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-5
MENDELEYEV THE PERIODIC LAW
549
one of the higher grades of oxidation, and the compounds of this type are distinguished by their great chemical instability, and split up into an element and the higher compound (for instance, Ag4 2 O). Many elements, moreover, form transition oxides whose composition is
O=2Ag+Ag
N
intermediate, which are able, like 2 O 4 , to split up into the lower and higher oxides. Thus iron gives magnetic oxide, Fe 3 4 which is In all respects (by its reactions) a compound of the suboxide FeO with the
O
oxide Fe 2 O 3
,
The independent and more or less stable saline compounds correspond with the following eight types: R 2 O; salts RX, hydroxides ROH. Generally basic like 2 O, Na 2 O, Hg 2O, Ag2 O, Cu 2 O; if there are acid oxides of this composition they are very rare, are only formed by distinctly acid elements, and even then have only feeble acid properties; for example, C1 2 O and 2 O. .
K
N
R 2 O2 or RO; salts RX2 hydroxides R(OH) 2 The most simple basic salts R2 OX2 or R(OH)X; for instance, the chloride Zn 2 OQ 2 also an .
,
;
almost exclusively basic type; but the basic properties are more feebly developed than in the preceding type. For example, CaO, MgO, BaO,
PbO, FeO, MnO,
R9O3
;
salts
,
&c.
R(OH) 3 RO(OH),
hydroxides
,
the most simple basic
B 2 O3
;
O
bases are feeble, like A1 2 3 , Fe 2 3 , T1 2 8 , The acid properties are also feebly developed; for instance, in but with the non-metals the properties of acids are already .
.
O
O
ROX, R(OH)X3 The
Sb 2 O 3
R2O
RX3
salts
O 3 P(OH) 3
clear; for instance, P 2 4 or 4 or 2 ; salts
RX
RO
,
ROX 2
.
R(OH) 4 , RO(OH) 2 Rarely bases (feeble), like ZrO 2 , PtO 2 , more often acid oxides; but the acid SO 2 , SnO 2 Many inter2> properties are in general feeble, as in mediate oxides appear in this and the preceding and following types. ,
hydroxides
.
CO
R2O 5
;
RO
ROX RO
the types 2 (OH), S, 2 X, RO(OH) 3 , character (X, a halogen, simple or complex; for Cl, &c.) is feeble, the acid character predominates, as P 5 , C1 B , then OK, &c., for example, 5
salts principally of
rarely
.
RX5 The basic .
NO
instance, is seen in
N02 (OK).
3,
N2 O
,
O
O
X=OH,
and hydroxides generally of the type RO 2 X2 RO 2 of an acid character, as SO 3 CrO 3 MnO 3 Basic and rare feebly developed as in UO 3 properties R2 O 7 salts of the form RO 3 X, RO3 (OH), acid oxides; for instance, C12O 7>
R2 O6 or RO 3 salts (OH) 2 Oxides
,
;
.
,
,
.
.
;
Mn2 O 7
.
Basic properties as feebly developed as the acid properties in
the oxides
R 2 O.
very rare type, and only known in OsO 4 and RuO 4 evident from the circumstance that in all the higher types the PO 4 ) and salts with a acid hydroxides (for example, HC1O 4 , 3 2 SO 4 , like the higher saline type RO 4 , not element one of atom contain, single more than jour atoms of oxygen; that the formation of the saline oxides a certain common principle which is best looked for in the is
R2O8
RO 4 A
or
.
.
It is
H
H
governed by fundamental properties of oxygen, and in general of the most simple comRO22H 2 O pounds. The hydrate of the oxide RO 2 is of the higher type RH 4 O4 R(HO) 4 Such, for example, is the hydrate of silica and the salts
=
=
.
MASTERWORKS OF SCIENCE
550
(orthosilicates) corresponding with sponds with the hydrate R 2 O 5 3H 2 O
thophosphoric acid,
PH 3 O 3
RH2 O 4 = RO 2 (OH) 2
.
Si(MO) 4
it,
.
__^
The oxide R 2O 5
= 2RH 3 O 4 = 2RO(OH) 3
The hydrate
RO 3
of the oxide
is
.
Such
=
is
or-
RO 3 H 2 O =
The hydrate
for instance, sulphuric acid.
corre-
corre-
RO 3 (OH) for example, perchloric sponding to R 2 O 7 is evidently RHO acid. Here, besides containing O 4 it must further be remarked that the amount of hydrogen in the hydrate is equal to the amount of hydrogen in the hydrogen corn-found. Thus silicon gives SiH 4 and SiH 4 O 4 , phosphorus PH 3 and PH 3 O4 sulphur SH 2 and SH 2 O 4 chlorine C1H and C1HO4 This, if it does not explain, at least connects in a harmonious and general system the fact that the elements are capable of combining with a greater amount of oxygen, the less the amount of hydrogen which they ,
,
,
.
are able to retain. In this the key to the comprehension of all further deductions must be looked for, and we will therefore formulate this rule
RH
in general terms. An element R gives a hydrogen compound M the hydrate of its higher oxide will be W 4 and therefore the higher oxide will contain 2RHW O 4 #H 2 O R 2 O 8_n For example, chlorine gives C1H, hydrate C1HO4 , and the higher oxide C1 2 O 7 Carbon gives 4 and CO 2 So also, SiO 2 and SiH 4 are the higher compounds of silicon with hydrogen and oxygen, like CO 2 and 4 Here the amounts of oxygen and hydrogen
=
RH O .
CH
.
CH
,
,
.
.
Nitrogen combines with a large amount of oxygen, forming 2 O 5 , but, on the other hand, with a small quantity of hydrogen in 3 The sum of the equivalents of hydrogen and oxygen, occurring in combination with an atom of nitrogen, is, as always in the higher types, equal to eight. It is the same with the other elements which combine with hydrogen and oxygen. Thus sulphur gives SO 3 consequently, six equivalents of oxygen fall to an atom of sulphur, and in SH 2 two equivalents of hydrogen. The sum is again equal to eight. The relation between C1 2 O 7 and C1H is the same. This shows that the property of elements of combining with such different elements as oxygen and hydrogen is subject to one common law, which is also formulated in the system of the elements 1 presently to be described. are equivalent.
N
NH
.
;
a
The hydrogen compounds, RaH, in equivalency correspond with the type of the suboxides, IUO. Palladium, sodium, and potassium give such hydrogen compounds, and it is worthy of remark that according to the periodic system these elements stand near
H
R2 appear, the are also present. Not wishing to complicate the explanation, I here only touch on the general features of the relation between the hydrates and oxides and of the oxides among themto each other,
and that in those groups where the hydrogen compounds
quaternary oxides
R*O
Thus, for instance, the conception of the ortho-acids and of the normal acids be considered in speaking of phosphoric and phosphorous acids. As in the further explanation of the periodic law only those oxides which give salts will be considered, I think it will not be superfluous to mention here the following facts selves.
will
Of the peroxides corresponding with hydrogen peroxide, the known: HaOs, Na2O2 S 2O 7 (as HSCX,?), KaO*, KaOa, CaO2) Ti03 Cr2 7 CuQa(?), Zn02 Rb 2O 3 SrO 2 Ag2 O2 CdO 2 Cs0 2 Cs 2O2 BaO2 Mo 2Or, SnOs, WsOr, UO*. It is probable that the number of peroxides will increase with further relative to the peroxides.
following are at present ,
,
investigation.
,
,
A
periodicity
is
,
,
seen in those
,
now known,
,
,
,
,
for the elements (excepting
MENDELEYEV
THE PERIODIC LAW
g51
In the preceding we see not only the regularity and simplicity which govern the formation and properties of the oxides and of all the compounds of the elements, but also a fresh and exact means for recognising the analogy of elements. Analogous elements give compounds of analogous types, both higher and lower. If 2 and SO 2 are two gases which
CO
closely resemble each other both in their physical and chemical properties, the reason of this must be looked. for not in an analogy of sulphur and
carbon, but in that identity of the type of combination, RX4 , which both oxides assume, and in that influence which a large mass of oxygen always exerts on the properties of its compounds. In fact, there is little resemblance between carbon and sulphur, as is seen not only from the fact that CO 2 is the higher form of oxidation, whilst SO 2 is able to further oxidise into SO 3 , but also from the fact that all the other compounds for example, SH 2 and are entirely unlike both in type and 4 SC1 2 and CC1 4 , &c. in chemical properties. This absence of analogy in carbon and sulphur is especially clearly seen in the fact that the highest saline oxides are of
CH
,
CO
different composition, 2 for carbon, and SO 3 for sulphur. Previously considered the limit to which carbon tends ifi its compounds, and in
we
a similar
manner
there
is
for every element in
RX
its
compounds a tendency
to attain a certain highest limit W This view was particularly "developed in the middle of the present century by Frankland in studying the metallo-organic compounds, i.e. those in which is wholly or partially .
