combined radar-visual work cannot be ascribed solely to human inaccuracy, as the report on such combined radar-visual observations given by Millman and McKinley would imply [108]. If hyperbolic meteors, in general, either fail to produce detectable radar targets in the M region or enter this relatively low-lying critical zone only after their extra-atmospheric speeds have been reduced to nonhyperbolic values, then clearly a heavy handicap rests on attempts to solve the hyperbolic meteor velocity question by means of radar. That such a handicap actually exists is shown by the following evidence: Not only the visual meteor data collected by the Harvard-Arizona Expedition [log], but also the significant results of Millman and McKinley’s radar investigations of the percentage of faint meteors in the sporadic background (see [107], p. 338) indicate that the eztraatmospheric frequency distribution of hyperbolic material, as regards size, is such that little of it exceeds the critical micrometeorite limit established by the early studies of opik [110] and the recent work of Whipple [lll]. As the micrometeorites produce no ionization whatever (see [96], p. 53), particles but slightly exceeding the micro-meteorite size limit must present extremely difficult radar targets, particularly since the M-zone for such tiny particles has its minimum extent [112]. Whatever the extra-atmospheric frequency distribution of the hyperbolic material as to size, after the first few kilometers of atmospheric transit, all but the most resistant masses, as a result of the comminuting action of high-speed atmospheric bombardment, will be near to or steadily approaching the micrometeorite size limit. For material moving with hyperbolic speeds, the relative velocities at which such atmospheric bombardment occurs may greatly exceed the velocities envisioned by Whipple at the time he made the following comments on the destructive effects of air molecular bombardment :

. . . the atmospheric molecules must penetrate deeply below the surface, disassociate, and damage the lattice structure of the solid. Since the total air mass encountered before the velocity becomes greatly reduced is comparable to the mass of the micro7 The limitation of radar meteor observations to such a restricted M-zone is not always as clearly pointed out as has been done by Millman and McKinley (cf., for example, Lovell’s recent book, ‘ I Meteor Astronomy” [104]);however, the reader who consults the raw data of observation given in Lovell’s references will speedily discover that the M-zone limitation exists.

EFFECTS OF METEORITES ON THE EARTH

283

meteorite, this damage may .be considerable. A crude estimate places the critical velocity in the neighborhood of 30 km/sec Il8.6 mi/sec]. Above this velocity the damage probably becomes appreciable, and near 70 km/sec, may become quite destructive.

As the writer has already pointed out (see [29], pp. 378-379), such considerations as the above offer a natural explanation not only of the discovery made by Opik [113] and Boothroyd [114] that the fraction of hyperbolic meteors increases in the fainter magnitudes, but also of opik’s discovery that more hyperbolic meteors have direct than retrograde motions (opik quoted by Watson [21], p. 101; compare also opik [115]). The latter discovery clearly reflects the influence of such excessive highaltitude disintegration as must result from head-on collisions between the earth and retrograde particles moving with hyperbolic heliocentric velocities. Furthermore, if the above considerations are kept in mind, the reader will be able properly to appraise the significance of the following statement made by one of the foremost authorities in the field in regard t o some of the reasons that have served as a basis for rejection of “strongly hyperbolic ” radar-meteor velocities : “If the treatment is confined to one part of the year, a fair case can be made for the presence of strongly hyperbolic heliocentric velocities, but the hyperbolic meteors must be assumed to be moving almost entirely in direct orbits of low inclinations. The analysis breaks down completely when applied to another time in the year, unless one can put forward convincing reasons why hyperbolic meteors coming from outside the solar system should have direct motions all year round and should lie close to the plane of the ecliptic” [116].

Finally, one may question the validity of the assumption made by the radar experts that, even in the case of particles moving with hyperbolic heliocentric velocities, one can ignore the decelerative effects of the violent intera,ction between particle and atmosphere which takes place all the way down t o the M-zone. From the viewpoint of ballistician and meteoriticist, i t seems most unlikely that any considerable number of hyperbolic objects succeed in retaining their full extra-atmospheric velocity all the way down to the M-level. A numerical example worked out by the writer in 1952 (see [29], p. 380) on the basis of a modification of the inverse acceleration method of Section 4.3.1 above clearly shows how great a decelerative handicap must be imposed on the smaller meteoritic projectiles, particularly if their interaction with the earth’s atmosphere begins a t exceptionally high speeds.

4.4. T h e Hyperbolic Comet Question and Its Relation to the Problem of Meteoritic Velocities Those readers whose interest in the vexed meteor-velocity question has been aroused by the account given in Section 4.1 would be well

284

LINCOLN LAPAZ

advised to read a critique of both radar- and photographic-velocity determinations recently published by Opik [98]. Opik points out, for example, that whereas the hyperbolic velocity first calculated for meteor No. 663 leads t o a result for the luminosity of the meteor per unit mass conforming well with the “general line of correlation of luminosity and velocity’’ the corresponding result under assumption of an elliptic orbit for No. 663 “falls 6 mag[nitudes] below the line, or is ‘out of tune’ in a ratio 250 :1.” Opik’s detailed critique may well arouse curiosity as t o how a fact as well established as the existence of interstellar meteorites has come t o be seriously questioned by many scientists. Two factors seem to have operated to sway astronomical opinion in favor of accepting the doctrine, widely promulgated in recent times, that all meteorites are of solar system origin. The first of these factors is general acceptance by astronomers of the thesis associated with Stromgren’s [117] name to the effect that, irrespective of the orbit-form observed near perihelion, all of the comets approaching the sun “were originally travelling in elliptical orbits.” Armellini [118] long ago pointed out the invalidity of this conclusion, but his sound criticism seems to have passed almost unnoticed. The error resides in what amounts t o an indefinite (and therefore illegitimate) extrapolation backward in time from results derived by approximate calculation of the perturbations experienced by a comet during, a t most, a few decades preceding its perihelion passage. A temporally limited investigation of this sort proves nothing about where the comet originally came from, establishing only that, a t a particular moment, namely, the remotest instant to which the calculations extended backward in time (at most a few score years preceding perihelion passage in all cases so far treated), the comet was going about the sun in a nonhyperbolic orbit. The writer [119] has published the following analogy in an effort to drive home a point already too long overlooked by the Stromgren school: Many collegiate race tracks are, approximately, ellipses with tangent initial and final straight-aways. A latecomer to a race notes the runners on the terminal straightaway and observes that 10 seconds backward in time these runners were moving along a n elliptical path. With Stromgren, he now illegitimately extrapolates to the conclusion that the runners had always been pursuing the same closed track until a perturbing force (appearance of the flag for the final lap) sent them onto the terminal straight-away. Track officials, however, having observed the entire race, are in position to point out that originally the runners (comets) entered the closed track (solar system) from the initial open straight-away (interstellar space).

Evidently, claims t o have solved Stromgren-type problems cannot be taken seriously until, along with calculations of the osculating ellipse at times t more and more remote in the past, an Abschutzung valid for

EFFECTS OF METEORITES ON THE EARTH

285

all t’s is provided for the total error accumulated during solution of the perturbation problem by the particular numerical process, and under the specific simplifying assumptions, adopted in carrying through the computations. The second factor alluded to at the beginning of this section is the rather widely held view that C. C. Wylie has proved ‘( . . . that meteorites before encountering the earth move in orbits of small inclination t o that of the earth and with small aphelion distances within the orbit of Jupiter . . . ” [120]. A critical examination of the procedures employed by Wylie in calculating meteorite orbits will show that the blanket conclusion just quoted is without foundation. As an illustration of these procedures, consider Wylie’s treatment of the exceptionally well-observed Pultusk fall, for which he reduced the beginning heights H corresponding to the reports of actual eyewitnesses of the fall to one-half or even to less than of the observed values as a preliminary t o computation of the orbit followed by the meteorite in question. Nielsen [121] has recently emphasized that such arbitrary reductions in H stand in “strange contradiction” to precisely the most dependable observations of the Pultusk fall, including one made by the astronomer Kayser, who observed the Pultusk fireball through a window; and for whom the point of appearance was marked by Rigel and the point of disappearance by Sirius. Wylie himself has pointed out [122] that an observer “who sees the entire path in the limited region of sky marked by familiar objects . . . ” exhibits no such tendency t o overestimate the length of path as, in Wylie’s opinion, is generally shown by less favorably situated eyewitnesses who see the path in an open sky devoid of landmarks. Certainly then, in this respect, Kayser’s observation (favored by the fortunate circumstances that he observed the Pultusk fall in the limited portion of the sky bounded by a window frame and that two of the brightest and most familiar stars served to delimit precisely the segment of the apparent path seen by him) leaves nothing to be desired. Nevertheless, it was rejected-apparently because its use would have led inescapably to a hyperbolic velocity for Pultusk, as is clearly shown in Nielsen’s detailed computations. This interpretation of Wylie’s procedure is supported by the following evidence : Two years prior to overhauling the Pultusk observations, Wylie published a paper [123] purporting to show that everything “From ordinary shooting stars t o detonating meteors dropping meteorites . . . 11 exhibited a constant height of appearance, namely H = 68.9 mi. Since, in treating the Pultusk fall, Wylie saw fit to reject not only the most dependable observations of the whole apparent path, but also all observed determinations of the beginning height H of this path, it would seem obligatory for him t o adopt his own universally applicable height of

286

LINCOLN LAPAZ

appearance, H = 68.9 mi, in discussing the Pultusk case. Instead, he arbitrarily adopted for N in this case the much smaller value, 52 mi, a height having no relation whatever to the observed fall at Pultusk, but appertaining rather to Wylie’s “determination” of the beginning height of the Paragould, Arkansas fall of February 17, 1930 (see [122], p. 310). This procedure becomes understandable only when calculation shows that the choice of Wylie’s universal constant, H = 68.9 mi, leads, as Kayser’s value led, to a hyperbolic orbit for Pultusk. The adoption of the small Paragould H value for the H of Pultusk and the selection for H.M.P. meteor No. 663 of an improbably early time of apparition T with subsequent reduction in H(663) from 120.2 km to 102.4 km [124], in each case led to a reduction in the observed velocity V . Such reduction was to be expected in view of the well-known fact (see [29], pp. 354-355) that observed speeds V and observed beginning heights H are closely correlated. The existence of such a relationship, however, should warn the computer that he cannot manipulate H values and still legitimately contend that he is calculating the value of V . (To indulge in guesswork about the value of H inescapably (‘predetermines” the derived value of V.) No compulsion would have existed to adopt the special H values to which attention has been directed, if the velocity problem had been envisaged from the viewpoint favored by the writer (see [29], pp. 353355), namely, that the earth collides with high velocity meteorites as well as with low velocity meteoroids, to adopt the H.M.P. term for the slowermoving bodies. Since the missiles in the high velocity category have, for easily understandable reasons, so far remained almost undetected except by the visual observer (see [29], pp. 374-381)’ no contradiction exists between the hyperbolic velocities so often found from visual observations and the generally, but by no means universally, elliptical velocities found by photographic and radar methods. 4.5. Nonvisual Methods of Meteoritic Velocity Determination 4.5.1. The Inverse Acceleration Method. The point B of initial visibility for carefully observed nocturnal meteorite falls has always been found to be at heights greatly in excess of those found for ordinary meteors and fireballs.8 The higher B is taken, the longer the path over which the infalling meteorite experiences retardation from the earth’s atmosphere. 8 Consequently, Wylie’s choice of onIy 52 mi as the beginning height for the large, high velocity Pultusk meteorite fall is out of line with the photographic evidence presented in reference [97]. The average beginning height determined by Whipple for the 144 small and generally low velocity bodies recorded on the H.M.P. photographs is in exces~of 58 mi.

287

EFFECTS OF METEORITES ON THE EARTH

To avoid any suspicion that high velocities are simply the result of observers involuntarily reporting too great heights for B [122], suppose that, for each meteorite considered, the observed point B is shifted downward along the real path of the meteorite until its altitude is reduced to the small height (74.4 km) of the midpoint B’ of the photographed path of H.M.P. meteor No. 670. The speed determined for the meteorite from the shortened path thus obtained will provide a lower bound for its true extra-atmospheric speed. To calculate this lower bound, we employ one of the standard artifices of the ballistician and express the deceleration, A, experienced by the meteorite in terms of the deceleration 6 = -heDt determined from the H.M.P. photographs of No. 670 (see [29], pp. 360-363). Since this particular H.M.P. meteor was purposely chosen because of its very low velocity, the expression for A, which is of the same form as 6 but with k replaced by a suitably determined new constant K , will give an underestimate of the deceleration actually experienced by the meteorite. Solution of the inverse acceleration problem [125] corresponding to the A thus determined leads to the relations K

+ s(to) (eDt - 1) + t s(t0) - eDto [ D

s ( t ) = - [eDt- eDto]

D

(4.1)

s(t) =

K

D

-

I+

SO

If we suppose that at t = 0, the meteorite is passing through the 3’ position on its path, and that at t = t o it has reached the end point H’ of its path, a position which even Wylie admits [126] can be satisfactorily determined from the numerous concordant visual observations always at hand in the case of a widely observed meteorite fall; then its velocity at B‘ is given by K (4.2) ~(0= ) [I - eDtol s(t01

+

Consequently, the velocity, s(O), of the meteorite a t this point, can be calculated from equation (4.2) when t o is known; but when u ( t 0 ) and SO are known, the value of t o can be obtained as accurately as desired by solving the transcendental equation

(4.3)

K

- [eDto- 11 0 2

+ to

obtained from the second relation in equation (4.1) by setting t = t o , since s(t0) = 0, if we choose H’B’ as the s axis, with origin a t H’, the positive direction being toward B’. In the applications, nonvisually determined values of s(&) generally are lacking (although, as the writer has

288

LINCOLN LAPAZ

pointed out, there are many easily ascertainable data, such as measures of the depth of penetration into the earth target, knowledge of which would enable the meteoriticist to calculate Iv(to)l rather closely for a recovered meteorite of known geometrical and physical characteristics). Consequently, we shall be obliged to take the terminal speed \v(t,)l as zero; and employ the process outlined above to determine a lower bound on the extra-atmospheric speed Iv(0) Finally, since the extra-atmospheric velocity, urn, obtained by evaluating

I.

(4.4)

K D

Lim [ v ( t ) ] = - - eDto

t--r--oo

+ v(to)

in most cases differs inappreciably from v(O), we shall generally refer to the absolute value of the latter as the extra-atmospheric speed of the meteorite, although it actually is a lower bound for this speed. In the case of the three famous meteorite falls of Prambachkirchen, Austria; Pultusk, Poland; and Treysa, Germany, application of the inverse acceleration method to paths, H’B’, all having the same beginning height (B’ = B’(670)), but terminated by the points of disappearance H t 9 determined from the best of the numerous visual observations led to the speeds recorded in Table X (compare [29], p. 375). Earlier speed determinations for these meteorites are also exhibited, together with a determination of the heliocentric speed of the Kybunga, Australia, fireball by a photographic method described in the next section, 4.5.2. In view of the great current importance of the so-called “re-entry problem” for rockets and artificial satellites, attention should be directed to an important by-product of the above application to the Treysa meteorite of the formula-given in the writer’s 1938 paper in the Astronomische Nachrichten [58]-connecting the extra-atmospheric mass M , and the impacting mass M for a nonfragmenting siderite. The value thus obtained for the extra-atmospheric mass of Treysa, viz., M a = 97.53 kgm, implies an ablation-loss for this iron meteorite of approximately 35 %. Since the formula in question was regarded as only a first approximation to the true relation between M , and M , a check on the ablationloss value just given was made by an independent method. This method consisted of reconstruction of the extra-atmospheric Treysa-octahedron, and was based on the clear evidence that this was the original crystallographic form of this meteorite revealed by careful study of the meteoritic mass of 63.28 kgm actually recovered. Results obtained in this manner indicate that the ablation-loss may have approached 41% for the relatively small, swiftly moving Treysa octahedrite. The ablation-loss values juet cited stand in sharp contrast to a loss as low as lo%, the only 9

In the case of the daylight Treysa fall, H’

=

0.

289

EFFECTS OF METEORITES ON THE EARTH

numerical estimate given by Rinehart and O’Neil [126a] in their investigation of the quite small (4 kgm) Algoma siderite. 4.6.2. The Coma Method. In the case of the Kybunga, Australia, fall an excellent photograph showing the coma about the falling meteorite was secured by a well-placed and alert amateur photographer [127]. As in the case of lined, shaped-charge jets penetrating air [128], the highspeed meteoritic projectile is shown to be surrounded by an onchnoidal TABLE X. Meteoritic speeds (km/sec) (nonhyperbolic values are underscored).

Name of meteorite Prambachkirchen

Speed by inverse Other Helio- accelera- Time speed centric tion of flight deterspeed method (sec) minations 73.0 93.6

Pultusk

Treysa

Kybunga Shower meteors

65.

3.08

56. 36. 56. 63.1

36.

3.45

37.5 47.4

30.7

3.29

45.8 34.541 . O 37.4 ~

Asteroidal meteors

45.

27.5 13.6 30.

19.8

36.661.2 13.3 -

Authority

Remarks

Schadler & Rosenhagen Author

visual

Whipple

photographic

inverse acceleration Galle-von Niessl visual visual C. C. Wylie visual Nielsen inverse Author acceleration visual Wegener Author inverse acceleration Author coma method Whipple photographic

coma composed of hot vapors derived from its volatilization, admixed with colliding and trapped air molecules. The projection of this pearshaped coma on a plane containing the tangent to the fireball trajectory is found to be a curve, the vertex portion of which can be closely approximated by a suitable parabola. Let us denote by w(t) the speed with which the meteorite penetrated the air, and by 5 ( t ) the effective speed of sidewise escape of the highly compressed gaseous cap built up between the swiftIy advancing meteorite and the static layers of air resisting its progress toward the earth. In contrast t o the familiar shock-wave situation encountered in ballistics, neither of these speeds can be treated as constant. We shall, therefore,

290

LINCOLN LAPAZ

seek t o obtain two relations from which the average values, 5 and Z of ir(t) and w(t>,respectively, a t least for sufficiently short intervals of time, can be calculated. In line with fundamental results obtained by Epstein [ 1291 in investigations of an analogous two-dimensional shock-wave problem, the first relation between 5 and .w‘ may be taken in the form

-

(4.5)

-

6 = hLi)

where h is a constant. The second desired relation between Z and 5 is secured, after suitable choice of a wv-coordinate system, by a limiting process applied t o the equation v 2 = cw of the approximating parabola (see [29], p. 372). The final result obtained can be summarized as follows. For given h, the mean values of w and ir within sufficiently short intervals of time can be calculated as soon as the value of the parameter c has been obtained from a study of the parabola approximating the vertex portion of the projection of the coma on the wv-plane. In the application to the Kybunga photograph, h was taken equal to one-third, in line with opik’s evaluation of this parameter for Epstein’s I( ideal case.” Because, as opik has stressed, in the actual case the speed of escape sidewise is smaller than in Epstein’s ideal case, it can be shown that use of h = will lead to a lower bound for the speed of the Kybunga meteorite a t the time a t which it was photographed. Although the Kybunga fireball was deep in the atmosphere a t this time (in fact, its height was only 31.3 km), nevertheless, the lower bound obtained by the coma method was found to lead to a value in excess of 45.8 km/sec for the heliocentric velocity of the Kybunga meteorite. This meteorite was therefore certainly moving in a strongly hyperbolic orbit before it became entrapped in the earth’s atmosphere (see [29], p. 374). 4.6.3. A Method Which M a y Be Applicable to High-SpeedrCarbonBearing Meteorites. All ballisticians are familiar with the fact that the appearance of a cloud of black smoke after the explosion of a charge of T N T is a certain indication that the charge actually detonated and did not merely burn a t low pressure. The extremely high pressure consequent on genuine detonation acts t o produce solid (uncombined) carbon. It is also well known that for many organic powders the conditions of pressure and temperature under which carbon, that is to say, black smoke, will be produced have been calculated [130]. Visual observations of meteorite falls show that certain types of meteorites produce spectacular clouds of black smoke when so-called “explosions” occur prior to or a t arrival of the meteorite at the Hemmungspunkt (point of retardation). Since this “ black-smoke” phenomenon has been chiefly remarked in connection with the carbon-bearing carbona-

EFFECTS OF METEORITES ON THE EARTH

291

ceous chondrites (Kc), it is a t least conceivable that an observed cloud of black smoke from such a meteorite is an indication of the very high pressure t o which the meteoritic vapor in the cloud is subjected. The carbonaceous chondrites are notoriously fragile and it is therefore reasonable to expect that as the head resistance on such a meteorite peaks up near the point of retardation, the whole (or a large portion) of the stone may quite suddenly be comminuted into powdery form. The result is a shower of very tiny meteorites moving through relatively dense air not a t the moderate speed that each meteoritelet would have attained had it penetrated as an individual t o such low levels in the atmosphere (see [29], p. 380), but, rather, endowed with the very great kinetic energy corresponding to the high velocity possessed by the main mass of the meteorite just before its disruption. The subsequent almost instantaneous transformation of the large kinetic energy carried by each tiny particle must lead to what could more aptly be called a “meteoritic detonation” than the characteristic meteoritic noises for which this term already has been preempted, If the pressure developed in this “detonation” of a carbon-bearing meteorite is in excess of what the ballistician calls the “smoke-formation pressure,” then it may be anticipated that a cloud of black smoke will be produced. This conjecture has been tested on one of the most recent wellobserved carbonaceous chondrite falls-that near Murray, Kentucky in 1950-in connection with which a single but notable cloud of black smoke was reported, The Murray meteorite was chosen for the test in question not only because of its recency, but also because Olivier [131], by use of the classical methods, and the writer (see [132], p. 115, footnote (*)), by use of the inverse acceleration method, had found strongly hyperbolic velocities for the Murray fall. The Murray meteorite was found by Horan [132] t o contain 2% of carbon. Available data on the smoke formation pressures for low carboncontent high explosives indicate that, since the temperature in the Murray fireball was certainly of the order of 3000”K, the smoke formation pressure p for the material in the Murray meteorite would fall in the high pressure range 6.9 x 10” dynes/cm2 < p < 6.9 X 1 O I 2 dynes/cm2. If these limiting values for the pressure p are introduced into a retardation formula of the type rpVn = p , where y is taken as 1 (see [124], p. 252) and p is the atmospheric density in gm/cc a t an altitude of 46 km (the height a t which the Murray black smoke cloud appeared), it is found that n = 2 leads to values for V so far in excess of even the largest hyperbolic velocities reported for telescopic meteors by Boothroyd [114] as to merit no consideration. For n = 2.5 and n = 3, the values of V in km/sec are given in Table XI.

292

LINCOLN LAPAZ

I n view of the wealth of concordant real path data collected in the case of the Murray fireball, the very low V values given by the choice n = 3 are clearly inadmissible. The smaller value, 88 km/sec given by the choice n = 2.5 is near the first velocity value (77 km/sec) found by Olivier for the Murray meteorite; as well as near the value 70 km/sec given by the inverse acceleration method as a lower bound on the speed of the Kentucky meteorite. TABLE XI. Velocities computed from the retardation formula p = 6.915 X 10"

V(2.5) V(3)

8.812 X 10 krn/sec 6.131 km/sec

ypVn =

p.

p = 6.915 X 10**

2.214 X lo2km/sec 1.321 X 10 km/sec

Since the meteoritical importance of the particular velocity-exponent n = 2.5 has already been signalized in another connection [133] it would seem that the velocity method of this section, with n chosen as 2.5, although obviously speculative, merits consideration. 5. THE HYPERBOLIC METEORITE VELOCITYPROBLEM. I1

Two quite incompatible points of view are revealed by the account of the meteorite velocity controversy given in Section 4. One holds that meteoritic material is observed to move with high (hyperbolic) as well as with low (elliptic) velocities, while the other, in effect, denies that a hyperbolic component exists a t all. Since there seems little possibility of securing agreement as to the relative importance of either instrumental peculiarities and limitations or of the role of the personal element, it is natural t o cast about for some crucial test capable of disclosing in an unambiguous way whether the meteoritic universe displays the comparative uniformity that would characterize a system of bodies all moving with low (elliptic) velocity about the sun, or rather is comprised of two categories of objects as diverse dynamically as would be a low-speed solar system component and a high-speed interstellar component. Obviously, such a crucial test, to be of any value in resolving the heated controversy, must be completely divorced from the many and varied velocity methods already devised, each with its own partisan champions. I n view of the well-established uniformity not only of the material basis of the known universe, but also of the physical processes operative within this universe, it seems clear that the most significant observable difference between the interstellar and the solar system meteorites would be in their different mean velocities a t the earth's distance from the sun.

EFFECTS OF METEORITES ON THE EARTH

293

Since the wide variety of observational techniques already applied t o detect such velocity differences has led only to the controversy briefly reviewed in the previous section, it may seem hopeless to hunt for a method that will successfully reveal the existence of these differences. A clue, however, is to be found in a remarkable paper of Lowell’s [134]. His highly interesting dynamical analysis clearly shows not only that the velocity due to the sun’s attraction and that due to the earth’s upon a particle falling to the latter under the action of both are not simply additive, but also that the increment in meteoritic speed produced by the action of the terrestrial gravitational field is very much greater for slow meteorites than for fast ones, the ratio of the speed increments in the particular case treated by Lowell having the value 5 . If changes in the directions rather than in the magnitudes of the meteoritic velocity vectors are considered, the same differential effect is present. These facts suggest that if we replace the three-body problem considered by Lowell (involving the sun, the earth, and a meteorite) by an analogous threebody problem (involving the earth, the moon, and a meteorite), the differential in the disturbing effects exercised by the moon on fast and slow meteorites may lead to observable differences in behavior between these two categories of bodies. For example, one would anticipate that the moon would have little or no effect on the fall to earth of swift hyperbolic meteorites passing through the earth-moon system; whereas, our widely roving satellite might be capable of diverting numbers of slow-moving solar system meteorites into the more or less void torus which, as opik [135] has pointed out in an important paper, is essentially the nature of the track now swept out by the earth. If the above reasoning is valid, evidence of a moon effect should be most notable for the very slowest meteorites intercepted by the earth. Consequently, one should seek such evidence first in the case of processional fireball falls like the famous Canadian incident of February 9, 1913,’O for which an exceedingly small initial velocity relative to the earth has been found by most investigators of the phenomenon. Influenced by these considerations, the writer made a search of the literature which disclosed that as long ago as 1923, Pickering [138]had already noted with some surprise that both the Canadian procession and a later occurrence quite similar in character but involving much fainter meteors had developed when the moon was in essentially the same position on the celestial The vaIidity of Chant’s [I361 satellitory interpretation of the Canadian fireball procession recently has been questioned by Wylie [137]. The procedures adopted and the conclusions reached in Wylie’s papers on the Canadian incident are discredited in two papers (one by A. D. Mebane and the other by the present writer) which have appeared in issue No. 4 of the journal Meteoritics, pp. 402-421.

2 94

LINCOLN LAPAZ

sphere. In fact, on the basis of the near identity of the lunar positions a t the two times of fall, Pickering was led to hazard the conjecture that the moon had played an important role in bringing both processions down into the earth’s atmosphere. Since it is, of course, possible that the near identity in lunar position which attracted Pickering’s attention was simply a fortuitous coincidence, an extensive statistical investigation is necessary to establish whether or not the moon is actually capable of increasing the probability of fall of meteorites or at least of certain categories of meteorites. In the present section, the results of such a statistical inquiry, based on examination of the times of fall of 317 meteorites are presented. In the writer’s opinion, these results leave no doubt that the frequency of fall of one subclass containing 165 meteorites is strongly dependent on the moon’s nearness in direction to that of the line of apsides of Jupiter’s orbit. On the contrary, the 152 members of the remaining group of meteorites constitute a quite distinct subclass of meteorites, the frequency of fall of which is affected but little or not at all by the position of the moon in the sky. It is the writer’s belief that the first category comprises the solar system meteorites and the second consists of the much faster interstellar meteorites. 5.1. The Frequency Distribution of Meteorite Falls as a Function of the Right Ascension of the Moon at the T i m e of Fall

The time interval selected for the statistical test suggested in the previous paragraph was a half-century 1896-1945, inclusive. Choice of this interval was dictated by the fact that an examination of the literature of meteoritics disclosed that a larger percentage of dependable meteoritic classifications and times of fall were available for the more recent falls; and, furthermore, that the half-century in question contained almost as many critically evaluated meteorite orbits as the preceding 500 years 11391. Within the half-century chosen, 269 meteorites fell [140]. Of these, 265, or 98.5%, are included in the totality of 317 meteorites to be reported on in this section. Times of fall or classifications, or both, of the necessary accuracy were lacking for the remaining 1.5% of the meteorites in question. In addition t o the 265 meteorites just referred to, 17 meteorites that fell after January 1, 1945, and 36 meteorites that fell before January 1, 1896, are included in the group of 317 meteorites treated in this section. Details on the manner in which these additional 53 meteorites came into consideration (given in Appendix 11) will make clear that they stand on exactly the same footing as those meteorites that fell in the half-century to which the investigation originally was limited. The conclusions t o be

295

EFFECTS O F METEORITES ON THE EARTH

announced below would not be significantly altered if the 53 meteorites in question had been excluded from consideration. In Table XII,the distribution of the totality of 317 meteorite falls with respect to the right ascension of the moon a t the time of fall is given, together with other relevant data such as the year, month, day, and hour of fall, the name, and the meteoritic classification. It is necessary to specify that the time “Noon?” has been used in every case where the day but not the hour of fall was the only information that could be found. In every such case, the tabulated a may, of course, be in error, but by no more than one-quarter of the moon’s daily motion for the date in question. The effect of errors of this magnitude is of no importance in the present connection. In view of the manner in which the tabular data in Table XI1 are grouped, it is easy to verify that the number of meteorites in the four quadrants, Q1, Q 2 , Q 3 , and Q4, centering in sequence on a = 0”, a = 90”, a = 180”, and a = 270”, is, respectively, n(Ql) = 98, n(Q2) = 60, n(Qa)= 88, and n(Q4)= 71. The remarkable nonuniformity of this distribution with respect to a certainly would not seem to be the result of chance. To verify this common-sense judgment mathematically, we may proceed as follows: The probability p that a meteorite falling at random would belong in (Q1 Q3)is p = 48,as is the counter probability q = 1 - p . One would therefore expect 3 1 7 4 of the meteorites in Table XI1 to fall in (Q1 Q3). The discrepancy d between this number and the number actually observed has the large value d = 27.5. To ascertain the probability of occurrence of a discrepancy of this magnitude, we shall employ Laplace’s theorem to the effect that if in a single trial the probability for success is p and that for failure is q, then the probability, P, that in n trials the discrepancy will not exceed numerically the number d is very nearly equal to

+

+

(5.1)

In our case calculation gives d / d = = 2.184, from which it follows that the corresponding value of P = 0.998. One can therefore infer that there are less than two chances in a thousand for occurrence of the observed discrepancy, d = 27.5. It should be emphasized that this significantly nonuniform distribution has been deduced from observational data affected by all of the potent and highly variable terrestrial factors that preclude recovery of more than a small fraction of the meteorites actually seen to fall [26, 1411. For further progress, it is essential that standard smoothing techniques be applied to such rough observational data as those in Table XII. Application

296

LINCOLN LAPAZ

TABLE XII. The right ascension

a of the moon at the time of fall of each of 317 meteorites.

No.

(a)

Year

Mo. Day

Hour

*I *2 3 4 5 *6 7 *8 *9 *lo 11

316% 31834 319 319% 319% 320 320M 323 324 32434 32534

1917 1905 1903 1937 1911 1922 1929 1932 1908 1911 1868

Feb. Apr . July Sept. Sept. Apr. Feb . Nov. Apr . June Mar.

20 8:30 A l:oo P 27 12 1O:OO A 17 11:45 P 6 3:30 P 20 7:45 P 9 12:45 A 5 1o:oo P 25 2:OO A 16 5:OO P 20 Noon?

12 13 *14 15 16 17

326 32654 326% 32735 329t.4 330

1914 1930 1926 1931 1938 1903

July July Dec. Aug. Feb. Apr.

10 Noon? 13 Noon? 10 9:30 A 27 3:OOP 1 5:OO P 22 11:30A

18 19 *20 *21 22

33035 33235 335% 336 33734

1932 1933 1898 1927 1903

May Apr. Jan. Apr. Jan.

5:30 P 26 19 8:30 P 24 2:30 P 27 1:00 A 3 11:OO P

23 *24 *25 *26 27 28 *29 30

339 339 34134 344 34435 345 345t.i 34534

1915 1927 1869 1882 1920 1869 1933 1933

Jan. June May Aug. Aug. Sept. July Mar.

19 Noon 21 6:OO A 5 6:30 P 29 Noon? 30 11:15 A 19 9:oo P 11 9:30 A 24 5:OO A

31 *32 33 34 *35 *36 *37 38 39

3463i 346% 347 34834 348t.i 34934 350% 351 35135

1897 1896 1931 1933 1889 1913 1905 1882 1927

June Apr . Apr. Oct. June Jan. May Aug. Apr.

20 8:30 P 9 6:15 P 14 11:53 A 2 6:OO A 18 8:30 A 12 6:OO P 27 10:45 A 2 5:OO P 28 9:00 A

Name Ranchapur, India Karkh, India Valdinizza, Italy Mabwe-Khoywa, Burma Demina, Siberia Hedeskoga, Sweden Padvarninkai, Lithuania Prambachkirchen, Austria Novy-Projekt, Lithuania Kilbourn, Wisconsin, USA Daniel’s Kuil, South Africa Saint-Sauveur, France Miller, Arkansas, USA Ojueltos Altos, Spain Yukan, China Aztec, New Mexico, USA Jackalsfontein, South Africa Kuenetzovo, Siberia Brient, USSR Mjelleim, Norway Sopot, Romania St. Mark’s Mission, S. Africa Visuni, India Trysil, Norway Krahenberg, Bavaria Pirgunje, India Merua, Iridia TjabB, Java Athens, Alabama, USA Pasamonte, New Mexico, USA Lanpon, France Ottawa, Kansas, USA Pontlyfni, Wales Pesyanoe, USSR Mighei, Ukraine Banswal, India Minnichhof, Hungary Pavlovka, Russia Aba, Japan

Classification cg cg Ci AE Chyi ChYW Aleu sh Chy Cg Cg Cenk Cenk Ceng Chy Civ AE Ci Ci Aleu AE C cc Cck cw Chyib (Cho) cwv Cbrg Chyk Cgb Aiho Civ Cgb(Cho) AE Aiho Cr cg Cw Aiho AE

297

EFFECTS OF METEORITES ON THE EARTH

TABLE XII. The right ascension 01 of the moon a t the time of fall of each of 317 meteorites. (Continued) ~

No.

(a)

Year

Mo. Day

Hour

*40 *41 42

3523.6 1882 Mar. 353 1933 Aua. 3533.i 1933 Aug.

19 1:00 P 8 8:OO P 8 10:30 A

43

3533.6 1919 June

20

*44 45

356% 1929 Oct. 35755 1927 Dec.

15 11:30 P 30 11:30A

46 47 48 49 50 *51 52 53 54 55 *56 57 58 *59 60 *61 62 *63 64 *65

3583.6 3583.6 358% 3593i 35955 1 3 33 i 3 36 3% 43.6 5 35 6 3.i 6% 7 3.6 7%

June May Sept. Sept. Mar. Mar. Nov. Apr. Mar. June Oct. Dec. July Sept. Oct. June Aug. June Aug. June

10 11:oo P 26 3:OO P 19 l:oo P 24 Noon? 31 Noon? 31 8:45 A 12 1:oo P 14 11:25 A 12 10:30 P 30 1o:oo P 1 2:oo P 22 5:OO P 11 7:15 P 29 5:OO P 9 2:OO A 1 1o:oo P 5 7:30 A 15 Noon 22 8:OO P 11 8:56 P

66 67

1901 1916 1910 1942 1938 1908 1902 1923 1899 1918 1868 1868 1868 1928 1938 1902 83.5 1898 9 1906 9% 1902 11 1939

6:OO P

1917 July 1865 Mar.

11 26

Noon 9:OOA

68 69 *70

11% 1910 Oct. 13 1907 May 13 1933 Jan.

17 9 31

Noon? 1:30 P 4:30 P

*71 *72 *73 *74 *75 *76 77

133.6 143.6 15% 213.i 213.4 22 223.5

Sept. 10 Feb. 2 Jan. 30 Apr. 3 Apr. 13 Oct. 30 Aug. 6

2:15 P Noon? 7:OOP 3:30P 7:30 A 5:OO P 9:00 P

11 11

1930 1922 1868 1916 1896 1944 1939

Name

~

Classification

Fukutomi, Japan cgv Repeev Khutor, Russia 0 Sioux County, Nebraska, Alho USA St. Mary’s County, Md., Ceng USA Beardsley, Kansas, USA Cg Oesede, Hanover, Cbrc Germany Sindhri, Bombay, India Cc Calivo, Philippine Islands A Khohar, U.P., India ccg Maziba, Uganda Ci Kasamatsu, Japan AE Avce, Italy H Kamsagar, India Ci Holetta, Abyssinia AE Bjurbiile, Finland Chyc Richardton, N.D., USA Cbrc Lodran, India S Moti-ka-nagla, India Ck Ornans, France Chyc Naoki, India cg Civ Zhovtnevyi, USSR Marjalahti, Finland LPa Andover, Maine, USA Cc Kijima, Japan C Caratash, Smyrna AIam Dresden, Ontario, cg Canada Nan Yang Pao, China Cc Vernon County, Cbr Wisconsin, USA Palahatchie, Miss., USA Cc Chainpur, India cc S Dyarrl Island, New Guinea Oldenburg, Germany Cw Baldwyn, Miss., USA Cwv Pultusk, Poiand Cbrgv Treysa, Germany Om Lesves, Belgium Chyg Valdavur, India cg Andura, India Ci

298

LINCOLN LAPAZ

TABLE XII. The right ascension CY of the moon at the time of fall of each of 317 meteorites. (Continued) No.

(01)

78 *79 80 *81 *82 83 84 85 86

2635 26% 28% 29% 32 33 33 36% 37

87 88 *89 *90 91 *92 *93 *94 295 96 *97 98

37 37% 39 39% 4034 41 41 35 42 43 43 ?4

99 100 101 102 103

Year 1925 1921 1944 1921 1939 1933 1865 1932 1921

1897 1916 1868 1932 1865 1930 1938 1933 1947 1914 43f4 1944 44% 1924 46)i 47 48)i 48% 49%

1941 1868 1943 1899 1938

Mo. Day Sept. June Mar. Jan. Sept. Dec. Aug. Aug. Oct.

Hour

6 Noon? 30 3:OO P ,26 10:15 A 17 9:oo P 3 Noon 26 6:OO P 12 7:OO P 22 3:OO P 17 11:oo P

Sept. 15 Noon? 5 2:30 A Apr. Nov. 27 5:OO P Apr. 8 Noon? May 23 6:OO P May 27 Noon Jan. 11 2:30 P 2 8:33 P Feb. Feb. 26 3:45 P July 17 Noon? Feb. 1 2:oo P June 27 3 3 0 P July Feb. July Sept. June

18 4:OO P 29 11:OO A 25 5:35 P 23 3:OO P 24 6:30 P

*lo4 105 * 106 107

51fi 1914 May 5236 1919 May 54% 1906 Mar. 553i 1902 Nov.

24 1 29 15

Noon? Noon Noon? 6:45 P

108 109 *110 *111 112

57% 6l)i 65% 67 68%

1934 1920 1939 1936 1948

Mar. Dec. Dec. July Feb.

20 23 24 15 18

6:30P 5:30 P 7:40 P 4:45 P 4:56 P

*113 *114 *115 *116

70)i 7154 7235 76%

1926 1905 1937 1868

Apr. Jan. May May

16 Noon? 17 9:30 P 12 8:45 P 22 10:30A

Name

Classification

Numakai, Japan C Tuan Tuc, China Chyg Tulung Dzong, Tibet AE Haripura, India Cr Santa Cruz, Mexico Cr Pervomaisky, USSR Cenivk Dundrum, Ireland Cbrk Douar Mghila, Morocco Chyi Rose City, Michigan, Cbrsb USA Gambat, India Civ Ekh Khera, India Civ Danville, Alabama, USA Chygbv Khor Temiki, Sudan cw Gopalpur, India Cbrc Kurumi, Japan C Lavrentievka, USSR cw Zemaitkiemis, Lithuania Chywv Seldebourak, North Africa Cg Nyirabrhny, Hungary AE Hallingeberg, Sweden Cg BBrBba, French West Aleu Africa Phuoc-Binh, Annam Cbrg Motta di Conti, Italy Cc Benoni, South Africa Cbr Donga Kohrod, India Ci Chicora, Pennsylvania, Chy USA Kisvarshy, Hungary AE Adhi Kot, India cs Kulp, Caucasus C Bath Furnace, Ci Kentucky, USA Tirupati, India Ci Atarra, India cs Nyaung, Upper Burma 0 Nassirah, New Caledonia Cbrgv Norton County, Kansas, Alno USA Urasaki, Japan AE Tomakovka, Ukraine Chyg Kaptal-Aryk, USSR cgv Slavetic, Yugoslavia Cgb

299

EFFECTS O F METEORITES ON THE EARTH

TABLE XII. The right ascension (I of the moon at the time of fall of each of 317 meteorites. (Continued) Year

Mo. Day

No.