X
X=CH
a hydrocarbon radicle; for instance, ample, antimony, Sb, gives, with chlorine,
3
or
C2H5
&c. Thus, for ex-
compounds SbCl and SbCl 5
and corresponding oxygen compounds Sb 2 O 3 and Sb 2 O 5 whilst under the action of CH 3 I, C 2 H 3 I, or in general El (where E is a hydrocarbon radicle of the paraffin series), upon antimony or its alloy with sodium there are formed SbE 3 (for example, Sb(CH 3 ) 3 boiling at about 81), which, corresponding to the lower form of combination SbX 3 are able to combine further with El, or C1 2 , or O, and to form compounds of the limiting type ,
,
,
SbX5
for example,
;
SbE4 Cl corresponding
to
NH4 C1 with the substitution
of nitrogen by antimony, and of hydrogen by the hydrocarbon radicle. The elements which are most chemically analogous are characterised by the fact of their giving compounds of similar form W The halogens
RX
which
are analogous give both higher
.
and lower compounds. So
also
do
group, which give RsO, form peroxides, and then the elements of the also to be particularly inclined to form peroxides, RaO?; but at present it is too early, in my opinion, to enter upon a generalisation of this subject, not only because it is a new and but little studied matter (not investigated for all the elements), but also, and more especially, because in many instances only the hydrates are known the
Li) o sixth
first
group seem
for instance, MoaHaOs and they perhaps are only compounds of peroxide of hydrogen 2MoOs HaOa since Professor Schone has shown that for example, MoaH^Os
=
+
possess the property of combining together and with other oxides. Nevertheless, I have, in the general table expressing the periodic properties of the elements, endeavoured to sum up the data respecting all the known peroxide compounds
HaOa and BaOa
whose
characteristic property is seen in their capability to
under many circumstances.
form peroxide of hydrogen
MASTERWORKS OF SCIENCE
552
the metals of the alkalis and of the alkaline earths. And we saw that this analogy extends to the composition and properties of the nitrogen and compounds of these metals, which is best seen in the salts.
Many hydrogen such groups of analogous elements have long been known. Thus there are analogues of oxygen, nitrogen, and carbon, and we shall meet with many such groups. But an acquaintance with them inevitably leads to the questions, what is the cause of analogy and what is the relation of one group to another? If these questions remain unanswered, it is easy to fall into error in the formation of the groups, because the notions of the degree of analogy will always be relative, and will not present any accuracy or distinctness. Thus lithium is analogous in some respects to potassium and in others to magnesium; beryllium is analogous to both aluminium and magnesium. Thallium has much kinship with lead and mercury, but some of its properties appertain to lithium and potassium. Naturally,
where it is impossible to make measurements one is reluctantly obliged to limit oneself to .approximate comparisons, founded on apparent signs which are not distinct and are wanting in exactitude. But in the elements is one accurately measurable property, which is subject to no doubt namely, that property which is expressed in their atomic weights. Its magnitude* indicates the relative mass of the atom, or, if we avoid the conception of the atom, its magnitude shows the relation between the masses forming the" chemical and independent individuals or elements. And according to the teaching of all exact data about the phenomena of nature, the mass of a substance is that property on which all its remaining properties must be dependent, because they are all determined by similar -conditions or by those forces which act in the weight of a substance, and this is directly proportional to its mass. Therefore it is most natural to seek for a dependence between the properties and analogies of the elements on the one hand and their atomic weights on the other.
there
This is the fundamental idea which leads to arranging all the dements according to their atomic weights. periodic repetition of properties is then immediately observed in the elements. We are already familiar with examples of this:
A
F
=19,
Na=23
,
Mg=24,
01=35.5, =39,
Br=8o,
I
Rb=8 5
Cs=i 33
Ca=40,
Sr=87,
K
,
=127, ,
Ba=i37*
The essence of the matter is seen in these groups. The halogens have smaller atomic weights than the alkali metals, and the latter than the metals of the alkaline earths. Therefore, // all the elements be arranged in the order of their atomic weights, a periodic repetition of properties is obtained. This is expressed by the law of periodicity; the properties of the elements, as well as the forms and properties of their compounds, are
dependence or (expressing ourselves algebraically} form a periodic function of the atomic weights of the elements? Table I of the
in periodic s
ln laying out the accumulated information respecting the elements, I had occasion to reflect on their mutual relations. At the beginning of 1869 I distributed among many
MENDELEYEV--THE PERIODIC LAW
553
periodic system of the elements is designed to illustrate this law. It is arranged in conformity with the eight types of oxides described in the preceding pages, and those elements which give the oxides, R 2 and consequently salts RX, form the ist group; the elements giving R 2 O 2 or as their highest grade of oxidation belong to the 2nd group, those giving R 2 O 3 as their highest oxides form the 3rd group, and so on; whilst the elements of all the groups which are nearest in their atomic weights are arranged in series from i to 12. The even and uneven series of the same groups present the same forms and limits, but differ in their properties, and therefore two contiguous series, one even and the other
O
RO
uneven
for instance, the 4th and 5th form a period. Hence the elements of the 4th, 6th, 8th, loth, and i2th, or of the 3rd, 5th, 7th, 9th, and nth,
chemists a pamphlet entitled 'An Attempted System of the Elements, based on their Atomic Weights and Chemical Analogies,' and at the March meeting of the Russian Chemical Society, 1869, I communicated a paper 'On the Correlation of the Properties and Atomic Weights of the Elements.' The substance of this paper is embraced in the following conclusions: (i) The elements, if arranged according to their atomic weights, exhibit an evident periodicity of properties. (2) Elements which are similar as regards their chemical properties
have atomic weights which are either of nearly the same value or which increase regularly (e.g. potassium, rubidium, of the elements or of groups of elements in the order of
(platinum, iridium, osmium) csesium). (3)
The arrangement
atomic weights corresponds with their so-called valencies. (4) The elements, which most widely distributed in nature, have small atomic weights, and all the elements of small atomic weight are characterised by sharply defined properties. They are their
are the
therefore typical elements.
character of an element.
The magnitude of the atomic weight determines the The discovery of many yet unknown elements may be
(5)
(6)
expected. For instance, elements analogous to aluminium and silicon, whose atomic weights would be between 65 and 75. (7) The atomic weight of an element may sometimes be corrected by aid of a knowledge of those of the adjacent elements. Thus the
combining weight of tellurium must lie between 123 and 126, and cannot be 128. (8) Certain characteristic properties of the elements can be foretold from their atomic weights.
The
entire periodic law is included in these lines. In the series of subsequent papers for example, in the Transactions of the Russian Chemical Society, of the
(187072,
Moscow Meeting
of Naturalists, of the St. Petersburg Academy, and Liebig's Annalen) find applications of the same principles, which were after-
on the same subject we only
wards confirmed by the labours of Roscoe, Carnelley, Thorpe, and others in England; of
Rammelsberg (cerium and uranium), L. Meyer (the specific volumes of the elements), Zimmermann (uranium), and more especially of C. Winkler (who discovered germanium, and showed its identity with ekasilicon), and others in Germany; of Lecoq de Boisbaudran in France (the discoverer of gallium == ekaaluminium) of Cleve (the atomic weights of the cerium metals), Nilson (discoverer of scandium ekaboron), and Nilson and Pettersson (determination of the vapour density of beryllium chloride) in Sweden; and of Brauner (who investigated cerium, and determined the combining weight of tellurium 125) in Austria, and Piccini in Italy. ;
=
=
consider
it necessary to state that, in arranging the periodic system of the elements, I made use of the previous researches of Dumas, Gladstone, Pettenkofer, Kremers, and Lenssen on the atomic weights of related elements, but I was not acquainted with the works preceding mine of De Chancourtois (vis tellurique, or the spiral of the ele-
I
ments according to
their properties
and equivalents) in France, and of
J.
Newlands
MASTERWORKS OF SCIENCE
554
series form analogues, like the halogens, the alkali metals, &c. The conjunction of two series, one even and one contiguous uneven series, thus forms one large period. These periods, beginning with the alkali metals, end with the halogens. The elements of the first two series have the lowest atomic weights, and in consequence of this very circumstance, although they bear the general properties of a group, they still show many peculiar
and independent properties. Thus fluorine, as we know, differs in many points from the other halogens, and lithium from the other alkali metals, and so on. These lightest elements may be termed typical elements. They include
H. Li, Be, B, C,
Na,
N, O, F.
Mg
In the annexed table
all the remaining elements are arranged, not in but according to periods. In order to understand the essence of the matter, it must be remembered that here the atomic weight
groups and
series,
gradually increases along a given line; for instance, in the line commencing with K=39 and ending with Br=8o, the intermediate elements have
intermediate atomic weights, as is clearly seen in Table elements stand in the order of their atomic, weights.
II,
where the
Rb Cs
The same degree of analogy that we know to exist between potassim, rubidium, and caesium; or chlorine, bromine, and iodine; or calcium, (Law of Octaves for instance, H, F, Cl, Co, Br, Pd, I, Pt form the first octave, and O, S, Fe, Se, Rh, Te, Au, Th the last) in England, although certain germs of the periodic law are to be seen in these works. With regard to the work of Professor Lothar Meyer respecting the periodic law (Notes 5 and 6), investigation,
and from
commencement
it is
from the method Band 7, 1870, 354),
evident, judging
his statement (Liebig's Annalen, Supt.
of at
which he cites my paper of 1869 above mentioned, that he accepted the periodic law in the form which I proposed. In concluding this historical statement I consider it well to observe that no law of nature, however general, has been established all at once; its recognition is always the very
hints; the establishment of a law, however, does not take place when recognised, but only when it has been confirmed by experiment, which of science must consider as the only proof of the correctness of his conjecture
preceded by its
the
many
significance
man
of
and opinions.
is
I
therefore, for
my
part, look
upon Roscoe, De Boisbaudran, Nilson,
Wirikler, Brauner, Carnelley, Thorpe, and others who verified the adaptability of the periodic law to chemical facts, as the true founders of the periodic law, the further development of which still awaits fresh workers.
MENDELEYEV
THE PERIODIC LAW
555
strontium, and barium, also exists between the elements of the other vertical columns. Thus, for example, zinc, cadmium, and mercury present a very close analogy with magnesium. For a true comprehension of the matter 3 it is very important to see that all the aspects of the distribution 8
Besides arranging the elements (a) in a successive order according to their atomic weights, with indication o their analogies by showing some of the properties for both of the eleinstance, their power of giving one or another form of combination
ments and of their compounds (as is done in Table II), (b) according to periods (as and (c) according to groups and series or small periods (as in the same tables), I am acquainted with the following methods of expressing the periodic relations
in Table I),
of the elements: (i) By a curve drawn through points obtained in the following manner: are arranged along the horizontal axis as abscissae at distances from zero
The elements
proportional to their atomic weights, whilst the values for all the elements of some property for example, the specific volumes or the melting points, are expressed by the ordinates. This method, although graphic, has the theoretical disadvantage that it does not in any way indicate the existence of a limited and definite number of elements in
each period. There is nothing, for instance, in this method of expressing the law of periodicity to show that between magnesium and aluminium there can be no other element with an atomic weight of, say, 25, atomic volume 13, and in general having properties intermediate between those of these two elements. The actual periodic law does not correspond -with a continuous change of properties, with a continuous variation of atomic weight in a word, it does not express an uninterrupted function and as
the law is purely chemical, starting from the conception of atoms and molecules which combine in multiple proportions, with intervals (not continuously), it above all depends on there being but few types of compounds, which are arithmetically simple, repeat themselves, and offer no uninterrupted transitions, so that each period can only contain a definite number of members. For this reason there can be no other elements between magnesium, which gives the chloride MgCls, and aluminium, which forms AlXs; there is a break in the continuity, according to the law of multiple proportions. The periodic law ought not, therefore, to be expressed by geometrical figures in which continuity is always understood. Owing to these considerations I never have and never will express the periodic relations of the elements by any geometrical figures. (2) By a plane spiral. Radii are traced from a centre, proportional to the atomic weights; analogous elements lie along one radius, and the points of intersection are arranged in a spiral. This
method, adopted by De Chancourtois, Baumgauer, E. Huth, and others, has many of the imperfections of the preceding, although it removes the indefmiteness as to the number of elements in a period. It is merely an attempt to reduce the zomplex relations to a simple graphic representation, since the equation to the spiral and the number of not dependent upon anything. (3) By the lines of atomicity, either parallel, as in Reynolds's and the Rev. S. Haughton's method, or as in Crookes's method, arranged to the right and left of an axis, along which the magnitudes of the atomic weights are radii are
counted, and the position of the elements marked oil, on the one side the members of the even series (paramagnetic, like oxygen, potassium, iron), and on the other side the
members
On
of the uneven series (diamagnetic, like sulphur, chlorine, zinc, and mercury). up these points a periodic curve is obtained, compared by Crookes to the
joining
oscillations of a pendulum, and, according to Haughton, representing a cubical curve. This method would be very graphic did it not require, for instance, that sulphur should be considered as bivalent and manganese as univalent, although neither of these elements gives stable derivatives of these natures, and although the one is taken on the basis of the lowest possible compound 8X2, and the other of the highest, because
manganese can be
referred to the univalent elements only
by the analogy of
KMnO*
to
MASTERWORKS OF SCIENCE
556
of the elements according to their atomic weights essentially express one 4 and the same fundamental dependence periodic properties. The followit. in be remarked must then ing points "
KC1CX, Furthermore, Reynolds and Crookes place hydrogen, iron, nickel, cobalt, and others outside the axis o atomicity, and consider uranium as bivalent without the least foundation. (4) Rantsheff endeavoured to classify the elements in their periodic rela-
by a system dependent on solid geometry. He communicated this mode of expression to the Russian Chemical Society, but his communication, which is apparently not void of interest, has not yet appeared in print. (5) By algebraic formula?: for example,. tions
E.
J.
Mills
(1886) endeavours to express
which the
all
the atomic weights by the logarithmic
and t are whole numbers. For oxygen 72=2, t=i; hence A=i5'94; for antimony n=$, /=ro; whence A=i20, and so on, n varies from i to 16 and t from o to 59. The analogues are hardlydistinguishable by this method: thus for chlorine the magnitudes of n and t are 3 and 7; for bromine 6 and 6; for iodine 9 and 9; for potassium 3 and 14; for rubidium 6 and 1 8; for caesium 9 and 20; but a certain regularity seems to be shown. (6) A more
function
A=:i5
(n
0-93 752), in
variables n
instance, for
method
dependence of the properties of elements on their obtained by trigonometrical functions, because this dependence is periodic like the functions of trigonometrical lines, and therefore Ridberg in Sweden (Lund, 1885) and F. Flavitzky in Russia (Kazan, 1887) have adopted a similar method natural
atomic weights
of expressing the
is
of expression, which must be considered as worthy of being worked out, although it does not express the absence of intermediate elements for instance, between magnesium and aluminium, which is essentially the most important part of the matter. (7) The investigations of B. N. Tchitcherin (1888, Journal of the Russian Physical and
Chemical Society) form the first effort in the latter direction. He carefully studied the metals, and discovered the following simple relation between their atomic volumes: they can all be expressed by A(2 0-0428 An), where A is the atomic weight for potassium, and n=.i for lithium and sodium, for rubidium, and for caesium. If n always I, then the volume of the atom would become zero at A 46%, and would reach its maximum when A=23%, and the density increases with the growth of A. In order to explain the variation of n, and the relation of the atomic weights of the alkali
%
=
%
%
alkali metals to those of the other elements, as also the atomicity itself, Tchitcherin
supposes
all
atoms
to
be built up of a primary matter; he considers the relation of the
central to the peripheric mass, and, guided by mechanical principles, deduces many of the properties of the atoms from the reaction of the internal and peripheric parts of each atom. This endeavour offers many interesting points, but it admits the hypothesis
up of all the elements from one primary matter, and at the present time such an hypothesis has not the least support either in theory or in fact.
of the building
4
Many natural phenomena exhibit a dependence of a periodic character. Thus the phenomena of day and night and of the seasons of the year, and vibrations of all kinds, exhibit variations of a periodic character in dependence on time and space. But in ordinary periodic functions one variable varies continuously, whilst the other increases to a limit, then a period of decrease begins, and having in turn reached its limit a, period of increase again begins. It is otherwise in the periodic function of the elements, Here the mass of the elements does not increase continuously, but abruptly by as
steps, also the valency or atomicity leaps directly from to 2 to 3, &c., without intermediate quantities, and in opinion it is these propers
from magnesium to aluminium. So i
ties
my
which are the most important, and
their periodicity which forms the substance of the periodic law. It expresses the properties of the real elements, and not of what may be termed their manifestations visually known to us. The external o it is
properties
MENDELEYEV THE PERIODIC LAW
557
1. The composition of the higher oxygen compounds is determined the groups: the first group gives R 2 O, the second R 2 2 or RO, the by third R 2 3 , &c. There are eight type of oxides and therefore eight groups. Two series give a period, and the same type of oxide is met with twice in a period. For example, in the period beginning with potassium, oxides of the composition RO are formed by calcium and zinc, and of the com-
O
O
RO
tellurium. The oxides of the even series, 3 by molybdenum and position of the same type, have stronger basic properties than the oxides of the uneven series, and the latter as a rule are endowed with an acid character. Therefore the elements which exclusively give bases, like the alkali metals, will be found at the commencement of the period, whilst such purely acid
elements as the halogens will be at the end of the period. The interval be occupied by intermediate elements. It must be observed that the acid character is chiefly proper to the elements with small atomic weights
will
exhibited by the heavier give acids chiefly predominate among the lightest (typical) elements, especially in the last groups; whilst the heaviest elements, even in the last groups (for instance, thallium, uranium), have a basic character. Thus the basic and acid charin the
uneven
series,
elements in the even
whilst the basic character series.
is
Hence elements which
by the type of oxide, (b) the atomic and uneven even or the weight. The groups series, (c) by by are indicated by Roman numerals from I to VIII. 2. The hydrogen compounds being volatile or gaseous substances which are prone to reaction such as HC1, 2 O, 3N, and 4 C are only formed by the elements of the uneven series and higher groups giving acters of the higher oxides are determined (a)
RO
O
H
H
H
oxides of the forms R 2 n , RO 3 , R 2 O 5 , and 2 a hydrogen compound, 3. If an element gives
compound
of the
.
RXm
same composition, where
,
it
forms an
X=CnH 2n4
_ 1; organo-metallic is the radicle of a saturated hydrocarbon. The elements of the that is, uneven series, which are incapable of giving hydrogen compounds, and com3 , also give organo-metallic 2, give oxides of the forms RX, zinc forms the Thus oxides. the to this form of higher proper pounds oxide ZnO, salts ZnX , and zinc ethyl Zn (C 2 H5) 2 The elements -of the
X
RX RX
.