((I)

117 *118 119

78 1923 Oct. 78% 1935 Mar. 7936 1942 Aug.

120 *121 *122 123 124 *125

79% 81% 8335 89ji 89% 95%

*126

963/4 1930 Apr.

127 '128 129 130

96>/4 96% 98>/4 983/,

1899 1904 1917 1907

Oct. Oct. Apr. Nov.

*I31 *132 133 *134 *I35 *136 *137 *138

99)/4 99j6 lOlj4 10334 104 10535 105% log>/,

1916 1913 1803 1918 1947 1935 1916 1899

Jan. Apr. Apr. Jan. Dec. Apr. Oct. Jan.

139

109% 1094/4 llO!i 11255 115 116 117 120 12136

1942 1900 1897 1950 1935 1803 1908 1925 1925

Apr. July Oct. Oct. July Oct. June July Apr.

140 *141 142 *143 *144 *145 146 *147

1933 1946 1925 1910 1940 1925

Jan. May June Jan. Dec. Dec.

148 12:3j/4 1911 June *149 12634 1919 Oct.

*150 *I51 152 *IC3

127 12755 129>q 13054

1944 1920 1917 1914

June Aug. hc. Oct.

Hour

Classification

Name

1 11:OOA Serra de Mag6, Brazil 12 12:52 A Lowicz, Poland 7 3:OO P Forest Vale, New South Wales 9 4:30 P Phum Sambo, Cambodia 4 Noon? Krasnyi Klyuch, USSR 20 3:oo P Renca, Argentina 22 9:30 P Vigarano, Italy 15 2:30 P Ramnagar, India 29 5:OO P Newtown, Connecticut, USA 6 2:OO P Gundaring, Western Australia 24 7:OO A Peramiho, East Africa 29 4:OO P Pfullingen, Germany 26 1O:OO A Troup, Texas, USA 22 10:30 A Bali Mission Station, W. Afr. 18 9:OOA Baxter, Missouri, USA 13 Noon? Sakouchi, Japan 26 1:00 P L'Aigle, France 25 2:30 P T a d , Japan 28 8:OO A Reliegos, Spain 10 7:30A Sungach, USSR 18 11:47A Boguslavka, Siberia 25 7:45 A Zomba, British Central Africa 22 7:OO P Kapoeta, Sudan 25 Noon? 0-Feherto, Hungary 18 Noon? Delhi, India 5 4:lO A Monse, Africa 29 2:20 P Patwar, India 8 10:30 A Apt, France 30 7:OO A Kagarlyk, USSR 20 7:OO P Villarrica, Paraguay 30 8:OO P Queens Mercy, South Africa 28 9:00 A Nakhla, Egypt, 16 8:OO A Bur-Gheluai, Ital. Somaliland 23 Noon? Fort Flattcrs, Algeria 13 Noon? Nanseiki, China 3 1:15 P Strathmore, Scotland 13 8:45 P Appley Bridge, England

Aleu S C Cbri C ChY ccs AE D Og Aleu 0 Ci

cs

C 0 Chyih cw cg Cga H Chyw Ci C cw ChY S cgv cw AE Cbrg Alna Cg AE LPa Chyi Chyg

300

LINCOLN LAPAZ

TABLE XII. The right ascension (Y of the moon a t the time of fall of each of 317 meteorites. (Continued) No.

((Y)

Year

Mo. Day

Name

Hour

Classification

.-

2:OO P Cherveltaz, Switzerland 8:30 P Hainaut, France 9:30 A Santa Isabel, Argentina

Nov. Nov. Nov. Feh. July Aug. Sept. May Apr. Apr. Feb. Jan. Apr. Apr.

30 26 18 26 10 23 19 23 6 2 3 9 13 !I

168 143$/a 1869 Jan. 169 146 1868 Dee. 170 147j/2 1949 Jan.

1 5 16

1230 P

26 3 1 li

Noon? Noon? Noon? 7:42 P

*175 15274 1929 July

9

3:00 P

June May June Dec.

30 22 29 26

11:30 P 1O:OO A 11:58 A

180 16036 1949 Sept. 21 6 181 160% 1924 July

1:45 A 4:20 P

154 155 *156 *157 158 *159 *160 161 *162 163 164 *165 *166 167

$171 172 *173 *174

176 177 178 *179

*182

183 *184 I85 186 187 *188 *189 190 *191

13034 13014 131 13235 133j.i 135 1363/4 13615 137 138M 13955 141 14235 143

14934 1493.5 150 1503/4

1553i 15636 15735 159

1613/4 162 163>/4 164 165 165 16536 167 167 170>/4

1901 1934 1924 1896 3899 1900 1949 1950 1914 1936 1882 1947 1916 1919

1940 1926 1873 1936

1903 1904 1903 1934

1932 1928 1897 1910 1926 1869 1949 1907 1924 1944

Oct.

May June Aug.

July Aug. Aug. Nov. Dec. Jan. Sept. Feb. Mar. May

Noon? 8:OO A 9:OO P 9:00 A 2:OO P 7:OO A 1:OO A 4:OO P 7:OO A Noon? Noon

3:oo P 4 3 0 I’

Noon?

8 1:00 P 16 7:OO P 1 11:30A 24 6:OO P 25 6:50 A 30 5:OO A 21 Noon? 1 Noon? 19 11:30 P 3 Noon?

Atemajac, Mexico Allegan, Michigan, USA Leonovka, Ukraine Karewar, Nigeria Madhipura, India Kuttippuram, India Yurtuk, USSR Mocs, Transylvania Git Git, Nigeria Tomita, Japan Cumberland Falls, Ky., USA Hessle, Sweden Frankfort, Alabama, USA Benton, New Brrinswick, Canada Semarkona, India Chaves, Portugal Virba, Bulgaria Crescent, Oklahoma, USA Bald Mount,ain, N. Car., USA Kerrnichel, Francc Altai (Barnaul), Siheria Uberaba, Brazil Fayet,teville, Arkansas, USA Beddgelert, North Wales Johnstown, Colorado, USA Khanpur, India Utzenstorf, Switzerland Zavid, Yugoslavia Lakangaon, India Ulmiz, Switzerland Angra dos Reis, Brazil Akaba, Transjordan Domauitch, Asia Minor La Colina, Argentina Mike, Hungary

Cck Cib Chyw ChYg Cbrc Cenw cw ChY cwv Atam Chywv cw C Wht, Cbrc Aiho C AE A,am cwv Crs

cfv Ck AE ccv AE Cks A d Cwb Chyi Chygb Aleu Chykc Alan cw AE Cbrg C

30 1

EFFECTS O F METEORITES O N THE EARTH

TABLE X I I . The right ascension

Q of the moon a t the time of fall of each of 317 meteorites. (Continued)

NO.

(a)

Year

192 193 194 195 *196 *I97 198

171 171 172 17235 172% 173>/4 1743/4

1946 1939 1931 1936 1935 1908 1903

Mo. Day

Hour

Jan. June June May July Dec. June

21 23 22 29 7 15 30

Noon? 1:OO P 3:OO A 7:34 P Noon*? Noon? 2:oo P

1912 June

21

2:oo P

*200 1763/4 1904 Aug.

13

8:OO P

201 *202 203 *204 205 206 *207 *208 209 210 *211 *212 213 214

27 12:45 P 9 150 P 21 9:30 B 12 7:25 P 12 3 : 3 0 P 14 11:OO P 20 9:00 A 25 Noon? 26 Noon? 19 7:15 P 24 5:44 A 23 5:00 A 2 5:OO P 1 9:42 A

199 176!/4

17835 182)/4 1823/4 183 183% 18634 18635 187 191% 192!/4 193>/4 193% 194j/4 195>/4

1918 1914 1916 1910 1906 1935 1921 1928 1929 1912 1909 1873 1945 1933

Feb. Apr. Nov. July Nov. May Apr. June Feb. July July Sept. Feb. July

6:49 P Noon

215 1953i 1950 Oct. *216 198 1865 Jan. 217 198$/4 1946 Aug.

11 19 2

3:oo P

218 20055 1865 Sept. *219 20094 1904 Apr. *220 2013/4 1930 Feb.

21 28 17

7:OO A 6:20 P 4:50 A

*221 *222 223 224 225 226 227 *228 229

202?4 203>/4 204ji 20436 205>/4 205j/4 20536 206>/, 206j/,

1865 1938 1865 1909 1930 1939 1869 1921 1939

Aug. Dec. Aug. May Mar. May May Aug. Apr.

25 11:30 9 16 5:30 P 25 9:00 A 30 10:30 P 17 Noon? 2 7:25 P 22 1o:oo P 9 9:OO A 5 6:OO P

Name

Classification

Krymka, Ukraine C Chervony Kut , Ukraine Aleu Malotas, Argentina Cbr Ichkala, Siberia ccg Sakurayama, Japan O Sete Lagbas, Brazil AE Rich Mountain, N. Car., Chyiv USA Leeuwfontein, South Chyi Africa Shelburne, Ontario, Chygvb Canada Glasatovo, Russia Civ Ryechki, Ukraine Chyg C Rampurhat, India St. Michel, Finland Chyw Kirbyville, Texas, USA ‘42 Perpeti, India Cen Pitts, Georgia, USA 0 Yoshiki, Japan AE Olmedilla, Spain Chyvb Holbrook, Arizona, USA Chykc CW Gifu, Japan Cenk Khairpur, India Cih Meru, Kenya Cherokee Springs, Ci S. Car., USA c: Vengerovo, Siberia Supuhee, India Cgh Pena Blanca Spring, Aran Texas, USA Muddoor, India Chyr Gurnoschnik, Bulgaria ChY R Paragould, Arkansas, cg USA Aumale, Algeria CVW Ivuna, Tanganyika. Cr Shergotty, India Aish Blanket, Texas, USA C Zindoo, Korea C Kendleton, Texas, USA CdJ Cbrkv KernouvB, France Shikarpur, India cwv Ekeby, Sweden cg

302

LINCOLN LAPAZ

TABLEXII. The right ascension CY of the moon at the time of fall of each of 317 meteorites. (Continued) ~~

No.

(01)

230 231 *232 *233 *234 *235 *236 237 238 239 *240 *241 242 243

207% 2093i 209% 209% 210% 21135 21336 21436 215 218 221 22 1 22 1 2213i

244 221% 245 222 *246 222%

Year

Mo. Day

1930 1869 1943 1905 1787 1911 1924 1920 1916 1942 1921 1947 1929 1913

May Oct. Nov. Sept. Oct. Jan. Aug. Sept. July Aug. May Feb. Mar. Apr.

Hour

11 4:OO P Lillaverke, Sweden 6 11:45 A Lumpkin; Georgia, USA 7:OO P Leedey, Oklahoma, USA 25 9:30 P Modoc, Kansas, USA 2 12 3:OO P Kharkov, Ukraine 22 3:55 P Tonk, India 7 2:30 P Muraid, India 16 Noon? Kushiike, Japan 10 11:OO A Sultanpur, India 18 Noon? Kamalpur, India 5:30 P Samelia, India 20 12 10:38 A Sikhote-Alin, USSR 1 5:24 A Khmelevka, USSR 21 5:OO P Moore County,

4 15 16

1934 Dec. 1928 Oct. 1898 Oct.

247 *248 249 250 *251

225% 22835 2303/4 231x 23136

1905 1928 1903 1900 1928

Oct. 29 Nov. 12 Oct. 22 8 July 8 Apr.

*252 *253 254 *255 256

232>/4 23236 234 235 235

1940 1922 1910 1873 1920

Mar. Jan. Jan. Sept. Jan.

*257 258 *259 *260 *261 '262

235% 235% 239 241% 245% 248%

1937 1934 1932 1938 1900 1918

Dec. Mar. Aug. June May May

'

27 21 7 26 15 29 7 10 11

15 26

283 249% 1944 Sept. 23 264 251 265 251%

1803 Dec. 1902 July

13 17

266 252%

1906 Dec.

15

Classification

Name

N. Car., USA Noon? Farmville, N. Car., USA 3:OO P Oter~jy,Norway mdt. Mariaville, Nebraska, USA 8:30 A Bholghati, India 7:30 A Isthilart, Argentina 7:OO P Dokachi, India 4:OO P Alexandrovsky, Ukraine 7:15 P Narellan, New South Wales Noon? Bhola, Pakistan 8:OO P Florence, Texas, USA 11:30 A Mirzapur, India Noon? Santa Barbara, Brazil 8:00 P Aguila Blanca, Argentina 1O:OO A Rangala, India 12:45 P Mangwendi, Rhodesia 4:30 P Archie, Missouri, USA 2:OO P Kukschin, Ukraine 11:30 A Felix, Alabama, USA 9:40 A Witklip Farm, South Africa 12:30 P Torrington, Wyoming, USA 10:30 A Mtissing, Germany 9:30 A Mount Browne, New South Wales 9:30 A Vishnupur, India

cv Chyck cw

Chywv cwv Cr cw C cs AE og H Ck Aleu AE Ci 0 Aiho ChY Chyiv C Chyw AE Chygb Cibv Cho Chyi Chywv Chyib cg

cw

Chycr cg C

Atho Cbrc Cib

303

EFFECTS OF METEORITES ON THE EARTH

TABLE XII. The right ascension of the moon at the time of fall of each of 317 meteorites. (Continued) No.

(a)

Year

Mo. Day

Hour

12 2:oo P Forsbach, Prussia 29 9:00 A Benld, Illinois, USA 9 l:oo P Ashdon, England 23 9:30 P Bahjoi, India 3 12:45 P Changanorein, India 28 11:30 A Ellemeet, Holland 23 Noon? Po-Wang Chbn, China 23 8:00 A Macibini, South Africa 8 10:30 P Nio, Japan 7 Noon? Unkoku, Korea 28 7:25 P Lanzenkirchen, Lower Austria 278 2663i 1937 Sept. 13 2:15 P Kainsaz, USSR 279 2673/a 1949 Jan. 25 7:56 P Mezel, France *280 270 1908 Nov. 26 12:30 P Mokoia, New Zealand 2 5:30 P Jajh deh Kot Lalu, India 281 270% 1926 May 282 27336 1931 July 27 1:30 A Tatahouine, South Tunisia *283 275% 1907 Jan. 12 8:OO P Leighton, Alabama, USA 7 6:35 A Okano, Japan $284 2773i 1904 Apr. *285 27836 1927 July 13 l:oo P Tilden, Illinois, USA 1 9:15 A Simmern, Prussia *286 279% 1920 July 5 6:22 P Fenghsien-Ku, China *287 280)i 1924 Oct. *288 283 1926 June 26 4:30 P Lua, India 4 6:30 P Colby, Wisconsin, USA 1917 July 289 285 290 2853i 1897 May 19 7:45 P Meuselbach, Germany *291 285% 1896 Feb. 10 9:30 A Madrid, Spain "292 286 1790 July 24 9:oo P Barbotan, France 1938 June 16 8:45 A Pantar, Philippine 293 293 Islands 9 3:OO P Tromoy, Norway 1950 Apr. 294 293 2 7:35 A Washougal, Washington, 1939 July 295 294 USA 1:30 P Boriskino, USSR $296 297 1930 Apr. 20 *297 29736 1945 Sept. 17 Noon? Soroti, Uganda 1 Noon? Sharps, Virginia, USA 298 297% 1921 Apr. *299 29835 1900 June 15 Noon? N'Goureyma, French W. Africa 300 299 1924 June 19 8:00 A Olivenza, Spain *301 29936 1902 Sept. 13 10:30 A Crumlin, Ireland 1930 Nov. 25 10:53 P Karoonda, South 302 300 Australia *303 301 1934 June 28 8:OO P Saeovice, Czechoslovakia 304 30191 1924 July 16 5:45 P Forksville, Virginia, USA 267 *268 *269 *270 *271 272 $273 274 275 *276 *277

25236 25436 25435 259 25934 260ji 261% 261% 26235 264M 265

1900 1938 1923 1934 1917 1925 1933 1936 1897 1924 1925

June Sept. Mar. July July Aug. Oct. Sept. Aug. Sept. Aug.

Classification

Name

Ci ChYW Chyw og cg Azan AE Aleu cc C ChY

cs Chyiv Cr Ckv A d

Cr 0 Chykc Ob Chygc Chyg Cc(Asiderite) ChYW Chyc

304

LINCOLN LAPAZ

TABLE XII. The right ascension a! of the moon a t the time of fall of each of 317 meteorites. iContinued) No.

(a)

*305 302 *306 *307 *308 *309 310 311 *312 313 314

Year

1932 D e r .

1897 1940 303)/4 1910 30636 1794 30635 1901 306)5 1922 1898 307 309>/4 1915 31055 1941 30255 303

*315 311 316 312% *317 3133i

Mo. Day 1

Hour

Name

5:OO P

Witsand Farm, S.W. Africa Higashi-KGen, Japan Erakot, India Baroti, India Siena, Italy Hvittis, Finland Tjerebon, Java Quesa, Spain Meestcr-Cornelia, Java Black Moshannon Park, Pa., USA Plantersville, Texas, USA Beyrout, Syria Majorca, Balearic Isles

Aug. 11 Noon? June 22 5:OO 1' Sept. 15 1O:OO A June 16 7:OO P Oct. 21 Noon July 10 10:30 P Aug. 1 9:oo P June 2 6:OO A July 10 6 3 0 A

1930 Sept. 1921 Dec. 1935 July

4 31 17

4:OO P 3:45 P 11:35 A

Classification Chyw Cg Cr Chyw Cho Ccnk ChY Of Cbr Cck Chywv Chyb 0

of such techniques not only provides data showing discrepancies d much less probable than the d = 27.5 of the unsmoothed data; but also discloses a new feature of great significance. I n Fig. 3 (111), the upper (dotted) and the lower (dashed) curves exhibit the smoothed distributions of the group, CrIr,of 317 meteorites in 5' and 30" sectors, respectively. The sinusoidal dependence on the moon's nearness in direction to that of Jupiter's line of apsides shown in the lower curve in Fig. 3 (111) is so pronounced that, in view of the wellknown concentration of the perihelia of asteroidal bodies near Jupiter's perihelion, i t might be concluded that all of our 317 meteorites belong t o a slow, solar system category of asteroidal meteorites. There is, however, a possibility that must not be overlooked. While one might expect asteroidal type meteorites to show such a dependence as that exhibited in the lower curve in Fig. 3 (111),it would be anticipated t,hat the infall of swift interstellar meteorites, being unaffected by the moon, would show a nearly constant frequency for all values of a. Clearly, a subgroup, Cr, of meteorites possessing a frequency of fall independent of a, if present in our totality of 317 meteorites would not mask the sinusoidal distribution curve which it is natural to attribute to the subgroup, CII, of solar system meteorites present in CIrr. Furthermore, if C, were removed from CIII,the remaining subgroup, CII, should exhibit the sinusoidal dependence t o be expected in the case of a group of solar system meteorites There thus arises the question as to whether any appreciable subgroup,

EFFECTS OF METEORITES ON THE EARTH

305

7

6 5 4

3 2

1 0

30 20

10

0

z ui

%

4

2

3

z

E

-

n $

2

1

s o z 20 10

0

3 2

1 0

20 10

0 0

30 60

90 120 150 180 210 240 270 300 330 01,

0

30 60

in degrees

FIG.3. Distribution of 152 interstellar meteorites (I),of 105 solar system meteorites (11),and of the totality of these 317 meteorites (111) with respect to the right ascension, 01, of the moon a t the time of fall.

306

LINCOLN LAPAZ

Cr, exhibiting a frequency of distribution essentially independent of a, can be removed from the group, CIII,without destroying such sinusoidal type dependence as that shown in the lower curve in Fig. 3 (111). On the basis of objective criteria which are described in detail in Appendix 11, a subgroup, CI, of 152 meteorites (those whose numbers carry prefixed asterisks in Table X I I ) was removed from the original group, CIII,and then smoothed distribution curves were prepared not only for Crbut also for the remainder subgroup, (711, of 165 meteorites, in exactly the same way as were the curves shown in Fig. 3 (111). Inspection of the resulting distribution curves in Fig. 3 (I) and (11), respectively, will disclose that the frequency of fall of the 152 meteorites in CIis very nearly independent of a, while that of the other subgroup, CIr, of 165 meteorites exhibits more perfect sinusoidal dependence on a than was shown by the original group, CIII,of 317 meteorites. I n fact, an even more exact dependence on the moon’s nearness in direction to that of Jupiter’s line of apsides is shown by the lower curve in Fig. 3 (11) than was shown by the analogous curve in Fig. 3 (111). In view of the fact (pointed out in Appendix 11) that, with very few exceptions, the meteorites entering into the subgroup Cr have orbital characteristics proclaiming them of interstellar origin, or present mineralogical or other features consonant with a nonsolar system origin; and that precisely the reverse may be said in regard t o almost all of the meteorites entering into the subgroup, CII, it would seem permissible to conclude that we have obtained rather convincing evidence of the existence of both solar system and interstellar meteorites. 6.6. B-Processes and the Hyperbolic Velocity Problem

The existence of two distinct meteoritic subgroups, CI and CrI,validates conclusions long ago reached by such pioneer investigators as G. von Niessl and W. F. Denning. Futhermore, examination of the positions on the celestial sphere of the cosmic quits of fireballs associated with certain of the most intensively investigated meteorite falls in CI, will only be found to redirect attention t o specific areas of hyperbolic radiation whose existence was signalized by von Niessl and Denning more than 75 years ago. At that early date, no notions of B-associations and B-processes were in existence. The writer wishes to conclude this section by pointing out the near coincidence in position between one of the most prolific ecliptic centers of hyperbolic radiation of von Niessl and Denning and the nearest of the aggregates, I1 Sco, contained in a tabulation recently published by Morgan et al. [142]. The significance of this relationship can best be appreciated in terms of the recent remarkable papers by Blaauw and Morgan [143, 1441 on the space motions of AE Aurigae and

EFFECTS O F METEORITES ON THE EARTH

307

Columbae. Blaauw and Morgan have shown that the observational data suggest that these two stars were formed in the same physical process 2.6 million years ago and that they now are moving away from their common point of origin in almost exactly opposite directions, each with the same high speed of 127 kmlsec. It is inconceivable that B-processes of such extreme violence should fail to eject, along with those giant masses rendered visible by their stellar character even in empty space, an enormous quantity of lesser, invisible debris, the smaller and far more numerous members of which comprise a new addition to the category of interstellar meteoritic material. It seems reasonable t o assume that equally potent B-processes must have occurred, possibly a t various times and at many centers in a n association a s rich and as widely extended as I1 Sco. If this be granted, then we have in the 11 Sco-aggregate a relatively nearby source of hyperbolic material situated, it must be emphasized, in proximity t o the ecliptic. I n view of the ultra-high-speed of masses ejected by B-processes, as revealed by Morgan and Blaauw’s study of AE Aurigae and p Columbae, one may infer that only rarely will meteoritic ejecta from the I1 Sco source survive, more than momentarily, head-on flight through the earth’s atmosphere. The great preponderance of direct orbits for the hyperbolic Scorpionids is thus immediately explained. The reader will recall that precisely the preponderance of direct over retrograde motions and the concentration t o the ecliptic shown by hyperbolic meteors have been cited in attempts t o discredit the very existence of interstellar meteorites. Two points remain that seem to merit emphasis. I n the first place, the results of this section give ample evidence that most meteor-orbit problems ought t o be regarded as three-body problems and not as the much simpler two-body problems alone attacked and solved by those classical procedures that have flooded the literature of both visual and photographic meteoric astronomy with extensive lists of assertedly highly accurate orbits. I n the second place, the ballistic potential of even the tiniest meteoritic particle, if i t be endowed with a strongly hyperbolic velocity, is formidable. p

6. CRATER-PRODUCING METEORITEFALLS

The refusal by scientists of the eighteenth century to give serious consideration t o the possibility that “stones might fall from the sky” is frequently cited as a prime example of learned blindness. One may feel sure, however, that scientific opinion of the future will concur in crediting meteoritics with the dubious honor of providing two still more inexplicable examples of scientific obtuseness: First, the failure to recognize until

308

LINCOLN LAPAZ

well into the twentieth century that certain remarkable topographic features had their origin in large-scale meteoritic impact and represent, indeed, an impressive and permanent testimonial t o the sensational nature of the effects produced by the most violent of all the interactions between the earth and infalling meteoritic material; and, second, the even more astonishing refusal of some geologists as late as 1953 to accept as a meteorite crater the first, terrestrial feature t o be recognized as such [145]. This refusal is the more singular because the crater in yuestion, that near Canyon Diablo, Arizona, is certainly a textbook example par oxcdlence of a meteorite crater, presenting as it does in clearly recognizable form almost all of the characteristics of this unique category of topographic. features. The current situation is rendered even more confused by the fact that, simultaneously with refusal to recognize the most obvious meteorite crater as such, recently both scientific and popular journals uncritically have publicized as meteorite craters a number of topographic features, none of which properly qualify for such as identihcation. The authentication of every meteorite crater recognized as such by meteoriticists rests on fulfillment of one or both of the following identification criteria: ( I ) Actual discovery in or near the crater of meteorites, either unaltered or, possibly, oxidized t o a lesser or greater degree (as a t IJssuri (Sikhote-Ah), Canyon Diablo, Wolf Creek), or of metamorphosed materials definitely known t o have resulted from meteoritic impact (e.g., the nickel-iron-bearing silica glass a t the Henbury and Wabar meteorite craters). (2) Actual observation of meteorite falls having earth-impact points in the watered areas (as in the case of the unparalleled Podkamennaya Tunguska fall of June 30, 1908, in Siberia).

In addition to the above-named principal criteria, auxiliary criteria which must be satisfied include the presence of bilateral symmetry (since strictly vertical infall is most improbable) and convincing evidence th a t the actual impact and explosion of a large meteorite is involved, such as a more or less regular decrease in the amount and the size of ejectamenta with distance outward from the crater; faulting, often roughly radial in character; the presence of radial percussion ridges or radially aligned jets of ejectamenta, including not only rock debris, but meteoritic fragments as well, or both; and the upturning and even the overthrow of strata, a t least where the impact has occurred in sedimentary beds. I n the case of such widely publicized craters as New Quebec (Chubb) in Canada, the Crater Elegante of Sonora, Mexico, and other craters recently asserted to be of meteoritic origin, neither the principal nor the

EFFECTS OF METEORITES ON THE EARTH

309

auxiliary criteria are satisfied. hi fact, in lieu of such evidence as is customarily presentfed to warrant assignment of a meteoritic origin to a crater, only less natural and less cogent reasons have been given for designating the Chub2, crater as a meteorite crater. For example, the mere existence of magnetic anomalies in rock admittedly rich in segregations of magnetite and allied minerals has been advanced by Meen (see [(ill, p. 24) as proof that Chubb is a meteorite crater. Again Millman, in summarizing the results of his exhaustive and valuable study of the profile of the Canadian crater [146],cites, as evidence considerably strengthening the meteoritic impact hypot’hesis of the origin of Chubb, what he regards as “ t he close agreement between the New Quebec crater and the normal series of explosion craters . . . ”-specifically, the series of terrestrial and lunar craters studied i n detail by Baldwin [147]. Both Baldwin’s ident’ification of the craters on the moon as explosion features resulting from the infall of meteorites and Millman’s extension of Baldwin’s argument to include the New Quebec crater rest, on a supposed concordance between various geomet>ricrat,ios exhibited by t he craters on t,he moon and the values of analogous geomet,ric ratios as measured in terrestrial craters known to have originated from explosions. The crucial point in establishing the supposed correlabion, as Baldwin himself recognized (see [147], p. 131), lay in bridging over the vast gap between relatively small military explosion cratjers, having diameters of at most a few hundred feet,, and lunar craters, having diamet’ers ranging from a few miles to as much as 146 mi. Baldwin asserted that the gap in question could be bridged over by use of the four terrestrial meteorite craters listed in his Table 5 (see [147], p. 125). But, if the correct measurements made at the most t’horoughly invest’igat>edof t’hese terrestrial meteorit,e crat.ers are employed, t,he concordance he sought to establish is found t.o break down completely. In view of t.he wide-ranging theore& ical considerations which Urey [148] and others have based on the coiicordance supposedly established by Baldwin, it seems well worthwhile t,o indicate precisely why it is invalid. Reference t o Table 5 and to the details concerniiig the main Odessa crat,er given in Chapter 4 of The Face qf the Moon, will disclose that by depth, Baldwin means t,he original interior relief of a crat>er;l* for example, in the case of the main crater at Odessa, he combines his estimak of -10 ft 11 Where several terrestrial meteorite craters of widely differing agcs and suhjec~t to a n annual aggraclat,ion variable within wide limits are under consideration, it is perfectly obvious t,hat use of any “depth ” other t.han t,he original interior crater relief cannot possibly he justified. So much the more so is this true as regards a cornparison involving not only several t,errestrial meteorite craters, but, also a series of crat,ers on a remote satellite where the very notion of aggradation is undefined and its annual rate is wholly unknown.

310

LINCOLN LAPAZ

for the original rim height above the surrounding plain (see [147], p. 73) with a figure of 90 ft for the distance at which the crater bottom originally lay below this plain, to obtain the depth of 130 ft entered in Table 5. It will be noted with surprise that this is not at all the procedure used to obtain the depth figure given in this table for the Barringer meteorite crater a t Canyon Diablo. Baldwin’s own estimate of the original rim height here is 300 ft. The original depth below the surrounding plain of the bottom of the Barringer meteorite crater is shown by the logs of the numerous drill holes put down inside the crater to amount to at least 1200 ft. Consequently, the original interior relief at the Barringer crater was at least 1500 f t [1491. In place of 1500 ft, however, Baldwin uses only 700 ft as the depth, thereby obtaining a (log-depth-log diameter) point whose coordinates (2.845, 3.618) place it exactly on the fundamental correlation curve he is seeking to establish (see [147], p. 132, Fig. 12). The correct (log depth-log diameter) point (3.176, 3.618), however, falls nowhere near the correlation curve in question-how wide is its departure from this curve will not be appreciated until one replots the data on a (depth-diameter) rather than on a (log depth-log diameter) diagram. Furthermore, the results obtained from the exhaustive program of drilling and excavation a t the Odessa meteorite crater, discussed in Section 6.1.2, quite discredit the almost perfect fit to the correlation curve of the main Odessa crater point, as plotted by Baldwin in his Fig. 12. Consequently, the concordance basic to all of Baldwin’s conclusions breaks down precisely in the region he recognized as critical. Even had Baldwin been successful in explaining Ebert’s Rule, and similar empirical relationships long ago discovered by the German selenographers, as consequences to be expected in case the lunar craters were of meteoritic impact origin, he would not have proved that all the craters on the moon are meteorite craters; for, as has been pointed out by J. Wasiutynski, relationships like those discovered by Ebert are also corollaries of another quite different theory of the origin of the lunar craters, namely, Wasiutynski’s convection-current theory of these features [150]. In the writer’s opinion, Wasiutynski’s new theory not only is physically the most plausible so far advanced (resting as it does on the fertile laboratory experimentation conducted by H. Benard and his associates) ; but also has the great additional advantage of not requiring (as the meteorite impact theory necessarily does) a random distribution of the centers of the lunar craters. That the distribution of the ordinary (i.e., the nonray) craters on the moon is not a random one was proved in 1942 by Scott [151]. Finally, as the writer has recently pointed out [152], Wasiutynski’s theory not only leads t o such empirical relations as Ebert’s

EFFECTS O F METEORITES ON THE EARTH

311

Rule, but also predicts both hexagonal crater shapes of the sort observed for many of the best preserved lunar craters and the highly significant rhomboidal network of dikes and rills-Puiseux’s network-discovered in 1907 by the French astronomer, P. Puiseux [153]. Unquestionably, a feature as remarkable as the Chubb crater merits the most exhaustive investigation, particularly on the part of those who seem determined to prove it is of meteoritic origin. It has been suggested that glaciation has obscured or destroyed all decisive evidence of the sort detailed in the principal criteria (1) and (2) given earlier in this section. However, as the writer recently pointed out [154], even as regards the exterior of Chubb crater, no support can be given to such a suggestion in view of discovery of typical meteorite-crater glass a t Mount Darwin in Tasmania in an area where the crater whence the glass in question was ejected is presumed “ t o have been destroyed by glacial erosion” (see Prior and Hey [22], p. 423). Certainly the suggestion in question is totally inapplicable t o the interior of the Chubb crater in view of the convincing explanation which has been given by Harrison [155] as to why the New Quebec crater was not filled with glacial debris; namely, that the continental ice sheet in part was deflected by the rim of the Chubb crater, and in part simply slid across the smooth, impenetrable ice floor provided by the frozen lake within this crater so that relatively little, if any, glacial debris was introduced into the crater by passage of the ice sheet. Furthermore, this ice sheet itself, together with the climatic conditions existing in far-northern Ungava, has spared the interior of the Canadian crater from such massive accumulations, chiefly of eolian origin, as mask much of the interior of the Barringer meteorite crater. Consequently, if the Chubb crater is a meteorite crater, it must contain within itself in relatively unadulterated state such evidences of meteoritic impact origin as have been found in profusion in the Barringer meteorite crater and in other recognized meteorite craters (see Sections 6.1 and 6.2). Of course, the deep water fill in Chubb constitutes a handicap to exploration of the interior of the Canadian crater, but modern devices and techniques for submarine sampling have overcome much more formidable obstacles. Consequently, until (and unless) systematic probing of the interior of the Chubb crater reveals undoubted evidence of a meteoritic origin, this remarkable Canadian feature should be excluded from the category of authenticated meteorite craters. 6.I . The Barringer Meteorite Crater

Approximately 20 mi west of Winslow, Arizona, near the Canyon Diablo, the large bowl-shaped depression of the Barringer meteorite

312

LINCOLN LAPAZ

crater is located. From a distance, the rim of this feature appears to the ground observer as a chain of low, hummocky hills, lighter in color than the surrounding reddish terrain. Viewed from the crest of the rim, the depression exhibits an approximately circular outline. This circularity is, however, largely illusory as air views of the crater have shown it to be

FI(:.4. Air view showing the plan-form of the Barringer meteorite crater.

squarish in shape (see Fig. 4), a fact recently stressed by Zimmerman 11561. This curious depression attracted the attention of the earliest settlers in the region and, as long ago as 1873, was named “Franklin’s Hole” by George M. Wheeler in honor of a well-known guide and Indian scout of this period. The topographic feature did not come under scientific scrutiny, however, until 1891, when the discovery of numerous masses of meteoritic iron scattered about the rim of the crater was announced by

EFFECTS O F METEOIZIT’ES Oh’ T H E EARTH

313

Footc [ 1571. Ititerest in the locality so011 \vas intensified by Moissaii’s subsequent ronfirmation of the discovery of small black diamonds in the sideritic material recovered a t the crater [158]. The Arizona depression has a major diameter of 3950 ft and a minor diameter of 3850 ft. The outer slopes of the crater rim rise a t a very gentle gradieut from the level of the dcscrt plain into which the crater is depressed; the itiiicr slopes, 011 the coiitrary, are exceedingly precipitous, so much so that only their lower portions have been covered by the widebpread deposit of talus bottoming the crater (see fiig. 5 ) . The height ot

FIG.5 The interior of thr Barringrr xnrteoritr cmtcr.

the rim above the surrounditig pl:iiii varies from 120 t o 160 it, while the greatest depth of the basin, measured from the crest of the rim t o the lowest point in the bed of the lake which occasionally occupies the basin, is approximately 570 ft. This depth is, however, only a fractioii of the original depth of the crater, as revealed by the mining operations carried 011 w i t h it; for thc ~ ~ u n i c r o u shafts s and bow holrs sunk in the interior of the carat er, after traversing crushed and metamorphosed masst’s of country rock aiid acwmiulations of rock flour, have in many cases penetrated into solid horizontally-bedded sedirnciitary strata. Undisturbed sandstone has thus been located a t depths of 800 ft or more below the central portion of the present crater floor (see [149], pp. 461-498). The country rock of the level plain on which the crater is located WHsists of the following horizontally-bedded geological formations: (1) The

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LINCOLN LAPAZ

Kaibab (Permian) limestone, which in the Canyon Diablo area is approximately 250 ft thick, forms the surface of the plain. (Upon this surface, a few remnants of the reddish-purple Moenkopi (Triassic) formation are present as small, flattish hills, rising but slightly above the general level of the plain surrounding the crater.) (2) Below the Kaibab limestone lies approximately 1000 feet of soft, white Coconino (Permian) sandstone. (3) The Supai redbeds (Lower Permian), of variable thickness, underlie the Coconino sandstone. The outer slopes of the crater consist of loosely consolidated, generally angular, fragmental material, unquestionably derived from beds once filling the space now occupied by the crater. These outer slopes are covered with rock ejectamenta varying in size from great masses of limestone weighing approximately 4000 tons (such as Monument Rock and Whale Rock) to microscopic particles of crystalline quartz, known as “silica” or rock flour. The latter, as Barringer, Tilghman, and Merrill first clearly pointed out, had its origin in the comminution of the Coconino sandstone by the violence of the meteorite impact forming the crater. Some limestone fragments weighing from 50 to 100 pounds have been found a t distances of 1% to 2 mi from the crater, and both rock ejectamenta and meteorites have been found out to distances of at least 6 mi. The amount of rock material dislodged and wholly or partially thrown out of the crater has been estimated at between 300,000,000 tons [159] and 1,000,000,000 tons [160]. The extraordinary violence of the crater-forming process is shown not alone by the estimates just quoted from Barringer and t)pik; but also by such evidence as the following: (1) I n the south wall of the crater, a block of country rock, extending for half a mile as measured along the crater rim, and estimated by Barringer to weigh between 20 and 30 million tons, has been bodily uplifted through a vertical distance of approximately 100 ft. (2) As previously noted, the strata in the Canyon Diablo area, where undisturbed, are horizontally bedded. But, as exposed in the steep, inner walls of the crater, these same strata everywhere dip radially outward at angles ranging from 5” to 80” or even more. (3) At a number of locations, the entire succession of rock beds several hundred feet thick is observed to be faulted. With one exception, all of the many scientists who have closely examined the structure exposed a t the Barringer meteorite crater have reached the conclusion that these faults either are roughly radial, or are approximately at right angles to crater radii. The striking bilateral symmetry, which is evident not only in the dips of the uptilted stratified beds exposed along the inner walls of the crater, but also in the distribution of the major rock ejectamenta, was early noted by Barringer (see [159], p. 5). To some extent, this same bi-

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lateral symmetry also is present in the distribution of the tens of thousands of pieces of meteoritic iron that have been found on the outer slopes of the rim and on the plain surrounding the crater; although nothing analogous to the very rich concentration of relatively small sideritic specimens present in the northeast quadrant has, as yet, been found elsewhere about the crater. The solid irons recovered about the Barringer meteorite crater range in mass from tiny gravel-sized specimens to individuals weighing as much as 1406 pounds. In addition to the almost unaltered nickel-iron, the meteoritic debris found at the Barringer meteorite crater includes an enormous number of fragments, large and small, of reddish-brown to chocolate-brown iron oxide, occasionally exhibiting a greenish stain as a result of the presence of nickel hydroxide; and, in far less profusion, rounded or pear-shaped masses of more or less incompletely oxidized meteoritic material-the so-called “ shale balls”-ranging in size from that of a marble to huge masses weighing hundreds of pounds. Specimens of all these types of meteoritic material, but particularly of the last variety, have been found buried not only in the heterogeneous aggregate of rock fragments and rock flour constituting the rim, but also in the moraine-like ridges of similar composition flanking the outer slopes of the crater. The attentive observer of the helter-skelter manner in which sizeable fragments of sandstone and limestone, “ rock flour” composed of particles of microscopic dimensions, and masses of meteoritic material of far greater density than that of the country rocks occur in the deposits just alluded to, will concur without hesitation in the following pronouncements of G. P. Merrill (see [149], pp. 466 and 495), one of the ablest and most critical students of the Barringer meteorite crater: The position they [ = the various components of the deposits under consideration] occupy is such as can be accounted for only on the supposition that all the material composing the deposit was in the air at the same moment of time and was deposited “pel1 mell,” wholly without order or reference to gravity . . . It is impossible to account for the position of these last [ = the shale ball irons] in any other way than to assume that they fell a t the same period of time as the material in which they lie embedded. The difference in specific gravity of the various materials is such that it is inconceivable that they should have traveled together for any great distance. Their association may be best explained on the assumption that all were poured out together over the crater rim . .

.