2
even
series
do not seem
to
form organo-metallic compounds
at all; at
elements and compounds are in periodic dependence on the atomic weight o the elements only because these external properties are themselves the result o the properand the compounds. ties of the real elements which unite to form the "free" elements To explain and express the periodic law is to explain and express the cause of the law of multiple proportions, of the difference of the elements, and the variation of their what mass and gravitation are. In my atomicity, and at the same time to understand the cause of gravitation, it opinion this is still premature. But just as without knowing aims of chemistry it is possible is possible to make use of the law of gravity, so for the able to explain to take advantage of the laws discovered by chemistry without being defitheir causes. The above-mentioned peculiarity of the laws of chemistry respecting has not yet nite compounds and the atomic weights leads one to think that the time come for their full explanation, and I do not think that it will come before the of such a primary law of nature as the law o gravity.
explanation
MASTERWORKS OF SCIENCE
558
least all efforts for their preparation
have
as yet
been
fruitless
for in-
stance, in the case of titanium, zirconium, or iron. of elements belonging to contiguous periods 4. The atomic weights Cr<Mo, Br
K
elements of the typical series show much smaller differences. Thus the difference between the atomic weights of Li, Na, and K, between Ca, Mg, and Be, between Si and C, between S and O, and between Cl and F, is 16. As a rule, there is a greater difference between the atomic weights of two elements of one group and belonging to two neighboring series (Ti Si S=Mn Cl=Nb As, &c.=2o); and this difference attains ssrV P=Cr a maximum with the heaviest elements (for example, Th Pb=26, Bi Ta =26, Ba Cd=25, &c.). Furthermore, the difference between the atomic increases. In fact, weights of the elements of even and uneven series also the differences between Na and K, Mg and Ca, Si and Ti, are less abrupt than those between Pb and Th, Ta and Bi, Cd and Ba, &c. Thus even in the magnitude of the differences of the atomic weights of analogous elements there is observable a certain connection with the gradation of their 5
properties.
According to the periodic system every element occupies a certain the group (indicated in Roman numerals) and position, determined by series (Arabic numerals) in which it occurs. These indicate the atomic and of weight, the analogues, properties, and type of the higher oxide, the hydrogen and other compounds in a word, all the chief quantitative and qualitative features of an element, although there yet remains a whole series of further details and peculiarities whose cause should perIf in a haps be looked for in small differences of the atomic weights. certain group there occur elements, R, R 2 R3 and if in that series which contains one of these elements, for instance R 23 an element Q 2 precedes it and an element T2 succeeds it, then the properties of R 2 are determined the atomic by the properties of R I} R 3 Q 2 and T 2 Thus, for instance, = %(Ri+R3+Q2+T2 ). For example, selenium occurs in weight of R 2 the same group as sulphur, S = 32, and tellurium, Te = 125, and, in the 5.
,
,
>
,
.
^The relation between the atomic weights, and especially the differ ence:=i6> was observed in the sixth and seventh decades of this century by Dumas, Pettenkofer, LMeyer, and others. Thus Lothar Meyer in 1864, following Dumas and others, grouped elements nitrogen, together the tetravalent elements carbon and silicon; the trivalent phosphorus, arsenic, antimony, and bismuth; the bivalent oxygen, sulphur, selenium, and tellurium; the univalent fluorine, chlorine, bromine, and iodine; the univalent metals lithium, sodium, potassium, rubidium, caesium, and thallium, and the bivalent metals beryllium, magnesium, strontium and barium observing that in the first the difference is, in generals 1 6, in the second about=46, and the last about= 87-90. The first
germs
of the periodic
law are
visible in
such observations as these. Since
its
estab-
has been most fully worked out by Ridberg (Note 3), who observed a periodicity in the variation of the differences between the atomic weights of two contiguous elements, and its relation to their atomicity. A. Bazaroff (1887) invesand tigated the same subject, taking, not the arithmetical differences of contiguous that analogous elements, but the ratio of their atomic weights; and he also observed this ratio alternately rises and falls with the rise of the atomic weights.
lishment
this subject
MENDELEYEV
THE PERIODIC LAW 559 and Br = 80 after Hence the atomic 7th series As = 75 stands before near weight of selenium should be % (32+125+75-1-80) = 78, which it
it.
is
Other properties of selenium may also be determined in this manner. For example, arsenic forms bromine gives HBr> and 3 As, it is evident that selenium, which stands between them, should form 2 Se, with properties intermediate between those of 3 As and HBr. Even the physical properties of selenium and its compounds, not to speak of their composition, being determined by the group in which it occurs, may be foreseen with a close approach to reality from the properties of sulphur, tellurium, arsenic, and bromine. In this manner it is possible to foretell the properties of still unknown elements. For instance, in the position IV, 5 that is, in the IVth group and 5th series an element is still wanting. These unknown elements may be named after the preceding known element of the same group by adding to the first syllable the prefix e\a-, which means one in Sanskrit. The element IV, 5, follows after IV, 3, and this latter position being occupied by silicon, we call the unknown element ekasilicon and its symbol Es. The following are the properties which this element should have on the basis of the known properties of silicon, tin, zinc, and arsenic. Its atomic weight is nearly 72, higher oxide EsO 2 lower oxide EsO, compounds of the general form EsX4 and chemically unstable lower compounds of the form EsX2 Es gives volatile organo-metallic compounds for instance, Es(CH 3 ) 4 Es (CH 3 ) 3 Cl, and Es(C2 5 ) 4 which boil at about 160, &c.; also a volatile and liquid chloride, EsCl 4 boiling at about 90 and of specific gravity about 1-9. EsO 2 will be the anhydride of a feeble colloidal acid, metallic Es will be rather easily obtainable from the oxides and from K 2 EsF 6 by reduction, EsS 2 will resemble SnS 2 and SiS 2 and will probably be soluble in ammonium sulphide; the specific gravity of Es will be about 55, EsO 2 will have a density of about 4-7, &c. Such a prediction of the properties of ekasilicon was made by me in 1871, on the basis of the properties of the elements analogous to it: IV, 3, = Si, IV, 7 Sn, and also II, 5 = Zn and V, 5 = As. And now that this element has been discovered by C. Winkler, of Freiberg, it has been found that its actual properties entirely 6 correspond with those which were foretold, In this we see a most importo the truth.
H
H
H
,
.
,
H
,
,
,
,
=
e The laws of nature admit of no exceptions, and in this they clearly differ from such rules and maxims as are found in grammar, and other inventions, methods, and relations of man's creation. The confirmation of a law is only possible by deducing consequences from it, such as could not possibly be foreseen without it, and by verifying those consequences by experiment and further proofs. Therefore, when I conceived the periodic law, I (1869-1871) deduced such logical consequences from it as could serve to show whether it were true or not. Among them was the prediction of the properties of undiscovered elements and the correction of the atomic weights of many, and at that time little known, elements. Thus uranium was considered as trivalent,
U=i2o; but to
double
its
as such
it
did not correspond with the periodic law. I therefore proposed 11=240, and the researches of Roscoe, Zimmermann, and
atomic weight
It was the same with cerium, whose atomic weight it change according to the periodic law. I therefore determined its heat, and the result I obtained was verified by the new determinations of
others justified this alteration.
was necessary specific
to
MASTERWORKS OF SCIENCE
560
tant confirmation of the truth of the periodic law. This element is now called germanium,, Ge. It is not the only one that has been predicted by 7 the periodic law. Properties were foretold of an element ekaaluminium, El 68, and were afterwards verified when the metal termed "gal-
III, 5,
=
lium" was discovered by De Boisbaudran. So also the properties of scandium corresponded with those predicted for ekaboron, according to Nilson. 6. As a true law of nature is one to which there are no exceptions, the periodic dependence of the properties on the atomic weights of the elements gives a new means for determining by the equivalent the atomic weight or atomicity of imperfectly investigated but known elements, for which no other means could as yet be applied for determining the true atomic weight. At the time (1869) when the periodic law was first pro-
posed there were several such elements. It thus became possible to learn their true atomic weights, and these were verified by later researches. thus concerned were indium, uranium, cerium, Among the elements 8 and others. yttrium, Hillebrand. I then corrected certain formula: of the cerium compounds, and the reRammelsberg, Brauner, Cleve, and others verified the proposed alteration.
searches o
was necessary to do one or the other either to consider the periodic law as comand as forming a new instrument in chemical research, or to refute it. Acknowledging the method of experiment to be the only true one, I myself verified what I could, and gave everyone the possibility of proving or confirming the law, and
It
pletely true,
did not think, like L. Meyer (Liebig's Annalen, Supt. Band 7, 1870, 364), when writing about the periodic law that "it would be rash to change the accepted atomic weights on the basis of so uncertain a starting point." In my opinion, the basis offered by the periodic law had to be verified or refuted, and experiment in every case verified it. starting point then became general. No law of nature can be established without
The
such a method of testing it. Neither De Chancourtois, to whom the French ascribe the discovery of the periodic law, nor Newlands, who is put forward by the English, nor L. Meyer, who is now cited by many as its founder, ventured to foretell the properties of undiscovered elements, or to alter the "accepted atomic weights," or, in general, to regard the periodic law as a new, stricdy established law of nature, as I did from the
very beginning (1869). 7
When in 1871 I wrote a paper on the application of the periodic law to the determination of the properties of hitherto undiscovered elements, I did not think I should live to see the verification of this consequence of the law, but such was to be the case. Three elements were described ekaboron, ekaaluminium, and ekasilicon and now, after the lapse of twenty years, I have had the great pleasure of seeing them discovered and named Gallium, Scandium, and Germanium, after those three countries where the rare minerals containing them are found, and where they were discovered. For my part I regard L. de Boisbaudran, Nilson, and Winkler, who discovered these elements, as the true corroborators of the periodic law. Without them it would not have been accepted to the extent
it
now
is.