The above well-considered conclusions, voiced without qualification by a most conservative scientist who had had unparalleled opportunities to gain first-hand knowledge of subsurface conditions at the Barringer meteorite crater, are in striking contrast to the precipitate pronouncements of those few crater investigators who have advanced the unsup-

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ported conjecture that the wealth of meteoritic materials of diverse types found a t this crater stand in no causal relation to its origin; and, in fact, fell tens of thousands of years after its formation. I n addition to the mac,rometeoritic specimens considered above, a great deal of what might be termed micrometeoritic material, both metallic and oxidized, was first discovered half a century ago in and around the Barringer meteorite crater by its pioneer investigators, Barringer and Tilghman. The latter, in particular, as early as 1905 by use of a magnetic separator, recovered nickel-iron‘grariules not only from the fill inside the crater, butj also from samples collected on the north and south slopes of the crater rim. H e estimat’edthat the metallic nickel-iron granules thus isolated occurred ill the proportion of 1/80 t o 1/4 ounce per ton of material worked, results in line with modern determinations of the average concentration of such granules. The cJaims recently made by H. H. Nininger t-o have first identified such granules in 1948 after they had eluded all earlier investigators can best be judged against the background of the many earlier publications dealing with the collection, study, and identification of such granules collated and published by the present writer in 1953 [63]. Equally unjustified is t8hecredence accorded in some quarters to claims that work a t the Barringer meteorite crater in 1948 first suggested that, the impact of giant, crat>er-forming meteorites with our globe develops heat sufficient t o fuse and partially to vaporize immense masses of both projectile and target material with the consequence that much of the resulting melange is ejected from the impact crater and widely scattered about it. All of these ideas not only were carefully discussed in Merrill’s pioneer paper of 1908 on the Barringer meteorite crater [149], but were again elaborated in great, detail in the classical 1933 paper of Spencer [lSl] on the millions of tiny metallic nickel-iron spherules found in the closest association with masses of congealed silica glass a t the Wabar and Henbury meteorite craters; and on the curious, roughly globular, somewhat altered “crinkled peas” of similar origin and association found in the vicinity of the latter craters. If confirmation were needed of the validity of the interpretation which Barringer, Merrill, and others long ago placed on the then quite unique meteoritic granules, rock flour, and silica glasses discovered a t the Barringer meteorite crater, it is to be found in Spencer’s exhaustive discussions of similar meteoritic impact evidence later discovered a t the Henbury and Wabar craters. Only the few who now hypothecate a nonmeteoritic origin for the Barringer meteorite crater seem to have overlooked the peculiarly significant role played in discrediting all such hypotheses by the early discovery a t this crater of meteoritic granules associated not, only with rock flour (unquestionably derived from the

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317

Coconino sandstone not by simple disintegration but, in the opinion of Merrill (see [149], p. 473), “through some dynamic agency acting like a sharp and tremendously powerful blow,” a view concurred in by Rogers [ 1621 and all other mineralogists, pet,rologists, and geologists who have carefully examined the rock and rock powder in question), hut also with heat-metamorphosed sandstone showing all gradations from the unaltered Cocoriino to various types of silica glass [l(i8]. As will be pointed out in the next sect,ion, certain significant resemblances bet,ween the Barringer meteorit,e crater and the second crater i n the world identified as of meteoritic origin, that near Odessa, Texas, can be notJiced at, once. Radiometric devices like the met>eoritedetectors, as well as visual observation, have cont~ributedto the list of similarities bet,ween t,he first two terrest,rial craters recognized as meteorite craters; for, as was noted during the instrumentd searches far buried meteorit.es made by the Ohio State University Meteorite Expeditions of I939 and 1941 t o Arizona and Texas, in addition t,o the quite localized signal maxima testifying to the presence of buried meteoritic material, the meteorit,e detectors occasionally revealed radiometric anonialies extending over areas of hundreds and even thousands of square feet. Several of the most marked anomalies found near the Odessa crater in September, 1939 later were rediscovered during a magnetometer survey of this region made by the Humble Oil and Refining Company as a contribution to the crater-exploration program initiated by the Bureau of Economic Geology of the University of Texas. Two of tfhemost prominent of these anomalies were later excavated and shown to be associated with subsidiary meteorite craterlets that had been so completely filled up by ejectamenta from the main crater and normal aggradation subsequent t o the infall of the Odessa meteorite that no trace of their existence was visible on the surface. In July, 1950, the Institute of Meteoritics of the University of New Mexico conducted a radiometric survey of one of the most pronounced of the anomalies earlier located near the Barringer meteorite crater. The isogramI2 derived from this survey (Fig. 6) confirmed that in extent, 12 The secondary (northern) high shown in this isogram was discovered before the primary but less symmetrical southern high was detected. The latter was, i n fact,, found during a systematic survey about the northern high. In the expanded survey of the entire anomalous area then undertaken, it proved expedient to choosr the intersection of the axis of the northern high with the axis of the southern high as t,he origin of the zy-coordinate system to be employed in the final survey. The directions given for these axes are only approximate since they are based on magnetic directions and the needle is not to be trusted over such terrain as that shown in Fig. 5. The scale of Fig. 5 can be det>ermined from the fact that t,he center of the circularly symmetrical northern high is 100 f t northeast of the origin of the xucoordinate system.

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shape, and radiometric relief, the Arizona anomalies were quite similar to those earlier discovered in Texas which were later proved to be the surface indications of small buried meteorite craters. To date, only shallow surface trenching has been conducted on the Pluto anomaly, as the feature shown in Fig. 6 is now called. Pending such

FIQ. crater.

a program of excavation as was instituted in and around the Odessa crater, the cause of the Pluto anomaly must remain undecided. It is, of course, possible that long-continued circulation, through subsurface fissures produced by the shock of the main crater-forming impact, of rain wash and of such scanty ground water as characterizes the Canyon Diablo region has brought about concentrations of oxidized and hydrated meteor-

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319

itic materials sufficient to produce the anomalies detected a t the surface in the Canyon Diablo area. The close similarities between the radiometric indications observed about the Arizona and Texas craters, however, strongly suggest that both sets of anomalies have similar origins. On the basis of such evidence as that briefly summarized above, the Barringer meteorite crater universally is adjudged by meteoriticists as the best authenticated and the most representative of t,he recognized meteorite craters of the worId. 6.1. The Odessa Meteorite Crater

Located about 10 mi west-southwest of Odessa, Texas, is a much smaller and unquestionably a much older meteorite crater than the one near Canyon Diablo, Arizona. The Odessa crater now consists of a shallow basin, somewhat elliptical in outline, with an average diameter of about 550 ft. Scarcely noticeable from a distance, the crater rim rises only about 5 to 8 ft above the surrounding plain. Viewed from the rim, however, the interior of the crater is more impressive. As at the Barringer meteorite crater, the rim is an assemblage of loosely consolidated, generally angular fragmental material, unquestionably derived from beds once filling the space now occupied by the crater. Also as in the case of the Barringer crater, the inner walls are much steeper than the external slopes. Many solid iron meteorites, varying in size from the most minute fragments to specimens weighing hundreds of pounds, have been found on or outside the rim of the main crater or in smaller subsidiary craters located nearby. The siderites found at the Odessa crater seem to be identical in composition and structure with the Canyon Diablo octahedrites. Furthermore, as at Canyon Diablo, the octahedrites so far recovered at Odessa can be separated into two quite distinct categories: the first, comprised of individuals hurled out of the main crater in parabolic paths by the explosion of the principal crater-forming mass; and the second, consisting of what the writer [164] has termed ‘‘ outriders,” i.e., subordinate masses that trailed the principal mass in its swift flight through the atmosphere and reached the earth with some appreciable fraction of their original cosmic velocities. In most cases, the outriders were shattered to a greater or lesser degree by their impact with the earth target and thus became subject to excessive oxidation which resulted in the formation of shale balls identical in appearance and internal structure with those found in profusion near the Barringer meteorite crater. In one exceptional case, however, a metallic Odessa outrider, weighing approximately 200 pounds, was found buried at a depth of 43 in. in apparently solid rock which showed indisputable evidence of intensive metamorphic action where it was in contact with the meteorite. In fact, this outrider, as finally

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chiseled out of the surrounding rock, was found to be completely coated by a n armor apparently consisting of a genuine melt of country rock and nic kel-iron. The Bureau of Economic Geology of the University of Texas, to which great credit must go for taking the initiative in thoroughly investigating the Odessa crater, has reported that on the basis of the elaborate program of excavation and drilling which began as a W.P.A. project, the following materials have been recognized : (1) Impact ejecta thrown completely out of the crater; ( 2 ) folded, faulted, elevated, tilted, thrust, and otherwise dislocated rock strata in the rim of the crater; (3) post-meteorite impact fill, consisting chiefly of silt and fine sand, within the crater itself; (4) impact ejecta which fell back into the crater opening shortly after its formation; (5) BarringerMerrill type “rock flour” formed in place inside the crater; and (6) undisturbed country rock beneath the rock flour zone ( 5 ) . We shall discuss each of the above categories in sequence, calling attention to the chief similarities between the phenomena observed a t Odessa and those earlier detected a t the Barringer meteorite crater: (1) The accumulation of rock debris ejected by the impact of the Odessa meteorite completely surrounds the main crater in a deposit thickest in the rim and quite uniformly thinning out with distance from the crater. The surface debris consists chiefly of blocks of limestone often solidly cemented together by caliche. Pits and trenches extending outward from the rim disclose that large masses of shale are included among the limestone blocks, the maximum size of the blocks in each case being of the order of 3 to 4 ft. The existence of secondary accumulations of caliche cementing the ejected rock is evidence of the remoteness in time of the crater-forming impact. The peripheral deposit of ejecta contains rock specimens which have beeii identified as coming from Cretaceous formations t ha t must have been buried a t depths of nearly 100 ft prior to the meteorite impact. Except for the difference in scale incident to the quite different masses of the meteorites that fell a t Canyon Diablo and a t Odessa, there is the closest similarity between the out-throw deposits around the two craters. (2) The Cretaceous formations underlying t,he Odessa crater normally have the same horizontal positions as the strata in which the Barringer meteorite crater was formed. As a result of the impact of the Odessa meteorite, all strata in and immediately adjacent to the present Odessa crater, down t o a depth of approximately 90 ft, were moved from their original positions. As revealed in the inner walls of the Odessa crater, the rock strata were lifted, broken, folded, and faulted. I n particular, one massive limestone, the top of which normally lies about 22 ft below the level

EFFECTS O F METEORITES ON THE EARTH

32 1

of the Odessa plain, was uplifted to a maximum extent of approximat,eIy 25 ft, evidence of the violence of the meteorite impact strictly comparable with that revealed in the arched-up south wall of the Barringer crater. Again, limestone strata once horizontally bedded show dips ranging up to go", analogous to those observed at the Barringer crater. Outside the crater, the dips in the rock strata produced by meteoritic impact) rapidly flatt>enout, as has been conclusively shown by the logs of test wells drilled on the north and south rims of the Odessa crater. In fact, in the north crater rim, the limestone stratum levels out t20almost, its normal position within a horizontal distance of no more than 110 ft. The extensive excavations carried out in the Odessa crater reveal rock beds so shattered, compressed, and disturbed that it is now quite impossible to determine accurately their original thickness or even to interpret their original st,ructural attitude. As evidence of the extreme structural dislocation present in rock formations a t the Odessa crater, a section of beds, including a resistant, fossiliferous limestone, has been folded into an asymmetrical a1it.icline, and evidence of thrust-faulting also is clearly shown. ( 3 ) The original depth, below outside ground level, of t.he impact. crater a t Odessa was about 106 ft. At the present time, the basin is filled to within 5 or 6 ft of the level of the surrounding plain, another indication of the great age of the basin. The lens-shaped fill within the cratclr (+onsists of fine sand mixed with red, incoherent silt,. Underlying t h r silt layer is a light-colored stratum consisting in part of silt,, hut, includitig material washed in from the rim of the crater, the whole bciiig partially cemented by caliche which has formed a t t'his level. The total thickness of these two post-met,eorite impact deposits is approximately 7lj ft. (4) Below the 75-ft t,hickness of upper fill iii t,he central part of t.he crat,er, there has been found a stratum of fragnieiitJalrock exteiidiiig down a distance of riot more t,hari 15 or 20 ftJto the original hottom of the crater. While this fragmental rock material is coarser in outlying areas aiid finer in the central portion of the crater, it is always easily dist.inguishable from the still finer material above and helow it,. (5) Exactly as a t the Barringer meteorite crater, rock flour has been formed from sand grains completely and suddenly shattered by the violent impact of t,he crater-forming meteorite. The rock flour exhibits the same almost incredible fineness earlier commetited on by Barringer, Tilghman, and Merrill in connection with their investigations a t the Arizona crater. The zone of rock flour at Odessa is thickest close to, butJ somewhat northeast of, the center of the original floor of the crater, thinning out in all directions so as to form a lens-shaped deposit lying well within the outer margins of the crater. Near the center of the crater the accumulation of rock flour underlies t,he zone of fragmental rock,

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indicating that in this region everything above the ceiling of the rock flour lens was thrown out by the impact of the meteorite. As the outer margins of this lens are approached, however, a few feet of unaltered sandstone and limestone are found to overlie the rock-flour layer. In fact, some of the exploratory bore holes within the crater penetrated Cretaceous rock underlain by rock flour, thus conclusively proving that the rock flour had been formed in situ. This fundamentally important discovery of rock flour in place in the Odessa crater, taken in conjunction with the essential identity of the rock flours found not only in the Barringer and Odessa craters but in other meteorite craters as well; and supplemented by the close similarities in the nature of the rock flour accumulations within those two meteorite craters most exhaustively explored, will enable the reader to appraise the likelihood of the suggestion recently made that the rock flour deposits at the Barringer meteorite crater are water-laid (see [145], pp. 846849). TABLE XIII. Thickness in feet Average ground level around crater, sea level datum 3050 Top of fill in crater at location of shaft 3044 First silt, top crater fill 0 . 0 to 2 5 . 5 Second stratum of crater fill 2 5 . 5 to 7 5 . 5 Ejecta which fell back into the crater 75.5 to 9 4 . 0 Rock flour in place 9 4 . 0 to 100 Undisturbed strata at depth 100 ft Bottom of shaft at depth 170 ft

25.5 50.0 18.5 6.0

(6) The depth to undisturbed rock strata, as well as the thickness and depth of burial of the other formations encountered during the construction of a shaft located near the center of the Odessa meteorite crater can be inferred from Table XIII. I n addition to the exhaustive excavations carried out at the main Odessa crater itself, two subordinate craters detected not only during the radiometric survey of the Odessa crater conducted by the Ohio State University Meteorite Expedition of 1939, but also by a magnetometer survey later made by the Humble Oil and Refining Company, were excavated under the supervision of the Bureau of Economic Geology of the University of Texas. The most interesting of these auxiliary craters was found to be approximately circular in outline and to have a diameter of about 70 ft and a depth of approximately 17 ft. This craterlet had been completely filled up, in part by ejecta, but also to a considerable extent by wash from its sides and from the rim of the main crater close to which

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323

it was located. Unlike the main crater, the craterlet had not penetrated far enough down to encounter solid rock, but had been formed entirely in clay-like, relatively incoherent materials. 6.3. Determinations of the Mass of Crater-Producing Meteorites and of the Age of the Craters

Stimulated by the identification of the Barringer and Odessa craters as meteorite craters, intensive search for other craters of meteoritic impact origin has been prosecuted all over the globe. Up t o the present, craters, generally recognized as meteoritic in origin by the date indicated, have been found a t the following 14 localities: 1905 1929 1932 1932 1933 1933 1933 1933 1937 1937 1938 1947 1948 1952

Barringer, Coconino County, Arizona Odessa, Ector County, Texas Henbury, McDonnell Ranges, Central Australia Wabar, Rub' a1 Khali, Arabia Campo del Cielo, Gran Chaco, Argentina Haviland, Kiowa County, Kansas Mount Darwin, Tasmania Podkamennaya Tunguska, Yeniseisk, Siberia Box Hole Station, Plenty River, Central Australia Kaalijarv, Oesel, Estonia Dalgaranga, Western Australia Sikhote-Ah, Eastern Siberia Wolf Creek, Wyndham, Kimberley, Western Australia Aouelloul, Adrar, Western Sahara

In addition to the numerous meteorite craters of prehistoric fall listed above, two meteorite crater-producing falls have been witnessed within the last half century within the U.S.S.R. The first of these, that of Podkamennaya Tunguska, occurred in Siberia on June 30, 1908. The writ8erand his collaborators in the Meteorite Bureau a t The Ohio State University and, later, in the Institute of Meteoritics of the University of New Mexico, have published translations of and critical commentaries on a considerable number of the papers in the very extensive literature that has appeared in the Russian language concerning the Podkamennaya Tunguska fall [165]. Among the many almost incredible phenomena produced by the Podkamennaya Tunguska meteorite, not the least intriguing was apparently complete annhilation of the impacting mass. So inexplicable on classical grounds was its disappearance without leaving even a trace of recognizable meteoritic debris in the area of fall, that its behavior led to the first suggestion of the possible existence of contraterrene meteorites [166]. The hypothesis of the existence of meteorites composed of

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reversed matter has received support from several different directions, the favorable evidence culminating quite recently in laboratory production of the final fundamental particle necessary for the fabrication of ‘‘ inside-out ” matter. On February 12, 1947, a second hardly less extraordinary meteoritecrater producing fall occurred in the Sikhote-Aliii mountain range not far from Vladivostok (see Fig. 7). The investigation of this so-called Ussuri, or Sikhote-Ah, fall, sponsored by the Meteorite Committee of the Academy of Sciences of the U.S.S.R., is by far the most elaborate and exhaustive of any meteoritical research project ever attempted, not excepting those at the Barringer and Odessa craters. Unfortunately, only Russians have participated in the Sikhote-Aliii investigations and, until 1956, none of the very numerous scientific papers written by those actually participating i n the investigations in the Sikhote-Alin area had appeared in any laiiguage other than Russian. A translation of and critical c.ommentary on a very important paper by E. L. Krinov was published by Boldyreff and the writer in 1950 [167]. Several other Russian papers relating tjo the Ussuri fall will soon appear in translation in forthcoming issues of the journal Mdeoritics. Had the Podkainenriaya Tunguska or Sikhote-Alin meteorites been of less exceptional iiature, they would have provided what might be described as very coiivenient if somewhat awebome field tests of the competency of meteorites of great mass to blast out full-scale meteorite craters. Such tests would have proved invaluable in deciding between rival theories concerning the impacting mass necessary to produce a meteorite crater of assigned magnitude [168, 1691. Fortunately, military development of lined shaped charges [128] and the concurrent perfection of satisfactory physical arid mathematical explanations of target penetration by 1.s.c. jets [170] have permitted attainment of a satisfactory solution of the very difficult problems of this sort posed by each recognized meteorite crater. For example, as regards the Barringer meteorite crater, a paper of fundamental importance by Rostoker [ 1711 discredits Rinehart’s assumption that crater volume is proportional to the kinetic energy of incident particles moving with velocities up to and including those of meteoritic order [172]. In striking contrast to the mass estimates of a few thousand tons which had been derived under the assumption that Rinehart’s postulate was valid, Rostoker has confirmed that the Canyon Diablo meteorite had a mass of several million tons, a figure of the same order of magnitude as that first found by Opik (see [160], p. 11) using a hydrodynamical approach. We come finally to the equally difficult problem of age determination

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325

Fro. 7. The fall of the Sikhote-Alin (Ussuri) meteorite, as painted by the Russinn artist, Medvedev, an eyewitness of the phenomenon.

for meteorite craters. Rough estimates of the age of the Barringer meteorite crater have been based on tree ring counts for the oldest cedars found on its rim [173] or on the dating of artifacts found in pit houses built, in part, of rock debris ejected by the explosion that produced the Barringer crater [174]. On the basis of paleontological and geological evidence, ages

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for the Barringer meteorite crater ranging between 20,000 and 50,000 years have been suggested by Blackwelder [175] and others; and the discovery of a fossil horse (Equus conoersidens) in the crater fill at Odessa implies a much greater age for the Texas crater. These latter figures at once place the age determination problem for the Arizona and Texas craters well beyond the range of accuracy of the C-14 method. This is only one of the reasons for current interest in and intensive work upon a C1-36 analog of the C-14 method; for, if such a C1-method could be developed, accurate age determination for meteorite craters even as ancient as the one at Odessa would become possible. Lack of dependable radioactive age determination methods applicable to the meteorite crater problem would appear to justify the consideration given to an admittedly rough and provisional crater age determination method which will be dealt with in the next section. 6.4. The Diffusion of NiO in the Soil and the Age of the Rrenham

Meteorite Craters In a work on the oxidation and weathering of meteorites which has appeared as No. 3 in the Meteoritical Monograph Series of the University of New Mexico, J. D. Buddhue gives a tabulation of the percentage C of NiO found at various horizontal distances z from a large, buried Brenham, Kansas, meteorite. The graphical representation of C as a function of 2 given by Buddhue struck the writer as resembling a typical Fick diffusion curve. One purpose of this section is to show that, in spite of the complexity of the process detailed by Buddhue, whereby in time the nickel in buried iron meteorites leaches out into the encompassing soil, the concentrationdistance relation, at least for the compound NiO discussed by Buddhue, is well represented by the Fick diffusion curve C = C ( 2 ) shown in Fig. 8, in which the observed pairs of values (z, C) as given by Buddhue are at the centers of the small circles. Later in this section, the explicit form of the function C ( x ) defining the curve in Fig. 8, will be derived on the basis of an idealization of the Brenham diffusion problem described by Buddhue. The primary purpose of this section, however, is to point out that, once the equation C = C(z) is known for such a compound as NiO diffusing outward from a leaching meteorite, we are in position to make a determination of the approximate length of time the meteorite has been buried, provided only we have available a dependable numerical estimate of the average value, over the interval of burial, of the Fick diffusion coefficient D relevant to the particular compound and the particular subsoil in which diffusion of the meteoritic compound has occurred.

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It will be recalled that if it be assumed that the coefficient of diffusion D, a quantity representing the amount of substance in grams diffusing through a n area of one square centimeter in one second under a unit concentration gradient, is independent of the concentration C ; then, on the

RADIAL DISTANCE

-

CM

FIG.8. The Fick diffusion Curve for NiO in the soil around a buried 336,500-gram Brenham meteorite.

basis of Fick’s law of diffusion, the following partial differential equation can be derived :

ac -- D-a w _ at

ax2

Laboratory experiments on the validity of the assumption that D does not depend on C, clearly indicate that this assumption must be quite closely fulfilled in the case of the diffusion of compounds originating in a leaching meteorite, for the concentration in the subsoil of such compounds is very low indeed. Furthermore, since temperature changes in the subsoil are quite limited in extent, the coefficient D may be treated as independent of the temperature of the soil in which the leaching meteorite is buried. If we idealize the diffusion-problem posed by the buried Brenham

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meteorite described by Buddhue in the same manner as has been done by Van Orstrand and Dewey in a related case [176], then the relationship between Buddhue’s variables C and x can be obtained by solving the Fick partial differential equation (6.1). In this wise, we are led to the relation

C(x) =

co

[

X ~

1 - G: ~

1

cw2 dw

/:dG

where Co is the value of the function C(z) a t L = 0. It is expedient to express the solution (6.2) in tterms of Gauss’ error function, Erf ( 2 )in t)he form (6.3)

C ( x ) = Co[l - Erf ( Z ) ] ,

Z

=

9: ~

2f i t

Our problem is now so to determine the parameters COand Z that the resulting expression (6.3) will give a curve C = C(.c) fitting the observed pairs of (C, s) values as well as possible. Since the N O determination for J: = 1 ft was regarded as the most accurate of the observed C’s, 2 was evaluated for various choices of Co with .c always assigned the value 30.5 em. I n this manner, the associated pair of values (Co = 0.19%, 2 = 0.34) was found to give a reasonably satisfactory fit to all of the observed data, as may be seen from Fig. 8 which is based on the choice indicated. If we suppose that the numerical value of the diffusion constant D is known, then the total time t required for diffusion t o build up the concentration observed at a distance x = 30.5 cm can be calculated a t once from the relation (6.4)

I n the sequel, reasons for taking D = cm2/sec in the Brenham case will be giveii. With this choice of D,one finds t = 637,000 years, a value consonant with the almost complete effacement of the Brenharn craters by the very slow action of aggradation and rim weathering. There remains the problem of justifying the choice just made for the value of D a t Brenham. Evidently, if a Fick diffusion curve of the sort pictured in Fig. 8 is available for a crater of k n o w n age, then by simply reversing the argument. of the last paragraph, we can determine the numerical value of the diffusion constant D. The Odessa crater has tentatiuely been assigned an age of t = 200,000 yr on the basis of the discovery of bones of Equus conversidens buried in the crater fill.

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329

I n the case of the Odessa crater, the relation analogous t o (6.4) is 03.5)

=

Hence, adoption of the value t

=

D

=

16.55 200,000 years leads to

0.837 X 10-'" cni2/sec

Values of D determined in diffusioii experiments ill the laboratory have a wide range but the few values ('orresponding to such low temperatures as those i n the earth a t Brenham, duster around

D = 10-'" cni2/ser the value adopted above. The first serious objection that can be raised against the age-deterniinatioii method developed above is that we have replaced a threedimensional physical situation by a one-dimensional idealization. ,Justification for limiting attention t o the simplified problem is given by such results as those of Van Orstrand and Dewey (see [176], p. 90) who found that predictions based on the one-dimensioiial idealization ' I represented the observed facts t o a high degree of precision," a t least for solid gold diffusing into solid lead a t moderate temperatures. A much more serious objection, can be based on the fact that ube was made of a value of D that may very poorly represent the average diff usiori conditions existing i n the Brenham subsoil over the interval cxt ending from the time the meteorite fell there t o the present. No defeiibe against this objection will be attempted. The writer prefers t o cite the objection in question as evidence of the urgent need for laboratory and field programs directed toward accurate determination of 11 for various compounds of meteoritic origin, diffusing under R wid(. iraric+y of wbsurfaw conditions. APPENDIX

I.

n/lETEORITICAL P I C T O G R A P H S 4 N D T H E \'ENERATIQY

EXPLOITATION O F METEORITES A first purpose of this section is t o describe meteoritical pictographs and petroglyphs of undoubted authenticity and considerable age, and to suggest that a meteoritical significance can with propriety be attached to certain pictographs of very much greater age. A4second purpose is to present briefly evidence of meteorite worship, and t o show that, meteorite cults have persisted up t o the present time. The section concludes by pointing out that while the more imaginative among primitive and medieval men venerated the objects that fell from heaven, the more practical had no hesitation in utilizing the heaven-sent material i n the fabrication of ornaments, weapons, and tools. AND

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‘ Those pictographs and petroglyphs left by Paleolithic man do not suggest that the moon, the planets, the fixed stars, or the sun in any notable way forced themselves upon the developing consciousness of Man. Soundless and endowed with languid motion, these bodies remained relatively unnoticed by him in the remoteness of the sky. The sudden, startling appearances of meteor showers and meteorite falls, however, must have had an entirely different effect upon him. Darting swiftly out of the heavens, shooting stars fall like a fiery snowstorm in the very faces of the beholders, and earth-shaking tumult accompanies the passage of a meteorite through the atmosphere. T o these unfamiliar and violently obtrusive visitations, early man no doubt reacted with frightened curiosity, as do the peoples of today. Because meteor showers and meteorite falls alarmed him, however, it does not follow that he would refrain from permanently recording them. Poisonous snakes and ferocious animals must have similarly terrified him, yet drawings, paintings, and carvings of snakes and wild beasts were made by him in profusion. It is to be expected that the records of primitive man’s attempts a t the earliest depiction of meteoritical phenomena will be much rarer than those devoted t o the animals and reptiles with which he fought for food and place. Even in Paleolithic times, meteor showers and meteorite falls were no doubt infrequent, and still less frequently would such phenomena be witnessed by men having the ability, the facilities, and the opportunity to make faithful and enduring likenesses of them. Such rarity may explain the failure, so far, to discover meteoritical pictographs among the artistic records preserved from the earliest times, but it seems likely to the writer that this failure may be due in part to misinterpretation of some of the evidence actually a t hand. Certain undoubtedly genuine meteoritical pictographs of moderate age are known. It seems probable that a meteoritical significance properly can, and should, be associated with other known pictographs of much greater age. Active collaboration between specialists in archeology, anthropology, ethnology, and meteoritics in exploring this promising and apparently neglected field would prove of much value. Today, when studies of radioactive carbon in the bones of a long-dead artist may serve indirectly to date one of his representations of a meteor shower, or when measures of the effects produced in a meteorite by exposure to cosmic radiation may, reciprocally, serve to determine the age in which a paleolithic artist painted the meteorite’s fall, i t is clear that close cooperation between those who study ancient man and those who investigate early meteorite falls and meteor showers is likely to be of mutual profit. As a modern instance of the pictorial recording of a n event of meteoritical importance, it may be noted that the Navajos of the Four Corners

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area of New Mexico, Arizona, Colorado, and Utah turned to pictographic means in describing the phenomena accompanying the fall of the meteorite of October 30,1947, in that region. Lacking words, other than “moving star,” with which to characterize this remarkable fall, the Navajos proved surprisingly adept a t tracing in the dust, or on wooden, rock, or paper surfaces, pictures that told the story more effectively than their speech could have done. Stimulated by the tendencies observed among the Navajos, the writer undertook a study of the relevant literature. This investigation disclosed that (1) a great meteorite fall occurring in the winter of 1821-1822 and (2) the spectacular Leonid meteor shower of November 13, 1833, were permanently recorded by historians of the Dakota tribe in the Winter Counts, by means of which the Indians established a chronological system. These Winter Counts were pictographic records, i.e., paintings, arranged on a spiral or similar curve on the tanned inner skin of a buffalo robe, of the year-characters whereby the Dakotas established a continuous designation of the years without having to resort to a scheme involving assignment of consecutive numerals to them [177]. Scientific records of the actual fall of a meteorite in the winter of 1821-1822 seem t o be lacking. As Mallery remarks, “There were not many correspondents of scientific institutions in the Upper Missouri region a t the date mentioned.” Furthermore, because of the enormous territory ranged over by the various tribes or bands of the great Dakota Nation, it is difficult to decide which one of several almost unweathered meteorites found in Dakota-land in the later 1800’s is most likely to have been associated with the fall the Indians observed in 1821-1822. The Fort Pierre, South Dakota (CN = 1003,344), and the Iron Creek, Alberta, Canada (CN = 1115,530:), octahedrites would seem to deserve careful consideration in this connection. As regards the Leonid shower of 1833, however, a wealth of hiRtorica1 and descriptive material is preserved in scientific journals and elsewhere. Intercomparison of the white- and red-men’s records of this meteor shower shows that both received the same impression of a veritable snowstorm of stars, descending into the very faces of the observers. Furthermore, the printed testimony justifies the Dakotas in representing the individual Leonid paths as luminous hairlines ending in bright bursts or flares similar to those observed for about 15% of the brighter Nu-Draconid meteors seen during the recent meteor shower of October 9, 1946. The crescent shown in the Dakota record of the 1833 Leonid shower may have been intended to represent the young moon, which set about an hour after the sun in the early evening of November 12, 1833. If this interpretation is indeed correct, then the association of this crescent with

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the Leonids indicates that in Dakota-land, as a t certain other places in the United States, the forerunners of the Leonid shower were observed in sufficient numbers t o attract attention even before moonset. It is more likely, however, that this crescent was intended to represent an extremely bright, long-enduring Leonid train. Such trains attracted universal attention among white observers and led to such printed descriptions as the following: " . . . it was then very brilliant, in the form of a pruning hook . . . I first saw it at 5 o'clock, when it resembled a new Moon, 2 or 3 hours high, shining thru a cloud . . . ) l I n addition to the portraitures of meteorite falls and meteor showers painted by the Amerinds-crude examples of a process of direct representation which culminated in such magnificent fireball paintings as those of Raphael [178] and Medvedev [179]-meteoritical pictographs of a conventionalized form have been found in the records left, for example, by the ancient Mexicans. These people used symbols to represent meteors which are reminiscent of those employed by the Europeans of the Middle Ages to portray comets. I n plates 29 and 30 of the first volume of Lord Kingsborough's compendious work on Mexican antiquities [180], one device-figure is reproduced which contains a circle enclosing an %pointed star with black spiraling plumes trailing from it, and another such figure shows a serpent darting out of a bowl of stars. I n the codex Telleriano Remensis (see [180], Vol. 6, p. 138), the first of these symbols is referred to as a smoking star, and the second as a serpent descending from the sky. Mallery believes that the first symbol represents a meteor that fell in 1534 (the year that Don Antonio de Mendoqa became Viceroy of New Spain, according to the codex quoted), and that the second symbol represents a meteor that fell in 1529 (the year that Nuiio de Guzman set out to conquer the Province of Yalisco, according to the same codex). Doubtless a careful search of the voluminous records left by the ancient Mexicans would disclose many other meteoritical pictographs. The examples just given show that meteoritical pictographs may be either portraitures or conventionalized forms. If, with this fact in mind, an examination is made of such pictographic collections as those published by Kingsborough and Mallery, a considerable number of drawings and paintings will be noted that appear t o have meteoritical significance. Furthermore, certain petroglyphs, or rock carvings, believed t o be of greater antiquity than the Mexican and Amerind pictographs, also seem to have such significance. Thus, a petroglyph found near San Marcos Pass, California, pictures two star-like figures joined by a trail, suggesting the path of a meteor from one position in the sky to another; a rock carving in Kansas shows a five-pointed star surrounded by a cloud; and

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333

a petroglyph a t Ojo de Benado, New Mexico, depicts what appears to be a crescent moon crossed by a hairline path with a terminal burst, closely resembling Dakota pictographs of typical bright Leonid meteors. Finally, although published collections of late Paleolithic pictographs (devoted as they primarily are to the more remarkable of innumerable animal portraitures) can scarcely be regarded as giving a typical sample of the work of the artists of that period, nevertheless they contain many forms suggestive of meteors and meteorites. One type in particular seems worthy of consideration in this connection, namely, the category of socalled radiate structures (figures rayonnantes) found in the cavern at Altamira, Spain, and studied with much care by Cartailhac and Breuil [181]. These investigators point out that, in spite of their best efforts, the meaning of these drawings is not understood. Various interpretations of these figures have been given, ranging from “ a bit of reed-grass” (see [181], p. 637) to a “magic weapon” [182]. It would seem quite possible that some of the “sheaves of rays” at Altamira-namely, those associated with certain reddish markings-are portraitures of auroral wreathes (i.e., incomplete auroral crowns) ; but others may be portrayals of showers of shooting stars during which a few curved and otherwise abnormal paths and several nonconforming meteors also were seen. The fact that the represented meteors are not shown shooting outward in all directions from the radiant is not fatal to this interpretation, for a similar-although somewhat less restrictive-limitation in directions of departure from the radiant is shown, e.g., in the Greenwich drawing of the Leonid shower of November 13, 1866, reproduced in Chambers’ “Astronomy” [183]. Furthermore, the artist may have observed only that limited portion of the shower visible through the entrance arch of the grotto of Altamira. If we seek to establish the identity of the shower which may have beeii depicted in the Altamira pictograph, it is interesting to note that twice within the period during which it is believed the artists of the Reindeer Age were active, the radiant of the annual Lyrid shower was near the north celestial pole for long intervals of time. Hence, as seen from the latitude of the Pyrenees Mountains, it would have occupied a nearly stationary position high in the northern sky, quite favorably placed for observation from the old entrance of the cavern at Altamira, since, according to Cartailhac and Breuil, this cavern opened toward the north a t the top of a hill (see [181], p. 626). As there is convincing evidence that earlier, richer showers of the Lyrids can be traced back into the past for more than 2500 yr 11841, it is not inconceivable that spectacular Paleolithic returns of this perennial shower inspired such portraitures as the Altamira pictograph. Much later in the evolution of mankind than the Altamira paintings,

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LINCOLN LAPAZ

the development of religious instincts led the more cultured people of antiquity to regard the stars as the domiciles of deity. Consequently, the fall of a meteorite was not unreasonably interpreted as the arrival on earth of divinity or an image thereof. Meteorites of observed fall were received with all due honor, and often were embalmed, draped, housed, and worshipped in temples built especially for them. As late as December 2, 1880, a new worship of this sort was inaugurated as a result of the fall of the Andhara, India, aerolite. Immediately after the fall and recovery of this meteorite, two Brahmans established themselves as its ministering priests and many thousands of the natives flocked to see it and to contribute funds for the construction of a temple in which to house it [185]. The meteorite temples of India and Japan, traceable to local meteorite falls like the one at Andhara, have such African analogs as the himmas or fetish temples of the Ashanti Negroes, the sacred stones of which are also meteorites or reasonable facsimilies thereof (see [2], pp. 50-51). Here, however, the origin of the cult apparently is lost in remotest antiquity. Since the giant water-filled crater, Lake Bosumtwi, has been seriously considered to have originated in large-scale meteoritic impact 11861, it is conceivable that the widespread and tenacious character of Ashantian meteorite worship is connected with racial memory of a past event of colossal proportions, lethal to many of the country’s early inhabitants. Among the most highly cultured Greek and other Mediterranean races, practices analogous to the worship of the Black Stone of Kaaba in Mecca (which persists even to the present day [187]) flourished and are recorded not only in the historical chronicles, but in more permanent, if less profuse, form in the various medals or Betyl coins struck to commemorate the arrival of meteorites on the earth. In his treatment of “numismatic meteoritics,” Brezina regards the term “ Betyl” as derived, by the way of the Greek PETVXOS,from the early Hebraic ‘‘Bethel,” or “home of God” [188]. As in the case of the pictographs earlier discussed, these Betyls, or meteoritic medals, show a transition from a primitive form-in which, for example, a black, conical aerolite found a naturalistic expression on the coin struck to commemorate its falllg-to a more sophisticated phase in which the meteoritical representations were increasingly conventionalized. But if man venerated meteorites, as the above evidence shows, he also exploited their properties of malleability and durability. In an inter1s Brezina gives the following description by Herodotus in regard to the Betyl of Emisa: “A large stone, which on the lower side is round, and above runs gradually to a point. It has nearly the form of a cone, and is of a black color. People say of it i n earnest that it fell f ~ o mHeaven.”

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esting paper, Rickard stresses that primitive man everywhere used meteoritic iron in the earliest stage of his metal culture [189]. As evidence proving that meteoritic iron was used in antiquity, Rickard calls attention to a number of the ancient names for iron:11 The Sumerian name for iron was an-bar, meaning “fire from heaven.” The Hittite ku-an has the same meaning. The Egyptian name, ‘bia-en-pet, has been variously translated; probably the first meaning of bia was “thunderbolt” . . and pet stands for “heaven,” so here also we have the plain intimation that the earliest iron was of celestial origin. A Hittite text says that whereas gold came from Birununda and copper from Taggasta, iron came from heaven Likewise the Hebrew word for iron, parZil, and the equivalent in Assyrian, barzillu, are derived from barZu-ili, meaning “metal of god” or “of heaven.” Even today the Georgian name for a meteorite is his-natckhi, meaning “fragment of heaven” (see “91, p. 55).

.

...

Various interesting uses of meteoritic iron may be cited: Fragments considered to be parts of a dagger found by Woolley at Ur of the Chaldees in 1927 have been ascribed to the first dynasty of Ur before 3000 B.C. According to Desch, these fragments upon analysis, were found to contain 10.9% nickel [191]. Furthermore, the predynastic iron beads found by Wainwright in 1911 at Gerzah, Egypt contained 7.5% nickel [192]. Similarly, microanalysis of a minute fragment of a thin blade of iron inserted into a small silver amulet in the form of a Sphinx head (XI dynasty) showed that iron and nickel were present in about the ratio 10 to 1 [193]. Atilla and other early conquerors of Europe possessed swords from heaven”; and the weapons of the Caliphs were of the same meteoritic material as the Kaaba stone. Emperor Jehangir (1605-1627) has put on record in considerable detail the circumstances of the fall on April 10, 1621, of the Jalandhar meteorite, from which by his orders two sword blades, one knife, and one dagger were smelted [194]; and as late as the beginning of the 19th century, J. Sowerby manufactured a sword from the Cape of Good Hope meteorite for presentation to Alexander, Emperor of Russia [195], while the Javanese armourers worked up the Prambanan siderite into weapons for royalty [196]. In various primitive areasSenegal, Mexico, and Chile-the natives have long utilized meteoritic iron €or agricultural implements, spurs, stirrups, spearheads, and knives. 14 In connection with the transition from picture writing to cuneiform script, it is interesting to note that one of the symbols in the earliest Egyptian hieroglyphic term for iron (min) is a good depiction of the teardrop shape of a falling fireball [190]. Some question has been raised as to whether or not the primitive Egyptians knew of the origin of meteoritic iron at the time this term was in use. This issue is still unresolved by Egyptologists. The resemblance of the hieroglyphic form to the actual phenomenon depicted would seem to indicate a “holdover” from the earlier picture writing of a people possessing knowledge a8 to the origin of meteoritic iron.

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The Eskimos of Greenland, using the famous Cape York meteorites as their source of supply, made metal knives, harpoon points, and other implements. Many artifacts composed of meteoritic iron have been found in the mounds erected by the prehistoric inhabitants of the central United States. Rickard (see [189], p. 59) has noted that, “The most remarkable objects found in these mounds were copper ear-ornaments, of spool shape, that had been covered with a thin plate of meteoric iron.”l6 The analyses of this overlaid material made by Kinnicutt [197] proved the presence of nickel in the proportion characteristic of meteoritic iron. More recently, members of the Illinois State Museum, excavating a group of Indian burial mounds in the Havana, Illinois area, discovered “22 rounded bead-like objects, composed of strongly oxidized iron, together with slightly more than 1000 ground shell and pearl or pearl slug beads” [198]. Several of the metal beads were analyzed, ground, and etched. They showed not only the characteristic nickel content of meteoritic iron, but also an interesting relict Widmanstatten structure. The examples cited here are but a few of the many well-substantiated instances of man’s utilization of meteoritic iron for practical and ornamental purposes. They clearly show, however, the important role played by cosmic materials in primitive, ancient, and medieval cultures. APPENDIX11. BASICMETEORITIC DATAAND CLASSIFICATIONAL IN SECTION5 CRITERIAEMPLOYED The reasons for selection of the half-century between 1896 and 1945 to provide the main body of data tested in Section 5 have already been given, together with the circumstances under which 17 meteorite falls of later data (1946-1950) came to be included during progress of the investigation. Use of Astapowitsch’s valuable summary of critically evaluated orbital elements in connection with work on the 1896-1950 data led t o the decision to take advantage of other orbits included in Astapowitsch’s paper, specifically those of the famous falls of Barbotan, L’Aigle, Pultusk, Hessle, MOCS,and Khairpur, occurring in the years 1790, 1803, 1868, 1869, 1882, and 1873, respectively. Nautical almanacs for these early years (none of which were in the files of the University of New Mexico Library) were very kindly loaned to the Institute of Meteoritics by the Yale University Observatory. Availability of these almanacs permitted treatment not only of the falls for which orbits had been computed, but 16 Through the courtesy of the Ohio State Museum, typical artifacts of this sort were displayed by the Society for Research on Meteorites at the American Association for the Advancement of Science convention in Columbus, Ohio, in December, 1939.

’

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also for all meteorite falls witnessed in the particular year covered by each almanac. Furthermore, since some of the bound volumes loaned by Yale contained almanacs for several years in addition t o the one requested, advantage also was taken of the opportunity thus afforded to treat several additional early witnessed falls. These facts make clear the quite fortuitous manner in which the meteorites with dates of fall prior t o those of the main body of data came to be included in our list. Furthermore, one can easily verify that exclusion from Table XI1 of the 36 meteorites with dates of fall prior to January 1, 1896, would produce no significant change in the results stated in Section 5. Much more important than the fortuitous circumstances determining the composition of the group C,,,, are the criteria deliberately chosen to effect a subdivision of CrIIinto the subgroups, CI and CII, of Section 5. First, it must be emphasized that objective considerations, which will be discussed below, led to adoption of these criteria; and, second, that the criteria were adopted before the subdivision of CIII was attempted and, once chosen, were transgressed only 7 times in the treatment of the totality of 264 classified meteorites. The reasons for the 7 transgressions will be given below. I n the writer’s considered opinion, the reasons given are valid ones; but, whether they are or not, it cannot be too strongly emphasized that the exceptions permitted, amounting t o only 2.6% of the total number of classified meteorites, are too few in number to affect materially the validity of the conclusions based on consideration of the subgroups CI and CII, as finally constituted. For 53 of the 317 meteorites treated, only such indefinite classifications as stone (AE), chondrite (C), etc., were known. For the remaining 264 meteorites, definite meteoritic classifications, often involving numerous qualifiers-to employ Leonard’s useful term [ 1991-were available. Except for 7 of the 264 classified meteorites, certain of these qualifiers (those italicized in the summaries given below) were taken as providing criteria of decisive importance in allocating a given meteorite either t o C, or to CIr.I n this manner, the following assignments were made of all meteorites for which a classification was known:

To the Subgroup, CI All 26 irons and iron-stones; all 10 carbonaceous chondrites; all 4 howarditic chrondrites of Brezina; all 38 white chondrites; and 44 of the 46 gray chondrites. I n addition, 3 mineralogically quite similar bronzite chondrites (Pultusk, Nassirah, and Queen’s Mercy) and 2 mineralogically quite similar enstatite chondrites (Khairpur and Leonovka) , which normally would have been allocated t,o Crr were placed in Cr because, in the writer’s

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judgment, the evidence that the extra-atmospheric velocities of these bodies were strongly hyperbolic outweighs all other considerations.

To the Subgroup, CII All 31 achondrites; all 17 spherulitic chondrites; all 37 intermediate chondrites; all 5 crystalline chondrites; all 7 black or veined chondrites; all 14 classified hypersthene chondrites not previously allocated; 17 of the 20 bronzite chondrites; and 7 of the 9 enstatite chondrites. In addition, 2 mineralogically quite similar gray chondrites (Ekeby and Kendleton), which normally would have been allocated to CI were placed in CII because, in the writer’s opinion, there is compelling evidence that the extra-atmospheric velocities of these meteorites were definitely elliptic. Choice of the criteria employed above in subdividing the 264 classified meteorites did not rest solely on such evidence as that furnished by compilations of meteorite orbits (like that of Astapowitsch) and the writer’s determinations of extra-atmospheric velocities for various meteorites. In addition, careful consideration was given to such convincing non-orbital evidence as the following: Watson’s [a001 laboratory demonstration that exposure of lightish-colored chondrites to a temperature of 800°C will turn them into black chondrites, and his sound probabilistic argument that the agency responsible for the heat darkening of the chondrites picked up by the earth is the sun and not the stars; and arguments, some dating back to Sorby [201] and Cohen [202]-and others recently published by Urey [148]-which indicate that the spherulitic chondrites had their origin in the crowded confines of the solar system. There remains to be considered the manner in which the 53 unclassified meteorites were allocated to either CI or CII.Since in these 53 cases, no clue whatever could be found permitting use of the precepts employed on the other 264 meteorites, the only alternative was t o leave the matter to chance. The 53 unclassified meteorites appeared in alphabetical order in the meteorite catalog employed in drawing up a polar diagram which served as a basis for preparation of Table XII. As each of the stones in question was encountered in the catalog, the toss of a coin determined whether the meteorite was to be allocated to CI or to CII.As a result, 25 of the unclassified meteorites went into the first of these subgroups and 28 into the second. Interestingly enough, the ratio 25/28 is very close to to that in which the classified chondrites were distributed between CI and CII.Since reliance on chance to distribute the unclassified meteorites conforms to the natural random fall of interstellar meteorites with respect to a, there is no reason to believe that the 25 stones assigned to CI by this process could significantly alter the distribution with respect to a of

EFFECTS OF METEORITES ON THE EARTH

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the classijied component of this subgroup. Similarly, since, as the reader can verify, chance provided a fairly uniform distribution with respect to cy of the 28 stones assigned to CII, the unclassified component of CIr cannot be held responsible for the sinusoidal excellence of the lower curve in Fig. 2 (11) of Section 5. LIST OF SYMBOLS (According to the Section in which they appear)

Section Symbol 1.2.1 HTA N

P

P

e

n

P* 1.2.2 BTA

N P P e

1.2.3 VTA d V

V II

3.2

R

Definition human target area number of meteorites reaching the surface of the earth per century probability t h at at least one of these N meteorites will strike the specified HTA area of HTA (in square miles) divided by 2 x 108 Naperian base of logarithms number of centuries after 2100 A.D. probability t h at in a t least one of the n centuries after 2100 A.D. at least one meteorite will hit in the HTA of the world built-over target area number of meteorites reaching the surface of the earth per century probability that at least one meteorite will hit in the New York City area in the 20th century area of BTA (in square miles) divided b y 2 x 108 Naperian base of logarithms vehicular target area diameter of rocket cruising speed of rocket velocity of visual meteors space density of visual meteors region within which the fallen meteorites constitute a n essentially homogeneous group total number of meteorites in R independent, equally intensive searches of R number of meteorites found during first search S1 number of meteorites found during second search Sn number of discoveries common to both SI and 5 2

nl/N ndN PZ X n: = (n2. n d / N pl X nl = (nl n z ) / N a real number such that 0

<e 6 1 integer nearest to the fraction, f recovery index actual number of individuals recovered in a strewn field of which the (probable) population is N

LINCOLN LAPAZ

Section

Definition

Symbol

3.4.2 P'

tangent plane to earth a t a point, 0, chosen as origin of an xyz-coordinate system of which the y and z axes lie in the plane P' inradius of spherical cap with center 0 on earth's surface area of circle with center 0 in plane P' radius of spherical iron meteorite the distance beneath the plane P' of the center of a spherical iron meteorite of radius r radius of the smallest meteorite which just attains a penetration of depth x into the earth radius of the largest meteorite which does not penetrate too far into the earth to touch the plane, x = x (ra - [ d ( r ) - zI2)% density of meteoritic nickel-iron number of years of sideritic infall number of iron meteorites with radius between r and T dr striking the entire earth annually depths in the earth beneath the plane I" ratio in right member of equation (8) of this section total observed increase in the length of the day a real number such that 0 < e 5 1 moment of inertia of earth and corresponding duration of diurnal rotation a t any time t value of Z at beginning of year for which we seek to calculate the meteoritic accretion, and corresponding duration of diurnal rotation increment in I due to the infall of meteoritic material radius of earth mean density of the earth thickness of shell of meteoritic dust density of meteoritic dust density of the fictitious auxiliary deposit D defined in Section 3.5 number of meteoritic particles falling on the earth annually average mass of these meteoritic particles mass of the earth when Z = ZO total observed annuaE increase in the length of the day radius in centimeters of interplanetary particle number of interplanetary particles per cubic centimeter in the vicinity of the earth's orbit with radii between r and r +dr electron density Harvard Meteor Program angular velocity time of apparition observed velocity eccentricity point of initial visibility midpoint of the photographed path of H.M.P. meteor No. 670

+

lo, 7 0 AI

r PO

A? P P'

N -

m

M AT

3.6.3 r n(r ) dr

4.2

n. H.M.P. w

T VO

e

4.5.1

B B'

EFFECTS OF METEORITES ON THE EARTH

Section

Symbol

H' A 6

4.5.2

4.5.3

5.1

6.4

c

= C(z)

co = C(0) D t

z=

341

Definition end point of meteorite path deceleration experienced by the meteorite deceleration determined from the H.M.P. photograph of meteor No. 670 constants time value of t when meteorite reaches end point H i velocity as a function of t position as a function of t velocity of meteorite a t the point H' Naperian base of logarithms coordinates of meteorite a t time t in the wv-coordinate system speed with which meteorite penetrates air effective speed of sidewise escape of compressed gaseous cap average values of 6 ( t ) and i ( t ) taken over the short time interval, AT constants smoke formation pressure atmospheric density in grams per cubic centimeter constants velocity of meteorite right ascension of the moon quadrants centering on CY = O", QO",180", 270°, respectively probability of success counter-probability = 1 - p number of trials discrepancy probability that in n trials the discrepancy will not exceed numerically the number d percentage of NiO found at horizontal distance z from buried meteorite Fick diffusion coefficient time X

2

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Coon Butte) in Northern Central Arizona,” p. 4. Privately printed. Read before the National Academy of Sciences meeting, Princeton Univ. November 16, 1909. 160. opik, E. J. (1936). Researches on the physical theory of meteor phenomena. I. Theory of formation of meteor craters. Acta et Comment. Univ. Tartu. A XXX1, 3-12. 161. Spencer, L. J. (1933). Meteoric iron and silica glass from the meteorite craters of Henbury (central Australia) and Wabar (Arabia). Mining Mag. (London) 23, 387-404. 162. Rogers, A. (1930). A unique occurrence of lechatelierite or silica glass. A m . J . Sci. 19, 195-202. 163. Blackwelder, Eliot (1953). Crater mound-meteor crater. Bull. A m . Assoc. Petrol. Geol. 37, 2577. 164. LaPaz, L. (1944). Meteoritical position problems. Contrib. SOC.Res. Meteorites 3, 152, footnote 2. 165. LaPaz, L., and Wiens, G. (1935). “On the History of the Bolide of 1908, June 30,” by L. Kulik. Contrib. SOC.Res. Meteorites 1(1), 29-34; (1935) “On the Fall of the Podkamennaya Tunguska Meteorite in 1908,” by L. A. Kulik. Ibid. 1(1), 3539; (1936). “Preliminary Results of the Meteorite Expeditions Made in the Decade 1921-31,” by L. A. Kulik. Ibid. 1(2), 15-20; (1937). “Instructions for the observations of [High Temperature Effects due to] Lightning [and other agencies],” by L. A. Kulik. Zbid. 1(3), 29-33; (1940). “New Data Concerning the Fall of the Great [Tungus] Meteorite on June 30, 1908 in Central Siberia,” by I. S. Astapowitsch. Ibid. 2(3), 203-226. 166. LaPaz, L. (1941). Meteorite craters and the hypothesis of the existence of contraterrene meteorites. Contrib. SOC.Res. Meteorites 2(4), 246. 167. Boldyreff, A. W., and LaPaz, L. (1950). Some characteristic features of the Sikhota-Alin (Ussuri) iron-meteorite shower [of the U.S.S.R.: ECN = T 1347,4621. Contrib. Meteorit. Soc. 4(4), 264-269. 168. Wylie, C. C. (1943). Calculations on the probable mass of the object which formed Meteor Crater. Popular Astron. 61, 97-99; (1943). Applying mine-crater formulas to Meteor Crater in Arizona. Ibid. 61, 220-222. 169. LaPaz, L. (1943). Probable mass of Canyon Diablo meteorite. Contrib. SOC.Res. Meteorites 3, 95. 170. Birkhoff, G., McDougal, D. P., Pugh, E. M., and Taylor, G. (1948). Explosives with lined cavities. J . Appl. Phys. 19, 563-582. 171. Rostoker, N. (1953). The formation of craters by high-speed particles. Meteoritics 1, 11-27. 172. Rinehart, J. S. (1950). Some observations on high-speed impact. Contrib. Meteorit. SOC.4, 299-305. 173. Barringer, D. M. (1905). Coon Mountain and its crater. Pror. Acad. Sci. Phila. 67, 868. 174. LaPae, L. (1950). A preliminary report on Indian ruins discovered near the crest of the Barringer Meteorite Crater, Arizona. Contrib. Meteorit. SOC.4(4), 285-286. 175. Blackwelder, E. (1932). The age of Meteor Crater. Science 76, 557-560. 176. Van Orstrand, C. E., and Dewey, F. P. (1916). Preliminary report on diffusion of solids. U.S. Geol. Surv. Profess. Pap. 96, 83-96. 177. Mallery, G. (1893). Picture writing of the American Indian. Ann. Rept. Bur. Am. Ethnol. 10, 25-777. 178. DaubrBe, G. A. (1891). Bolide peint6 par Raphael. Astronomie. Revue mens. populaire 10, 201-206; Newton, H. A. (1891). Fireball in the Madonna di Foiigno. Am. J . Sci. [3] 41, 235-239.

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LINCOLN LAPAZ

179. A black and white reproduction of Medvedev’s painting appears as a frontispiece in E. L. Krinov’s “Bases of Meteoritics,” Moscow, 1955. 180. Kingsborough, E. K. (1831-1848). “Antiquities of Mexico,,’ 9 vols. Have11 and Colnaghi, London. 181. Cartailhac, E., and Breuil, H. (1904). Les peintures et gravures murales des Cavernes Pyreneennes. Anthropologie Paris 16, 625-644. 182. Raphael, M. (1945). ‘[Prehistoric Cave Paintings,” p. 78. Pantheon, New York. 183. Chambers, G. F. (1877). “Handbook of Descriptive Astronomy,” 3rd ed., p. 805. Oxford Univ. Press, London and New York. 184. Biot, E. (1841). Catalogue general des Qtoiles filantes et des autres met6ores observhs en Chine pendant 24 siitcles. Mbm. Savants Etrangers 1, 74. Academie des sciences morales et publiques, Paris. 185. Cunningham, A. (1883). The Andhara meteorite. Repls. Archaeol. Surv. Zndia (new Imperial series) 16, 32-34. 186. Maclaren, M. (1931). Lake Bosumtwi, Ashanti. Geograph J . 78,270-276; Junner, N. R. (1933). Lake Bosumtwi. Rept. Geol. Survey. Gold Coast 4-7; (1937). The geology of the Bosumtwi caldera and surrounding country. Bull. Gold Coast Geol. Surv. 8,5-38. 187. Sheikh, A. G. (1953). From America to Mecca on airborne pilgrimage. Natl. Geograph. Mag. 104(1), 1-60 (especially 26-27). 188. Brezina, A. (1889). Darstellung von Meteoriten auf antiken Munzen. Monatsbl. Numismat. Ges. Wien 70, 212-214. 189. Zimmer, G. F. (1916). The use of meteoritic iron by primitive man. J. Iron Steel Inst. (London) 94(2), 306-356; Rickard, T. A. (1941). The use of meteoric iron. J . Roy. Anthropol. Inst. Gt. Brit. and Ireland 71, 55-66. 190. Mellor, J. W. (1932). “ A Comprehensivc Treatise on Inorganic and Theoretical Chemistry,” Vol. XII, p. 484. Longmans, New York. 191. Desch, C. H. (1928). Report on the Metallurgical examination of specimens for the Sumerian Committee of the British Association. Rept. Brit. Assoc. Adu. Sci. 437-441. 192. Wainwright, G. A. (1932). Iron in Egypt. J . Egypt. Archaeol. 18, 3-15. 193. Coghlan, H. H. (1941). Prehistoric iron prior to the dispersion of the Hittite Empire. M a n 41, 74. 194. Khan, M. A. R. (1934). “Meteors and Meteoric Iron in India.” Privately printed by Moses and Co., Secunderabad. 195. Sowerby, J. (1820). Particulars of the sword of meteoric iron presented b y Mr. Sowerby to Emperor Alexander of Russia. Phil. Mag. 66, 49-52. 196. Berwerth, F. (1907). Javanische Waffen mit “ Meteoreisenpamor.” Tschermak’s Mineralog. u. petrog. Mitt. 26, 506-507. 197. Kinnicutt, P. (1884). Report on the meteoric iron from the Altar Mounts in the Little Miami Valley. Ann. Rept. Peabody M u s . 3, 381. 198. Grogan, Robert M. (1948). Beads of meteoric iron from an Indian mound near Havana, Illinois. Amer. Antiquity 13, No. 4, 302. 199. Leonard, F. C. (1948). A simplified classification of meteorites and its symbolism. Contrib. Meteorit. SOC.4, 142, 200. Watson, F. G. (1956). “Between the Planets,” rev. ed., p. 161. Harvard Univ. Press, Cambridge, Mass. 201. Sorby, H. C. (1877). On the structure and origin of meteorites. Nature 16, 496498. 202. Cohen, E. (1894). “Meteoritenkunde,” Vol. 11. Koch, Stuttgart.

SMOOTHING AND FILTERING OF TIME SERIES AND SPACE FIELDS J. Leith Holloway, J r . U. S.

Weather Bureau, Washington

D.C.

Page Introduction.. . . . . . . . . . . . ............................. 351 Time Smoothing and Filtering., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Equalization, Pre-emphasis, and Inverse Smoothing. . . . . . . . . . . . . . . . . . 353 Smoothing and Filtering Functions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 Frequency Response of Smoothing Functions and Other Filters.. . . . . . . . . . . 355 Design of Smoothing Functions and Filters with Specified Frequency Response. . . . . . . . . . . . . . . . . . . . . . . . . . . .... 363 7. High-Pass and Band-Pass Filtering Functions. . . . . . . . . . . . . . . . . . . . . . . . . . 365 8. Elementary Smoothing and Filtering Functions. . . . . . . . . . . . . . . . . . . . . . . . . . 369 9. Design of Inverse Smoothing Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 10. Design of Pre-emphasis Filters.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 11. Filtering by Means of Derivatives of Time Series.. . . . . . . . . . . . . . . . . . . . . . . 378 12. Space Smoothing and Filtering.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 Acknowledgments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 List of Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388

1. 2. 3. 4. 5. 6.

1. INTRODUCTION

Time and space smoothing are widely used in the study of geophysical problems. For example, the drawing of smooth isolines through data plotted on a map of some geophysical variable is a type of space smoothing. The computation of consecutive monthly mean values of a series of measurements and the use of long-lag instruments for suppressing rapid fluctuations in readings are examples of time smoothing. The purpose of this paper is t o give the reader a better understanding of just what these smoothing methods really accomplish so as to provide a rational basis for the selection of any particular smoothing method. Smoothing will be shown t o be a special type of filtering, and the analysis will therefore be extended t o cover numerical filters of all types. Much of the information in this paper is not new, but is scattered rather widely in the mathematical, statistical, and scientific literature. An attempt is made here to combine all pertinent information on smoothing and filtering in a concise, simple, underst,andable form for the benefit of geophysicists concerned with these problems. Since this paper is pri351

352

J. LEITH HOLLOWAY, JR.

marily a survey of the field, rigorous mathematical derivations of the equations are not given. 2. TIMESMOOTHING AND FILTERING In statistical work a series of data arranged chronologically is commonly called a time series. For example, a series of daily mean temperatures in order of date is a time series. Generally the data in time series are equally spaced in time, and therefore all time series discussed in this paper will have equally spaced data. The variations in the data with time may be relatively smooth and orderly or may be rather complex and without apparent pattern. It is convenient to consider that the variations in time are produced by superimposed sinusoidal waves of various amplitudes, frequencies, and phases. The Fourier theorem states that no matter how complicated the fluctuations in the data may be they can be accounted for by the superposition of a number of simple component sinusoidal waves [l]. The amplitudes, frequencies, and phases of these waves are generally changing constantly with time. The exception to this is where fixed cyclic processes such as diurnal and annual influences tend to induce waves of constant frequency (one cycle per day or per year) into the data. The purpose of time smoothing is to attenuate the amplitudes of high-frequency waves in the data without significantly affecting the lowfrequency components. The attenuation is roughly proportional to frequency. Above some high frequency, depending upon the properties of the smoothing method used, the attenuation is complete for all practical purposes. The assumption upon which the use of smoothing is justified is that high-frequency oscillations in the data are either random error (“noise”) or are of no significance to the particular type of evaluation of the data to be carried out after the smoothing. Smoothing thus enables one to concentrate on the low frequencies without the distraction caused by high-frequency noise and other irrelevant fluctuations. A smoothed value of an observation in a time series is merely an estimate of what the value would be if noise and other undesired high frequencies were not present in the series. Smoothing is a special case of the broader general process of filtering, a concept brought into the field of time series analysis from electrical engineering. An electrical filter, such as a simple resistance-capacitance network, separates various sinusoidal components of an “ electrical time series” according to frequency. An electrical analog of a numerical time series is a continuously varying voltage or current-usually referred to as a “signal” in electrical engineering. Electrical filters can be designed to pass only low frequencies of the signal while attenuating or eliminating

SMOOTHINQ AND FILTERING

353

high frequencies. This type of filter is commonly called a “low-pass filter.” Thus smoothing of a numerical time series is analogous to lowpass filtering of an electrical signal. Filters can also be designed to pass only high frequencies and attenuate low frequencies (“ high-pass filter ”). Finally other filters pass a band of intermediate frequencies ( ‘ I band-pass filter”) and attenuate both very low and very high frequencies in the input signal. Numerical band-pass and high-pass filters will be described in Section 7. 3.

EQUALIZATION, PRE-EMPHASIS, AND

INVERSE SMOOTHING

Two other terms which may be borrowed from electrical engineering and applied to time series analysis are “equalization” and “pre-emphasis.” Equalization is the process of restoring the original balance of amplitudes of sinusoidal waves in a signal which has previously been altered by filtering or pre-emphasis. Pre-emphasis is the amplification before transmission of certain bands of frequencies in a signal above a standard amplification. For example, the high audio-frequencies are pre-emphasized before transmission by a frequency-modulation transmitter to override high audio-frequency noise introduced by the transmitter, the atmosphere, and the receiver. This can be done since high audio-frequencies are generally of low amplitude in the original signal. At the receiver the correct balance of frequencies in the audio signal is restored by an equalization filter (“de-emphasis” filter) which in this case is merely a low-pass filter having an attenuation which is the inverse of the frequency characteristics of the pre-emphasis at the transmitter. A second example of electrical equalization is the compensation for the attenuation of high frequencies in a long transmission line. I n this case the line itself acts as a low-pass filter. The original balance of frequencies in the signal is approximately restored at the end of the line by an equalization amplifier which has greater amplification a t high than at low frequencies. As long as some fraction of the signal a t a given frequency is received above the noise in the line, the original relative amplitude at this frequency can be approximately restored. Of course, in order to equalize properly it is necessary to know how much the line attenuates the signal a t each frequency. It follows that it should be possible to equalize a time series previously smoothed provided that the characteristics of the smoothing were known. Later in this paper, a method for performing this equalization numerically will be given. The term “inverse smoothing” will be used for the numerical equalization used for accentuating high frequencies in respect to low frequencies in order to restore the original balance of frequencies to a smoothed time series. A good deal of work on inverse smoothing already

354

J. LEITH HOLLOWAY, J R .

has been done in several scientific fields, notably in radio-astronomy 12-10].

4. SMOOTHING AND FILTERING FUNCTIONS Smoothing of a time series is performed by a type of numerical or mathematical operator which will be termed a ‘‘ smoothing function” in this paper. Generally the smoothing function consists of a series of fractional values, called weights. I n this paper, the term “filtering function” will be applied t o operators which perform filtering of time series other than smoothing. Filtering functions also generally consist of various weights similar t o those of smoothing functions. The weights determine in what proportion each observation in the time series contributes to the estimate of the smoothed or filtered value. In the process of smoothing or filtering, successive observations in a time series are cumulatively multiplied by these weights. The smoothed or filtered value corresponding t o the observation x t in the time series is computed from observations xt-,, through xt+, by the following linear equation: (4.1) & =

5

k=-n

Wkxi+k

= w-nX1-n

+

’ ’

+

+

w-1%-1

+

W O X ~ WlXt+l

+

*

*

+

+

WmXt+m

where w k is a particular weight in the smoothing or filtering function. The weight W O , which is multiplied by the observation xt, will be termed the principal weight in this paper. The principal weight is the central one in the case of the equally-weighted running mean where all weights are identical and equal to 1,” where N is the number of observations used in computing the mean. The use of smoothing and filtering functions is illustrated in Fig. 1. The weights of the smoothing function in the block shown in this figure are cumulatively cross-multiplied by the adjacent values in the time series and the resulting product is entered opposite the time series value multiplied by the principal weight. Then the smoothing function is moved down one time increment (data interval) along the time series and t h e cross-multiplication is repeated t o obtain a second smoothed value. This process is repeated unt,il the lowest weight in the smoothing function reaches the end of the series. The sum of the weights of a smoothing or filtering function determines the ratio of the mean of the smoothed or filtered series t o the mean of the original series assuming that these means are computed over periods long enough to insure stable results. I n smoothing it is generally desired

355

SMOOTHING AND FILTERING

t o leave the mean. of the series unchanged, and consequently the sum of the weights of most smoothing functions is made equal t o unity. With some filters to be discussed later it is not necessary to preserve the mean of the series, and in these cases the sum of the weights may be different from unity. For theoretical evaluation of smoothing and filtering functions it is often useful t o consider th at these functions are continuous rather than composed of discrete weights. The continuous analytic form of the smoothing or filtering function will be some function w(t) describing the envelope of the discrete weights. The time origin here is the time of the principal weight; namely, the time of the observation for which a smoothed value is being computed. The area under the continuous Time Series Smoothing Function\ Principal Weight

--f

,016 +.094 +.234 +.312 +.234 +.094 +.016

X X X X X X X

Time Series

28 23 21 24+ 22.3 22 20 17 18 29 35

.016 + . 094 + . 234 + . 312 + . 234 + . 094 +.OlS

X X X X X X X

28 23 21 Smoothed 24 2 2 . 3 Values 22 4 2 1 . 4 20 17 18 29 35

FIG. 1. Illustration of smoothing a time series by means of a typical smoothing function.

smoothing or filtering function corresponds t o the sum of the weights of a discrete-valued function. Thus the ratio R of the mean of the filtered series t o that of the original series is

R

=

-w

w(t) at

in the case of continuous functions.

5. FREQUENCY RESPONSE OF SMOOTHING FUNCTIONS AND OTHERFILTERS The ratio of the amplitude of a wave of a given frequency in the time series after filtering t o the original amplitude before filtering is the frequency response of the filter a t this frequency. The frequency response is a function of frequency. For example, the value of the frequency response of a smoothing function is near unity at low frequencies and near zero a t high frequencies.

356

J. LEITH HOLLOWAY, JR.

The frequency response of a mathematical filter such as a smoothing function can be derived by determining the effect of this filter on a unitamplitude sinusoidal wave of frequency f. This wave may be represented by a unit vector rotating about the origin with angular velocity of 27rf in the complex plane. The projections of this unit vector on the real and imaginary axes define the phase of the unit amplitude wave a t any time. The projection of this vector on the real axis is cos (27rft), and on the imaginary axis, sin (27rft), where t is time.' After smoothing or some other form of filtering, the modified wave can be represented b y another vector rotating about the origin in the complex plane with the same angular velocity but having a magnitude and phase angle generally different from that of the original unit vector. The amplitude of the smoothed or filtered wave and its phase angle a t any time is determined by the instantaneous projections of this modified vector on the real and imaginary axes. These projections can be shown to be merely the weighted mean of the projections of the original unit vector on these axes averaged over the interval during which the smoothing or filtering function is operating, hereafter t o be referred t o as the filtering intervaL2 The weighted mean projection of the unit vector on the real axis averaged over the filtering interval is obtained by summing the products of each weight and the corresponding value of cos (27rf.t) a t time t. The weighted mean projection on the imaginary axis is obtained in a similar manner but with the sine substituted for the cosine. I n the case of continuous analytic forms of the smoothing and filtering functions these mean projections must be computed by integration. The ratio of the magnitude of the modified vector t o the magnitude of the unit vector (unity) is the frequency response of the filter. Thus, the magnitude of the modified vector is the frequency response. This magnitude is the absolute value of the complex quantity R ( f ) given by

The cosine term of (5.1) is a weighted time mean projection of the unit vector on the real axis, and the sine term is the simultaneous weighted time mean projection of this vector on the imaginary axis. This equation will be recognized as the inverse Fourier transform of w(t). Therefore, the inverse Fourier transform of the smoothing or filtering function is the filter's frequency response function. The absolute value of R ( f ) is the The arguments in this paragraph are valid for any time origin in addition to tha t used in the last section. * For example, the filtering interval in Fig. 1 is seven data intervals.

357

SMOOTHING AND FILTERING

square root of the sum of the squares of the real and imaginary parts of R ( f ); namely

IR(nl = uw-w" + [ I m { R ( f ) W

(5.2)

The angle between the original and the modified vector is the phase shift which the filtering function w(t) produces at frequency f. This angle 4 is given by

4 = tan-' [Im(R(f))/Re{R(f)Jl

(5.3)

+ +

For smoothing and filtering functions having (n m 1) discrete weights the frequency response is computed by the following form of equation (5.1)

where units of frequency f are cycles per data interval. The absolute value of R(f) obtained from the above equation is again computed by equation (5.2). It is desirable that smoothing and filtering functions not shift the phase of waves of any frequency. The phase shift angle can be made equal to zero by requiring that the numerator of the argument in equation (5.3)(namely, the specified weighted time mean projection of the unit vector on the imaginary axis) be zero. This in turn can be accomplished by requiring that the function w(t) be even (namely, that w(-t) = ~ ( t ) ) , ~ for if w(t) is even, the terms containing the sines in equations (5.1) and (5.4) are zero, and R ( j ) is a pure real quantity computed by

R(f)

(5.5)

=

w(t) cos (27rft) dt = 2

/om

w(t) cos (27rft) dt

for continuous w(t) functions or

+

for smoothing and filtering functions having ( 2 n 1) discrete weights. The frequency response of an equally-weighted running mean of (2n 1) consecutive terms may be computed from equation (5.6) be-

+

* I n the case of discrete-weighted is that

W-E

=

smoothing and filtering functions this condition wk.The smoothing function in Fig. 1 is even.

358

J. LEITH HOLLOWAY, JR.

cause w-k = wk; in fact, in this case every weight Equation (5.6) gives R ( f ) = wo 2 ~ cos 1 (2~jA.t) 2 ~ cos 2 (&!At) (5.7)

+ = (2n +

wk

+

l)-I[l

= 1/(2n

+ 1).

+. + 2w, cos (2n7rfa.t) + 2 cos (27rfAt) ++2 cos (&!At) . . . + 2 cos (2n?rfAt)] *

where At is the data interval. The use of At here avoids the requirement that the units of frequency be cycles per data interval; the units of frequency in (5.7) are thus cycles per particular unit of time used. A convenient approximation of the frequency response of the equallyweighted running mean can be computed from equation (5.5) by using the analytic form of the envelope of the weights, w ( t ) ; namely, (5.8)

where T is the filtering interval. Equation (5.5) gives (5.9)

R(O

=

2

,l""z T-'

cos (2n;fl) c~t=

(Z!T)-~

sin

(.trf~)

Equation (5.9) gives a very accurate approximation of the frequency response of equally-weighted running means.4 The exact frequency response of an equally-weighted running mean having five weights of one-fifth each is shown in Fig. 2 as a dotted line. This response is computed from equation (5.7) assuming a data interval of T/5 so as to make the filtering interval equal to T. For comparison, the approximate frequency response for this type of running mean computed from equation (5.9) is shown in this figure as a solid line. Notice that the agreement between these two curves is quite good; the agreement would be even better with running means of more than five terms. The physical meaning of the negative response a t some frequencies in Fig. 2, is that the input waves of these frequencies are reversed in polarity in addition to being changed in amplitude. A reversal of polarity of a wave means that its maxima are changed into minima and vice versa.6 Positive and negative values of the frequency response above the frequency of the first zero response point are undesirable because they will introduce many unwanted and misleading high-frequency ripples into the smoothed output. A method for suppressing or eliminating these undesirable responses By L'Hopital's rule this function has the value unity at f = 0. Reversal of the polarity of a wave corresponds to a reversal of the direction of rotation of the vector representing this wave. This is equivalent to a 180-degree phase shift of the wave. 4 6

359

SMOOTHING AND FILTERING

1.0

w u)

0.5

z P 0

W u) K

0

0.0

I .o

2.0

FREQUENCY IN CYCLES PER FILTERING INTERVAL

T

FIQ.2. Frequency responses of equally-weighted running means and of a normal probability curve smoothing function. Solid line is response of the running mean computed from equation (5.9). Dotted line is response of the five-term running mean computed from equation (5.7). Dashed line is response of normal curve smoothing function having u = T / 6 computed from equation (5.11).

is t o provide a smoothing function having weights decreasing in magnitude outward from the principal weight. For example, the smoothing function weights may be made proportional t o the ordinates of the normal probability curve. A continuous analytic form of this smoothing function is (5.10)

w ( t ) = (27rg2)-%exp ( - t 2 / 2 a 2 )

The area under the above function is unity so that the mean of the smoothed series will be conserved. The frequency response of this smoothing function is obtained from equation (5.5); namely, (5.11)

R ( j ) = exp (-2?r2a2f2)

360

J. LEITH HOLLOWAY, JR.

The frequency response given by equation (5.11)for the normal curve smoothing function decreases smoothly with increasing frequency and asymptotically approaches zero. Thus it avoids the negative values of response exhibited by the equally-weighted running mean. Although zero response is theoretically never reached, for practical purposes this smoothing function has a finite “cutoff frequency.” The “cutoff frequency” of a smoothing function will be defined as the lowest frequency at which the response reaches zero for all practical purposes and remains zero for all higher frequencies. Thus in cases like this where the response function approaches zero asymptotically the cutoff frequency can be taken as that frequency where the response drops to some arbitrarily chosen low value, say one per cent. The cutoff frequency of the normal curve smoothing function is controlled by the value of the parameter u in equation (5.10). The response of the normal curve smoothing function having a filtering interval of T is plotted in Fig. 2 as a dashed line for comparison with that of the equally-weighted running mean having the same filtering interval. The filtering interval of a normal curve smoothing function is taken to be 6u, for beyond 30-from the origin the normal curve ordinates have negligible value. The equations in this section may also be used t o compute the frequency response of an exponential smoothing function; namely, one having the analytic form:

(5.12) where X is the so-called time constant or lag coefficient. The area under this function is unity so that the mean of the series is unaffected by the smoothing. This type of smoothing is that which is performed by physical instruments which are viscous-damped and have constant X and by simple, two-element resistance-capacitance low-pass electrical filters. An example of an instrument which smooths in this manner is the simple mercury-in-glass thermometer. Since this smoothing function defined above is continuous and not even,6 equation (5.1)must be used for determining its frequency response. This equation gives

+

(5.13) R(f) = (1 h Z f 2 X “ ) - ’ and from (5.2),’ (5.14) IR(f)I = (1

- (2nifX)(1 + h 2 f Z X 2 ) - ’

+

47?f2X2)-%

This smoothing function has zero values for t > 0 since no physical instrument can take future variations into account in its smoothing. 7 Middleton and Spilhaus obtain this same result by means of differential equations [Ill.

361

SMOOTHING AND FILTERING

Since the imaginary part of R(f) is not zero owing to the unsymmetrical distribution of weighting about the origin, the smoothed series has phase error which is computed from equation (5.3) and given below

4

(5.15)

=

tan-' (-27rfX)

The frequency response and phase shift for exponential smoothing is shown in Fig. 3 where X equals unity. Notice that this frequency response also approaches zero asymptotically. Smoothed data are often obtained by deliberately increasing the viscous damping of the measuring instrument [I21 or by use of simple resistance-capacitance electrical filters. The fact that this type of smoothing introduces phase error into the data suggests that a better smoothing

1.0

-+ c

6'0

r

Y !

0.5

30'

/

I

I

I

I

I

I

I

FREQUENCY

FIG. 3. Frequency response R ( f ) and phase shift function having a lag coefficient of unity.

I

I I .o

0.5

+ of

I

1

an exponential smoothing

procedure would be to obtain the d ata from the fastest response instrument available and to smooth these data later by means of smoothing functions having no phase error, such as the normal curve smoothing function. However, no matter how fast its response is, any physical instrument smooths the data to some extent. It is only necessary th a t the time constant of the instrument be short in comparison with the wavelength of variations in the data whose amplitudes and phases are desired to be recorded accurately. The results of smoothing a time series by the three methods described above are compared in Fig. 4 where the original unsmoothed series is shown as a solid line and equally-weighted running means of five consecutive observations are connected by a dotted line. The dashed line in this figure shows the series smoothed by a discrete-weighted approximation data interval; the of a normal curve smoothing function having u =

362

J. LEITH HOLLOWAY, JR.

weights of this function are 0.03, 0.23, 0.48, 0.23, and 0.03 in that order. The frequency responses of the running means and the normal curve smoothing function are given by the dotted and dashed lines, respectively, in Fig. 2 when the filtering interval is taken to be 5 data intervals. The dot-dashed line in Fig. 4 represents the series smoothed by a discreteweighted approximation of an exponential smoothing function having X = 2.5 data intervals. The frequency response of this exponential filter versus frequency in cycles per data interval is obtained from Fig. 3 by multiplying the values on the abscissa by X-’ = 0.4. The filtering intervals and u’s and X’s of these three smoothing functions were chosen so that the degree of smoothing of each of the three methods would be about

I

0

5

I

10 TIME

IN

I

I

I

15 20 25 30 DATA INTERVALS AFTER ARBITRARY ORIGIN

I

35

-

40

FIG.4. Time series (solid line) and the same series smoothed by means of an equallyweighted running mean (dotted curve), by a normal curve smoothing function (dashed curve) and by exponential smoothing (dot-dashed curve).

the same. Fig. 4 illustrates the unfortunate polarity reversals effected by equally-weighted running means at some frequencies (for example, at point A ) and the phase shift produced by exponential smoothing (at points B and C).The normal curve smoothing does not exhibit either of these two shortcomings. The frequency response of many other smoothing and filtering functions may be determined from the equations in this section. When the exact response function of a particular discrete-weighted smoothing or filtering function is desired, equation (5.4) or (5.6) must be used. However, as illustrated in this section, equations (5.1) and (5.5) may be used for determining estimates of the response of such functions having a relatively large number of weights, provided the envelopes of these

SMOOTHING AND FILTERING

363

weights can be expressed in simple integratable analytic forms. If the smoothing or filtering function is intrinsically continuous (as is the case with exponential smoothing by an electrical filter, for example), either equation (5.1) or (5.5) will be required for computing the exact frequency response function. Other methods for computing frequency response functions will be discussed later in this paper. 6. DESIGN OF SMOOTHING FUNCTIONS AND FILTERS WITH SPECIFIED FREQUENCY RESPONSE

The procedure in the last section may be reversed and a smoothing or filtering function w(t) having a specified frequency response function of R(f) may be obtained by solving the integral equation (5.1). This solution is8

For a n even response function R(f), equation (6.1) reduces t o (6.2)

w(t) = 2

lom R(f) cos (27rft) df

These equations may be recognized as those for Fourier transforms of

R (f)*

An example of the use of equation (6.2) is the determination of the smoothing function having a flat response of unity out t o some cutoff frequency fc and zero response beyond; namely,

(6.3) R(f)= Use of equation (6.2) gives (6.4)

w(t) = 2

( 0:1

OSflfC f

> fc

f cos (27rft) df =

(Tt1-1

sin (2Tjct)

This smoothing function is a damped wave extending forward and backward in time from the origin. However, because the damping is rather slow, this function will often be impractical t o use, since it will extend over so much of the series to be smoothed. The function can, of 8A wave of negative frequency is merely one of the corresponding positive frequency with reversed polarity. Ordinarily frequency is not thought of as having negative values; the above definition is given only to clarify equations such as (6.1) where frequency is allowed to take on negative values. From the above it is clear that a t least the absolute value of all frequency response functions must always be even functions, for it would be contradictory for a filter to have a different response to a negative frequency than to the corresponding positive one. When l R ( f ) (is not even, w(l) will generally be a complex function (composed of both real and imaginary parts) and therefore will have no physical meaning as a filtering function.

364

J. LEITH HOLLOWAY, JR. I

1

I

I

I

I

I

I

I

1.2

I .o

\

0.8

-c

LT

0.6

0.4

I

I I \

.

0.2

i \

*.