^Taking indium, which occurs together with zinc, as our example, we will show the principle of the method employed. The equivalent of indium to hydrogen in its oxide is 37*7 that is, if we suppose its composition to be like that of water; then In:=37-7, and the oxide of indium is InsO. The atomic weight of indium was taken as double the equivalent that is, indium was considered to be a bivalent element and
MENDELEYEV THE PERIODIC LAW The
7.
561
periodic variability of the properties of the elements in de-
pendence on their masses presents a distinction from other kinds of periodic dependence (as, for example, the sines of angles vary periodically and successively with the growth of the angles, or the temperature of the atmosphere with the course of time), in that the weights of the atoms do not increase gradually, but by leaps, that is, according to Dalton's law of multiple proportions, there not only are not, but there cannot be, any between two neighbouring ones (for 28, or C example, between 40, or Al 27 and Si 39 and Ca 12 and 14, &c.). As in a molecule of a hydrogen compound there
transitive or intermediate elements
K=
N=
=
=
=
=
be either one, as in HF, or two, as in H 2 O, or three, as in NH 3 &c., atoms of hydrogen; but as there cannot be molecules containing 2% atoms of hydrogen to one atom of another element, so there cannot be and O, with an atomic weight any element intermediate between greater than 14 or less than 16, or between K and Ca. Hence the periodic
may
,
N
dependence of the elements cannot be expressed by any tinuous function in the same way that it is possible, for
algebraical coninstance, to ex-
press the variation of the temperature during the course of a day or year. 8. The essence of the notions giving rise to the periodic law consists in a general physico-mechanical principle which recognises the correlaindium only formed an oxide, RO, it should be placed in group appears that there would be no place for indium in the system of Sr Zn the elements, because the positions II, 5 87 were 65 and II, 6 already occupied by known elements, and according to the periodic law an element with an atomic weight 75 could not be bivalent. As neither the vapour density nor the of indium crystallise with great specific heat, nor even the isomorphism (the salts
In=2X37 7 =75'4F
II.
But in
If
:
this case it
=
=
=
=
'
difficulty), of the
ering
of indium were
to be a bivalent metal,
it
be
rivalent, &c. If it is
compounds
InaOs,
and of
trivalent,
its salts
and therefore
then
known, there was no reason for considmight be regarded as trivalent, quad-
it
In=3X377
InXs. In this case
it
at
I]C 3
once
anc* the composition of the oxide Jails into its place in the system,
namely, in group III and 7th series, between Cd=ii2 and Sn=n8, as an analogue of 2 in Sanskrit). All the properties observed in aluminium or dvialuminium (dvi 8-6, indium correspond with this position; for example, the density, cadmium
=
indium
=
7-4; tin
=.
=
7-2; the basic properties of the oxides
CdO,
In^Os, SnOs, succes-
CdO
between those of sively vary, so that the properties of In2Os are intermediate SnsO*. That indium belongs to group III has been confirmed
SnOa or CdsOa and
and by the
its specific heat, (0-057 according to Bunsen, and 0-055 according to by the fact that indium forms alums like aluminium, and therefore belongs to the same group. The same kind of considerations necessitated taking the atomic weight of titanium as nearly 48, and not as 52, the figure derived from many analyses. And both these for Thorpe found, corrections, made on the basis of the law, have now been confirmed, titanium to be that foreseen by a series of careful experiments, the atomic weight of by the periodic law. Notwithstanding that previous analyses gave 05=1997, 11=198, and Pt=i87, the periodic law shows, as I remarked in 1871, that the atomic weights should rise from osmium to platinum and gold, and not fall. Many recent researches, and especially those of Seubert, have fully verified this statement, based on the law. Thus a true law of nature anticipates facts, foretells magnitudes, gives a hold on nature,
determination of
me) and
and
also
leads to improvements in the
methods
of research, &c.
562
MASTERWORKS OF SCIENCE
tion, transmutability, and equivalence of the forces of nature. Gravitation, attraction at small distances, and many other phenomena are in direct
dependence on the mass of matter. It might therefore have been expected would also depend on mass. A dependence is in fact shown, the properties of elements and compounds being determined by the masses of the atoms of which they are formed. The weight of a molecule, or its mass, determines many of its properties independently of its composition. Thus carbonic oxide, CO, and nitrogen, 2 are two gases having the same molecular weight, and many of their properties that chemical forces
N
,
(density, liquefaction, specific heat, &c.) are similar or nearly similar. differences dependent on the nature of a substance play another part,
The
and form magnitudes of another order. But the properties of atoms are mainly determined by their mass or weight, and are in dependence upon it. Only in this case there is a peculiarity in the dependence of the properties on the mass, for this dependence is determined by a periodic law.
As
the mass increases the properties vary, at first successively and reguand then return to their original magnitude and recommence a fresh period of variation like the first. Nevertheless here as in other cases larly,
atom generally leads to a small variation of properties, and determines differences of a second order. The atomic weights of cobalt and nickel, of rhodium, ruthenium, and palla-
a small variation of the mass of the
dium, and of osmium, indium, and platinum, are very close to each other, and their properties are also very much alike the differences are not very perceptible. And if the properties of atoms are a function of their weight, many ideas which have more or less rooted themselves in chemistry must suffer change and be developed and worked out in the sense of this deduction. Although at first sight it appears that the chemical elements are perfectly independent and individual, instead of this idea of the nature of the elements, the notion of the dependence of their properties upon their mass must now be established; that is to say, the subjection of the individuality of the elements to a common higher principle which evinces itself in gravity and in all physico-chemical phenomena. Many chemical de-
ductions then acquire a new sense and significance, and a regularity is observed where it would otherwise escape attention. -This is more particularly apparent in the physical properties, to the consideration of which we shall afterwards turn, and we will now point out that Gustavson first, and subsequently Potilitzin, demonstrated the direct dependence of the reactive power on the atomic weight and that fundamental property which is expressed in the forms of their compounds, whilst in a number of other cases the purely chemical relations of elements proved to be in connection with their periodic properties. As a case in point, it may be mentioned that Carnelley remarked a dependence of the decomposability of the hydrates on the position of the elements in the periodic system; whilst L. Meyer, Willgerodt, and others established a connection between the atomic weight or the position of the elements in the periodic system and their property of serving as media in the transference of the halogens to the hydrocarbons. Bailey pointed out a periodicity in the sta-
ivi
JS1N JJ
JC,
JL
X
,
,
V
1JHLJ
J^
K I U JU 1 (J
LAW
563
bility (under the action of heat) of the oxides, series (for instance, 3, 3, 3 , and
namely: (a) in the even ) the higher oxides of a given group decompose with greater ease the smaller the atomic weight, while in the uneven series (for example, CO 2 GeO 2 SnO 23 and PbO 2 ) the contrary is the case; and (b) the stability of the higher saline oxides in the even series (as in the fourth series from K O to Mn O decreases
MoO
CrO
WO
UO 3
,
,
2
2
7)
in passing from the lower to the higher groups, while in the uneven series it increases from the 1st to the IVth and then falls from the
group,
In O 3 SnO 0? and K. Winkler looked for and" actually found
IVtrh to Vllth; for instance, in the series
then
SnO2 Sb 2 O 5 TeO3 ,
,
,
I
2
O7
.
Ag 9 O, CdO,
,
(1890) a dependence between the reducibility of the metals by magnesium and their position in the periodic system of the elements. The greater the attention paid to this field the more often is -a distinct connection found between the variation of purely chemical properties of analogous substances and the variation of the atomic weights of the constituent elements and their position in the periodic system. Besides, since the periodic system has become more firmly established, many facts have been gathered, showing that there are many similarities between Sn and
Pb, B and Al, Cd and Hg, &c., which had not been previously observed, although foreseen in some cases, and a consequence of the periodic law. Keeping our attention in the same direction, we see that the most widely distributed elements in nature are those with small atomic weights, whilst in organisms the lightest elements exclusively predominate (hydrogen, carbon, nitrogen, oxygen), whose small mass facilitates those transformations which are proper to organisms. Poluta (of Kharkoff), C. C. Botkin, Blake, Brenten, and others even discovered a correlation between the physiological action of salts and other reagents on organisms and the positions occupied in the periodic system by the metals contained in
them. As, from the necessity of the case, the physical properties must be in dependence on the composition of a substance, i.e. on the quality and quantity of the elements forming it, so for them also a dependence on the atomic weight of the component elements must be expected, and
consequently also on their periodic distribution. We will content ourselves with citing the discovery by Carnelley in 1879 of the dependence of the magnetic properties of the elements on the position occupied by them in the periodic system. Carnelley showed that all the elements of the even series (beginning with lithium, potassium, rubidium, caesium)
belong to the number of magnetic (paramagnetic) substances; for examaccording to Faraday and others, C, N, O, K, Ti, Cr, Mn, Fe, Co, Ni, Ce, are magnetic; and the elements of the uneven series are diamagnetic, H, Na, Si, P, S, Cl, Cu, Zn, As, Se, Br, Ag, Cd, Sn, Sb, I, Au, Hg, H, Pb, Bi. Carnelley also showed that the melting point of elements varies periodically, as is seen by the figures in Table II (nineteenth column), where ple,
all
the
most trustworthy data are collected, and predominance having maximum and minimum values.