'i. \

0.0 I

I

I f

c

2fc

FREQUENCY

FIG.5. Theoretical frequency response of a smoothing function having the shape of the damped wave defined by equation (6.4)(dashed line), and the actual response of this function truncated beyond the first negative lobes on either side of the central positive lobe (solid curve). The dotted curve is the response of the normal curve 1 smoothing function having u = -. 3fc

course, be taken to be zero (truncated) at some convenient distance on each side of the origin, but this alters the response in an undesirable way, and the closer t o the origin it is truncated, the less desirable the response becomes. For example, the frequency response of this function truncated at t = kl/fc is shown in Fig. 5 as a solid line. This condition specifies two negative lobes on each side of the central positive weights. The desired frequency response specified by (6.3) is shown in this figure as a

SMOOTHING AND FILTERING

365

dashed line. Notice that the truncation causes the actual frequency response of the smoothing function to differ considerably from the desired response a t most frequencies. In fact, there is actually amplification a t intermediate frequencies and undesirable negative response at certain higher frequencies. For comparison, the frequency response of a normal 1 3fc

curve smoothing function having u = - is also shown in Fig. 5 as a dotted line. The filtering intervals of these two smoothing functions are essentially the same. It is seen that the cutoff frequency of this normal curve smoothing function as defined in the last section is lower than that of this truncated version of the function designed to have sharp cutoff characteristics. It should be mentioned here that in performing mathematical filtering it is tacitly assumed that the periodicities present at the time for which the filtered variable in the time series is being estimated are unchanged in amplitude and phase during the filtering interval. Thus, i t is advisable to have this filtering interval as short as possible so as to have this assumption reasonably justified. Smoothing functions having negative weights beyond the positive central values do stretch this assumption rather far owing t o their longer filtering intervals for given cutoff frequencies. 7.

HIGH-PASS A N D

BAND-PASS FILTERING FUNCTIONS

Earlier in this paper electrical band-pass and high-pass filters were described. The same type of frequency separation can be accomplished numerically by a modification of the smoothing procedures. If smoothed values are subtracted from the corresponding values in the original unsmoothed time series, only high frequencies will remain; thus, this operation is equivalent to high-pass filtering. If well-smoothed values in a time series are subtracted from values smoothed to a lesser extent, only intermediate frequencies will remain, for the high frequencies will have been smoothed out and the low frequencies will have been subtracted out of the original series; this operation then is equivalent t o band-pass filtering. Therefore, by use of these methods the oscillations in a time series can be separated into three time series each containing a particular band of frequencies-high, intermediate, and low. For example, let xt represent the observation in a time series at time t , and f t and Zt be the smoothed values computed by normal curve smoothing functions having u = % day and u = 5 days, respectively (see equation (5.10) for a definition of u). Only low frequencies of the original data will appear in the time series of Zt values. The intermediate frequencies will appear in the series resulting from the subtraction of 3,from I t , and

J. LEITH HOLLOWAY, JR.

366

only the high frequencies will remain in the series computed by subtracting & from zt. The frequency response of the intermediate frequency band-pass filter is given by R(f)z-2 =

(7.1)

R(f)z - R ( f h

where the R(f)'s are frequency responses and the subscripts indicate the filters to which they correspond. The frequency response of the high-pass filter is

R(fL-3 = 1 - R(nz

(7.2)

The frequency responses of these filters in the above example are shown in Fig. 6. Notice that there is considerable overlap in the response

I'

1

1

1

1

1

1

I

1

PERIOD

IN

I

I

l

l

1

1

I

DAYS

FIG.6. Frequency responses of a low-pass filter (solid curve), a band-pass filter (dashed curve), and a high-pass filter (dotted curve) generated by two normal curve smoothing functions having u 36 day and u = 5 days, respectively. =i

curves of the three filters, and the transition between the appearance of a wave in the output of one filter and in the next filter is smooth with a uniform change of the frequency of the wave. If & and Zt had been computed by equally-weighted running means instead of by normal curve smoothing functions, this transition would have been less smooth and the response of each filter would have been more irregular owing to the negative response characteristics of running means to certain frequencies. To illustrate this filtering technique a series of twice daily barometric pressures a t the Washington National Airport for spring 1956 are filtered by means of the filters described above. The pressures a t the National Airport at 0100 and 1300 EST are plotted in Fig. 7(A), and a solid line is drawn connecting them. These values are smoothed by the normal curve smoothing function having u = 5 days, and the resulting smoothed series is represented by a dashed line in Fig. 7(A). The weights for a discretevalued approximation of this smoothing function are given in Table I. The

367

BMOOTHING AND FILTERING

process of smoothing individual half-day observations by this smoothing function would be laborious. However, it is only necessary to compute thesezwell-smoothed values for every tenth observation (every fifth day) becauseathe resulting smoothed series contains no waves of shorter period thanltenrdays. Intermediate smoothed values needed as the subtrahends of the band-pass filter can be obtained by graphical interpolation. The series resulting from the band-pass and high-pass filtering are shown in

W

f

I

29.0

I

I

I

I

30

5

10

I

I

I

-0.5

\-I I

15

20

25 APRIL 1956

15 MAY 1956

20

25

FIG.7. Illustration of low-pass, band-pass, and high-pass filtering of station pressures a t the Washington National Airport. A. I n this the original pressures are indicated by the solid line and the output of the low-pass filter is dashed. B. I n this the solid line is the output of the high-pass filter and the dashed line tha t of the band-pass filter.

Fig. 7(B) as dashed and solid lines, respectively. The weights of the normal curve smoothing function having CT = 4% day used in computing the lesser smoothed values are given in Table I. The low-pass filtered series in Fig. 7(A) appears to have a low amplitude wave of about 30 days period. Since the band-pass filter has appreciable response to waves of this period, this wave also appears weakly in the output of this filter along with waves of much shorter period. Likewise there are also waves which appear in the output of both the band-pass and high-pass filters. Thus, the partition of the waves according to period is not perfect, but it is adequate to facilitate greatly the analysis of complicated fluctuations in data such as are exhibited by the original pressure series in Fig. 7(A).

368

J. LEITH HOLLOWAY, JR.

TABLE I. Weights for discrete-valued approximations of normal curve smoothing functions having = 5 days and 35 day.* (I

u =

5 days

0.001 0.001 0.001 0.001 0.002 0.002 0.003 0.004 0.004 0.005 0.007 0.008 0.010 0.011 0.013 0.015 0.017 0.020 0.022 0.024 0.027 0.029 0.031 0.033 0.035 0.037 0.038 0.039 0.040 0.040 (Principal weight) 0.040 0.039 0.038

o =

35 day

0.004 0.054 0.242 0.400 (Principal weight) 0.242 0.054 0.004

t?tC.t

* Values are rounded t o a few significant places for convenience in computation.

t Rest of the weights of this smoothing function are identical with the ones above the principal weight but in reverse order.

Similar sets of filters with different frequency ranges could be designed for studying other scales of atmospheric phenomena such as atmospheric turbulence. For example, Panofsky [13] used this type of filtering for making a crude spectral analysis of wind fluctuations at the Brookhaven National Laboratory. If desired, the operation of smoothing and subtracting may be com-

369

SMOOTHING AND FILTERING

bined into a single filtering function. The appropriate weights for the high-pass filter are the negative of the weights for the associated smoothing function except for the principal weight which is one minus the principal weight of the smoothing function. For example, a high-pass filter generated by the subtraction of values smoothed by a smoothing function having weights of ?46, 34, and Ks in that order (where 36 is the principal weight) would have the weights: -).is, +34, -%, and -%S. Notice that the sum of the weights of a high-pass filter such as this will be zero because it does not pass the mean of the original series (a component of zero frequency). Therefore, the output of this high-pass filter will be a series having a mean of zero. Two smoothing functions are used in the derivation of the band-pass filter. The weights for the band-pass filtering function are merely the weights of the smoothing function having the lowest cutoff frequency subtracted from the corresponding weights of the other smoothing function, This filter also does not pass the mean of the original time series.

x, x,

-x,

8. ELEMENTARY SMOOTHING AND FILTERING FUNCTIONS

A useful approach t o the design of smoothing functions and other mathematical filters is t o build up filtering functions from elementary filtering functions consisting of only three weights each. The two outer weights of the elementary filtering functions are made equal,g and the sum of the weights is made equal to unity for smoothing functions and zero for filters not passing the mean of the original series. The frequency response of an elementary smoothing or filtering function is obtained from equation (8.1) below, which is derived from equation (5.6) (8.1)

R(f)= WO

+2

~ cos 1 (2~jAt)

where wo is the central (and principal) weight, w1 is the value of each of the two outer weights, and At is the data interval. If one elementary filtering function provides insufficient filtering, a time series may be successively1° smoothed or filtered by this same elementary filtering function until the desired smoothing or filtering is 9 Each elementary filtering function is made even (namely, wP1 = wl)so that it will produce no phase error and so that more complicated filters built up from a combination of these elementary filters will also be even and therefore produce no phase error. 10 By “successive” filtering here is meant the repeated filtering of the entire series by the same or different filter-not the normal application of the filter to the series centered on each successive observation which is required for computing the filtered series.

370

J. LEITH HOLLOWAY, JR.

accomplished. Also different elementary filtering functions may be used on succeeding filterings. It can be shown that the frequency response of the sequential application of these elementary filtering functions is the product of all the responses of the individual elementary filtering functions used; namely, M

R(fh

- .

R(f)M By use of this equation it is possible to specify certain features of the resultant frequency response R ( f ) R desired at given frequencies and t o solve for the various weights required in the elementary filtering functions to be used to give this response. This type of procedure has been successfully used by Shuman [14]. Once the elementary filtering functions have been designed, a composite filtering function can be generated which will circumvent the operation of sequential application of each elementary filtering function and give the resultant filtered series in one step. This is accomplished by first computing the cumulative cross-products of the weights of the first and second elementary filtering functions at various lags. Then the resulting series of weights is multiplied in a similar manner by the third elementary filtering function and so on until all the elementary filtering functions have been multiplied as many times as they would have been used in the sequential filtering operation. The final resulting series of weights is the composite filtering function. For example, when two three-weight elementary filtering functions having principal weights of wo and WOand outer weights of w1 and WI, respectively, are combined, the composite filtering functions will have weights of wlWI, wowl wlW0, 2wlW1 WOWO,wowl wlWo, and wlWl in that order with the principal weight being 2wlW1 wowo. After combining a number of elementary filtering functions, often many of the outer weights of the composite functions will become insignificantly small and may be neglected. However, it will be necessary to adjust the remaining weights in the composite function to insure that their sum is correct (namely, unity in the case of a smoothing function). A method of smoothing that has been discussed by Brooks and Carruthers [15] is to compute running means of pairs of observations in a time series and in turn to take running means of pairs of these smoothed values and so on until the time series is smoothed sufficiently. This procedure may be considered as the repeated application of a two-weight elementary smoothing function having weights of one-half each. Composite smoothing functions generated solely from this elementary smooth=

+

+

*

R(f)2

*

*

*

+

+

371

SMOOTHING AND FILTERING

ing function will have weights proportional to the familiar symmetrical binominal coefficients; namely, the coefficients of the expansion of (P 4)". For example, the composite smoothing function generated from two of these two-weight elementary smoothing functions has weights of g, 36, and in that order, these weights being proportional to the coefficients (1, 2, and 1) of the second power expansion of ( p q ) . This particular three-weight elementary smoothing function will be referred to hereafter as the elementary binomial smoothing function. It is well known that the envelope of the coefficients in the expansion of ( p q) approaches the shape of the normal probability curve as a limit a s the exponent increases. Therefore, the above procedure of taking repeated running means of pairs of observations in a time series approximates the use of a normal curve smoothing function when the number of successive smoothings is large; this corresponds t o the use of a large number of weights in the composite smoothing function. The frequency response of the two-weight elementary smoothing function may be computed from equation (8.1) by setting wg = 0 and w1 = $5. However, the data interval t o be used in this equation, At', will obviously be one-half the actual data interval At of the time series. This substitution into equation (8.1) gives

+

+

+

(8.3)

R(f)

=

0 f 2(0.5) cos (27rfAt') = cos (.fat)

From equation (8.2) the frequency response of the elementary binomial smoothing function will be the square of the result in equation (8.3); namely,

(8.4)

R ( f ) = cos2 ( r f A t )

The above result can also be determined directly from equation (8.1) by setting wo = $5 and w1 = In general, the binomial smoothing function having weights proportional to the coefficients of ( p q)" has a frequency response of

x.

(8.5)

R(f) =

+

COS"

(rfAt)

The derivation of equation (8.5) assumes that the sum of the weights of the binomial smoothing function is made equal to unity a s is done with all smoothing functions considered in this paper. Some workers smooth time series by successive use of running means of more than two terms each. Brooks and Carruthers [15] give the following general expression for the frequency response of the operation of M

372

J. LEITH HOLLOWAY, JR.

successive smoothings by the equally-weighted running means of N terms each

With N set equal to two, this expression is equivalent t o equation (8.5).

9. DESIGN OF INVERSE SMOOTHING FUNCTIONS An application of the use of elementary filtering functions to the design of filters is the computation of weights for inverse smoothing functions. A composite inverse smoothing function can be generated from elementary inverse smoothing functions in the same way th a t composite smoothing functions can be generated from elementary smoothing functions; that is, cumulative cross-products of the weights of the inverse smoothing functions involved are computed for various lags. Unfortunately, it is not possible t o design a three-weight inverse smoothing function which has exactly the inverse or reciprocal frequency response of the elementary binomial smoothing function. If this were possible, the design of inverse smoothing functions for correcting for binomial and normal curve type smoothing would be facilitated. However, the three-weight elementary inverse smoothing function having a central weight of 2 and outer weights of -0.5 has a frequency response which is roughly the reciprocal of the response of the elementary binomial smoothing function (having weights of %, and )/4). The frequency response of this inverse smoothing function as computed by equation (8.1) is

x,

(9.1)

R(f)

=

2 - cos ( 2 ~ f A t )

This frequency response equals the reciprocal of the response of the elementary binomial smoothing function a t f = 0 where R ( f ) = 1 and a t 1 1 f = - where R ( f ) = 2. However, the response is three at f = - as 4At 2At compared with a value of infinity for the reciprocal of the zero response of the elementary binomial smoothing function a t this frequency. It is impossible to restore a wave to a time series by inverse smoothing if this wave was completely smoothed out previously. Some residual amplitude must remain in the smoothed series at each frequency t o be restored, and this residual amplitude has t o be greater than the noise for equalization t o be effected with relative freedom from errors owing to noise. For example, rounding of smoothed values would introduce a type of random error, called " quantizing error," into the smoothed series. High-frequency noise is amplified in addition to the true high-frequency

SMOOTHING AND FILTERING

373

fluctuations in the time series, and this noise can “drown o u t” not orlly true high frequencies but also all other components besides if the amplification at these high frequencies is too great. Overemphasis of noise or random nonsignificant variation in the time series t o be equalized creates a type of mathematical instability which plagues many attempts a t inverse smoothing. Thus, in designing inverse smoothing functions a compromise must be made between having a stable output and having a response nearly equal to the inverse of that of the original smoothing. 1 An amplification of three a t f = - instead of infinity in equation (9.1)

2At

is a n example of just such a compromise. By combining two of the above elementary inverse smoothing functions (having weights of -0.5, +2.0, and -0.5) a composite function can be designed t o reverse the smoothing by a binomial smoothing function generated from two elementary binomial smoothing functions; namely, the function having weights of H.~‘s,3.8, and W S .Although this inverse smoothing function would provide the correct restoration of 1 waves of frequency equal to -, it would overemphasize oscillations of

x, x,

4At

some of the lower frequencies by as much as 40%. I n order to eliminate this excessive overemphasis of low frequencies the composite inverse smoothing function should instead be generatjed from two elementary three-weight functions each having a central weight wo of 1.7 and outer weights w1 of -0.35. These weights were obtained empirically. This composite function would have the five weights: +0.12, -1.19, f3.14, -1.19, and +0.12 (with $3.14 being the principal weight), and its frequency response would be computed according t o equation (8.2)from the square of the right-hand side of equation (8.1); namely,

(9.2)

R(f)

=

+ +

+

4 ~ 0 cos ~ 1(2~fAt) 4201~COS’ (2~fAt) 2.89 - 2.38 cos (2~jAt) 0.49 C O S ~(2~fAt)

= WO’

At low frequencies, this response is approximately the inverse of that of the binomial smoothing function considered above, The frequency response of the latter is

(9.3)

R(f)

=

c0s4 (nfAt)

from equations (8.2)and (8.4)or (8.5). These frequency responses are compared in Fig. 8 to show the extent to which this type of inverse smoothing can restore the original balance of frequencies in the smoothed time series. A curve representing the product of the frequency response of the inverse smoothing function considered and that of the binomial smoothing function a t each frequency is also included in this figure.

374

J. LEITH HOLLOWAY, JR.

Ideally this product should be a straight line of unit response. Departure from this ideal product shows the extent to which this form of inverse smoothing fails to compensate for the previous binomial smoothing, Figure 9 showing three curves illustrates how well inverse smoothing

5

wa > 3 0

z

W 3

0 W

I

0.I

0.2

0.3

0.4

0.5

FREQUENCY IN CYCLES PER DATA INTERVAL

FIG.8. Frequency response of a five-weight binomial smoothing function, R ( f ) s , and that of a n inverse smoothing function designed to reverse this binomial smoothing, R ( f ) r . The product of these two responses is also shown.

performs on an actual time series. The solid line in this figure is the original time series; the dashed line is this series smoothed by the five-weight binomial smoothing function considered above; and the dotted line is the smoothed series inversely smoothed using the five-weight function described above. The departure of the dotted line from the solid line indicates the limitations to applying inverse smoothing t o this type of

375

SMOOTHING AND FILTERING

smoothed series. At point A in Fig. 9 where the original series contains primarily low frequencies there is nearly perfect restoration of the original series by the inverse smoothing. On the other hand, the inverse smoothing does not restore the high-frequency fluctuation at B in the original series because this component was completely smoothed out by the previous binomial smoothing. The examples in this section illustrate how inverse smoothing functions may be designed t o compensate for two types of binomial smoothing. These procedures may also be applied to the problem of reversing many other forms of smoothing. However, serious error can be made when inverse smoothing is applied to a series which has been smoothed by a method having appreciable negative response beyond the first cutoff frequency as is the case with equally-weighted running means. AS

0

5

10 15 20 TIME I N DATA I N T E R V A L S A F T E R A R B I T R A R Y ORIGIN

25

FIG.9. Time series (solid line), same series smoothed by a five-weight binomia smoothing function (dashed line), and the smoothed series inversely smoothed (dotted line).

has been mentioned in Section 5 such a smoothing function will introduce spurious fluctuations into the smoothed output, and these fluctuations will generally be amplified by the inverse smoothing process. A good way of remedying this condition is to smooth the series again by the same smoothing method applied originally. This will restore the original polarity t o all the waves in the series. Then this double smoothing may be partially reversed by an inverse smoothing function similar to those described earlier in this section. In this case inverse smoothing can a t best only partially restore the original series, for no procedure can restore waves previously completely smoothed out. Smoothing methods having negative responses generally completely smooth out waves of a number of relatively low frequencies. The fact that smoothing by equally-weighted running means is not very reversible is another good argument against using this type of smoothing.

376

J. LEITH HOLLOWI’AY, JR.

The concept of reversibility occurs in the field of thermodynamics in connection with entropy change. The more reversible a thermodynamical process is the less entropy is increased during this process. The concept of entropy, which is a measure of the disorder or randomness in a system, has been extended to statistical analysis by information theory where the negative of entropy change is taken as a measure of the information change occurring in statistical data. The foregoing implies that the less reversible a smoothing or filtering process is the more entropy is created, and therefore the more information is lost in the operation. No entropy would be created, and thus no information would be lost by perfectly reversible smoothing or filtering. In order for smoothing to be perfectly reversible several conditions must be fulfilled. First, the original smoothing cannot have completely smoothed out any wave of finite frequency. This is true in the case of exponential and normal curve smoothing. Second, the smoothed series must be continuous-not a series of discrete values. Third, the series must be completely free from noise. Finally, waves of all frequencies must remain unchanged in phase and amplitude during the filtering interval of the original smoothing function. This last condition is fulfilled in general only when the filtering interval is infinitesimal as is the case when the series is smoothed by the derivative method described in Section 11 of this paper. These last two conditions are so stringent that for all practical purposes no smoothing operation is completely reversible, although some (for example exponential and normal curve smoothing) are more reversible than others. 10. DESIGNOF PRE-EMPHASIS FILTERS

It may be desirable to amplify high frequencies in a time series more than the low frequencies for reasons other than for correcting for previous smoothing. For example, in statistical spectral analysis it is often desirable to pre-emphasize high-frequency components before computing the autocorrelation function of a series. This type of high-frequency preemphasis has been named “pre-whitening” by Tukey because it tends to equalize amplitudes at all frequencies [16]. This pre-emphasis prevents a great deal of instability in making spectral estimates when originally the amplitudes of waves of low frequency in a series are much greater than those of high frequency. After the spectral estimates have been obtained, they are then corrected by a factor which is the inverse of the frequency response of the pre-emphasis operation applied to the original series.11 “ T h e square of the frequency response is required for making this correction when the relative variance rather than the relative amplitude is computed in the spectral analysis.

SMOOTHING AND FILTERING

377

An inverse smoothing function similar to those described in the last section may be used for this type of pre-emphasis. However, in spectral analysis work a simpler two-weight filter is generally used which has a principal weight w o of unity and a weight wP1 of minus b. By means of this two-weight operator the pre-emphasized variable xi is computed from time series values xt and xt--l as follows:

(10.1)

~ t = ’

~t

-

brt.t-1

where the subscripts refer to the times of the observations. The weight b is generally made equal to 0.75 in studies involving atmospheric turbulence. This choice of b makes the sum of the weights of this filter equal t o one-quarter. Therefore, the mean of the resulting pre-emphasized series will be only one-fourth of that of the original series. However, in spectral analysis work the original series is usually made up of deviations from a mean and therefore has a mean of zero. Consequently, the effect of the pre-emphasis on the mean of the series is of no concern. Because this two-weight pre-emphasis filter is not a n even function, equations (5.2) and (5.4) must be employed for determining its frequency response; namely,

(10.2)

R ( f ) = [I - b cos (-2rfAt)I

and

IR(f)J = [ l - 2b cos (2rfat)

+ i[-b

sin (-2rfAt)l

+ b2]’$

This pre-emphasis filter also introduces phase error which may be computed from equation (5.3). However, this error is of no significance unless co- and quadrature spectra are t o be computed between the preemphasized series and another series which has either not been preemphasized or has been done so differently. A special case of this type of pre-emphasis is where b in equation (10.1) equals unity [17]. This filter is a finite difference approximation of the derivative of a time series. The response of this filter is given by equation (10.2) ;namely,

(10.3)

IR(f)I = [2 - 2

COB

(2rfAt)l”

=

2 sin (.!At)

When rfAt is small,

IW)I = %!At

(10.4)

The phase shift of this filter would be given by equation (5.3) as follows:

(10.5)

$I = tan-’ [1 = ?r/2

- rfA2

= =

90°(1

- 2fAt)

tan-’[cot (rfAt)]

378

J. LEITH HOLLOWAY, JR.

I n the limit as At goes t o zero, 4 becomes 90" which is the phase shift accomplished by differentiating any sine curve. An exactly opposite type of pre-emphasis also used in spectral analysis work consists of taking consecutive means instead of consecutive instantaneous values of a variable which is continuously recorded such a s wind [16, 181. These means are usually obtained by eye from a graphical record. This procedure emphasizes low frequencies and is used to reduce errors resulting from '' aliasing "-the process by which high-frequency waves appear as lower frequencies in a time series having a data interval too long to portray these shorter wavelengths. The spectral estimates obtained from the series generated in this manner are corrected by the inverse of the frequency response of the equally-weighted mean (computed by equation (5.9)). 11. FILTERING BY MEANSOF DERIVATIVES OF TIMESERIES

Additional insight into the operation of smoothing and filtering may be gained by considering what effects are produced on the time series by adding specified fractions of time derivatives of the series to the series itself. Consider a sine wave of angular frequency w = 27rf, amplitude a, and phase 4. A time series having only this one component would be defined as s(t) = u sin (wt

(11.1)

+ 4)

The second, fourth, sixth, and 2nth time derivaties of this series would be:

+

(11.2)

+ +

~ ( t =) d2x/dt2 ~ ~ = -aw2 sin (wt 4) z(t)$"= d4x/dt4 = aw4 sin (wt 4) x(t)"i = dsx/dta = - a m 6 sin (wt $1 ~ ( t ) ~=" dZnx/dt2n= (-l)nuw2n sin (wt

+ 4)

From the derivatives given above one can form a power series which defines a new modified time series as follows: (11.3)

+

+

+

Z(t) = ~ ( t ) k z ~ ( t ) ~k 4~~ ( t ) ~ '

*

..

+

k2n~(t)zn

Substituting values in equations (11.1) and (11.2) into equation (11.3) one obtains (11.4) Z(t) = [ l

- kzw2 + k4w4 - k~w' +

*

*

+ (- l)nkZnwzn]a sin (wt + 4)

Notice that the power series in brackets in equation (11.4) is actually the frequency response for the operation defined in equation (1 1.3) since it is the factor by which the original sine wave is multiplied in order to obtain the new filtered wave; namely,

379

SMOOTHING AND FILTERING

(11.5)

R(u) = 1 - kzw2 f k4w4 - k6we f

*

*

.

+ (-1)"ICZnUzn

If in equation (11.5) (11.6)

kz

=

k4

=

c2, c4/2!= c4/Z,

ks = c 6 / 3 ! = c S / 6 , kzn = c Z n / n !

this frequency response reduces to exp ( -czwz) which is the response of a normal curve smoothing function having u = c ~, Thus it follows that the addition of these fractions of each even time derivative to the original series is equivalent to normal curve smoothing of the series. The technique described here would be an alternate method for designing a filter with specified frequency response. The k's in equation (11.5) can be determined so that this power series would be equal to the desired frequency response. Many desired frequency responses may be expressed as power series, and in such cases the determination of the k's would amount merely to equating the coefficients in two power series. However, in practical application of this method only a small number of derivatives can be used, so that the actual frequency response of the derived filter is not exactly the same as the desired frequency response expanded into the complete power series. Furthermore, if the derivatives are computed by the method of finite differences, additional discrepancies between the actual and the desired frequency response will result owing t o the tendency for the finite difference method t o underestimate derivatives. This method is especially valuable for the design of inverse smoothing functions. For example, suppose that the original smoothing had a frequency response of (11.7)

R(w) = exp ( -c2wz)

The frequency response of the inverse smoothing function required t o reverse this smoothing should be the reciprocal of the above R(w) or (11.8)

R'(w) = [R(w)]-' = exp

(c2w2) = 1

Equating coefficients in equation (11.8) the power series in equation (11.5) one the k's: kz = -c2, ks = (11.9) kq = c 4 / 2 , kzn =

+ c2w2+ (2!)-'c4w4 +...

+ (n!)--1cZnw2n

with the corresponding ones in obtains the following values of

-ce/6, (-l)n~zn/n!

These k's are identical with those in (11.6) except that alternate ones have negative signs. When these values of k are substituted into equation (11.3), the required inverse smoothing operator is obtained.

380

J. LEITH HOLLOWAY, JR.

That derivatives can be used for inverse smoothing could have been inferred from the fact that smoothing itself is a form of integration over time and t,hat tlhe inverse of integration is differentiation. The most straightforward application of differentiation to inverse smoothing is that of the equalization of a time series smoothed by an exponential process such as is performed by an instrument with a constant lag coefficient. n For such an instrument the following well-known differential equation holds: (11.10)

(z - 2)

= X(dz/dt)

or

=

z - X(dz/dt)

where Z is the smoothed value of the variable x in the time series and X is the lag coefficient. If equation (11.10) is solved for 2, one obtains the so-called inverted lag equation after McDonald [19] (11.11)

2 =

z

+ X(dZ/dt)

From equation (11.11) it follows that perfect restoration of the original time series is theoretically possible given the smoothed values without noise, by differentiating the smoothed values with respect to time, multiplying this derivative by X, and adding this result to the original smoothed values. A finite difference form of equation (11.11) is (11.12)

zt =

Zt

+ X(Zt -

&-I)

=

(1

+ X)Zt - XZt-1

where X is in units of At, the data interval. Since the time derivative in equation (11.12) is estimated by the method of finite differences, it is necessary that the data interval be a small fraction of the lag coefficient, say smaller than one-fifth, in order for the results to be accurate. If the output of the instrument is electrical, the above equalization may be done by means of a resistance-capacitance network as shown by Hall [8]. This circuit performs the required differentiation electrically. A practical limitation to this method is that the lag coefficient is seldom constant but is a complicated function of many variables, Secondly, the record must be relatively free from noise for accurate results to be obtained by this procedure. 12. SPACESMOOTHING AND FILTERING

So far in this paper only smoothing and filtering of time series has been dealt with, The methods of time smoothing and filtering may, nevertheless, apply equally as well to space smoothing and filtering in one dimension, except, that the terms “wavelength” and ‘(wave number” (number of waves in a given distance) are used instead of period and frequency, 14

See Section 6 for a further discussion of this type of smoothing.

381

SMOOTHING AND FILTERING

respectively. Furthermore, these concepts may be extended t o space smoothing and filtering in two dimensions. I n space smoothing in one dimension, the term wave number response may be substituted for frequency response. However, with two-dimensional space smoothing the concept of wave number or wavelength is not very meaningful unless the waves are essentially one-dimensional. The term “scale size” is perhaps better t o use in this case. Scale size will be defined a s the average 2 81

1 81

-1 3

-1

-1

3

3

-1 4 -1 4

1 -

1 -

9

9

1 9

-1 4 1 4

1 -

16 2 16 1 16

-1 9

2 -

16 4 16 2 16

8 81

1 81

1 -

16 2 16 1 16

81

8 -

l5 81

8 81

2 81

2 -

8 81

8

sl

81

1 9

3 9

1 9

2 -

1 81

I -

81

81

2 81

8 81

1 81

2 -

81

1 81

1 256

4 256

6 256

4 256

1 256

4 256

16 256

24 256

16 256

4 256

6 256

24 256

36 256

24 256

6 256

4 256

16 256

24 256

16 256

4 256

4 6 4 1 256 256 256 256 256 FIG.10. Generation of composite space smoothing functions from the elementary space smoothing functions in the first column. The functions in the second column result from one iteration of those in the first; those in the third column, from one iteration of those in the second. 1 -

distance between adjacent centers of high values or between adjacent centers of low values. Space smoothing will decrease the ranges between values in high and low centers of small scale without much affecting these ranges between large-scale centers. Space smoothing and filtering functions are generally isotropic; namely, they are functions only of the radial distance from the origin. The function will usually have a maximum at the origin and decrease with radial distance outward from this origin. The scale response of twodimensional smoothing and filtering functions will be comparable t o the

382

J. LEITH HOLLOWAY, JR.

wavelength response of a one-dimensional filter which is a cross-section of this two-dimensional filter. Discrete-weighted space filters will have weights proportional t o the ordinates of continuous two-dimensional space filtering functions. The sum of these weights is made equal to unity

(A)

FIQ.11 (A,B,C,D). Space-smoothed Northern Hemisphere sea-level pressure maps. for smoothing functions and zero for filters not passing the mean of the field. As with most one-dimensional filters, the central weight of a twodimensional filter is the principal weight. If no weight is centrally located, the space-smoothed value corresponds to the location of the center of gravity of the filter’s weights. It is conceivable that nonisotropic space smoothing may be desirable for some purposes. For example, one may wish t o suppress north-south

SMOOTHING AND FILTERING

383

fluctuations more than those in the east-west direction. This could be accomplished with a space smoothing function whose weights decrease to zero faster in the east-west direction than t o the north and south. Composite space smoothing and filtering functions may be generated

(B) FIG.11. (Continued).

from elementary two-dimensional functions just as composite onedimensional smoothing and filtering functions were built up from elementary one-dimensional functions earlier in this paper. Such elementary functions could consist of either an array of three weights of one-third each at the corners of an equilateral triangle or a n array of four weights of one-fourth each at the corners of a square. Iterative cumulative multiplication of these elementary space functions a t various relative positions creates composite smoothing functions whose weights approach the circularly-symmetric bi-variate normal distribution (with standard de-

384

J. LEITH HOLLOWAY, JR.

viation the same in all directions from the origin) as is illustrated in Fig. 10. The bi-variate normal smoothing function has the same desirable characteristics in two dimensions that the normal curve smoothing function has in one dimension. One such desirable property is that the bi-

(C) FIG. 11. (Continued).

variate normal smoothing function will not reverse polarities of fluctuations of any scale whereas, for example, an equally-weighted space smoothing function will reverse the polarity of features at some scale sizes. The familiar Fjgrtoft method of space smoothing is merely the single application of the square elementary space smoothing function described above [20]. Therefore, by smoothing twice by the Fjgrtoft method a first approximation is made to circular bi-variate normal smoothing illustrated in Fig. 10.

SMOOTHING AND FILTERING

385

The use of space smoothing is illustrated in Fig. 11 showing four Northern Hemisphere sea-level pressure maps smoothed by a space smoothing function very similar to the one in the upper right of Fig. 10. The distance between the grid points on the triangular grid used averaged

(D) FIG. 11. (Continued).

about 500 miles. This smoothing almost completely attenuates features having a scale size of about 1500 miles, but it retains 4000-mile features at about 75% of their original amplitude. These smoothed maps thus display only large-scale pressure systems which are of particular interest to extended weather forecasters. The small-scale features of the pressure field 'can- be-isolated by-subtracting the smoothed map from the original unsmoothed pressures. This operation constitutes the space analog of the high-pass filter of time series terminology. An example of this process is shown in Fig. 12 where the

386

J. LEITH HOLLOWAY, JR.

FIG.12. Original North American sen-level pressures (left) and small-scale pressures (right) obtained by subtracting the space-smoothed map from the original map.

small-scale patterns of the January 1, 1953 North American surface map are isolated by subtraction of the smoothed map for this date obtained previously. This procedure essentially eliminates systems of greater extent than about 4000 miles. The original map is also shown in Fig. 12 for comparison. The filtered map has the same general appearance as the original map but gives slightly more emphasis t o certain smallerscale features. The fact that these maps look very similar suggests that in viewing a weather map we naturally concentrate more on small-scale features than on the large-scale ones and thus do high-pass filtering in our “mind’s eye.” ACKNOWLEDGMENT8 The writer wishes to acknowledge the helpful suggestions and assistance given during the preparation of this paper by the following people: Messrs. F. Hall, G. W. Brier, I. Enger, R. A. McCormick, and J. E. Caskey, Jr., of the U.S. Weather Bureau, Col. P. D. Thompson of the Joint Numerical Weather Prediction Unit and Dr. Max A. Woodbury of New York University.

SMOOTHING A N D FILTERING

387

FIG. 12. (Continued). LIST OF SYMBOLS amplitude of wave weight in pre-emphasis filter constant frequency cutoff frequency square root of minus one imaginary part of y summation variable n t h coefficient number of times a series is smoothed or filtered number of weights in smoothing or filtering function after principal weight number of terms in a n equally-weighted running mean number of weights in smoothing or filtering function before principal weight; arbitrary exponent arbitrary variables ratio of the mean of the filtered series to that of the original series frequency response function; frequency response when it is a pure real quantity absolute value of frequency response function; frequency response when R(f) is complex

J. LEITH HOLLOWAY, JR.

resultant frequency response frequency response of filter y frequency response as a function of W , the angular frequency real part of y filtering interval time data interval kth weight of a smoothing or filtering function principal weight of a smoothing or filtering function smoothing or filtering function unsmoothed or unfiltered discrete variable a t time t smoothed or filtered discrete variable a t time t well-smoothed discrete variable a t time t pre-emphasized discrete variable a t time t continuous function of time smoothed continuous function of time ith time derivative of x ( t ) lag coefficient normal curve dispersion parameter phase angle angular velocity or angular frequency = 2 ~ f REFERENCES 1. Carslaw, H. S. (1930). “Introduction to the Theory of Fourier’s Series and Integrals.” Macmillan, New York. 2. Bracewell, R. N. (1955). Correcting for Gaussian aerial smoothing. AustraZian J . Physics 8, 54-60. 3. Bracewell, R. N. (1955). A method of correcting the broadening of X-ray line profiles. Australian J . Physics 8, 61-67. 4. Bracewell, R. N. (1955). Correcting for running means by successive substitutions. Australian J . Physics 8,329-334. 5. BraceweIl, R. N. (1955). Simple graphical method of correcting for instrumental broadening. J . Opt. SOC.Amer. 46, 873-876. 6. Bracewell, R. N., and Roberts, J. A. (1954). Aerial smoothing in radio astronomy. Australian J . Physics 7, 615-640. 7. Burr, E. J. (1955). Sharpening of observational data in two dimensions. A u s tralian J . Physics 8, 30-53. 8. Hall, F. (1950). Communication theory applied to meteorological measurements. J . Meteorol. 7, 121-129. 9. Kovasznay, L. S. G., and Joseph, H. M. (1953). Processing of two-dimensional patterns by scanning techniques. Science 118, 475-477. 10. Kovasznay, L. S. G., and Joseph, H. M. (1955). Image Processing. PTOC.I.R.E. 43, 560-570. 11. Middleton, W. E. K., and Spilhaus, A. F. (1953). “Meteorological Instruments,” 3rd rev. ed. Univ. of Toronto Press, Toronto. 12. Amble, 0. (1953). A smoothing technique for pressure maps. Bull. Am. Meteorol. SOC.34, 293-297. 13. Panofsky, H. A. (1953). The variation of the turbulence spectrum with height under superadiabatic conditions. Quart. J. Roy. Meteorol. Sac. 79, 150-153. 14. Shuman, F. G.(1955). A method of designing finite-difference smoothing operators

SMOOTHING AND FILTERING

15.

16. 17. 18.

19. 20.

389

to meet specifications. Technical Memorandum No. 7, Joint Numerical Weather Prediction Unit, Washington, D. C. To be published in Monthly Weather Rev. 86. Brooks, C. E. P., and Carruthers, N. (1953). “Handbook of Statistical Methods in Meteorology,” H.M.S.O., London. Gifford, F., Jr. (1955). A simultaneous Lagrangian-Eulerian turbulence experiment. Monthly Weather Rev. 83, 293-301. Dedebant, G., and Machado, E. A. M. (1955). Effectos de ciertos 6ltros sobre la correlati6n. Meteoros 6, 163-176. Griffith, H. L., Panofsky, H. A., and Van der Hoven, I. (1956). Power-spectrum analysis over large ranges of frequency. J. Meleorol. 13, 279-282. McDonald, J. E. (1952). Lag effects in the measurement of turbulent temperature fluctuations. Scientific Report No. 1, Contract No. AF19(122)-440, Iowa State College, Ames, Iowa. FjBtoft, R. (1952). On a numerical method of integrating the barotropic vorticity equation. Tellus 4, 179-194. GENERALREFERENCES

Berry, F. A., Haggard, W. H., and Wolff, P. M. (1954). Description of Contour Patterns at 500 mb. Bureau of Aeronautics Project AROWA, U. s. Naval Air Station, Norfolk, Va. Goldman, S. (1953). “Information Theory.” Prentice Hall, New York. Jeffreys, H., and Jeffreys, B. (1950). “Methods in Mathematical Physics.” Cambridge Univ. Press, London and New York. Wiener, N. (1949). “Extrapolation, Interpolation, and Smoothing of Stationary Time Series.” Wiley, New York.

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EARTH TIDES

.

Paul J Melchior* Obrervotoire Royal de Belgique. Uccle. Brussels. Belgium

Page 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 2 Static Theory of the Tides . . ................................ 394 2.1. Calculation of the Attra ................................ 394 2.2. Deformations of the Level Surfaces Caused by Luni-Solar Effects . . . . . . 396 2.3. The Three Kinds of Tides According to Laplace ..................... 397 2.4. Numerical Values . . . . . .......................... 399 3 . Definition of Love’s Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 4 . Study of the Amplitude of Oceanic Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 4.1. Effect Due to the Deformations of the Crust . . . . . . . . . . . . . . . . . . . . . . . . 401 4.2. Application to Oceanic Tides of Long Period., . . . . . . . . . . . . . . . . . . . . . . 402 402 4.3. Application to Short Period Tides in Lakes . . . . . . . . . . . . . . . . . . . . . . . . . 5 Periodical Deflections of the Vertical with Respect to the Crust . . . . . . . . . . . 403 5.1. Effect Caused by Deformations of the Crust ........................ 403 5.2. The Horizontal Pendulu ......................... 404 5.3. Observations Obtained from Lar r Levels . . . . . . . . . . . . . . . . 5.4. Numerical Results of the ......................... 409 5.5. Discussion of the Observa t Effect of the Oceanic Tides 411 5.6. Method of Numerical Evaluation of the Indirect Effects . . . . . . . . . . . . . . 411 5.7. Empirical Method of Separation of the Two Effects . . . . . . . . . . . . . . . . . . 414 5.8. Effect of the Tides on High Precision Leveling Operations . . . . . . . . . . . . 417 6. Measurement of E1ast.ieTensions and Cubic Dilatations Due to Deformations

. .

.

6.2. The Sassa Exte

8.4. Results of the Observations., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5. Observations Made with Clock Pendulums . . . . . . . . .