to those
is
given
MASTERWORKS OF SCIENCE
564
There Is no doubt that many other physical properties will, when further studied, also prove to be in periodic dependence on the atomic weights, but at present only a few are known with any completeness, and we will only refer to the one which is the most easily and frequently determined namely, the specific gravity in a solid and liquid state, the more especially as its connection with the chemical properties and relations of substances is shown at every step. Thus, for instance, of all the metals those of the alkalis, and of all the non-metals the halogens, are the most energetic in their reactions, and they have the lowest specific gravity among the adjacent elements, as is seen in Table II, column 17. Such are sodium, potassium, rubidium, caesium among the metals, and chlorine, bromine, and iodine among the non-metals; and as such less
energetic metals as iridium, platinum, and gold (and even charcoal or the diamond) have the highest specific gravity among the elements near to them in atomic weight; therefore the degree of the condensation of
matter evidently influences the course of the transformations proper to a substance, and furthermore this dependence on the atomic weight, although very complex, is of a clearly periodic character. In order to account for this to some extent, it may be imagined that the lightest elements are porous, and, like a sponge, are easily penetrated by other substances, whilst the heavier elements are more compressed, and give way with difficulty to the insertion of other elements. These relations are best understood when, instead of the specific gravities referring to a unit of volume, the atomic volumes of the elements that is, the quotient A/d of the atomic weight A by the specific gravity d are taken for comparison. As, according to the entire sense of the atomic theory, the actual matter of a substance does not fill up its whole cubical contents, but is surrounded by a medium (ethereal, as is generally imagined), like the stars and planets which travel in the space of the heavens and fill it, with greater or less intervals, so the quotient A/d only expresses the mean is
.
the
mean
^
to the sphere of the atoms, and therefore A/d distance between the centres of the atoms. For compounds
volume corresponding
whose molecules weigh M, the mean magnitude of the atomic volume is obtained by dividing the mean molecular volume M/d by the number of atoms n in the molecule. The above relations may easily be expressed from this point of view by comparing the atomic volumes* Those comparatively light elements which easily and frequently enter into reaction have the greatest atomic volumes: sodium 23, potassium 45, rubidium 57, caesium 71, and the halogens about 27; whilst with those elements which enter into reaction with difficulty, the mean atomic volume is small; for carbon in the form of a diamond it is less than 4, as charcoal about 6, for nickel and cobalt less than 7, for iridium and platinum about 9. The remaining elements having atomic weights and properties intermediate between those elements mentioned above have also intermediate atomic volumes. Therefore the specific gravities and specific volumes of solids and liquids stand in periodic dependence on the atomic weights, as is
MENDELEYEV THE PERIODIC LAW
565
where both A (the atomic weight) and d (the specific (specific volumes of the atoms) are given (column 18). Thus we find that in the large periods beginning with lithium, sodium, potassium, rubidium, caesium, and ending with fluorine, chlorine, seen in Table
gravity),
II,
and A/d
bromine, iodine, the extreme members (energetic elements) have a small density and large volume, whilst the intermediate substances gradually increase in density and decrease in volume that is, as the atomic weight increases the density rises and falls, again rises and falls, and so on.
Furthermore, the energy decreases as the density rises, and the greatest density is proper to the atomically heaviest and least energetic elements; for example, Os, Ir, Pt, Au, U. In order to explain the relation between the volumes of the elements and of their compounds, the densities (column S) and volumes (column M/.?) of some of the higher saline oxides arranged in the same order as in the case of the elements are given on p. 566. For convenience of comparison the volumes of the oxides are all calculated per two atoms of an element combined with oxygen. For example, the density of Al 2 O 3 =4*o, weight Al 2 O 3 =i02, volume A1 2 O 3 =25'5. Whence, knowing the volume of aluminium to be n, it is at once seen that in the formation of aluminium oxide, 22 volumes of it give 255 volumes of oxide. A distinct periodicity may also be observed with respect to the specific gravities and volumes of the higher saline oxides. Thus in each period, beginning with the alkali metals, the specific gravity of the oxides first rises, reaches a maximum, and then falls on passing to the acid oxides, and again becomes a miniabout the halogens. But it is especially important to call attention to the fact that the volume of the alkali oxides is less than that of the metal
mum
contained in them, which is also expressed in the last column, giving this difference for each atom of oxygen. Thus 2 atoms of sodium, or 46 volumes, give 24 volumes of Na 2 O, and about 37 volumes of 2NaHO that is, the oxygen and hydrogen in distributing themselves in the medium of sodium have not only not increased the distance between its atoms, but have brought them nearer together, have drawn them together by the force of their great affinity, by reason, it may be presumed, of the small mutual attraction of the atoms of sodium. Such metals as aluminium and zinc, in combining with oxygen and forming oxides of feeble salt-forming capaccommon metals and non-metals, and esity, hardly vary in volume, but the when pecially those forming acid oxides, always give an increased volume oxidised that is, the atoms are set further apart in order to make room for the oxygen. The oxygen in them does not compress the molecule as in the alkalis; it is therefore comparatively easily disengaged. As the volumes of the chlorides, organo-metallic and all other corresponding compounds, also vary in a like periodic succession with a change
of elements, it is evidently possible to indicate the properties of substances yet uninvestigated by experimental means, and even those of yet undiscovered elements. It was possible by following this method to foreof the properties of scandium, tell, on the basis of the periodic law, many after gallium, and germanium, which were verified with great accuracy
MASTERWORKS OF SCIENCE
566
HaO
I'O
2-0
LiaO
M/J
Volume
18
?
15 16
BsOa
1-8
39
-J-
GO*
1-6
1-64
55 66
+ +
Na*O
2-6
24
MgaOa
3'5 4-0
23 26
SbO*
2-65
45
PaOs
2'39
59 82
1-96
CLO*
ScaOa
2-7
35
3*25
34
3 86
35
4-2
38
3 49
52
2 74
73
Cu^O
5 9
24
ZnaOa GasOa
5'7
AssO5
NbaOs
Ag2
TeOo BaaOa
LaaOa
TaaOs
Hg
2
2
PbaO*
.... .... ....
4'7 5-0 5'5 4*7 4*4
+ + + +
+ + + + + + + +
o 3
6-7 9'5 9'6 4'8 4
4'5 6-0 13
2
?
44 57 65
7-18
38
7-0 6-5 5-i
43
8-9 9*86
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8 ?
44
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n-i
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7'5 8-0
5*7 6-5 6-74 7'5 6-8
4
4'5
23
45
10*0 10-6
22
56
SraOa
MoOo
?
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4'7
9 2-6
+
95
K*0
Oxygen
22
3-06
ALOa
of
3i
+ + + + + +
49
6
6-8
3
2-7 2-7 2-6 4.7 10
52 50 50
59 68 39 53
54
+ + + + + + +
i
2
4-6 8-2
4-5 4-2 2
MENDELEYEV
THE PERIODIC LAW
567
had been discovered. The periodic law, therefore, has not only embraced the mutual relations of the elements and expressed their analogy, but has also to a certain extent subjected to law the doctrine of the types of the compounds formed by the elements: it has enabled us to
these metals
all chemical and physical properties of elements and compounds, and has rendered it possible to foretell the properties of elements and compounds yet uninvestigated by experimental means; thus it has prepared the ground for the building up of atomic and molecular mechanics.
see a regularity in the variation of
RADIOACTIVITY
MARIE CURIE
CONTENTS Radioactivity
The Discovery of Radioactivity and of the Radioelements The Rays of Uranium. The Rays of Thorium Method of Chemical AnalyRadioactivity an Atomic Property. New sis Based on Radioactivity. Discovery of Radium and Polonium Radium Spectrum and Atomic Weight of Radium. Metallic The Radioelements The Derivatives of Uranium: A. The Radium Branch B. The Actinium Branch The Derivatives of Thorium
The
Radioactive Ores and the Extraction of the Radioelements
The
Radioactive Ores Ores of Thorium and Uranium
MARIE CURIE 1867-1934
MARIE CUKIE was born Marie Sklodovska
in
Warsaw,
in 1867,
the youngest child of a poorly paid Polish teacher in the Russian-controlled schools of Warsaw. At three she had learned by herself to read; from an early age she displayed an infallible memory, quick comprehension, unbelievable powers of concentration. This precocity her parents, particularly her
father, after his wife's death when Marie was scarcely more than an infant, tried to curb. But the four other children in the family also had great gifts, and the atmosphere of the
household encouraged intellectual striving. At sixteen Marie finished the course at the gymnasium and had there won the gold medal the third to be carried off by the Sklodovski
had
children. And after a year of visiting her relatives in rural Poland, she began earning her living as a private teacher in
Warsaw. Like the other young people of her set, she devoted herComte, read Darwin and Pasteur, made an effort patriotic in origin to educate the illiterate poor, and joined
self to
secret classes for the study of science.
The
local university
being open only to men, she and her favorite sister, Bronya, yearned to go to Paris to study. Finally she persuaded Bronya to take their slender resources and to proceed to the Sorbonne. Their plan was that once Bronya had qualified for her degree, she would aid Marie. Meantime, Marie would contribute what she could earn to Bronya' s support.
There followed several years of service as a governess, in Warsaw, now in a country village miles from a town. In the intervals of her exacting duties Marie found time to
now
organize secret Polish classes for the children of the poor, to study mathematics, and to teach herself such chemistry and physics as she could dig out of textbooks without the aid of either teacher or laboratory. The dream of getting to Paris
MASTERWORKS OF SCIENCE
572
faded. Then Bronya finished her medical course, married a fellow Pole in Paris, and began to practice. Suddenly Marie was summoned to her opportunity.
In 1889, almost without financial resources, Marie was was entered at the Sorliving in Paris with her sister and bonne. Presently she felt that the gaiety of her sister's Polish friends even the occasional concert and the occasional theainterfered with her work. She moved to a lodging in the ter Latin Quarter. In that neighborhood, in one poor, unheated, almost barren room or another, she lived her student days. There, unable to cook, too poor to buy food and fuel, she studied early and late until she almost succumbed to overwork and malnutrition. In 1893, at the top of her class, she took her master's degree in physics; in 1894, her master's
degree in mathematics. About this time Marie undertook her first commission: to study the magnetic properties of steels. In the course of this she met Pierre Curie. He was a man of thirty-five, already a highly esteemed physicist. Like Marie, he came of a most cultivated, middle-class family; like her, he was devoted
work
to his science to the exclusion of people. The two were quickly in sympathy, and shortly they were close friends. Two years later they married. The Curies now began an amazing collaborative work at the School of Physics and Chemistry of the City of Paris,
where Pierre was chief
of laboratory. Marie, searching for a subject for a doctoral dissertation, had become interested in Becquerel rays and their sources. As she systematically exam-
ined
all
known
elements and minerals, she began to sus-
pect that in the pitchblende (uranium ore) she had studied there was a hitherto-unidentified element capable of radiation far stronger than that from uranium. Pierre at once his work with crystals to join in the study of the -
abandoned
Becquerel rays. In 1898 they together announced the probable few months later they announced radium. From 1898 to 1902 they devoted themselves to the long, arduous task of preparing a sample of pure radium from the existence of polonium; a
masses of pitchblende they were, with difficulty, able to obtain. Together they studied the physical and chemical properties of the new element. Finally, in 1902, Marie isolated pure radium salt and determined its atomic weight, 225. Meantime, Pierre had become a teacher at the P.C.N., an annex of the Sorbonne, and Marie had become a lecturer in physics at the girls' normal school at Sevres. Though these teaching duties constantly drained their energies, though
RADIOACTIVITY
CURIE
their earnings scarcely paid their modest bills, though Pierre's health failed, they never halted in their research. By 1904 they
had published twenty-nine papers on
radioactivity, most of so completely joint products that the work of one is indistinguishable from that of the other.
them
For her work on radium Marie won her doctoral degree same year the Curies began to receive the honors which, until Marie's death in 1934, never stopped in
1903; in the
coming. They visited London to present the results of their studies to the Royal Society, and Marie attended the meeting the first woman ever admitted; they were jointly awarded the Davy Medal in 1903, and a few months later, together with Becquerel, the Nobel Prize for Physics, Even this triscarcely persuaded them to pause in their labors long enough to visit Stockholm for the presentation of the prize
umph
scarcely paused to celebrate Pierre's election to the Academy of Science, or his elevation to a professorship at the Sorbonne. Suddenly, in 1906, after an idyllic Easter holiday in the country, Pierre died, the victim of a street accident.
money. They
The
was ended. and the genuine friendly sympathy which rose round Marie meant nothing to her. She was sustained only by that devotion to science which had persuaded her and Pierre several years before to refuse to patent their process for refining radium: by that devotion, and by her ingrained habit of work. Within a few months the Sorbonne entrusted her with Pierre's course, as his successor. She labored upon her lectures, and in November she delivered the first of them, beginning exactly where Pierre had left off. The great collaboration
The tremendous
first
woman
give the
official
ever to lecture at the Sorbonne, she soon began to and for long the only course in the world on
first
radioactivity.
From 1906 to 1914, as the fame of Marie Curie grew, she never stopped working hardly even for an occasional visit to Warsaw, such as that in 1913 to inaugurate a laboratory for the study of radioactivity, or for a quick trip to a foreign university to receive an honorary degree, or for a summer walking tour in the Engadine, or for a second excursion to Stockholm to receive in 1911 the Nobel Prize for Chemistry. She studied polonium exhaustively; she administered the fellowships for the study of radioactivity established by Carnegie; she prepared the first and only sample of pure metallic radium and redetermined its atomic weight; when the University of Paris and the Pasteur Institute jointly undertook the construction of an Institute for Radium, she supervised the execution of the scheme.
573
MASTERWQRKS OF SCIENCE
574
This building was just ready for occupancy when World I broke out in 1914. For the next five years Mme. Curie was occupied constantly with the war work she made peculat once that the army hospitals were iarly hers. She observed not equipped to use radiology. Almost unaided, and fre-
War
the end of the war quently in the face of official lethargy, by she had equipped two hundred radiological rooms, most of
them
in field hospitals,
and twenty radiological
cars.
She her-
performed prodigies in the field as an X-ray technician; she trained one hundred and fifty X-ray technicians, and she service. Her organized and operated the radium emanation her services and those of patriotic fervor blazed: not only but her prize winall the scientists she could commandeer nings and her whole fortune, she put at the disposal of the But immediately the war ended, she resumed her self
government.
investigative studies. Though the hard
work never ended, nor her eagerness
for
Curie's life for the next fifteen years had a brighter tone than before. She had wonderful summer holidays at Larcouest, a quiet spot in Brittany, with a group of congenial it,
Mme.
academic people from the Sorbonne. She watched the progress of her daughter and her son-in-law, the Joliot-Curies, who were rising to eminence in the world of science. She even occasionally accepted the world's homage; for she came to believe that whatever was offered her was in reality a tribute to science. Thus in 1921 she made a trip to America, an almost
the gift royal progress, to receive from the women of America of a gram of radium, and repeated the same tour for the same reason in 1929. (The first gift she immediately transferred to
Radium Institute, and the second to the Warsaw Institute, founded in 1925.) Thus she journeyed to Rio de Janeiro, to Italy, to Holland, to England, to Czechoslovakia, the Paris
The
learned societies of the world elected her to universities of the world conferred their the membership; honorary degrees upon her. She accepted everything with complete self-effacement. It even seemed to her that these exto Spain.
peditions, pleasurable as they sometimes were, cost overmuch in their interruptions of her work. Even when her health declined and her sight dimmed, her energy did not. Almost until the day of her death she was busy writing her last, her greatest, book. It
was
just finished
when
she died.
Mme.
Curie's story has been so colorfully told by her daughter Eve and so vividly presented on the movie screen that everyone knows of her, and thinks of her, probably, as a fairy-tale heroine of science. Yet her genius was not romantic. It
was a genius
had a passionate devotion a devotion which made her
for hard work. She
to accuracy, to truth, to science
CURIE but
RADIOACTIVITY
selfless. Even when she must credit herself with her achievements, as in the pages here translated from her last book, Radioactivity, she speaks of herself in the third person. For she cared nothing for personal glory, everything for labor and knowledge. all
own
575
RADIOACTIVITY THE DISCOVERY OF RADIOACTIVITY AND OF THE RADIOELEMENTS THE
STUDY of radioactivity includes the study of the chemistry of the radioelements, the study of the rays emitted by these elements, and the conclusions to be drawn from such studies relative to the structure of the atom. The radioelements can be defined as particular elements from which there emanate, spontaneously and atomically, rays designated as
alpha, beta, and gamma positive corpuscular rays, negative corpuscular rays (electrons in motion), and electromagnetic radiations. The emission
accompanied by an atomic transformation. Arranged according to their respective abilities to penetrate matter, the alpha rays are the weakest: they are stopped by a sheet of paper or by a leaf of aluminum o.i mm. in thickness; they travel through air a few centimeters. The beta rays travel farther in air and can penetrate several millimeters of aluminum. The is
rays can penetrate several centimeters of relatively opaque masuch as lead.
gamma terial
.
The Rays
of
Uranium. The Rays of Thorium.
Henri Becquerel discovered radioactivity in 1896. After the discovery of Roentgen rays, Becquerel began his researches upon the photographic effects of phosphorescent and fluorescent substances.
The
first
cathode.
The
tubes which produced Roentgen rays had no metallic antisource of the rays was the glass wall of the tube, rendered fluorescent by the action of the cathode rays. It was natural to inquire whether the emission of Roentgen rays did not necessarily accompany the production of fluorescence, whatever might be the cause of the latter, Henri Poincare suggested that it did, and various attempts were made to obtain photographic impressions on plates shielded in black paper, using zinc sulphide and calcium sulphide previously exposed to light; the re-
were finally negative. H. Becquerel made similar experiments with the salts of uranium, some of which are fluorescent. He obtained impressions on photographic plates wrapped in black paper with the double sulphate of uranyl and potassium. Subsequent experiment showed that the phenomenon obsults
CURIE
RADIOACTIVITY
577
served was not linked to that of fluorescence. The salt used need not be activated by sunlight; further, uranium and all of its compounds, whether fluorescent or not, act on the photographic plate in the same way, and metallic uranium is the most active of all. Becquerel eventually discovered that compounds of uranium, placed in complete darkness, continued for a period of years to make impressions on photographic plates wrapped in
He
then affirmed that uranium and its compounds emit sperays. These rays can penetrate thin metallic screens; as they pass through gases, they ionize them and render them conductors of electricity. The radiation from uranium is spontaneous and constant; it is independent of external conditions of light and temperature. The electrical conductivity caused in the air or other gases by the uranium rays is the same as that caused by Roentgen rays. The ions produced in both cases have the same mobility and the same coefficient of diffusion. Measurement of the current for saturation provides a convenient means of measuring the intensity of radiation under given conditions.
black paper. cial rays:
uranium
The Thorium Rays. Researches made simultaneously by C. Schmidt and Marie Curie have shown that the compounds of thorium emit rays like the uranium rays. Such rays are usually called Becquerel rays. The substances which emit Becquerel rays are called radioactive, and the new property of matter revealed by that emission has been named by Marie Curie radioactivity. The elements which so radiate are called radioelements.