429

* Reporter General for earth tides of the International Associations of Geodesy and Seismology . 391

392

PAUL J. MELCHIOR

Page 9. The Role of the Geologic Structure of the Crust in the Indirect Effects. . . . 432 9.1. Oceanic Effects. ...... 9.2.Atmospheric Effects.. ..................................... 434 10. Theory of Elastic Deformations of the Earth.. 10.1. Conclusions Drawn from the Obse .............................................. 435 ............................................... 435 . . . . . . . . . . . . . 435 10.3.Herglotz Theory. . . . . . . . . . . . . . . . 437 10.4.Note on the Relatio . . . . . . . . . . . . . . . . . . . 438 10.5.Dynamic Effects of Earth. . . . . . . . . . . . . 439 440 12. Program of the International Geophysical Year.. . . . . . . . . . . . . . . . . . . . . . . . . List of Symbols.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 References. . . .. .... ........................... 441

1. INTRODUCTION The concept of an earth not completely rigid but deformable came into being in the beginning of the nineteenth century. Simultaneously, astronomers began to suspect the existence of a variation of the latitudes (Brioschi a t Naples) and to study variations in the direction of the vertical and local deformations of the earth’s crust. The experiments made by d’Abbadie, beginning in 1837, on pools of mercury revealed some rather irregular variations which, near the Gulf of Gascogne in particular, seemed to correlate with the oceanic tide, although in a quite complex manner. Furthermore, classical theoretical considerations predicted the existence of small periodic variations of the vertical as well as small periodic displacements of the pole. The discrepancies, which will be discussed later, between this theory and the observations in both of these phenomena only indicate the existence of elastic deformations of the earth due to the influence of underlying disturbing forces. It will be necessary to consider these elastic deformations in the calculations in order to obtain results conforming to the observation. The static theory of the tide shows immediately that the direction of the vertical and the intensity of gravity do not remain constant but vary under the influence of the luni-solar attraction. Kelvin directed attention to the effect of the deformations of the earth; one is not able, in effect, to imagine it to be infinitely rigid and consequently has to admit that it ought to be deformed under the influence of a perturbation of the potential, similar to the ocean layer but in a lesser degree. The amplitude observed at the surface of the earth for all the phenomena dependent on this potential (oceanic tides, deviations of the vertical variations in the intensity of gravity) will thus be affected by the deformation of this surface, where all our measurements are made.

EARTH TIDES

393

Thus, the oceanic tides are observed by comparison with bench marks reputedly “fixed,” established on the “terra firma.” These bench marks would be fixed if the earth were perfectly rigid and the amplitudeobserved would be equal to that calculated. However, if the crust itself rises as a result of the action of the disturbing potential, the measured amplitude will be the difference between the tide of the ocean and that of the crust. One can apply the same reasoning to other manifestations of the phenomenon. For more than half a century, observations of all kinds have confirmed the views of Kelvin and, when compared with the data of seismology and of the motion of the pole, permit one to study the elastic properties of the earth with increasing precision. Before considering the analysis and the interpretation of the results of these observations, it is desirable to investigate whether it is possible to apply the static theory to tides of the “solid” earth. This theory, proposed initially by Newton and Laplace in order to attempt an explanation of the phenomena of oceanic tides, is based upon the hypothesis that at each instant the sea takes the equilibrium position which corresponds to the instantaneous distribution of the vertical (taking into account here the influence of the displacement of the mass of water itself). However, it is quickly apparent that this theory does not give a quantitative representation of the phenomenon, in particular for short period oscillations (semidiurnal and diurnal). Indeed, the liquid particles, not being rigidly connected, because of inertia exceed their equilibrium position and oscillations are initiated. Darwin, Kelvin, and Love have taken this effect into account and constructed a dynamic theory of the tides. This theory was still not entirely satisfactory and did not explain the large dissimilarities that the phenomenon presents from one ocean basin to another. A better approximation to reality is furnished by the theory of Harris who introduced the consideration of ocean basins where certain tidal oscillations may or may not be able to enter, in resonance with characteristic periods determined by the geometric form of the basin. In the case of the solid earth, the rigid connections (we will see below that the moduli of rigidity are of the order of that of steel and larger) between the molecules do not allow currents, and the particles are only displaced a few decimeters and equilibrium is thus rapidly attained. It is easy to show that the periods of tidal oscillations are long compared to the period of free oscillation of a liquid earth having the dimensions of the earth (1.5 hr), thus the phenomena of resonance will not be able to develop (cf. [l]). This can be seen by considering that the crust is comparable to a very deep ocean, which leads to a very short free period (function of fi).

394

PAUL J. MELCHIOR

On the other hand, a seismic impulse takes about 20 min to be propagated along one diameter. Compared with these periods, the semidiurnal period of the tides may be considered long, and the phenomena which are its manifestation may be treated by the static theory. We shall now develop the essential elements of this theory in order to compare the theoretical data with the results of observations which are described below.

2. STATICTHEORY OF

THE

TIDES

1.1. Calculation of the Attraction

Let L be the disturbing body of mass m (the mass of the earth being taken as unity) ; A , a given point a t the surface of the earth; and G, its center of gravity (Fig. 1). The attraction is exerted on G and A in the LGA plane. We separate the components parallel to the axes OX and O Y :

a

FIG.1.

where f / a 2 = g (acceleration of gravity). The relative attracting force acting on A is the resultant of these two forces which can be written

A pendulum suspended at A , when in equilibrium, would make an angle e with AG given by

395

EARTH TIDES

From Fig. 1 we notice that

(

7r2= 1 + 2 % o s z r a sin 2' = sin z -sin z cos z r a cosz' = cos z - -sin2z r

+

Thus, we obtain

and, neglecting small terms of an order greater than the third power of a/r, we obtain

(2.7) I n order to study the intensity of gravity, it suffices to consider equations (2.3) using values of r2/r" and cos 2' given by (2.5). Again neglecting terms of the 4th order these give:

The change in gravity is thus (2.9)

dg

=

Y t

gm -

(1 - 3 cos2 z )

=

a f m - (1 - 3 cos2 z ) r3

The expressions (2.7) and (2.9) of the horizontal and vertical components of the perturbing force are derived from a potential (2.10)

w2

fm a2 2 r

= - 7(3

cos2 z - 1)

This may be seen by forming (2.11)

1 aw2 - -~

g adz

and

dW2 aa

-

The quantity within the parentheses in (2.10) is the surface zonal harmonic function of the second order if one takes the direction between the center of the earth and of the disturbing body as the axis.

390

PAUL J. MELCHIOR

9.8. Deformations of the Level Surfaces Caused by Luni-Solar Efects

Alevel surface is defined as a surface normal to the direction of gravity at all points; that is, normal to the resultant of the gravitational force due to the terrestrial mass and the centrifugal force caused by rotation of the earth about its instantaneous axis. One notes that such a surface is equipotential and its equation may be written

v = C(h)

(2.12)

where h is the distance to a level surface chosen as reference. Helmert has called these surfaces level spheroids (these are not ellipsoids but irregular surfaces differing from a simple geometric surface because of the heterogeneous distribution of densities in the earth’s crust). The name “geoid” has been given to the level spheroid corresponding to the mean surface of the oceans, and its equation is

vo = C(0) Thus, the acceleration of gravity a t a point P may be expressed by g=

(2.13)

av -ah

where h represents the altitude of point P above sea level. Let us now consider the effect on the level spheroids, and in particular, on the geoid, of a perturbation caused by the luni-solar attraction whose potential will be W z (an harmonic function of second order). The equipotential surface passing through P is deformed; let P be the amplitude of the radial deformation (height of the tide). The potential of surface h f is

+

and the equation of the surface becomes (2.14)

Using in this relation equations (2.12) and (2.13),it follows that (2.15)

which is the theoretical height of the observed tides.

EARTH TIDES

397

d.3. The Three K i n d s of Tides According to Laplace

Beginning with expression (2.10) for the potential of the tides, one can separate the phenomenon into several distinct types of oscillations. In order to do this it suffices to introduce the well-known trigonometric relation (2.16)

cos z

=

sin cp sin 6

+ cos I$ cos 6 cos (0 - A)

giving the zenithal distance from the heavenly body as a function of its declination 6, its hour-angle e and the coordinates of the location (lati-

Fra. 2. The three types of tides according to Leplace.

398

PAUL J. MELCHIOR

tude 4, longitude X). One thus obtains cos2 4 cost 6 cos 2(0

- A)

+ sin 24 sin 26 cos (0 - A) + 3 (,sin2 4 - -k)

(sin2 6

-

k))

The three terms contained in the parentheses are surface spherical harmonic functions. Their significance is demonstrated in Fig. 2. (A) The first of these functions has as nodal lines (lines where the function is zero) only the meridians located a t 45" on either side of the instantaneous meridian of the body. These lines divide the sphere into four sections where the function is alternately positive and negative: regions where W is positive are those of the high tides (f > 0); the negative regions are those of the low tides (f < 0). This function is called the 8ectorial function, the period of the tides to which this corresponds is semidiurnal, and the amplitude is maximum a t the equator when the declination of the disturbing body is zero. These are Laplace's tides of the third type. (B) The second ,function has as nodal lines a-meridian (90";from the meridian of the disturbing body) and a parallel, the equator. This is a tesseral function. The regions into which it divides the sphere change in TABLE I. Principal short period terms of the potential which generates the tides. ~

Waves

Mean value of coefficient.

Relative amplitude to Mz

~~

~

~

-~

Hourly displacement

Semidiurnal terms

M z semidiurnal lunar N t large lunar elliptic L p small lunar elliptic Sz semidiurnal solar Kz semidiurnal luni-solar Diurnal terms

diurnal lunar diurnal luni-solar P diurnal solar & I large lunar elliptic; JIsmall lunar elliptic 00 second-order diurnal lunar 01

K1

0.45426 0.08796 0.0126 0.21137 0.05752

1 0.194 0.028 0.465 0.127

28'98410 28'43973 29'52848 30"00000 30'08214

0.18856 0.2655 0,08775 0.0365 0.0149 0.0081

0.4151 0.5845 0.1932 0.0803 0.0328 0.0178

13'94304 15"04107 14"95893 13"39866 15'58544 16'13910

General coefficient for semidiurnal terms: General coefficient for diurnal terms:

$4(:)'

ag cost

+ = r cos*+

sin 2+ = sin 24

399

EARTH TIDES

sign with the declination of the disturbing body. The period of the corresponding tides is diurnal and the amplitude is maximum at f45” when the declination of the body is maximum. It is zero at the equator and the poles. These are Laplace’s tides of the second type. (C) The third function depends only on the latitude. It is a zonal and -35’ 15’. Since it is function whose nodal lines are the parallels a function of the sine squared of the declination of the disturbing body only, its period will be about fourteen days in the case of the moon and six months in the case of the sun. These are Laplace’s tides of the first type. The level surface will be depressed about 28 cm a t the pole and elevated about 14 cm at:the equator. The effect of this permanent tide is to increase the constant flattening of the earth. Table I gives the characteristics of the principal waves of types (A) and (B).

+

2.4. Numerical Values

Introducing in the precedingformulas, (2.7) and (2.9), the ratios of the masses of the moon and sun to that of the earth: mL = 1181.45

m,

=

333,432

and expressing the distances in terrestrial radii: a/rL

=

1/60.27

u/r,

=

1/23,400

(cosec 1”

=

206,265)

we obtain for the amplitudes of deflections of the vertical and variations in the intensity of gravity for the moon for the sun

e = 0.0174” sin 22 e = 0.0080’’ sin 22

dg = 0.168 mgal dg = 0.075 mgal

Using the formula (2.15) we are also able t o calculate the tides of the geoid, which become

This equation gives a maximum elevation of 35.6 cm and a maximum depression of 17.8 cm, hence a total amplitude of 53.4 cm. At the time of a new or full moon, the lunar effect (54 cm) and solar effect (25 cm) combine to give a maximum tide of 79 cm. These results would apply to the oceans if sea water had zero density and no viscosity, if no continental barriers or islands existed, if the solid portion of the earth were a niveau. surface, and, finally, if no oscillations were produced in the liquid mass.

400

PAUL J. MELCHIOR

3. DEFINITION OF LOVE’SNUMBERS To characterize the various aspects of the tide of the solid earth, Love [3] introduced two dimensionless numbers which bear his name. Shida has shown that a third number is necessary to obtain a complete representation of the phenomenon. Their significance, as we are going to show, is very simple and each type of elastic deformation can be represented by a combination of these numbers, which, in turn, are bound to the distribution of moduli of rigidity and densities in the earth by rather complex differential equations which have been established by Herglotz. We shall return later to this theoretical aspect. The guiding idea of Love’s theory is that, the perturbation potential being represented with sufficient accuracy by a spherical harmonic function of the second order, all the perturbations produced on the earth by this potential may be represented by the same harmonic function multiplied by the proper numerical coefficient for each aspect of the phenomenon. This coefficient is a simple algebraic combination of Love’s numbers. The radial displacement U and the cubical dilatation D,produced a t all points in the solid by forces deriving from the potential of the second order, Wz, may be expressed in the form

where r is the distance from the point considered to the center of the earth. The coefficients considered depend only on the radial distance. One may indeed presume that below the level of isostatic compensation there exists hydrostatic equilibrium and a symmetrical distribution of the densities, moduli of the rigidity, and compressibility around the center. Likewise, the potential due to the variation of density accompanying the cubical dilatation and the surface displacement of material can be expressed in the form

v

K(T)W* Moreover, the horizontal displacements in the meridian and in the prime vertical will be expressed as functions of the derivatives of Wz with respect to the latitude and the longitude: (3.3)

=

(positive directions of displacement are those of increasing tj and A).

EARTH TIDES

401

For the surface of the earth, where the observations are made, one defines H(a) = h (3.5) K(a) = k L(a) = 1 as the three Love numbers: h represents the ratio of the height of the terrestrial tide to the height of the corresponding static oceanic tide at the surface; k represents the ratio of the additional potential produced by this deformation to the deforming potential; and I represents the ratio of the horizontal displacement of the crust to that of the corresponding static oceanic tide. The observations of the earth tides relate to six aspects of the phenomenon : 1. Reduction of amplitude of oceanic and lake tides 2. Deflections of the vertical with respect to the crust 3. Elastic tensions and cubical dilatations in the crust 4. Deflection of the vertical with respect to the axis of the earth 5. Variations of the intensity of gravity 6. Changes in the speed of rotation of the earth due to zonal tides. In approaching successively the examination of the results of each type of observation, we shall establish first how one can introduce the effect of the deformations of the earth in the theoretical prediction with the help of particularly simple combinations of Love’s numbers.

4. STUDY OF

THE

AMPLITUDE OF OCEANIC TIDES

4.1. Efect Due to the Deformations of the Crust

This phenomenon was the first method of approach and measure of earth tides suggested by Kelvin. This method has only historical interest because indirect effects distort the results. It is impossible to eliminate these effects through the calculations. Following the definitions of Love’s numbers, the total perturbing potential is evidently (1 k)Wz and the static oceanic tide will have an effective height (1 k)Wz/g. But the tide observed on the tide gauges is the difference between the tide of the ocean and that of the crust, hWz/g, to which the tide gauges are attached. The amplitude observed for the oceanic tide will therefore be

+

+

(=

(1

wz = y w2 + k - h) I7 J !

PAUL J. MELCHIOR

402

4.2. Application to Oceanic Tides of Long Period

The comparison of observations and the theory should, therefore, permit us to deduce the factor (1 k - h ) , but that will only be practically possible for tidal oscillations of long period. These, because of the slowness of the displacements and the presence of continental barriers, which prevent the formation of currents, are little affected by the inertia, little damped and thus obey the static theory. Darwin, in 1881, analyzed the records from 14 ports in Europe and in the Indies covering 33 years of observations; later Schweydar analyzed those of 43 ports distributed over the world and covering 194 years of observations. Their results are the following:

+

Darwin Schweydar

Fortnightly tides 0.675 c! 0.084m.e. 0.6265 f 0.043

y = y =

y = y =

Monthly tides 0 680 k 0.387 m.e. 0.6053 f 0.102

Meanwhile, some very serious objections can be raised against this procedure of evaluation of the factor y. One has neglected, in the theoretical predictions of the long period tides, the gravitational effect exerted on the water by the liquid layer raised by the tide itself. One can easily estimate this “secondary” effect in the case of an ocean covering the whole earth, which is assumed to be homogeneous. We find that the heights observed should be reduced by 10% and also the numerical values of the coefficient y to which they are related. But this correction is very uncertain, because the oceans cover only of the earth and are irregularly distributed. In addition, the presence of continental barriers modify the amplitude and phase of theoretical tides. Finally, some static tides of the second type (which result from the Coriolis force) can also exist, even in restricted oceanic areas appearing as permanent currents that neither the continental barriers nor friction seem able to impede. They are therefore superposed on the ordinary static tide and only observations will establish to what an extent they affect the phenomena. It is interesting to note that notwithstanding all these theoretical objections, the numerical values obtained by this method for the coefficient y are in quite good accord with those provided by the other methods which are free from these objections.

N

4.9. Application to Short Period Tides in Lakes In 1925, Proudman suggested attempting to obtain a value of y from the study of tides in narrow seas or large lakes. Grace attempted the test

EARTHITIDES

403

for the Red Sea but did not obtain a significant determination (the factor found being negative). The reason for this can be attributed to the connection of that sea with the Indian Ocean. On the contrary, study of tides of Lake Baikal and Lake Tanganyika gave satisfactory results. ~

Lake Baikal [4]? Bay of Pestchanaia von Sterneck wave M z wave K 1 Grace (semidiurnal tide) Aksentcheva (semidiurnal tide) Bay of Tankoi Aksentcheva (semidiurnal tide) Lake Tanganyika-Albertville [5] Melchior wave M P

y = 0.52

0.73 0.54 0.72

x = -3" +4"

0.55 y =

0.56

x = +go

' x = phase shift.

5. PERIODICAL DEFLECTIONS OF THE

THE VERTICAL WITH RESPECTTO CRUST

6.1. Efect Caused by Deformations of the Crust

The deflections are affected by the addition of the potential kW,, and also by the deformations of the ground with reference to which they are measured. Love's numbers again permit a simple expression for the proportion by which the amplitude of the deflection of a pendulum will be modified. The problem is to measure the angle between the vertical and the normal to the deformed surface. From the force acting on the pendulum

one must subtract this effect caused by the deformation, with the result that one will observe 1 aw, 1 IG - h a-w-2 g aae -Ti=

+

The deformation of the crust has the same sense as the force and thus offsets a part of its effect. We find the same coefficient, 1 k - h, as that for the amplitude of the oceanic tides. This could be expected since, in practice, the static tides result uniquely from deflections of the vertical. The ratio of the observed amplitude, for the deflections of the vertical, to the calculated static theoretical amplitude will give directly the factor y.

+

404

PAUL J. MELCHIOR

Two very different types of instruments are able to measure these deflections: horizontal pendulums and large water levels. One can easily see that the difference of potential, a t the two ends of a sufficiently long tube of water, ought to produce slight oscillations of the liquid which one could be able to detect with the aid of very sensitive measuring devices, which we will describe later. We shall first discuss briefly the elementary theory of the horizontal pendulum. 5.2. The Horizontal Pendulum

The deflections of the vertical are so small (0.02”) that a special instrument must be devised in order to record them with sufficient precision. If, for example, one should want to represent a variation of 0.02” by a displacement of 1cm a t the end of an ordinary pendulum, the length of this pendulum should be 103 km! In order to increase considerably the sensitivity of a pendulum to the small deflections of the vertical, a method of almost horizontal suspension of the boom has been developed. This concept dates back to the beginning of the nineteenth century. Subsequently, the idea was the object of much research by Zollner (1869) a t Leipzig, whose name is generally attributed to this type of instrument. The boom of the pendulum AG, of an average length of 20 cm, is weighed with a mass P of about 20 gm. The boom is supported by two wires (of quartz or of superinvar) in such a manner that it makes a very small angle with the horizontal (of the order of 1’). This type of suspension is such that only the component Mg sin i affects the boom of the pendulum, since Mg cos i is always perpendicular to it and its effect is sustained completely by the system of suspension. On the other hand, the angle that the component Mg sin i subtends with the boom is variable. This is the angle 0. It is necessary now to introduce g sin i in place of g in the well-known formula giving the period of oscillation of the pendulum. We have now (5.3)

:

T

= 2rJ-

L g sin i

Now, the sensitivity of the pendulum is proportional to T2, that is, to cosec i. The amplification of variations of inclination is very large and corresponds, as does the period of oscillation, to a fictitious increase in the length of the pendulum boom by a factor cosec i. I n practice, one carefully measures the periods of oscillation of the pendulum in two positions, in order to obtain exactly the value of sin i which will indicate the amplification of the variations t o be observed. A horizontal pendulum permits the study of the displacements of the

405

EARTH TIDES

vertical in a direction perpendicular to the direction of the boom at rest. If one desires to reconstruct the complete trajectory described by the base of the vertical, it will be necessary to utilize two horizontal pendulums preferably at right angles, in order to register the two components of movement (the pendulum directed toward Oz permits observation of the component following Oy and inversely). The amplification of the movements thus realized can be further increased optically by fixing to the boom of the pendulum a mirror which reflects a light beam on a cylinder rotated by a clock motor and carrying photographic paper. The difficulties encountered in the first models of the Zollner suspension system resulted from the poor quality of the wires which were available a t that time. Hengler had proposed nonspun silk or horsehair; Zollner used steel and torques were appreciable. Orlov used platinum wires.

>At & I

I

I

I

1 I I

I

I

I

I I

I

I

I

I

I' I

I

I

FIQ.3. Schematic representationof different types of horizontal pendulums.

Although similar in principle, several methods eliminated the use of suspension wires. E. von Rebeur Paschwitz achieved this result with the aid of two pins acting in two different directions on the boom of the instrument which had a weight of 42 gm. These instruments were, moreover, destined for additional research, e.g., the recording of seismic waves. For the latter, Milne and Shaw built an instrument where one of the suspension wires was replaced by a point. The different types of instruments are shown schematically in Fig. 3. Hecker perfected the design of von Rebeur Paschwitz by placing the pins in such a way that their axes and the direction of gravity, applied at the center of gravity, would be concurrent. Obviously, the difficult problem in this kind of suspension was to find the proper materials for the pins and their supporting plates. The makers generally used steel pins resting on cups of agate, but wearing of the pins created some serious difficulties. Also, for the horizontal pendulums, various workers have returned to the Zollner suspension, using wires of tunga@n, fused quartz (Ishimoto), superinvar (Nishimura-diameter 30 p ) ,

406

PAUL J. MELCHIOR

or strips of phosphorbronae (Schaffernicht). Use is primarily limited to instruments which are light and of small dimensions; for example, the apparatus used by Schaffernicht a t Marburg was built with an aluminum boom weighted with a mass of 30 gm. The numerous pendulums constructed by Ishimoto were made completely of quartz, including the frame (height of 20 cm, boom of 8.6 cm, and wires of 12 cm and 7 p

FIG.4. Horizontal pendulum of Tomaschek. radius) in order to render the thermal effects practically negligible. The latter instruments have been used in prospecting where it is not always possible to find locations protected from thermal variations. The suspension of Zollner presents several advantages in comparison with that of von Rebeur Paschwita: first in the simplicity of construction; also, according to OrIov, in greater stability of the zero position and the amplification factor; and in the fact that the period T is independent of the amplitude, which is not always the case for the von Rebeur Paschwitz. Finally, we note that Lettau has obtained even greater sensitivity by

EARTH TIDES

407

coupling two horizontal pendulums, in a manner shown schematically in Fig. 3. However, this arrangement is quite delicate, and it is not possible to “couple” any two horizontal pendulums in this manner. 6.3. Observations Obtained from Large Water Levels

As we have mentioned previously, the study of the reduction of the amplitude of the oceanic tides is greatly complicated by the irregular forms of the ocean basins and the existence of considerable perturbing effects that result therefrom. It is practically impossible to take account of these effects. Source

f

FIG.5. Michelson Interferometer on tube for tidal observations.

In 1914, Michelson and Gale proposed to observe the phenomenon in a specially constructed container (with a regular geometrical form) through microscopic measurements and, later, by measurements of interference effects [6]. They buried, to a depth of 1.80 meters, two tubes 150 meters long and 15 cm in diameter. These tubes were half-filled with water and oriented along the meridian and the prime vertical. The first series of experiments, designed to study variations of the level a t the two extremities of each tube, were executed by measuring, with the aid of a microscope, the distance separating the extremity of an immersed rod from its image obtained through total reflection in the liquid. More precise results were obtained in the course of a second series of observations using the interference method, with the aid of an apparatus shown schematically in Fig. 5, which was placed a t each end of the tubes.

408

PAUL J. MELCHIOR

A horizontal mirror is submerged in such a manner that it is covered by a half-millimeter thick layer of water, whose viscosity damps small perturbations. Variation of level will produce a modification of the optical path of the rays issuing from the source S, and one will observe a displacement of the interference fringes from the two light beams. The two beams are obtained a t the first of the parallel faced glass plates, L1, which is half-silvered on one of its faces and inclined a t 45’. The second plate, inclined a t 45”, is a compensating plate. It equalizes the thickness of glass traversed along the optical path of the two interfering light beams and serves, a t the same time, to seal the tube. The displacements of the fringes are recorded on a film transported a t a rate of 2 cm per hour. One is able to record the hours by means of automatic slits in the recorder which appear on the film in the form of a fine bright line. The observations covered one year (November 20, 1916 to November 20, 1917). The films were measured with a microscope, the displacement of the fringes being estimated to one-tenth. The difference in the movement a t the two ends of each tube give a measurement leading to the observed height of the tide. Instruments based on the same principle are going to be installed in a cave near Trieste, Italy, by Professor A. Marussi, in order to obtain observations during the International Geophysical Year. The theory of the tides in the tubes of water has been developed by F. R. Moulton. The authors have carried out a harmonic analysis on the theoretical calculated curve, as well as on the curve resulting from the observations, in order to eliminate distortion due to imperfect elimination of certain components. I n 1934 Egedal and Fjeldstad applied the same procedure in Europe, installing two tubes of water in a 125-meter tunnel a t Bergen, Norway [7]. Recording of the variations of level was obtained in a different manner. The apparatus used, which is called a “level variometer,” consists of a cylindrical vessel 14 cm in diameter and 7 cm high communicating with the water of the tube which partially fills it. I n order to prevent evaporation, the water is covered by a layer of Nujol, 1 to 2 cm thick on which floats a cylindrical glass float 5 cm in diameter and 1.7 cm high. Vertical movements of the float are transmitted though a vertical rod to a rotating mirror whose variations of inclination are observed in a small telescope. The same principle applies to the observation made by W. B. Zerbe in the basins situated a t Carderock (near Washington, D. C.) which were designed for testing of ship models (David Taylor Model Basin) [8]. These long and narrow basins are enclosed under an arched roof and are well suited t o observations of this type. The basin used by Xerbe is

EARTH TIDES

409

845 meters long, 16 meters wide, and 6.7 meters deep. It is oriented along direction W 16" N-E 16' S. One gauge is situated 17 meters from the west end and the other is 15 meters from the east end, thus, they are separated by a distance of 813 meters. Measurements made a t the two ends of the basin permit the elimination of changes in level caused by evaporation and thereby reduce observational errors. The gauges were read alternately each quarter of an hour and each time the small oscillations of the pointer were noted in the following manner: four readings of the minima and four readings of the maxima. The difficulties encountered in obtaining a precise leveling between various Danish islands lead Norlund to use since 1939 a new, hydrostatic procedure. This installation, resembling that of Michelson but considerably longer led, unquestionably, to observations of terrestrial tides. Two vertical glass tubes, graduated in millimeters, were mounted on the islands Fyn and Sjaelland and connected by a water-filled pipe, 18 km in length, submerged to 60 meters on the bottom of Store Belt. Because water surfaces in the two vertical tubes belong to the same level surface, one can thus observe differences of elevation between the different islands. The differences between the readings of the vertical tubes at the two terminal stations are not constant but change regularly with time. The semidiurnal oscillations show an amplitude of 2 to 3 mm and a period of 12 h 25 m. The great length of the pipe (18 km) aids considerably the observation, which gives a coefficient 1 k - h = 0.8.

+

6.4. Numerical Results of the Observations

Figure 6 represents the reconstruction of the trajectory described by the position of the vertical, obtained from records of two horizontal pendulums oriented along the meridian and the prime vertical a t Freiberg in Saxony. On January 9, 1912, the moon and sun being near to the quadrature, the amplitude of the movement was a minimum. On January 12 of the same year, the two bodies being about in opposition, the amplitude of the movement was obviously a maximum. Such records, extending over long periods of time, are analyzed following the procedures ordinarily applied to oceanic tides, and from them the amplitudes and phases of the various components are deduced (Table I). Figure 7 represents three of these components obtained a t Barim, Manchuria. The dashed curve is the theoretically predicted curve, while the solid curve has been deduced from the observations. The amplitude is thus reduced in the ratio (1 k - h) just as has been predicted in formula (5.2). Thus, a t each station one is able to deduce, in each direction (meridian

+

410

PAUL

J. MELCHIOR

West

South

South

West

10

-

0 0.005" 0.01"

January 9, 1912, Oh-January 10, 1912,2h

January 2, 1912, Oh-January 3, 1912,2h

FIQ.6. Reconstruction of the trajectory described by the base of the vertical from records of two horizontal pendulums at Freiberg (Saxony).

N

FIQ.7. Components Mp,

,632,

01

of the earth tide at Barim (Manchuria).

and prime vertical, in general), a value of the coefficient y and the corresponding phase for each one of the components that can be isolated from the observed curve by harmonic analysis. An exhaustive list was given in 1954, including all determinations (33 in number) that have been made up to that time since that of von Rebeur Paschwitz in 1892 [l]. This list contains the essential characteristics of the stations.

EARTH TIDES

41 1

From a series of observations recently made at Winsford, England, Tomaschek has obtained a value 0.72 [16]. J. Picha [17], analyzing the observations made by Cechura at Brkaov6 Hory, Czechoslovakia from 1935 to 1940, a t a depth of 1000 meters, obtained for the average of the oscillations MzNzS2 in the direction of the meridian and the prime vertical the values 0.701. We will refrain here from details about the values found for the coefficient y because they are of very unequal quality. The best values of this coefficient will be mentioned in the following paragraph. 6.6. Discussion of the Observations-the

Indirect Efect of the Oceanic Tides

The first statement that can be made is that there exists a systematic difference between values of the factor y along the meridian and along the prime vertical, the latter generally giving a higher value of y (approximately 20%). To our knowledge, Hecker first indicated in 1907 the origin of this disagreement, attributing it to “indirect effects” caused by the complex influence exerted on the vertical by the masses of water moving in nearby seas. This influence presents three aspects: (a) the attraction of the water masses on the vertical; (b) a variable deflection of the crust under the influence of the extra load of water imposed on it (this is the most important part of the indirect effect, cf. Fig. 8); (c) the variation of the potential caused by this supplementary deformation of the crust, an effect of smaller order but of opposite sense to the two preceding. T. Shida [9] calculated, for the first time, the effects (a) and (b) for the station a t Kamingamo (Kyoto). We have reproduced his very striking results in Fig. 8. Two methods, based on essentially different principles, permit the separation of the direct effect from the global indirect effect. We shall now describe these briefly. 6.6. Method of Numerical Evaluation of the Indirect Eflects

This method has been applied principally by Japanese workers. (a) Calculation of the attraction of the water

The distribution of ocean water varies with the tides and is represented on cotidal charts. Dividing the ocean surface into small sectors, of uniform water height, of which the station occupies the top, and which are limited by radii rl, r2 and azimuths 01, & (taken in a clockwise direction), one obtains the attraction that it exerts by the formulas:

412

PAUL J. MELCHIOR

(5.4)

Ax = ___ jPh (log r2 - log r,)(cos e2 - cos el) towards the east g sin 1“ A s = fPh (log r2 - log rl) (sin O2 - sin 0,) towards the south g sin 1” ~

( p being the density of the ocean water). In these formulas it is necessary to replace h by h cos (nt - 4) for each component of the tide.

(b) Calculation of the deformation of the crust caused by the burden of the water Already in 1878, J. Boussinesq had calculated the distortion of a plane elastic surface under the effect of an additional load and showed Kamigarno IS

s

s

FIG.8. Components Ms, 0,of the earth tide at Kamigamo, according to T. Shida. Curve a: observed deflections Curve b: calculated effect due to deformation of the crust Curve c: calculated effect due to attraction of the water Curve d: direct effect = a - (b -k c) Curve e: calculated effect, using the static theory

that the vertical displacement of the crust was, at each point, proportional to the gravitational potential of the load and a function of the elastic constants of the medium (A, p the Lam6 constants) [lo]. Writing the attraction in the form (5.5)

the deformation is written, following Boussinesq :

EARTH TIDES

413

if (5.7) (c) Variation of potential This effect is less than the two others and acts as if it were produced by a negative mass. Nishimura, who appears to be the only one to have taken it into consideration in the case of the tides, acknowledges that, in a first approximation, one is able to consider the effect to be proportional to A , and defines

v

(5.8)

- E A [Ill

=

The sum of the indirect effects is, thus, expressed by

I

(5.9)

=

(1

+ v - €)A

The Japanese authors T. Shida, R. Sekiguchi, R. Takahasi, E. Nishimura have attempted to take into account variations with depth of the elastic characteristics of the medium by observing that the depth p of the crust participating in the deformation depends upon the distance r to the disturbing mass. Since X and p are functions of p , one is able, here, to consider them as functions of r and write (5.10)

I

=

(1

+

y(r)

- €)A

In order to obtain empirically the numerical values of these coefficients, Nishimura has made observations simultaneously a t two Japanese stations: Aso and Kamigamo. The difference between the components M z (or 0,)obtained a t these two places by harmonic analysis of the observations is freed from the direct effect, which is practically the same, and contains only the indirect effects, which depend upon the position of the stations with respect to the surrounding seas. The interpretation of this difference with the aid of (5.10) permitted Nishimura to obtain the values (5.11)

v(r) =

12.6 r+3

-

E

= 0.5

r being expressed in degrees (distances computed in arcs). We have compared this experimental result with previous theoretical research due to L. Rosenhead [12]. That author, primarily interested in the movements of mobile air masses on the surface of the earth and their effect on the moments of inertia of the earth, attempted, in 1929, to evaluate theoretically the importance of the compensation A due to the deformation of the crust under the weight of these air masses.

414

PAUL J. MELCHIOR

Adapting the Herglotz theory of the elasticity of the earth to this particular case, he found 0.3 < B < 0.4 which is exactly the same order of magnitude as that found by Nishimura. Rosenhead adopted for the calculation a rigidity modulus of zero in the core and equal to 16.95 10" dynes/cm2 in the solid shell. In the present state of the theory of the elasticity of the earth and of the precision of the experimental results, one can consider this agreement as being quite remarkable. Serious objections have frequently been raised against this method and to its applications: (1) the theory of Boussinesq is related to the deformation of a plane surface and thus, is only valid in the case under consideration over a very small distance because of the curvature of the earth; (2) the rocks constituting the upper layers of the earth do not rigorously obey Hooke's law on which the theory of the elasticity is based; (3) the tides aTe poorly known on the open ocean and the pattern of cotidal lines presents many uncertainties, rendering the application of the method very uncertain; (4) we have not been able to take into account the heterogeneity of the geological structure of the crust (cf. [lo]).

-

5.7. Empirical Method of Separation of the Two Efects

This methodwas introduced by Corkan and Doodson [13]. It is based on an exceedingly probable hypothesis and presents the advantage of great simplicity while appearing extremely effective. One notices that, over vast oceanic expanses, the ratio of amplitudes of various oscillations of the same type (for example the semidiurnal components) remains essentially constant. This constant differs from that given by the static theory and can be deduced from tide gauge observations. Thus, for the region of Liverpool : A ( S 2 ) / A ( M 2 )= 0.320 (static theory 0.465) (5'12) A ( N 2 ) / A ( M z )= 0.190 (static theory 0.193) The fundamental hypothesis of the method acknowledges that this is valid for all of the phenomena resulting from the oceanic tides, and therefore in the indirect effects studied here. Let f = E cos ( A - b) a component given by the theoretical static terrestrial tide, f l = I cos ( A - L) the indirect effect resulting from the presence of this component in the ocean tides, and c0 = K cos ( A - K ) the same component deduced from the observations by harmonic analysis.

415

EARTH TIDES

Obviously, one can write To

=

rT

+

TI

from which one can deduce, by equating the coefficients of sin A and cos A , I COB i y E cos b = K cos K (5.13) I sin 1 y E sin b = K sin K

+ +

We know t ha t the phase lag of the static terrestrial tide is very small. We assume initially, as the first approximation, that it is zero: b=O and the equations become : (5.14)

I cos i f y E = K COS K I sin i = K sin K

By virtue of the fundamental hypothesis developed, we write amplitude of the oceanic tide ( M z ) amplitude of the oceanic tide (S2) (5.15) static amplitude (Sz) static amplitude ( M 2 )

I(Sz) - o.320 I(Mz) r E ( S z ) - 0.465 ~E(Mz)

and two analogous relations for the ratio of the oscillations N z / M 2 ,for which the numerical values are 0.190 and 0.193, respectively. To each value of the phase of the indirect effect L there corresponds, for each oscillation (Mz, SZ,N z ) , values of I and y B from which the values of I(M2) and yB(M2) can be deduced from the relations (5.15). I n order t o verify the hypothesis developed, one should find, for each oscillation, a suitable value of i which should lead to the same values of I ( M 2 ) and yB(M2). This is done graphically, with I ( M z ) as abscissa and y B ( M 2 )as ordinate. Each oscillation is represented by a characteristic curve. The three curves determine a triangle of which one takes the center of gravity (by weighting the curves in proportion to the amplitudes of the oscillations). Corkan has thus found as coordinates of the center of gravity for Bidston (Birkenhead-Liverpool) : (5.16)

I ( M z ) = 0.0593” E(M2) = 0.0059”

from which y = 0.77 results, with the restriction th a t b = 0 and th a t the hypothesis of Doodson-Corkan is correct. Corkan has attempted to solve the problem completely, th a t is t,o determine the phase b by calculating the values of y corresponding to various values of b for two different stations [14].

PAUL J. MELCHIOR

416

He analyzed, for this purpose, the results from Bergen following the same scheme as for those a t Bidston and obtained y = b =

0.65 8"

a somewhat surprising result since it was generally acknowledged that the phase b should be very small. However, according to Corkan himself, the station a t Bidston would not be very adequate for this kind of determination since the indirect effect is ten times greater than the direct effect, while at Bergen the two effects are of the same order of magnitude. Melchior has discussed Corkan's method [15]and has shown that its application is more difficult for a continental station than for a coastal station where one can pre-estimate the approximate phase of the indirect effects. He shows that the number of solutions offered by the method is rather variable, because the representative curves y = f(1)of each wave ( M I , 82,N 2 ) are hyperbolas with parallel transverse axes. On the other hand, it would be necessary to know a priori the exact role of each oceanic region in the indirect effects acting on the particular station, in order to weigh correctly the values observed for these relations in these oceans. Thus relations accepted for the north-south component and for the east-west component will in general be different. Finally, Melchior has obtained the following: Freiberg in Saxony Br6zov6 Hory Bidston

y y Y

= 0.704 (weight = 4) (observations of Schweydar [15]) = 0.709 (weight = 9) (observations of Cechura-Picha [17]) = 0.703 (weight = 8) (observations of Doodson-Corkan [13])

These values are in very good internal agreement and in satisfactory agreement with the results of measurements made in Japan. The most probable value of y would then actually be (5.17)

y =

0.706

a value which should be very close to the true value of the coefficient y. Zerbe [8] has obtained in America 0.742, while the results of studies by Japanese scientists seem to indicate a value a little smaller, undoubtedly in the neighborhood of 0.68. One can wonder if it is necessary to infer the existence of a regional heterogeneity in the crust or rather an incomplete elimination of the indirect effects resulting from the application af the formulas of Boussinesq and the cotidal charts. Furthermore, note that the phase b has not been reduced to zero a t any of the Japanese stations, the phase being very variable from one station to another and appreciably different between the NS and EW components.

417

EARTH TIDES

6.8. Effect of the Tides on High Precision Leveling Operations

The hydrostatic leveling operation accomplished by Norlund has attracted the attention of geodesists to the eventual advantage of applying a “tidal” correction to the raw results of precise leveling measurements. The Danish geodesists Jansen and Simonsen were the first to do this in a practical manner. Beginning with the classical formulas giving the perturbing action of a heavenly body on the vertical of the level surface, they have calculated the correction to be applied to the results of precise leveling recently carried out in Denmark. By way of example, and to establish an order of magnitude, the luni-solar correction was 2.49 mm for a leveling operation extending over 125 km. L. Jones has applied the same method to the Belgian base network near Tournai. He has observed : (1) That there is not necessarily an amelioration of the leveling results after luni-solar correction. (2) That the proposed method permits no definite conclusions; the experimental measurements, which would be investigated, would only be able to show that the precise levelings are in a position to contribute in the general study of tides. (3) That the study of the possible effect of the luni-solar action on the systematic errors is intimately connected with the study of all of the causes of systematic errors. The International Association of Geodesy has recommended, during its meeting a t Brussels in 1951, an exhaustive study of these problems. In this connection, the Instituto Geogrbfico y Catastral has undertaken, in Spain, a program of experimental leveling. The author believes, in agreement with the opinion of L. Jones, that the application of the classical formulas (provided with the coefficient y = 1 k - h ) appears extremely hazardous, especially in a region near the ocean. This is due to the importance of the indirect effects (at Bergen and at Winsford, for example, they are of the same importance as the direct effect, and at Liverpool, 10 times greater) whose phase can be very different from that of the direct effect. Furthermore, the local geologic structure in certain cases is able to induce flexures in an opposite sense to those which one would expect from the localization of the additional loads (cf. Section 10). It appears to us that one could simultaneously employ a horizontal pendulum during the course of a leveling operation. This horizontal pendulum would be oriented perpendicular to the direction of the survey and, thus, would give along this direction not only the direct effect and indirect effect but also the thermal effects on the crust, that is, perhaps the complete correction to be applied to the leveling. Such an operation appears possible with pendulums of the type of Nishimura or of Ishimoto.

+

418

PAUL J. MELCHIOR

6. MEASUREMENT OF ELASTIC TENSIONS AND CUBICDILATATIONS DUE TO DEFORMATIONS PRODUCED BY THE EARTH TIDES 6.1. Components of the Tension

The deformations resulting from the action of the luni-solar potential give rise in the earth to elastic tensions which one can measure, a t least a t the surface. Dependent on the amplitude of the deformation, they will constitute a new way of approach for the experimental determination of Love’s numbers. Using relations (3.4) and (3.5)the deformations of the earth’s surface may be written in the form along the meridian

aw,

i

following the prime vertical

The classical theory of elasticity is based on Hooke’s law according to which the tensional components are linked to those of the dilatation (derived from the deformation, u, Y, w)by linear relations. If in addition, one assumes restrictive conditions of isotropy, homogeneity, and incompressibility, the tensional components in the X Y plane are directly proportional to the corresponding dilatational components :

Y 3 = - au f - = - - av

dy

ax

1

aso + -1-asA = i ax u a6 ag sin 8 ~

a sin 0

. _a2wz _ aeax

and the tension, exerted in such a direction that the direction cosines are (m, n), will be proportional to (6.4)

+ ezn2+ yamn

elmZ

Measurement of these will allow direct determination of the number 1. 6.2. The Sassa Extensometer

The measurement of such weak stresses in the crust is not possible, but Professor Sassa of Kyoto University has arrived at a very elegant method of making them evident [18]. His instrument, simple and ingenious in concept, is the only one which actually measures the number

EARTH TIDES

419

I directly. A superinvar wire (1.6 mm in diameter) is stretched almost horizontally between two fixed supports about 25 meters apart and a weight of 350 grams is suspended from its center. Variations in the distance between the supports resulting from deformations of the crust will cause variations in the tension of the wire as expressed by equations (6.3) and (6.4) and vertical oscillations of the weight. This up and down movement is converted into rotation of a mirror through a bifilar suspension consisting of two superinvar wires, 0.5 mm in diameter, under torque. Figure 9 shows the disposition of a part of the apparatus in a room a t the Makimine station (one can also see a pair of Nishimura horizontal

FIG. 9. Instrument room at Makimine, Japan: extensometer of Sassa and two horizontal pendulums of Nishimura ,

pendulums). At the bottom is one of the supporting pillars, in the background to the left the device carrying the bifilar suspension on which the weight and the mirror may be seen. The apparatus is calibrated by displacing one of the suspension points by a quantity measured with a micrometer. Since the observation rooms are at great depth ( p ) , variations in temperature are very small (of the order 0.2"C per year). As shown by the theory [equation (6.4)] measurements in three different directions, to determine the components el , €2, y3,will allow a complete study of the stresses a t the surface. A complete set of equipment has been installed a t Osaka-Yama. The first results published by Sassa, Ozawa, and Yoshikawa relate to three different stations in Japan. These are shown in Table 11. The mean error in the value of the quantity 1 is of the order of +0.011.

420

PAUL J. MELCHIOR

The results marked with asterisks have had the indirect effect evaluated by Boussinesq's method and removed, the others are the raw results. Ozawa has tried to calculate the amplitude of the indirect effects beginning with the observed results, for various values of 1. These results are only preliminary and observations are still in progress. Ozawa [18a] has published the first detailed results obtained with the aid of a group of 13 extensometers placed in three stations and following different orientations and inclinations (cf. Table 111). TABLE 11. Numerical value of 1 number obtained with extensometer. Station

&

x

Time interval

P

Mitsubishi 35" 40' 135" 47' -800 Ikuno 32" 38' 121" 24' -165 Makimine Osaka-Yama 34" 54' 135" 51' -150 Tune1

9/19/43-10/5/43 12/7/49-12/8/50 10/24/47-10/29/48 9/2/52-10/1/52 5/19/52-5/3/52

Azimuth of wire

1

X

E 3" S 0.051 -40"* N 57" W 0.025 +74O S 38" W 0 . 0 5 -61°* 0.035 S 76" W 0.091 - 5" 0.021 -12" S 2" W

Studying first the direct effect, the author has developed the calculations of the tension according to its six components, cubic dilatation, and horizontal areal tension B = eee e4@. In order to take into account the indirect effects, he has calculated the corresponding tensions from the expressions for displacements given by Boussinesq's solution. He was able to show that for this solution the horizontal areal tension, cubic dilatation, and radial tension which are due to indirect effects, are nil at the surface. The recording of each instrument over a period of a month was subjected to harmonic analysis. Since the direct effect is approximately the same at the three stations the observed indirect effects were compared with the calculated effects by the formulas deduced from Boussinesq's solution, by taking the difference between the observed effects M zfor each pair of stations. This comparison makes evident an anomaly of the station a t Suhara in relation to the other two which are in agreement. However, Suhara is right on the seacoast. The direct effects are studied only in the representative combinations at the surf ace :

+

radial tension (6.5)

err =

2 [4h + a a$ dr

2 horizontal areal tension Z = - (h - 31)W~a ag

cubic dilatation

421

EIARTH TIDES

If Boussinesq's solution is accepted these combinations are free of indirect effects. The results obtained for the different combinations of parameters are listed in Table 111. From these data the author concludes that the weighted mean is: h - 31 = 0.434

Taking h

=

+ 0.026

0.600, Ozawa then deduces that 1

=

0.055.

TABLE 111. Results obtained from a group of extensometers. Distance from ocean

P

$J

x

Osakayama

34'59.6' N

135O51.5' E

- 150 m

65 km

Kishu Suhara

33O51.7' N 34" 2.6' N

135'53.4' E 135'21.7' E

-100 m - 30 m to - 60m

15 km 50 m to 90m

Station

Station Osakayama

Wave

Mn 82

Ki 0 1

Kishu Suhara

M1 M2

Extensometers 3 horizontal 2 vertical 2 oblique 3 horizontal 3 horizontal

Horizontal areal tension h - 31

Radial tension ah' 4h

+

Cubic dilatation ah' 6h - 61

0.427 0.572 0.294 0.511 0.304 0.521

-0.246 -0.615 -0.371 -0.402 -

0.604 0.616 0.221 0.644 -

+

Benioff has installed extensometers a t Dalton Canyon (Pasadena) and Isabella (Kern County), and positive results have already been obtained. He proposes to make additional installations in South America ~91. 6.3. Efect of Cubic Dilatations on Wells

This result of earth tides is demonstrated by variations in the water level in wells which are too far from the ocean to have any relation to it. The effects have been noticed positively a t fifteen points in Europe,

422

PAUL J. MELCHIOR

Africa, and America [23]. We will cover here only the two cases which have been rigorously analyzed.: These are the Kiabukwa well (Belgian Congo) and the Turnhout boring (Belgium) [23] which are located a t 7" south latitude and 51" north. They present the two extreme cases with respect to tidal theory since the diurnal tides are zero at the equator and maximum at 45". In both cases the temperature of the water was very high (92" t o 102°C). It should be noted, before discussing these phenomena, that one cannot predict from theory the absolute amplitude of the tide since one does not know the volume of water confined in the dilated beds nor the porosity of the beds, both of which factors will affect the results. Under these conditions two tests make the tidal effects clear. First, the various oscillations must have amplitude ratios which are related by the static theory. Secondly, the phases of the oscillations must be 180" since the effect of compression will invert the tide; there will be a contraction of the beds a t low crustal tide and this contraction will raise the water level in the spring and cause a high tide in it. Table IV demonstrates that this is the case at Kiabukwa and Turnhout. TABLE IV. Tides in wells. Turnhout

Kiabukwa 4 = -7'47'

6 = +51° 19' Relative amplitude

Oscillation Phase Semidiurnal Ma 185'1 N2 176'6

Lz

S2 Diurnal K1 01 &1

J1

001

Relative amplitude

Amplitude Static Amplitude Static cm Observed theory Phase cm Observed theory

-

-

-

0.198 0.073 0.524

0.194 0.028 0.465

242'4 209"3

1.48 0.24 0.04 0.68

0.154 0.025 0.455

- 183.7 0.194 170.8 0.028 235.1 0.465 182.6

161"6 151'2 178'5 238'9 179'5

1.41 1.20 0.23 0.09 0.08

0.952 0.810 0.157 0.063 0.057

1.460 At Kiabukwa the weak amplitudes 1.037 of the diurnal oscillations are not 0.201 significant, for want of data on the 0.082 atmospheric pressure 0.044

7.53 1.49 0.55 3.95

These phenomena constitute the most easily measured effect of earth tides since they involve quantities of the order of several centimeters. Perkeris' suggestion, of constructing an experimental dilatometer, deserves to be pursued. This is particularly interesting if one wishes to

423

EARTH TIDES

verify the recent theory of Jeffreys (see 1 0 . 5 ) which suggests that the diurnal oscillations are related to movements in the core. The diurnal oscillations should then have a different amplitude relation with the semidiurnal oscillations. The Turnhout observations appear to support a first experimental confirmation of this theory; the K 1 oscillation there has a slightly reduced amplitude nearly in the ratio predicted by Jeffreys theory [19]. K. Sperling [23a] has noticed a very sensitive effect of the earth tides on the yield of oil wells in Nienhagen, Germany (4 = 52'30'N, X = 1O"E). He made this clear for tides Mz and Sz. However, a rigorous harmonic analysis is not possible because priorities of production have not permitted recording of the data. Moreover, the level is often irregularly disturbed by accidents (fallen rock, paraffin, sands, etc.).

7. DEFLECTIONS OF THE VERTICAL WITH RESPECT TO THE EARTH

THE

AXIS OF

7.1. E$ect of Deformation of the Crust

The deflections of the vertical determined by horizontal pendulums or levels are related to the crust itself. With a horizontal pendulum the deviations of a light beam reflected by a mirror attached to a moving arm are compared on a recording drum with the trace of a light beam reflected from a mirror fixed to the instrument; i.e., to the deformed crust. The situation is quite different in the case of astronomical instruments. All deflections from the vertical a t a place must vary the astronomic coordinates, especially the latitude. This latter is determined by comparing the direction of the vertical measured by two levels (Talcott's method) or a mercury bath (Zenith Tube, Astrolabe) to the observed directions of a series of ((fixed" fundamental stars. In this case the deflections of the vertical are not fixed with respect to the crust but with respect to the direction of the axis of rotation of the earth in space. If the earth were perfectly rigid, there would be no difference between the results of the two methods of measurement, but it is clear that, if the earth deforms, the observed phenomena will be different for the two cases. We have expressed in (6.1) and (6.2) the respective components of the deviation of the vertical and the deformation of the surface in two directions chosen conveniently in the plane tangent to the surface. The deformation will also induce (Eq. 3.3) a supplementary perturbing potential, kW2, which will be added to Wz in the expressions (6.1) so that, finally, the deflection of the vertical with respect to the axis of the earth will be:

424

PAUL J. MELCHIOR

in the meridian

(7.1)

(1

in the prime vertical (1

1 awz + k - 1) ag a0

1 aw, + k - 1) ___ ag sin 0 ax

The intervening factor is no longer.?

=

1

+ k - h but

It would appear, a t first glance, to be impossible that astronomical observations of the meridian having a precision of the very most a tenth of a second of arc would reveal such weak phenomena. Despite this objection, highly precise measurements made using instruments especially equipped for the accurate measurement of latitude and carried out methodically over the course of many years have made it possible to evaluate this phenomenon and to obtain a relatively accurate value of the coefficient, A, which, while not reaching the precision attained by other methods of observation of earth tides, is nevertheless in good accord with the value that theoretical research indicates. 7.2. Indirect Efects From the principles governing the methods of observation in meridian astronomy arises a property which is important in the consideration of the indirect effects. It is evident that deformations of the crust, due to the varying load of the ocean waters, cannot play a part since they do not affect the direction of the vertical, which is the only reference used, and which is defined by the level bubble or the mercury bath. The observed phenomenon is then composed only of the oscillations of the vertical resulting from direct luni-solar action and of “indirect” oscillations resulting from the attraction of the waters and the effect on the potential of the deformations of the crust, the last acting as partial compensation for the effect of the attraction of the water (about 40%) cf. Section 5.6). 7.9. The Zenith Telescope This type of instrument, utilized since 1899 in the various stations of the International Latitude Service, has a mounting especially adapted to the precise determination of latitude by the method of Horrebow and Talcott. This method consists of successive observations of two stars symmetric with respect to the zenith and passing the meridian a t a few minutes interval.

EARTH TIDES

425

In this manner the latitude is obtained by the relation SNorth

(7.3)

4=

+2

88outh

ZN - 28 $7-

The measurement is made using only a micrometer screw and without the need of a divided circle and this makes the method superior. Several authors have attempted a t various times, and with different data, to analyze the observations in relation to the hour angle and the

7 8 9 1 0 1 1 O h 1 2 3 4 5

FIG.10. Apparent variations of latitude due to earth tides at stations of the International Latitude Service.

declination of the moon. (The sun does not play an important part here since the observations of latitude are always made in such a manner as to be centered a t local midnight.) Their results are given in Table V, and for an example we reproduce the figure given by E. Nishimura relating to five stations in the northern hemisphere (Fig. 10). This last has taken the indirect effects, evaluated by the cotidal chart method and Boussinesq’s formulas, into consideration. 7.4. The Photographic Zenith Tube

Markowitz and Bestul have discussed the observations made in Washington with this instrument. They have taken into account the indirect effect due to the attraction of the waters but not that arising from varia-

426

PAUL J. MELCHIOR

TABLE^ V. Factor A. Results obtained by analysis of the observations of variations of latitude." Station

A

Mizusawa Carloforte Ukiah Gaithersburg Tschardjui Cincinnati La Plat,a Greenwich Washington Pulkovo Poltava Pino-Torinese Rabelsberg a

0.68 1.07 1.00 0.56 1.06 1.33 2.23 1.16 1.27 1.05 1.25 1.37 1.60

Thew data are the weighted means of numerous results of analysis by several authors.

tions in the potential due to flexing of the crust. They obtained a coefficient of 1.30, but if the compensation of 40% of the attraction, due to the variation in potential, is taken into account, the coefficient will be 1.27. 7.5. Value Concluded for A It is difficult to decide on a value for A since the results are disparate. A careful correction for the indirect effects would be necessary but the cotidal chart method is uncertain. A weighted mean of all the valid results of Table V is

(7.4)

A = 1.13

(Tschardjui, Cincinnati, La Plata, Pino-Torinese, Babelsberg : weight

x,All the others: weight 1.)

It is generally accepted that A is between 1.1 and 1.2. 8. VARIATIONS IN

THE

INTENSITY OF GRAVITY

8.1, Effect of Crustal Deformation

The variations calculated in (2.15) are affected by elastic deformation of the globe with the resulting potential variations. With the help of Love's numbers the importance of this modification of the amplitude calculated from the classical theory may be evaluated. If V ois the initial potential, the gravitational acceleration will be

EARTH TIDES

427

The potential of the body under luni-solar action and deformed is (8.2)

V'

= w2

+ Wz' + r avo+ vo 7 & -

The variation of g will be that derived from the additional potential with respect to r, for (8.3)

91 - go = -

-+aT aw; (awz ar

+r$)

Here, Wz' represents the additional potential due to the deformation of the globe and is of the form R2/a3,while [ = h(Wz/g). Consequently,

and finally,

I t is this new combination of Love's numbers given as (8.5)

6 =1

+ h - 4gc

which allows us to determine the observations of the variations of g.

8.2,BiJilar Gravimeters The first effort to reveal this phenomenon was made by W. Schweydar in 1913. The observations, made a t Potsdam with a Schmidt bifilar gravimeter, gave a result ( 6 = 1.2) that recent observations tend to confirm. I n 1927, Tomaschek and Schaffernicht, having created a highly sensitive gravimeter, also of the bifilar type, made measurements at Marburg which gave quite a different result (6 < 1) that is even theoretically impossible. Ellenberger in Germany and T. Ichinohe in Japan have improved on these gravimeters by use of a double bifilar suspension giving a sensitivity which appears to be much greater, assuring a precision of better than a microgal. These instruments will be used during the International Geophysical Year. Apparatus of this type is not easily transportable.

: I. Prospecting Gravimeters

)

(:reat progress has been made in the development of portable grav' ters of high sensitivity. These are designed to disclose anomalies of le than 1 mgal and will measure tidal phenomena with amplitudes of 0. mgal.

428

PAUL J. MELCHIOR

3

FIQ.11. Askania Gravimeter GS.11.

Many variations are employed in the construction of the mounting, but the basic principle is the same (see Fig. 11). A mass is fixed a t the end of a beam making an angle a with the vertical and swinging about a horizontal axis. An inclined spring, also in the vertical plane, supports the beam so that rotation of the beam varies the pull of the spring. Thus,

EARTH TIDES

429

the moment of the force exerted by the spring will be equal to the couple due to gravity so that the moving assembly will be in equilibrium for all values of a and the sensitivity is great and constant over a large range. The addition of a supplementary spring allows compensation for gravitational variations and the shifting of the zero by a known amount in order to extend the range of the measurements (change of zone). Prospecting companies have taken the initiative in determining the factor (a), knowledge of which is necessary to correct their readings starting from tables or abacus giving the classical theoretical effect. However, these surveys cover too limited a period of time (15 days) to permit the harmonic analysis which would give the various components with the accuracy desirable for geophysical research. 8.4. Results of the Observations

It has meanwhile been verified that the value of 6 determined for the different isolated oscillations by harmonic analysis is almost systematically less than the value concluded from a global comparison with a calculated curve. W. D. Lambert explained this effect by recalling a statement of R. Harris: each perturbing phenomenon which is such that its origin increases the difference between the greatest maximum and the greatest minimum will be eliminated in harmonic analysis by separation of the various components. Harris evaluated the effect on the amplitude of a factor 1.02, but it has not been possible to find observations which would support this numerical coefficient. In the type of observation studied here it seems that it is a question of a coefficient of the same order. The study of the indirect effects acting on the acceleration of gravity has hardly been approached. This is due to the fact that their role is relatively smaller than in the study of the deflections of the vertical. They have manifested themselves clearly in certain stations near the ocean and have been noted by prospectors in the vicinity of the Gulf of Mexico. On the other hand, Bollo and Gougenheim believe that they do not have the effect, which might be presumed to be found in the form of a phase shift, a t La Chapelle Saint Laurent, a station very close to the coast. In the case of variations in the intensity of gravity, the indirect effects include the attraction due to water masses, the variation of distance to the center of the earth resulting from flexure of the crust, and the variation of the potential resulting from that flexure. The only solution, which is actually possible, is to take the mean of the results of a great number of stations dispersed over all regions of the earth. Harmonic analysis has been applied by A. J. Hoskinson to nearly

430

PAUL J. MELCHIOR

all of the results of the important field work of the Shell Company, and W. D. Lambert [20] calculating the vectorial mean for each oscilration concluded that: for Ma for Sz for K1 for O1

8

K

1.191 f 0.012 1.213 f 0.022 1.192 f 0.026 1.178 f 0.016

l"99 f O"95 4"92 f 1'41 -0234 f 0'86 O"70 f O"77

Following the views of Jeffreys and considering the semidiurnal and diurnal oscillations separately, W. D. Lambert accepted: 6 = 1.198 K = 2'97 for the semidiurnal oscillations for the diurnal oscillations 6 = 1.186 K = -0"22 The probable errors are too large for one to admit without reserve the existence of a difference between the two types of oscillations as experimentally established. In this regard it is interesting to compare the results obtained by two separate sets of apparatus functioning simultaneously at the same station (Houston, Edmonton, Los Angeles) or during different periods. The mean phase shifts obtained by W. D. Lambert result without doubt from an imperfect elimination of the indirect effects. The more important series of observations were recently made at Strasbourg (France) by Lecolazet with a revised North American gravimeter (improvements and automatic recording due t o the author). Eight months of observation were analyzed and the results are given in Table VI.

TABLE VI. Results of Global Analysis. Place of observation : Strasbourg X = 7'46'E). Original time: 6 A. M., G.M.T., Jan. 5, 1955.

($ = 48'35";

Wave

8

K1

1.204 f 0.006 1.178 f 0.006 1.150 f 0.017 1.20 f 0.03 1.16 f 0.13 1.16 f 0.09 1.6 f 0.2 1.211 f 0.005 1.217 f 0.013 1.27 f 0.05 1 . 2 1 f 0.02 1.4 f 0.2 1.3 f 0 . 2

01

P1 &I

MI J1

S1

M2 S2 K1 Na

LZ

2N1

Phase shift, in degrees

-

1.48 1.59 0.9 - 2.4 4.0 7.8 -22 0.16 - 2.95 - 2.9 1.9 1 1

f 0.27 f 0.27 f 0.9 f 1.5 f 6.5 f 4.3 f8 f 0.21 f 0.61 f 2.2 f 1.0 f 6 f 7

431

EARTH TIDES

One of the difficultiesin applying harmonic analysis to these observations arises from the drift that is generally significant for gravimeters (just as for horizontal pendulums), and particularly disturbances in the drift. Lassovsky has proposed a simple procedure to eliminate this consisting of noting the hours when the tides are theoretically zero and to mark the observed values of g a t these times. This series of values will give the drift simply [4].However, the methods of harmonic analysis generally eliminate linear drift on each interval of 24 hours; a method given by Lecolazet eliminates a parabolic drift. 8.6. Observations M a d e with Clock Pendulums

E. Brown and D. Brouwer first suggested studies on the existence of small variations in g during the course of a day using observatory clocks of high accuracy. This method of observation not only can yield a precision as high as t!hat of the gravimeters, if the observations are continued over several years, but also constitutes a remarkable test. Brown and Brouwer made continuous comparisons, on a Loomis chronograph of the operation of three Shortt clocks, whose rate is dependent on g, with a quartz clock based on the vibrations of a quartz crystal, which is independent of gravity. The phenomenon was clearly measured, the coefficient being 0.9 and the phase shift 17"30', a result which is not surprising when we see the scattering of gravimetric measurements. The problem has been taken up again recently by N. Stoyko [22] with four Leroy pendulums and one Shortt pendulum compared with a Belin tuning fork clock a t the Paris Observatory. Studying the terms of the sidereal day, for which the theoretical global amplitude is 0.0013 sec, he found for the coefficient 6 = 1.195 a value in excellent accord with that concluded from the field work of the Shell Company by W. D. Lambert. The results of Stoyko, detailed by year and pendulum and reproduced TABLE VII. Determination of factor 6 by pendulum clocks. 1940

1941

1942

1943

Average

44 Shortt 1185 Leroy 1228 Leroy 1229 Leroy 1372 Leroy

1.45 1.14 1.15 1.17 1.18

1.04 0.98 1.02 1.20 1.28

1.40 0.97 1.38 1.29 1.56

1.08 1.26 1.14 1.42 1.03

1.24 1.09 1.17 1.27 1.26

Average

1.22

1.10

1.32

1.19

1.21

Phase (0-C)

-0.8h

+O .9h

-1,lh

-0.4h

432

PAUL J. MELCHIOR

.

in Table VII, give us an idea of the precision which may be obtained in this type of measurement. P. Sollenberger and G. Clemence, having tried to determine a variation in the corrections of the pendulum clocks at Washington from observations made with a zenith tube, found in fact a combination of the effect affecting the observations themselves (with the factor A) and of the effect acting on the pendulum (factor 6) but one cannot determine what part of this belongs to each phenomenon (the coefficient found was 0.92). 9. THEROLE OF

THE

GEOLOGIC STRUCTURE OF INDIRECT EFFECTS

THE

CRUSTIN

THE

9.1. Oceanic Effects

Studies of the indirect effect show that it is necessary to consider the possibility that local flexures in the crust may have an important effect. If, in the general phenomenon of earth tides (direct effect), the whole earth participates in the deformation, and if, as a consequence, small local inequalities of structure do not have a measurable effect on the amplitude of the deformation, it will not be, a priori, the same in the case of local flexures due to oceanic or barometric loads where only the superficial crust floating on a viscous substratum participates in the deformation. Tomaschek has shown, in a penetrating discussion of the observations, that one must consider independent compartments more or less rigidly interconnected. The question becomes one of determining the limits of blocks capable of movements of their own. Nishimura has succeeded in demonstrating the effect of an active fault on the flexures of the superficial crust. His study is based on the fact that, near the ocean, the indirect effect is large compared to the direct effect, so that the behavior of the crust will give measurable information on the microstructure of the superficial beds. Nishimura [ll]placed six pairs of horizontal pendulums along the active fault of Beppu (3G016’N, 131”30’E, Kyushu) placed a t intervals from 400 to 1800 meters starting from the fault. Figure 12 shows, in one part (a) the observed effect at six points and, in the other part (b) the residue after elimination of the direct and indirect effects, the latter calculated by Boussinesq’s method. The points D and E show a very curious anomaly. But the region to the south of the fault ( T T )is mountainous and built of ancient volcanic rocks (point F ) , while the region to the north is an alluvial plain (points ABCD). An important subsiding movement of the plain has been detected which actually still continues according to the results of precise leveling. From this phenomenon Nishimura estimates that the fault behaves

433

EARTH TIDES

like the boundary of an elastic plane, with the result that certain neighboring points bend toward the fault rather than in the direction of the bay. This is shown in Fig. 12 by the arrows which indicate the time when high tide occurs in the bay. (The center of gravity of the block would be found to the north of the station and of the overloading water mass. The fault constitutes the border of this block.) Examining the records of the German stations a t Marburg, Pillnitz, Beuthen, and Berchtesgaden, Tomaschek considers that the Alpine chain is manifested by a predominance of north-south flexures. Similarly, studying the gravimetric observations which he has made in Great Britain (Peebles and Kirklington) the same author described these phenomena as follows [24].

0.005”

74 -.,

Bay of Beppu

la1

FIG.12A. Deflections observed a t Beppu. Fra. 12B. The same curves corrected for the direct effect and calculable indirect

effects (TT = fault).

“The tectonic block to which these stations belong is the Caledonian structure, comprising the Welsh mountains and the Pennines. Kirklington is situated in the Eastern basin, whereas Peebles rests on the northern spur of the Pennines. Observations with horizontal pendulums performed at Winsford (53’ 12’ N, 02” 20’ W) show, as do the observations of Gnass in the Alps, that this tectonic structure acts as a sort of long rigid bar, which is more easily tilted round an axis parallel to its length than an axis perpendicular to it. Peebles is situated on the longitudinal axis, whereas Kirklington lies on an axis which is perpendicular to the arc Welsh Mountains-Pennines. We have therefore to expect a different response to the loading tides in such a sense that Kirklington should be more influenced than Peebles. The higher value of 6 in Kirklington indicates that the movement is opposite to the loading of the Irish sea, that is, that the axis of this movement coincides nearly with the region of greater vertical thickness of the mountains.”

434

PAUL J. MELCHIOR

This observation is similar to that of Nishimura. By the application of Corkan's method t o the observations a t Freiberg and BrBzov6 Hory, Melchior shows that the indirect effects diverge greatly, notwithstanding the closeness of the two stations (distance: 145 km). The representative ellipses of the wave Mz due to indirect effects have their major axes perpendicular and the direction of revolution of the base of the vertical is reversed [15]. I n the course of deducing the indirect effects from the difference between the observed effect and the theoretical direct effect-the value of the coefficient being taken as 0.72-Professor Tomaschek had previously pointed out an analogous divergence between the two stations a t Freiberg and Pillnitz, which are very close to each other (distance: 40 km). It is established, therefore, that Pillnitz and BrBzovB Hory behave in exactly the same way. This obviously suggests a certain independence of movement of the various continental regions, constituting as many independent blocks. Unfortunately such an interpretation remains qualitative. 9.2. Atmospheric Efects

One can readily imagine that moving air masses can affect the direction of the vertical and the gravitational intensity just as is the case with the mobile ocean masses. As early as 1882 this effect was suspected, and G. H. Darwin wrote that i t did not appear impossible that, a t some future date, when very precise tidal and barometric observations could be attained, an estimation could be made of the modulus of rigidity of the upper 500 mi of the earth's mass (see reference [24a]). Assuming that the upper crust has a rigidity.slightly larger than that of glass, this author has calculated for a variation of pressure of 50 mm of mercury an inclination of the surface of the lithosphere by 0.012". In a recent paper by Tomaschek [25] the question has been reopened with the observation of a perturbation of almost 0.05" in the records of the horizontal pendulums a t Winsford simultaneously with the passage of a strong atmospheric perturbation on the British Islands (warm front followed immediately by a cold front and a zone of low pressure). However, the inclination observed is much too strong, and in the opposite sense, to be that given by the formulas of Darwin. The effect would likely be associated with the tectonic structure and of the type described above. Tomaschek envisages blocks with diameters of the order of 1000 km and explains the observations by stating that the Winsford station, as well as the low pressure center (58"N), are to the south of the center of gravity of the block and that Winsford is raised with the southern part of the block.

EARTH TIDES

435

10. THEORY OF ELASTIC DEFORMATIONS OF THE EARTH 10.1. Conclusions Drawn from the Observations of Various Efects of Earth Tides One can sum up the results of all relative measurements of earth tides which we have just described as follows: =

6

=

A

=

1 1 1

+ k - h = 0.706 f 0.01 + h - 3k/2 = 1.20 f 0.02 + k - 1 = 1.13 f 0.10 1

=

0.05 f 0.03

The two first relations, which are the best established, give

k

=

0.188 & 0.06

h = 0.482 f 0.07

and, admitting the results of the extensometer measurements, we obtain A = 1.13

i-0.09

so t ha t the four methods of measuring earth tides give coherent results. 10.2. Law of Elasticity Observations of deformations of the globe are related to various phenomena: earthquakes, tides, movements of the instantaneous pole of rotation with respect to the globe, isostasy. The periods involved in earthquakes and tides permit treatment of the phenomena as purely elastic, the raising of Fenno-Scandia under isostasy must be treated aq a viscous phenomenon. Between these two extremes with great differences in period it is necessary to resort to elastico-viscous theories which are not entirely satisfactory and do not conform to laboratory experiences [I]. Their application t o the movement of the pole, the period of which is about 1.2 years, is not very good and this movement has still not been satisfactorily explained [26]. 10.3. Herglotz Theory We limit ourselves here to the essential elements of the theory of elasticity as applied to earth tides. This theory is obviously based on Hooke’s law (proportionality between stress and deformation) and its object is to express Love’s numbers, h, k, I , as a function of the elastic constants and the density of the earth’s interior. The first attempt was made by Kelvin who adopted, as a first approxi-

436

PAUL J. MELCHIOR

mation, a globe which was homogeneous in density and modulus of elasticity and perfectly incompressible. Some simple and frequently reproduced formulas resulted:

but these formulas will not explain the observed phenomena since 0.73 will givep = 10 * 10” while 6 = 1.18 willgivep = 1.5 * loll cgs. Herglotz advanced the theory considerably by making the density and the modulus of rigidity functions of the distance, T , to the center of mass, the material remaining perfectly incompressible. He thus arrived at a differential equation of the sixth order which can only be integrated for certain particular cases. It is interesting to note that this equation is only a generalization of Clairaut’s equation relating to the flattening of concentric liquid layers in rotation, and it will revert to this equation if we set p equal to zero. This remark explains why forms of the type of Roche have been adopted for the distribution of modulus of rigidity and density within the earth in attempts to solve the Herglotz equation. However, these laws are only speculative and have no relation to the internal structure of the earth. Some applications have been made using Wiechert’s model by Jeffreys and by Rosenhead, assuming that the core and the mantle are homogeneous in density and elasticity. Finally, a very remarkable study has been made by H. Takeuchi [27] who developed the Herglotz equations by considering the compressibility of the earth. He succeeded numerically integrating for different models with the following characteristics: y =

Model 1 : Bullen’s second density law (published in 1940). Compressibility and rigidity from seismic wave velocities of Gutenberg, Richter, and Wadati; zero rigidity in the core. Model 2: Bullen’s first density law (1936). Compressibility and rigidity from Jeffreys’ seismic wave velocities from 0 to 500 km, discontinuity a t 500 km, then Gutenberg’s and Wadati’s velocities. Rigidity zero in the core. Models 3, 4, 5, 6: The same constitution for the mantle as in Model 2, but in the core (from 2900 km to center) : X = 11 * 1OI2 Model Model Model Model

3 4 5 6

p = p =

lo7 lo9

p = loll p =

1013

EARTH TIDES

437

The numerical results are as shown in TabIe VIII. Takeuchi states that the results are essentially constant for core rigidities between 0 and lo9. The results from the most recent observations indicate that the best value which may be expected is between lo9 and 10". This table shows principally, in our opinion, that the tidal observations, disturbed as they are by the indirect effects, and the motion of the pole (whose period appears as variable), are not known with sufficient precision to permit accurate deductions on the internal constitution of the earth. TABLE VITI. Theoretical values of Love's numbers for several earth models. Model

k h klh 1 Y

8 A Pcore

1

2

3

4

5

6

0.290 0.587 0.494 0,068 0.703 1.152 1.22 0

0.281 0.606 0.464 0.082 0.675 1.188 1.20 0

0.275 0.601 0.457 0.081 0.674 1.189 1.19 10'

0.275 0.600 0.458 0.081 0.675 1.188 1.19

0.243 0.530 0.458 0.083 0.713 1.167 1.16 10"

0.055 0.109 0.504 0.092 0.946 1.127 1.96 10'8

109

The work of Takeuchi has advanced the theory beyond the observations and makes better observations most desirable. 20.4. Note on the Relation between the Numbers h and k Kelvin obtained, as stated, a simple relation between Love's numbers, 3h/5 but by assuming that the earth is homogeneous from the standpoint of density and rigidity. Melchior [29] has found that it is possible to reach a simple relation between these numbers without this hypothesis. This is done by graphical integration based on Bullen's density distribution but keeping the hypothesis that the elastic deformations are homothetic with respect to the center of the earth. It is shown that in all casea k / h is less than 0.6, and the value established by this author is

k

=

(10.2)

k

= /2 l/h

Developing this argument G. Jobert [30] has shown that if homothety of the deformations is abandoned, one can no longer determine k / h but the value W is an upper limit of the relation. This condition is an interesting criterion and it can be shown that, among all the efforts to integrate the Herglotz equation, only those of Boaga (trinomial law of densities,

438

PAUL J. MELCHIOR

Roche type of rigidity law) and those of Takeuchi fulfill this condition

I %.jh

(10.3) (cf. Table V). 10.6. Dynamic Efects of the Core

A serious objection has been raised to developments based on the assumption of a fluid core. The inertia of the fluid has been neglected in the theories, postulating that rigidities must be high; thus it is incorrect to state then that the rigidity is zero in the core. Jeff reys, who developed this argument, arrived at very significant conclusions. It is known, from Poincard and Hough, that if the core were fluid and the crust completely rigid the Eulerian period would not lengthen but shorten (to about 270 days). Jeffreys has shown that the elasticity of the mantle reduces the movements of the core and that agreement can be restored between the data of pole motion, tides, and seismology by assuming a modulus of rigidity for the mantle of 19 10l1 dynes/cm2. However, a new difficulty arises; the fluidity of the core has an influence on the luni-solar nutation. The theoretical amplitude calculated for the nutation by classical mechanics is 9.2272” while the values given by observations are systematically less, the mean being 9.2109”. The fluidity of the core reduces the theoretical value but in such large proportions that the result this time is too low [as]. Jeffreys and Vicente [19] demonstrated moreover, for the case of a fluid core, that the diurnal tides do not follow the static law. The diurnal oscillations, which may be represented by tesseral harmonic functions, affect the position of the pole of inertia and induce movements in the core. The dynamic theory applied to these waves by Jeff reys and Vicente leads to different values of Love’s numbers, according to the oscillations studied: Semidiurnal oscillations Diurnal oscillations K1

P

0 00

Y

s

0.704 0.714 0.676 0.658 0.695

1.152 1.183 1.209 1.221 1.196

The experimental confirmation of this important discovery will be sought during the International Geophysical Year by observations on the 45th parallel where the diurnal oscillations are a maximum. The variations of level observed in the Turnhout boring [23] appear to show a first confirmation, as previously mentioned. The question remains and, as can be seen, it is far from being resolved

EARTH TIDES

439

satisfactorily. A great number of phenomena are involved and the effect of each is a t the extreme limit of instrumental accuracy. The unknown constitution of the core of the earth is a great obstacle, and recent discoveries by Bullen with regard to it are of the greatest importance. The other part, the problem of the movement of the pole (and particularly the variations of the period), is not resolved in a satisfactory manner.

11. EFFECT OF EARTH TIDESON THE SPEEDOF ROTATION OF EARTH

THE

A new theme has become ripe for discussion. It deals with the influence of the earth tides on the earth’s rotation. As early as 1928, Prof. H. Jeffreys suggested the possibility of this influence and giving it a numerical evaluation [31]. It is essential to state first, th at these variations in speed result exclusively from the largest moment of inertia C, and this constitutes a sufficient approximation. Given th at only deformations of the zonal type are capable of affecting the value of C , we will only consider here long period tides. The process of very simple calculation used by Jeffreys consists of writing the additional potential engendered by the deformation first 2.s a fuiic,tion of the luni-solar potential and of the number k , then as a function of the variations of the moments of inertia, in order to identify the two expressions with the introduction of the condition of incompressibility. I n 1938, Andersson [32] applied Jeffreys’ method in a detailed fashion, introducing all the zonal waves with long periods. Integration shows that the longer the period, the more noticeable the cumulative effect. Since then, the techniques of time services have undergone a veritable revolution (quartz crystal clocks, the photographic zenith tube). The obvious increase of precision demonstrates the variations of the earth’s speed of rotation with considerable reliability. Professors Mintz and Munk [33] have tried to link the semiannual component of the change of speed of the earth’s rotation with the Ssa tide (semiannual tide). They have resumed the theoretical development along a line which seems to us less elegant than that of H. Jeffreys, for it introduces the number h in place of the number k (these authors consider the distribution of the heights of the earth tide a t every point of the globe). This necessitates further the somewhat disguised introduction of the relation k = 0.486h The coefficient in this equation is not yet known with sufficient precision. Thus, Mintz and Munk arrive a t apparently the same numerical

440

PAUL J. MELCHIOR

results as those obtained by the method of Jeffreys, Anderson, and Stoyko [34] but the latter retains the advantage of introducing the number k directly, leaving no room for any uncertainty concerning the value of the relation k/h. Mintz and Munk showed that the liquid core could be considered absent; their calculation came again to adopt lc = 0.30. Under these conditions the amplitudes of the different waves are, in milliseconds:

Mf (fortnight1y)Tl.0 M m (monthly) 1.1 fl (18.6 years) 197.0

Ssa (semiannual) Sa (annual)

5.8 2.3

One might have surmised that this effect would be too weak for actual detection. However, Dr. W. Markowitz demonstrated it in observations of the photographic zenith tube in Washington and Richmond during the years 1951-1954 [35]. He found the following terms, expressed in milliseconds:

Mf:f 1 . 2 sin 2L M m : + 0 . 7 sin U

+ 0 . 4 cos 2L = 1 . 3 sin 2(L + 9") - 0 . 2 cos U

=

0 . 7 sin (U - 16")

where L is the mean*longitude of the moon (13.6 days) and U is the mean anomaly of the moon (27.6 days). For the annual and semiannual terms, Markowitz has obtained amplitudes of 10 msec and 30 msec, respectively. The annual term is almost entirely due to meteorological effects but it is seen that the Ssa tide accounts for 60% of the observed semiannual effect. 12. PROGRAM OF THE INTERNATIONAL GEOPHYSICAL YEAR

Great developments in the observation of gravimetric tides are foreseen during the International Geophysical Year [ 191. The Commission of Gravimetry of the CSAGI (Special Committee for the International Geophysical Year) has considered that the time variation of g responds to the spirit in which the IGY was conceived and has recommended the organization of concerted measurements. These measurements will be made using horizontal pendulums, Michelson tubes, extensometers, and especially, gravimeters having a precision of at least 0.01 mgal and automatic registration. The uninterrupted duration of the measurements will in no case be less than 31 days, permitting the application of Doodson's method of harmonic analysis, which can be considered as the most selective. These measurements will be made simultaneously for groups of stations situated in related tectonic zones in order to be able to discuss the indirect effects on the basis of very detailed information.

EARTH TIDES

441

During this campaign, use will be made of gravimeters of recent construction such as the Askania gravimeter GS 11, which has a sensitivity of 0.01 mgal (Fig. 11), and special gravimeters constructed for the study of earth tides such as that of Ichinohe which has already been mentioned and that of LaCoste-Romberg [21] which has a precision of nearly 0.001 mgal. In addition a number of gravimeters of old types have been modified by specialists and will permit, without doubt, the attainment also of a microgal [21]. Thus, important results may be expected from this world-wide effort. LIST OF SYMBOLS

f universal gravitational constant 2

9 T

U

V m

D W2

t e d h k 1 y = l - k + h

A = l + k - l 6 = 1

+ h - 3k/2 E K K

I L

x,

P P

zenith distance of a n astronomical body (sun or moon) acceleration of gravity radial distance mean earth radius terrestrial potential mass of attracting body (sun or moon) cubical dilatation potential of the exterior forces amplitude of the static tide colatitude latitude first number of Love second number of Love third number of Love factor affecting the amplitude of the crustal tides and the deflections of the vertical with respect to the crust factor affecting the amplitude of the deflections of the vertical with respect to the axis of the earth factor affecting the amplitude of the variations of gravity amplitude of theoretical tide amplitude of observed tide phase of observed tide amplitude of indirect effects phase of indirect effect!s Lam& constants density of the interior of the earth

REFERENCES A practically complete bibliography of the discussion will be found in reference [I] as well as in the general reports on earth tides 121 (IUGG, Association of Geodesy). 1. Melchior, P. J. (1954). Les mardes terrestres. Obs. Roy. Belg. Monographies 4, 134 pp. 2. Lambert, W. D. Rapports g6nCraux sur les mar6es terrestres. Association Internationale de GkodBie, successive assemblies of the IUGG. 3. Love, A. E. H. (1911). “Some problems of Geodynamics.”

442

PAUL J. MELCHIOR

4. Aksentjeva, Z. N. (1948). Sur les marbes du Lac Ba’ikal. T r u d y Poltavskoi Gravirnetritcheskoi Obs. 2, 106-120. 5. Melchior, P. J. (1956). Sur I’effet des mardes terrestres dans les oscillations du niveau du Lac Tanganika A Albertville. Obs. Roy. Belg. Commun. 96, Sdr. Gdophys. 36. 6. Michelson, A. A., and Gale, H. G. (1919). The rigidity of the earth. Astrophys. J . 60, 330-345. 7. Egedal, J., and Fjeldstad, J. E. (1937). Observations of tidal motions of theearth’s crust made at the Geophysical Institute, Bergen. Geojys. Publzk. l l ( 1 4 ) . 8. Zerbe, W. B. (1949). The tide in the David Taylor Model Basin. Trans. Am. Geophys. U n . SO, 357-368. 9. Shida, T. (1912). Horizontal pendulum observations of the change of plumb line a t Kamigamo-Kyoto. Mern. Coll. Sci. and Eng. Kyoto I m p . Univ. 4, 23-174. 10. Boussinesq, J. (1878). Equilibre d’6lasticitb d’un sol isotrope sans pesanteur supportant diffBrents poids. Cornpt. rend. 86, 1261-1263. 11. Nishimura, E. (1950). On earth tides. Trans. Am. Geophys. U n . 31(3), 357-376. 12. Rosenhead, L. (1929). The annual variation of latitude. Monthly Not. Roy. Ast. SOC.Geophys. Suppl. 2, 140-170. 13. Doodson, A. T., and Corkan, R. H. (1934). Load tilt and body tilt at Bidston. Monthly Not. Roy. Ast. SOC. Geophys. Suppl. 9, 203-212. 14. Corkan, R. H. (1953). A determination of the earth tide from tilt observations a t two places. Monthly Not, Roy. Ast. SOC.Geophys. Suppl. 6, 431-441. 15. Melchior, P. J. (1957). Discussion du procbd6 de Corkan pour la sdparation des effets directs e t indirects dans les markes terrestres. Obs. Roy. Belg. Cornrnun. 116, S h . Gdophys. 40. 16. Tomaschek, R. (1954). Variations of the total vector of gravity at Winsford. Monthly Not. Roy. Ast. SOC.Geophys. Suppl. 6, 540-556. 17. Picha, J. (1956). Ergebnisse der Geaeitenbeobachtungen der festen Erdkruste in Brbzovb Hory in den Jahren 1936-1939. Trav. Znst. Gdophys. Acad. Tchdcosl. Sci. 42, Gcofys. Sbornik. 18. Sassa, K., Osawa, I., and Yoshikawa, S. (1952). Observation of tidal strain of the earth. Disaster Prevention Research Znst. Kyoto Univ. Bull. S(l), 1-3; Osawa, I. (1952). Observation of tidal strain of the earth by the extensometer. Disaster Prevention Research Znst. Kgoto Univ. Bull. S(2), 4-17. 18a. Ozawa, I. (1957). Study on elastic strain of the ground in earth tide. Disaster Prevention Research Inst. Kyoto Univ. Bull. 16. 19. Commission pour I’btude des marbes terrestres (1956). Rapports et recommandations, Rdunion de Paris 7 sept. 1956. Obs. Roy. Belg. Cornrnun. 100,Sdr. Gdophys. 36. 20. Lambert, W. D. (1951). Rapport gbnbral sur les marbes terrestres. Presented a t the AssemblCe GEnbrale de I’UGGI B Bruxelles, Association de GdodBsie. 21. Bulletin d’informations sur les mar6es terrestres (1956-1957). P. Melchior, ed. Observatoire Royal Belgique, TJccle. 22. Stoyko, N. (1946). L’attraction luni-solaire e t lea pendules. Bull. Ast. Paris 14, 1-36. 23. Melchior, P. J. (1956). Sur l’effet des marbes terrestres dans les variations de niveau observdes dans lea puits, en particulier au sondage de Turnhout (Belgique). Obs. Roy. Belg. Cornmun. 108, Sdr. Gdophys. 37. 23a. Sperling, K. (1953). Gibt es Gezeiteneinflusse im Erdblforderbetrieb? Erdiil u. Kohle 6(8), 446-449.

EARTH TIDES

443

24. Tomaschek, R. (1952). Harmonic analysis of tidal gravity experiments at Peebles and Kirklington. Monthly Not. Roy. Ast. SOC.Geophys. Suppl. 6, 286-302. 24a. Darwin, C. H. (1907). On variations in the vertical due to elasticity of the earth’s surface. Sci. Papers I, 448. Cambridge Univ. Press, London. 25. Tomaschek, R. (1953). Non-elastic tilt of the earth’s crust due to meteorological pressure distributions. Geojk. Pura A p p l . 26, 17-25. 26. Melchior, P. J. (1955). Sur l’amortissement du mouvement libre du p81e instantan6 de rotation B la surface de la Terre. Atti. accad. naz Lincei cl. sci. fis. mat. nut. Se?. [8]19(34), 137-142. 27. Takeuchi, H. (1950). On the earth tide of the compressible earth of variable density and elasticity. Trans. Am. Geophys. Un.31 (5), 651-689. 28. Jeffreys, H. (1949). Dynamic effects of a liquid core. Monthly Not. Roy. Ast. Soe. 109(6), 670-687; (1950). Ibid. 110(5), 460-466; Jeffreys, TI., and Vicente, R. 0. (1957). The theory of nutation and the variation of latitude. Monthly Not. Roy. Ast. SOC.117(2), 142-173. 29. Melchior, P. J. (1950). Sur l’influence de la loi de r6partition des densit6s B l’inthieur de la terre dans les variations Iuni-solaires de la gravit6 en un point. Geojis. Pura Appl. 16(3-4), 105-112. 30. Jobert, C. (1952). Mardes terrestres d’un globe fluide hCt6rogBne. Ann. gbphys. 8(1), 106-111. 31. Jeffreys, H. (1928). Possible tidal effects on accurate time keeping. Monthly Not. Roy. Ast. SOC.Geophys. Suppl. 2, 56-58. 32. Andersson, F. (1937). Berechnung der Variation der Tagesliinge infolge der Deformation der Erde durch fluterzeugende Kriifte. A l k . Mat. Ast. Fys. 26A, 1-34. 33. Mints, Y., and Munk, W. (1954). The effect of winds and bodily tides on the annual variation in the length of day. Monthly Not. Roy. Ast. SOC.Geophys. Suppl. 6(9), 566-578. 34. Stoyko, N. (1951). La variation de la vitesse de rotation de la Terre. Bull. Ast. 16(3); (1950). Sur l’influence de l’attraction luni-solaire et de la variation du rayon terrestre sur la rotation de la Terre. Compt. rend. 230, 620-622. 35. Markowitz, W. Private communication to the author.

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AUTHOR INDEX Numbers in brackets are reference numbers and are included to assist in locating references in which the authors’ names are not mentioned in the text. Numbers in italics indicate the page on which the reference is listed. A Adel, A., 57, 58, 105, 106 Angstrom, A., 82, 107 Aitken, J., 65, 106 Aksentjeva, 2. N., 403[4], 431[4], 442 AlfvBn, H., 116, 122, 159, 170, 174, 176, 190[27], 211, 213 Almond, M., 278[103], 346 Amble, O., 361[12], 388 Anderson, F., 439, 443 1 Anderson, V. G., 81, 85[130], 107 Andrews, E. B., 225[19], 342 Aristotle, 110, 210 Armellini, G., 284, 347 Arnold, P. W., 58, 106 Arons, A. B., 201261, 103 Astapovich, I. S., 1141211, 211, 294[139], 32811651, 348, 349 Aubin, E., 46[60], 104

B Babcock, H. D., 174, 213 Babcock, H. W., 174, 213 Baer, F., 21[29], 103 Baker, G., 250, 344 Baldwin, R. B., 309, 310[147], 348 Barrett, E., 77, 107 Barringer, B., 220, 342 Barringer, D. M., 313[159], 314, 316, 325,

Bennett, W. H., 148, 149, 151, 812 Berry, F. A., 389 Berwerth, F., 335, 350 Biot, E., 33311841, 350 Birkeland, K., 111, 210 Birkhoff, G., 324[170], 349 Blaauw, A., 306, 348 Blackwelder, E., 317[163], 326, 349 Blackwell, D. E., 159, 182[53a], 189[53a], 212

Blanchard, D. C., 20[26], 75, 76[122], 103, 107

Blifford, I. H., 93, 108 Block, L., 177, 213 Bodenstein, M., 571871, 59[87], 105 Bornstein, R., 195[108],215 Boldyreff, A. W., 324, 34.9 Booker, H. B., 191, 214 Boothroyd, S. L., 283, 291, 347 Boussinesq, J., 412, 414[101, 442 Bowen, E. G., 270, 271, 272, 273, 346‘ Bowen, I. G., 51[74], 105 Bowley, H., 219, 34%’ Bracewell, R. N., 354[2, 3, 4, 5, 61, 388 Breuil, H., 333, 350 Brewer, A. W., 51, 52, 56, 105 Brezina, A., 219[4], 237[34],334, 341, S43, 350

Brodin, G., 77[126], 107 Brooks, C. E. P., 370, 371, 389 Brouwer, D., 269, 3.46 Brown, H. S., 241, 343 Buch, K., 46, 48, 104 348,349 Buddhue, J. D., 41[53], 104, 264, 265, Bartels, J., 168[64], 183[64], 190[64], 213 266, 3.46 Bates, D. R., 58, 106, 143, 193, 203, 211, Burkhardt, H., 19, 102 214 Behr, A., 159, 171151, 521, 182151, 521, Burr, E. J., 354[7], 388 Byers, H. R., 28, 103 189[51, 521, 212 445

446

AUTHOR INDEX

C Callendar, G. S., 45[571, 46[57], 47, 104 Canton, J., 110, 210 Capron, J. R., 111[8],210 Carmichael, R. D., 287[125], 347 Carruthers, N., 370, 371, 389 Carslaw, H. S., 352[1], 388 Cartailhac, E., 333, 360 Cauer, H., 18, 21, 66, 68, 71, 102, 106, 107 Chamberlain, J. W., 114[22],148[35], 193, 194, 195\105], 196[104], 198[105], 204, 205, 206, 211, 214, 216 Chambers, G. F., 333[183], 360 Chambers, L. A., 38[50], 69, 96[50], 104 Chant, C. A., 293, 348 Chapman, R. M., 61, 106 Chapman, S., 113, 147, 158, 160, 162, 164, 165, 166, 168, 169, 177, 183, 190, 221, 212, 21s

Cherwell, Lord, see Lindemann, F. A., 216

Cholak, C. E., 38[501, 69[50], 96[50], 104 Clegg, J. A., 282[112], 346 Code, A. D., 306[142], 348 Coghlan, H. H., 335[193], 360 Cohen, E., 338, 360 College, M., 85[137], 108 Corkan, R. H., 414, 415, 416, 442 Coste, J. H., 69, 70, 106 Courtier, G. B., 69, 70, 106 Cowling, T. G., 176, 213 Craig, R. A., 50[69], 106 Crooks, R. N., 72[120], 93[120], lOl[l20], 107

Crozier, W. D., 27[43], 103, 272, 346 Culbertson, J. L., 251[59], 344 Cunningham, A., 334[185], 360

D Daly, J. W., 258[65], 344 Darwin, G. H., 434, 443 DaubrBe, G. A., 332[178], 349 Davidson, I. A., 282[112], 346 Davies, J. G., 278[103], 346 Davis, L., 182, 213 DeBeck, H. O., 258[68], 346 Dedebant, G., 377[17], 389 De Mairan, J. J. D., 110, 210

Desch, C. H., 335, 360 Dessens, H., 5[5], 102 DeViolini, R., 294[140], 348 Dewey, F. P., 328, 329, 349 Dhar, N. R., 68, 106 Dodson, H. W., 115[23], 148[35], 211 Dodwell, G. F., 289[127], 347 Doherty, D. J., 5[2], 9[2], 101 Doodson, A. T., 414, 416, 442 Drischel, H., 82, 84, 85[131], 107 Dubin, M., 190, 205, 21.4 Dunbar, A,, 251[59], 344

E Eaton, J. H., 6511051, 106 Eaton, S. V., 65[105], 106 Edgar, J. L., 60, 96[98], 106 Edlund, E., 111, 210 Effenberger, E., 12, 102 Egedal, J., 408, 442 EgnBr, H., 21[32], 62, 63[102], 64, 66[32], 78[127], 88, 89[141], 90, 91, 92[141], 103, 106, 107, 108 Ehmert, A., 51, 53, 56, 106 Ehmert, H., 53, 106 Ellis, B. A., 69, 70, 107 Elsasser, H., 159, 171[51, 531, 182151, 531, 189[51, 531, 212 Elsasser, W. M., 185[84], 213 Emanuelsson, A., 88, 89, 90[141], 92, 108 Epstein, P. S., 290, 347 Eriksson, E., 48[63], 49, 62[102], 63[102], 64[102], 72, 82, 83[132], 84, 85[132], 87[1321, 88, 89[141], 9011411, 9211411, 104, 106, 107, 108

Esclangon, E., 222, 342 Evans, E. W., 2251191, 342

F Facy, L., 21, 76, 88, 103, 108 Farrington, 0. C., 225[20], 237[34], 242, 245,342, 343 Fath, E. A., 224, 342 Faucher, G. A., 43, 44, 10.4 Fenner, C., 289[1271, 347 Fenton, K. B., 182[75], 189[75], 213 Ferraro, V. C. A., 155, 158, 160, 162, 166, 168, 212, 213

447

AUTHOR INDEX

Finnegan, B. J., 237, 250, 343, 344 Fisher, E. M. R., 72[120], 93[120], 101 [120], 107 Fisher, W. J., 295[141], 348 Fjeldstad, J. E., 408, 442 FjZrtoft, R., 384, 389 Flach, E., 99, 108 Flohn, H., 19, 102 Fonselius, S., 49, 104 Foote, A. E., 313, 348 Foote, W. M., 250[55], 344 Forster, H., 18[23], 102 Foster, J. F., 251, 344 Fournier d’Albe, E. M., 22, 25, 103 Franklin, B., 110, 210

G Gale, H. G., 407, 442 Gartlein, C. W., 112, 211 Gerhard, E. R., 18, 65, 70[24], 102 Gifford, F., Jr., 376, 378[16], 589 Glavion, H., 40[52], 104 Gmelin, L., 62[101], 63[101], 65[106, 1071, 106

Gnevyshev, M. N., 149, 212 Goddard, R. H., 234, 343 Gotz, F. W. P., 49, 53, 54[81], 56, 104,

Harper, H. J., 85[137], 108 Harrison, J. M., 311, 348 Hart, H. C., 220, 342 Harvey, H. W., 76[125], 107 Hawkins, G. S., 273, 346 Haxel, O., 93, 108 Hedeman, E. R., 148[35], 211 Heiland, C. A., 258[66], 344 Henderson, E. P., 225[22], 246, 342, 344 Hettick, I., 87, 108 Hey, M. H., 225[22],235[30],311,3~2,343 Hogberg, L., 82, 107 Hoffleit, D., 264, 3.46 Hoffmeister, C., 269, 271, 3.46 Horan, J. R., 291, S47 Houghton, H., 87, 108 Hoyle, F., 159, 174, 177, 178, 181, 182, 212 Hulburt, E. O., 148, 190, 21.2, 214 Hutchinson, G. E., 45[58], 46[58], 47, 48 [58], 61[58], 67, 84, 104

I Isono, K., 24[381, 29, 103 Israel, H., 5[3], 6[3], 102

J

105

Gold, T., 186, 214 Goldberg, L., 57, 61[99], 67[111], 68, 106 Goldman, S., 389 Goldschmidt, V. M., 241, 343 Goldstein, E., 111, 210 Goody, R. M., 57, 58, 106 Gorham, E., 22, 87, 103 Gottlieb, M. B., 192[98],214 Goubau, F., 270, 345 Griffing, G., 193, 203, 214 Griffith, H. L., 378[18],389 Grogan, Robert M., 336[98], 350 Gustafson, P. E., 8311341, 107

H Eager, D., 308[145], 322, 348 Haggard, W. H., 389 Hall, F., 354[8], 380, 388 Harang, L., 193, 194, 214 Harkins, W. D., 240, 343

Jacobi, W., 15[19],102 Jacobs, M. B., 70[118], 107 Jakosky, J. J., 258[65], 344 Jeffreys, B., 389 Jeffreys, H., 389, 438, 439, 443 Jobert, G., 437, 443 Johnson, D. W., 225[19], S@ Jones, W. B., 225[23], 228, 342 Joseph, H. M., 354[9, 101, 388 Junge, C. E., 5[4], 6[8], 8[4, 81, 9141, 10 [ll],12[4, 8, 151, 15[17, 18, 191, 16 [17], 22, 25, 27[42], 29181, 30[8, 11, 491, 341111, 35[11], 60, 62, 64[111, 66, 69[11], 75[15], 79[8], 82[8], 83[1341, 93[37], 102, 103, 104, 107 Junner, N. R., 334[186], 360

K Kaiser, T. R., 273, 282[961, 346 KalIe, K., 92, 108

448

AUTHOR INDEX

Kasper, J. E., 192, 214 Kate, M., 69, 70, 71, 107 Katzman, J., 182[75],189[75],213 Kay, R. H., 51, 52, 56, 106 Kent, R. H., 290, 347 Khan, M. A. R., 33511941, 360 Kientsler, C. F., 20[26], 105 Kiepenheuer, K. O., 115[25],211 Kingsborough, E. K., 332, 360 Kinnicutt, P., 336, 360 Kohler, H., 15[16], 106 Koroleff, F., 491641, 104 Kovasznay, L. S. G., 354[9, lo], 388 Krinov, E. L., 265, 332, 346, 360 Krogh, M. E., 57, 106 Krumbein, W. C., 40[51], 104 Kulik, L. A., 224[17], 323[165],:342, S49 Kumai, M., 76, 107 . i Kuroiwa, D., 29, 74, 75, 104: Kvasha, L. G., 236, 237, 343

-

1 Lacroix, A., 218, 341 Lambert, W. D., 430, 441, 442 Landolt, H. H., 195[108],216 Landsberg, H. E., 5111, 11, 18[1], 19, 75 [l],80, 101, 107,272[90], 346 Landseer-Jones, R. C., 159, 212, 215 Langmuir, I., 79, 107 LaPaz, L., 222[12], 228[25], 235[29], 245 [44], 246[49], 250[49],251[12, 581, 253 [58], 254[60], 255[63], 257[58], 263 [72], 283[29], 284[119], 286[29, 1251, 288[29, 581, 290[29], 291[29], 310 [152], 311[154],316[63],319[164],323 [165, 1661, 324[167, 1691, 325[1741, s Q J 343,344,345,347,34, 349 Larson, T. E., 87, 108 Lebedinski, A. I., 178, 813 Leeflang, K. W. H., 88, 89, 92, 108 Lemstrom, K. S., 111, 204, 210 Leonard, F. C., 224[16], 236, 237, 238, 239, 294[140],337, 8-42, 34S, 348, 360 Liesegang, W., 84[136], 108 Lindemann, F. A., 112, 113, 148, 160, 210

Lippert, W., 15[19], 102 Lockhart, L. B., Jr., 93[144], 108

Lodge, J. P., 21[29], 22, 26, 103 Lomonosov, M. V., 110, 210 Love, A. E. H., 400, 441 Lovell, A. C. B., 234[28], 278, 282[1041, 343,346 Lowell, P., 293, 347 Lust, R., 188[87, 881, 214 Lynch, D. E., 101[151], 108

M MacCarthy, G. R., 223, 342 McDonald, J. E., 380, 389 McDougal, D. P., 324[170], 349 Machado, E. A. M., 377[17], 589 McKinley, D. W. R., 220, 281, 282, 283 [llsl, '4'J 346, 34r Maclaren, M., 334[186], 360 McMaster, K. N., 21[28], 103 McMath, R. R., 61[99], 106 Mallery, G., 331, 349 Malmfors, K. G., 177, 213 Maria, H. B., 190, $14 Markowitz, Pi.,440, 443 Martyn, D. F., 170, 213 Mason, B. J., 10[13], 11[13], 20, 21, 102, 103, 273, 346 Mason, M., 258[661, 344 Maxwell, J. C., 163, 2 f 3 May, K. R., 5[6], 102 Meen, V. B., 254[61], 309, 344 Meetham, A. R., 95[146], 96[146], 97 [146], 98[146], 100, 108 Meinel, A. B., 112, 114[22], 194, 198, 211, 816

Melcbior, P. J., 393[1], 403, 410[11, 416, 422[23], 434, 435[1, 261, 437, 438 ~31,441,449,443 Mellor, J. W., 335[190],360 Meredith, L. H., 192, 214 Merrill, G. P., 240, 245, 310[149], 315, 317,343, 348 Meunier, S., 218, 324[2], 341 Meyer, P., 182, 215 Michelson, A. A., 407, $42 Middleton, W. E. K., 360, 388 Migeotte, M. V., 59, 61, 67, 68, 106 Miller, A. M., 223[15], 348 Miller, L. E.,-57[89], 106

449

AUTHOR INDEX

Millman, P. M., 220, 266, 281, 282, 309, 342, 345,346,348 Milne, E. A., 115, 148, 211 Milton, J. F., 38[501, 69[50], 96[50], lo4 Minta, Y., 439, 443 Mohler, 0. C., 61, 106 Moissan, H., 313, 348 Moore, D. J., 10[13], 11[13],22, 25, 102, 103 Morgan, W. W., 306, 348 Mueller, E. A., 57, 106 Munk, W., 439, 443 Munta, A., 46[60], lo4

Petukhov, V. A., 142, 811 Picha, J., 411, 416, 442 Pickering, W. H., 293, 348 Plantb, G., 111, 210 Plass, G. N., 49, 10.4 Poincar6, H., 112, 122, 210 Preston, F. W., 225[22], 342 Price, W. C., 64[103], 106 Prior, G. T., 225[22], 235[30], 311, 3.42, 343 Pugh, E. M., 289[128],324[128, 1701,347, 349 Puiseux, P., 311, 348

N

Q

Neumann, H. R., 29[46], 90, 103 Neven, L., 59, 106 Newton, H. A., 332[178], 349 Nichols, H. W., 225[21], 266[21], 3.42 Nielsen, A. V., 285, 347 Nishimura, E., 432, 442 Noddack, I., 241, 343 Noddack, W., 241, 343 Nolan, P. J., 5[2], 9, 101 Nordenskiold, N. A. E., 265, 3.45

0 opik, E. J., 234[28], 248, 266, 273, 275, 279, 280, 281,282, 283, 284,292[133], 293,314,324,343,344,346,346,347, 349 OI’, A. I., 149, 212 Olivier, C. P., 291, 347 Omholt, A., 192, 195, 197, 199, 201, 203, 214,215 O’Neil, R. R., 289, 347 Osawa, I., 418[18], 442 Otake, T., 29, 74, 10.4 Ozawa, I., 420, 442 P Paetaold, H. K., 50[68], 105 Paneth, F. A., 60, 96[98], 106, 246, 257,

344

Panofsky, H. A., 368, 378[18], 388, 389 Parker, E. N., 182[74], 189, 113,214 Penndorf, R., 42, 43[55], 10.4

Quitmann, E., 71, 107

R Ram, A., 68, 106 Randolph, J. R., 225[22], 342 Raphael, M., 33311821, 350 Rau, W., 21, 103 Ray, E. C., 168[65], 213 Regener, E., 50[71], 51, 105 Regener, V. H., 511741, 53, 54, 56, 106 RBmusat, A., 219, S42 Renzetti, N. A., 56[76], 96[76], 981761, 106 Reynolds, W. C., 59, 60, 106 Richard, T. A., 335, 336, 350 Richards, E. H., 84, 108 Rinehart, J. S., 289, 324, 347, 349 Roberts, J. A., 354[6], 388 Rogers, A., 317, 349 Rose, D. C., 182[75], 189[75], 213 Rose, G., 2371341, 343 Rosenhead, L., 413, 442 Rosenstock, H. B., 93[144], 108 Rossby, C. G., 21[32], 66[32], 90, 91, 103 Rostoker, N., 324, 349 Russell, E. J., 84, 108 Russell, H. N., 240, 343

S Sagalyn, R. C., 43, 44, lo4 Sassa, K., 418, 44% Schaefer, V. J., 41, lo4

450

AUTHOR INDEX

Schmidt, A., 168, 21s Schulz, L., 5[3], 6[31, 102 Schumann, G., 93, 108 Schuster, A,, 113, 147, 183, 211, 213 Scott, William, 310, S48 Seaton, M. J., 192, 214, 273[96], 282[961, 346 Seely, B. K., 27, 10s Sheikh, A. G., 334[188], 960 Shida, T., 411, 4 2 Shirl Herr, 258, S46 Shklovski, I. S., 203, 216 Shuman, F. G., 370, 588 Siedentopf, H., 159, 171[51, 521, 182[51, 521, 189[51, 521, 212 Silberrad, C. A., 229[26], 231, 295[261, 349 Simpson, E. S., 219, S42 Simpson, G. C., 24, 10s Simpson, J. A., 182, 189[751, 21s Singer, S. F., 186, 193, 214 Slichter, L. B., 258[66], 344 Slobod, R. L., 57, 106 Slocum, G., 47, 48, 104 Sloss, L. L., 40[511, 104 Smith, J. L., 225[19], S42 Sorby, H. C., 338, 560 Sowerby, J., 335,560 Spencer, L. J., 246, 316, 344, 349 Sperling, K., 423, -4.42 Spilhaus, A. F., 360, 588 Spitzer, L., 116, 125, 126, 148, 151, 211 Stair, R., 501701, 106 Stearn, N. H., 258[66, 681, S44, 346 Stenz, E., 246, S44 Stewart, B., 111, 210 Stewart, N. G., 72[120], 93, 101[1201, 107 Stewart, R. H., 2541611, 3091611, 344 Stomgren, E., 284, 347 Stormer, C., 128, 133, 134, 135, 137, 140, 145, 211 Stoney, G. J., 267, 346 Storey, L. R. O., 159, 1711541, 182[541, 189[541, 212 Stoyko, N., 431, 440, 442, 4-63 Suess, H. E., 242, 343 Swanson, C. O., 258[681, 346 Swindel, G. W., 2251231, 228, S42 Swings, P., 112, 210

T Takeuchi, H., 436, 44s Taylor, G., 32411701, 349 Teichert, F., 54, 55, 56, 106 Theodorsen, T., 261, S@ Thomas, L. H., 148, 211 Thomson, E., 204, 216 Tomascheck, R., 411, 433, 434, 442, 443 Tonks, L., 149, 212 Turner, J. S., 75[123], 79, 107 Twomey, S., 16[20], 21, 27, 102, 103

U Udden, J. A., 220, 342 Urey, H. C., 241, 242, 309,338, 343, 348

v Van Allen, J. A., 192, 214 Van de Hulst, H. C., 234[281, 343 Van der Hoven, I., 378[18], 389 Van Orstrand, C. E., 328, 329, S49 Vegard, L., 112, 143, 147, 150, 193, 210, 211,214 Vestine, E. H., 183, 184, 185, 215, 270, 546 V'iunov, B. F., 190, $14 Volz, F., 10, 52, 53, 54[811, 56, 102, 106 von Fellenberg, T., 66, 106 von Heine-Geldern, R., 289[128], 324 [1W, 34'7 von Lasaulx, A., 265, 346 von Niessl, G., 276, 546

W Waerme, X., 49[64], 104 Wainwright, G. A., 335, 360 Walshaw, C. D., 57, 58, 106 Washington, H. S., 245, 544 Wasiutynski, J., 310, 548 Watson, F. G., 225[21], 262[71], 266, 283, 338, S/,8, 346, 560 Weaver, J. H., 287[125], S47 Wegener, A., 220, 342 Welander, P., 49, lo4 Wempe, J., 9191, 10% Wheeler, L. B., 27[43], 103

AUTHOR INDEX Whipple, F. L., 194[106], 214, 266, 273, 275, 276, 282, 285[120], 286, 29111241, $461 346,347 Whitford, A. E., 306[142], 348 Wiener, N., 389 Wiens, G., 323[1651, 949 Wilson, C. H., 2581651, 344 Wisman, F. O., 262[70], 346 Witherspoon, A. E., 58, 106 Wolff, P. M., S89 Woodcock, A. H., 6/71, 10, 12[12], 20, 22, 23, 25, 28, 75, 76[122], 102, 103, 107 Woodward, R. S., 267, 346 Wright, H. L., 24, 103 Wiirm, K., 112, 210 Wulf, 0. R., 184, dl9

451

Wylie, C . C., 285, 286, 287, 293, 349[1681, 9d7> 'd9

Y Yamamoto, G., 29, 74, 104 Yoshikawa, S., 418[18], 442

Z Zaslavskii, I. I., 245[47], 344 ZavaritskiI, A. N., 236, 237, 343 Zenncck, J., 270, 345 Zenzen, N., 218[1], 941 Zerbe, W. B., 408, 416, 442 Zimmer, G. F., 335[189], 336[189], 360 Zimmerman, W., 312, 348

SUBJECT INDEX A Achondrites, see Meteorites, achondritic Aerosols, 3 Aitken, 4, 11, 17 attaching of, to cloud droplets, 75 composition of, 19 nature of, 17 origin of, 17 sources of, 18 as condensation nuclei, 73 continental, 29 vertical distribution of, 41 definition of, 3 giant, 4, 6, 12 growth of, with relative humidity, 15, 16 curves for, 16 large, 4 natural, 3 definition of, 3 physical constitution of, 14 size distribution of, 4, 5 curves for, 8, 10, 13 limits of, 12 methods of determination of, 5 volume distribution of, 5, 10, 13 removal of, from atmosphere, 72 by fallout, 72 by impaction, 72 by washout, 72 sea-salt, 20 concentration of, 24-29 distribution of, 90 formation of, 20 role of, with respect to visibility, 24 size distribution of, 22 curves for, 23, 26 source of, 20 vertical mixing over land of, 91 washout through precipitation of, 90 Air pollution, 94, also see Polluted air Aitken particle, see Aerosols, Aitken 452

Ammonia, formation and role in soil, 63, also see under Trace gases Aurora(e), 109-215 electrical nature of, 111 excitation of hydrogen in, 196 main features of, 115 primary electrons in, 192 theory(ies) of, 109 Alfvbn’s, 174 electronic orbits in, 176 Bennett and H u Iburt’s .?elf-focused stream, 148 Chapman and Ferraro’s, 158 cylindrical sheet problem, 166 neutral ionized stream, 158 discharge, 204 Hoyle’s, 177 Lebedinski’s, 178 Lemstrom’s, 111 Maris and Hulburt’s ultraviolet light, 190 Martyn’s, 170 Parker’s, 189 Singer’s shock wave, 186 Stormer’s, 112, 113, 127-146 criticisms and modifications of, 147 equations of motion for meridian plane, 130 forbidden regions in the threedimensional problem, 134 V’iunov and Dubin’s meteor, 190 Wulf and Vestine’s dynamo, 183 typical display of, 116 Auroral arcs, 193 velocity dispersion of incident protons in, 202 Auroral excitation, 191, 194 luminosity curves, 194, 197 role of electrons in, 191 theories of, 191 Auroral forms, 143, 146 homogeneous arcs, 146

453

SUBJECT INDEX

rayed arcs, 146 single rays, 146 Auroral luminosity, 193 incident proton theory of arcs, 193 Vegard’s & Harang’s incident electron theory, 193 Zenith profile, 198 Auroral reflection, 191 Booker’s theory of, 191 Auroral zones, 115, 141

C Carbon dioxide, see Trace gases, atmospheric Carbon dioxide cycle, 46 Carbon monoxide, see Polluted air, main components of Also see Trace gases, atmospheric Charged particle(s), 116 motion of, 116 in dipole field, 128 in inhomogeneous magnetic field, 119 in monopole field, 122 in three dimensions, 136 in uniform electric and magnetic fields, 118 in uniform magnetic field, 116, 117 Stormer’s trajectories in equatorial plane, 131 motion of cylindrical stream of, 161 motion of plane slab of, 160 Chondrites, see Meteorites, chondritic Cloud droplets, 74, 75 size of, 75 Condensation nuclei, 73 size of, 75 distribution of, in clouds and fog, 74 Crustal deformation, effect(s) of, 401 on amplitude of tides, 401 long period, 402 short period in lakes, 402 on deflection of the vertical, 403 on intensity of gravity, variations in, 426

E Earth, elastic constants, see Elastic constants of the earth

moment of inertia, increase of, due to infall of meteoritic material, 267 Earth tides, 391 effect@) of, 417, 418 elastic measurement of, 418 on high precision leveling, 417 on speed of earth’s rotation, 439 on water level in wells, 421 indirect effect of oceanic tides on, 411 empirical method of separation of, 414 numerical evaluation of, 411 measurement of, from large water levels, 407 numerical results of observations of, 409 static theory of, 394 Elastic constants of the Earth, 435 derivation from earth tides, 435 Herglota’ theory, 435 Electric currents between the sun and the earth, 146

F Filtering functions, 354 band pass, 365 elementary, 369 high pass, 365 low pass, 367 Filters, 355 mathematical, see Mathematical filters pre-emphasis, 376 specified frequency response, 363 design of, 363 Formaldehyde, see Trace gases, atmospheric Frequency response(s), 355 negative, physical meaning of, 358 undesirable, suppression of, 358

G Geologic structure of the crust, role in indirect effects, 432 Gravity, variations in, 428 effect of crust.al deformation on, 426 measurements of, 427-432 bifilar gravity meters, 427 clock pendulums, 431

454

SUBJECT INDEX

recovered, 235 mineralogy of, 236, 238, 239 recovery index, 250, 251 siderites, 237 H siderolites, 237 auperficially buried, search for, 253 Halogens, see Trace gases, atmospheric worship of, 334 Herglotz’ equation, 436 Meteoritic abundances, 240, 243, 244 Takeuchi’s development of, 437 Meteoritic accretion, terrestrial, 240 Herglotz theory, 435 Meteoritic artifacts, 335, 336 Horizontal pendulum, 404 Meteoritic crater(s), 307 Hydrogen sulfide, see Trace gases, atmosage of, 323 pheric Barringer, 310, 311 Hyperbolic velocity problem, see MeteBrenham, 326 oritic velocities, hyperbolic diffusion of NiO in soil in, 326 Chubb, 308,311 I criteria for recognition of, 308 Odessa, 310, 319 Indirect effect, see Earth tides, indirect Podkamennaya Tunguska, 323 effect of ocean tides on Meteoritic dust, 264, 269 Intensity of gravity, see Gravity, variainfall of, 269 tions of light streaks due to, 269 Inverse smoothing functions, see Bmoothnoctilucent clouds due to, 269 ing functions, inverse rate of accretion of, 264 Meteoritic falls, 218 1 effects of, 218 ballistic headwave, 222, 223, 224 Level surfaces, deformation of, by lunidamage and injury, 225 solar effects, 396 ionization, 220 Lorents force, 116 seismic, 222 Love’s numbers, 400, 437 sound, 220 frequency of, as function of right ascenM sion of moon, 294 Meteoritic hits, 228 probability of, 228 Magnetic storms, 164, 186, 189 initial phase of, 164 on built-over target area, 230 Parker’s theory of, 189 on human targets, 228 sudden commencement of, 186 on rockets, 234 Meteoritic iron in the earth, vertical disMathematical filter, 356 tribution, 255 frequency response of, 356 Meteorite(s), 217 Meteoritic material, detection and recovachondritic, 237, 338 ery of, 252 aerolites, 237, 245 Meteoritic orbits, 273-278 ballistic potential of, 273 elliptic, 278 chondritic, 337 hyperbolic, 273, 274 classification criteria for, 336 parabolic, 281 contraterrene, 323 Stromgren type problems, 284 deeply buried, detectors for, 258 Meteoritic petroglyphs, 330, 332 effects of fall of, 219 Meteoritic pictographs, 329 mass of, crater-producing, 323 Meteoritic showers, 246, 247 prospecting gravity meters, 427 results of observations, 429

455

SUBJECT INDEX

relation with rainfall peaks, 272 strewn fields of, 246 Meteoritic velocities, 273 elliptic, 277, 278 hyperbolic, 273, 274, 282 B-processes, 306 comet question, 283 non-visual determination of, 286 black smoke method, 290 coma method, 289 inverse acceleration method, 286 radar detection of, 278 limitations of, 278, 281 Meteoroids, 218 Methane, see Trace gases, atmospheric Michelson interferometer on tube for tidal observations, 407

N Nitric oxide, see Trace gases, atmospheric Nitrogen dioxide, see Trace gases, atmospheric Nitrous oxide, see Trace gases, atmospheric

0 Ozone, see Trace gases, atmospheric

P Photographic zenith tube, 425 Pinch effect, hydromagnetic, 151 Pollutants, 95 concentration of, 96, 97 degree of, trends with time, 97 industrial origin, 98 Polluted air, 94 main components of, 94 carbon monoxide, 96 sulfur dioxide, 96 Pollution centers, area of influence around, 98

R Rain d r o m 79. 80 pH v a k e of individual, 80

size of, 80 correlation of, with chloride concentration, 75, 79 Rain water, 81, 88 continental components of, 81 ammonia and nitrogen trioxide, 82 change with latitude of, 82 long time variation of, 83 calcium, 86, 87 sulfur tetroxide, 85 change with latitude of, 85 long term variation of, 85 source of, 86 maritime components in, 88 chlorine, 88 concentration of, 89, 90 magnesium, 88 potassium, 88 sodium, 88 p H values of, 77 Ring current, theories of, 142, 168, 172 Chapman and Ferraro’s, 168 Martyn’s, 172 Stormer’s, 142

S Sassa extensometer, 418 Smog, cause of, 95 Smoke, composition of, 95 Smoothing, 351 binomial, 371 compensation for, 375 by resistance-capacitance electrical filters, 361 by viscous damping of measuring instrument, 361 exponential, 361 phase error due to, 361 Smoothing functions, 354 design of, 363 elementary, 369 frequency response of, 355 inverse, 372 design of, 372 frequency response of, 373 normal curve, 359, 361 Solar streams, 180 nature of, 181 Space filtering, 380

456

SUBJECT INDEX

Space smoothing, 380 Stormer’s theory of aurora(e), see Aurora(e), theories of Stormer’s trajections, 132, 133 forbidden regions, 134 Stromgren-type problem, 284 Sulphur dioxide, see Polluted air, main components of Also see Trace gases, atmospheric

T Tektites, 218 Theodorsen bomb detector, 261 Tides of the earth, see Earth tides Tides of the geoid, 399 Time series, 351 derivatives of, as means of filtering, 378 equalization of, 353 filtering of, 351 inverse smoothing of, 353 pre-emphasis of, 353 smoothing of, 351 Trace gases, atmospheric, 44-71 absorption of, in cloud droplets, 76 ammonia, 59, 61 soil as a source of, 84 carbon dioxide, 45 role of, in radiation balance of earth’s atmosphere, 49 secular changes in concentration of, 47 carbon monoxide, 67

concentration, decrease during precipitation, 81 formaldehyde, 67 hydrogen sulfides, 65 methane, 67 nitric oxide, 59 nitrogen dioxide, 59 nitrous oxide, 57 origin of, 58 ozone, 49 decomposition of, 52 distribution, 50 latitudinal, 50 stratospheric, 50 tropospheric, 51, 54 removal of, from atmosphere, 72 by escape into space, 73 by precipitation, 73 sulfur dioxide, 64 units for concentration of, 44

V Variation in gravity, see Gravity, variation in

W Wash out processes for cleansing of troposphere, 94 Wasiutynski’s theory of lunar craters, 310

Z Zenith telescope, 424