Radioactivity an Atomic Property. New Based on Radioactivity. Discovery of
Method of Chemical Analysis Radium and Polonium.
From BecquereFs
from
more
made
uranium
is
researches, it was clear that the radiation intense than that from its compounds. Marie Curie
a systematic study of all known metallic elements and their compounds to investigate the radioactivity of various materials. She pulverized the various substances and spread them in uniform layers on plates of the same diameter which could be inserted into an ionization chamber. Using the current propiezo-electric quartz method, she measured the saturation and B (see p. 578). With duced in the chamber between the plates of plates 3 cm. in diameter, placed three centimeters apart, an even layer
A
n
of about 2Xio~ amperes, which scarcely increases as the thickness of the layer increases after it exceeds a fraction of a millimeter; the emanations are almost all alpha rays of uranium, absorbed. Measurements made upon the compounds of uranium
uranium oxide gives a current
easily
have
certified that the intensity of radiation increases with the uranium The same thing is true for the thorium compounds. The radio-
content.
is therefore an atomic property. the contrary, a substance such as phosphorus cannot be considered radioactive because to produce ionization it must be in the state of
activity of these elements
On
MASTERWORKS OF SCIENCE
578
white phosphorus; in the red state, or in a compound such as sodium phosphate, it does not produce ionization. Similarly, quinine sulphate, which produces ionization only while it is being heated or cooled, is not radioactive, for the emission of ions is produced here by the variation in temperature and is not an indication of radioactivity of any one of the constituent elements. It is, indeed, a fundamental characteristic of radioactivity that it is a spontaneous phenomenon and an atomic property. These considerations played an important part in the discovery of radium.
Marie Curie carried on her measurements, using both the widely distributed elements and the rare elements, and as many of their compounds as possible. In addition to pure substances, she also examined a great many samples of various rocks and ores. For simple substances and their compounds, she demonstrated that none except thorium showed an activity equal to i% of that of uranium. the ores examined, several were radioactive: pitchblende, and some others. Since all of these contain either uranium or thorium, it was natural to find them active; but the intensity of the phenomenon with certain minerals was unexpected. Thus some pitchblendes (oxide of uranium) were four times as active as metallic uranium. Chalcolite (copper phosphate and crystalline uranium) was twice as active as uranium. These facts did not agree with the results from the study of simple substances and their to
Among
chalcolite, autunite, thorite,
compounds, according which none of these minerals should have shown more activity than uranium or thorium. Furthermore, double phosphate of copper and uranium, of the same formula as chalcolite, prepared from uranium salts
CURIE
RADIOACTIVITY
579>
and pure copper, showed an activity quite normal (less than half that of uranium). Marie Curie formed the hypothesis that pitchblende, chalco-. lite, and autunite each contain a very small quantity of a very stronglyactive material, different from uranium, from thorium, and from alreadyknown elements. She undertook to extract that substance from the ore bythe ordinary processes of chemical analysis. The analysis of these ores,, previously made in general to an accuracy of nearly i% or 2%, did not destroy the possibility that there might occur in them, in a proportion of that order, a hitherto unknown element. Experiment verified the proph-. ecy relative to the existence of new, powerfully radioactive radioelements;
:
much smaller than had been sup-posed. Several years were required to extract one of them in a state of-"
but their quantity turned out to be purity.
The research upon the radioelement hypothesized was Pierre Curie and Marie Curie together, using pitchblende. The
research
method had
to be based
upon
made
radioactivity, for
first by-
no
other*
property of the hypothesized substance was known. Radioactivity is used in a research of this kind in the following way:; the activity of a product is measured; it is then subjected to chemical, separation; the radioactivity of each resulting product is measured, and it is observed whether the radioactive substance now remains integrallyin one of the products or is divided among them, and if so, in what pro-, portion. The first chemical operations carried out showed that an enrich-,
ment
in active material
was
possible.
The
activity of the solid products
.
well-dried and spread in a powdered state on plates was measured undercomparable conditions. As more and more active products are obtained,,
necessary to modify the technique of measurements. Some methods, of quantitative analysis for radioactive materials will be described lateron in this work. it is
The method of analysis just described is comparable to spectrum, analysis from low to high frequencies. It not only discovers a radioactive-, material, but also distinguishes between the various radioactive elements,. For they differ from one another in the quality of their radiations and in their length of
life.
The
pitchblende from St. Joachimstahl which was used in the first experiments is an ore of uranium oxide. Its greatest bulk is uranium oxide, but it contains also a considerable quantity of flint, of lime, of magnesia, of iron, and of lead, and smaller quantities of some other ele-. ments: copper, bismuth, antimony, the rare earth elements, barium, silver^ and so on. Analysis made by using the new method showed a concentra-, tion of the radioactive property in the bismuth and in the barium ex-, tracted from the pitchblende. Yet the bismuth and the barium in com-, mercial use, which are extracted from non-jradioactive ores, are not themselves active. In agreement with the original hypothesis, Pierre and Marie Curie concluded that there were in the pitchblende two new radioactive elements: polonium and radium. The first of these they took to be analog to barium,. gous in its chemical properties to bismuth, and, tb,e_ second
MASTERWORKS OF SCIENCE
580
_^
these conclusions in 1898. At the same time, they indicated that polonium could be separated from the bismuth by such chemical treatments as the fractional precipitation of the sulphides or the nitrites, and that radium could be separated from barium by the frac-
They announced
tional crystallization of the chlorides in water, or their fractional precipitation by alcohol. Theoretically, they claimed, such processes should lead to the isolation of the new radioelements.
A
specimen of radium-bearing barium chloride, sixty times as active uranium, was submitted to spectral analysis by Demargay. He found, accompanying the spectrum of barium, a new line of 3815 Angstrom units. Later, examining a specimen nine hundred times as active as the oxide of uranium, he found the line of 3815 A. much strengthened, and two other new lines. Examination of polonium-bearing as the oxide of
bismuth, though the specimen was very active, revealed no new lines. It had become clear that the new elements occurred in the ore in very small proportions, and that they could be isolated only by treating hundreds or even thousands of kilograms of the ore. To accomplish this labor, it was necessary to have recourse to industrial operations, and to treat the concentrated products thus obtained. After several years, Marie Curie succeeded in obtaining several decigrams of a pure radium salt, in determining the atomic weight of that element, and in assigning to it a place in the periodic table hitherto vacant. Still later, Marie Curie and A. Debierne isolated radium in the metal state. Thus the chemical individuality of radium was established in the most complete and rigorous way. The application of the new method of investigation later led to the discovery of other new radioelements: first, actinium (discovered by A. Debierne), then ionium (by Boltwood), then mesothorium and radiothorium (by O. Hahn), then protoactinium (by O. Hahn and L. Meitner), etc. There have also been identified radioactive gases called emanations.
Among all these substances, radium is the most widely known and most widely used. Practically unvarying because of the slowness of its transformation, it is now industrially prepared, especially because of the medical applications of the gamma radiations to which it apparently gives rise, and which
are, in reality, only indirectly attributable to it. Radium produces, apparently continuously, a radioactive gas named radon, and this gas gives birth to a series of substances: radium A, radium B, radium C. The last of these emits particularly penetrating gamma rays. Radium and the derivatives which usually accompany it furnish intense sources of
alpha, beta, and gamma radiations. These have been and are the principal ones used in researches upon such radiations. From the point of view of chemistry, the studies of radium have confirmed the atomic theory of radioactivity and have provided a solid foundation for a theory of radioactive transformation.
CURIE
RADIOACTIVITY
581
Spectrum and Atomic Weight of Radium. Metallic Radium. is an alkaline-earth metal, it is extracted from its ores with the barium also found there, or combined with it. simultaneously The mixture of radium and barium is submitted to a series of operations
Since radium
of which the result is the separation of the radium from the barium in the form of a pure salt. As the products of these operations are successively enriched in radium, their radioactivity increases, the intensity of the spectral lines for radium increases as compared with the barium lines and the mean atomic weight increases. When the radium salt is wholly pure, the phoshows only the lines characteristic of radium; spark
spectrum
tographed
A line
the strong 4554.4
hard to
elimina-te, is
of barium, of such sensitivity that scarcely discernible.
it is
extremely
now
A radium salt introduced into a flame gives it a carmine-red color, and produces a visible spectrum composed of the characteristic radium lines (Giesel).
In general, the appearance of the radium spectrum resembles that of the alkaline-earth metals. It includes bright, narrow lines and also cloudy bands. The principal lines of the spark spectrum and of the flame spec-
trum follow: Flame Spectrum
Spectrum 4821.1 faint
6653
4682.3 very bright 4533*3 faint
6700-6530 63 29 6330-6130 4826
4340.8 bright 3814.6 very bright
band
band
3649.7 bright 2814.0 bright 2708.6 bright
The spark spectrum shows two intensity at 4627.5
and 4455.2
bright, nebulous bands,
with
maximum
A respectively.
The spectral reaction of radium is very sensitive. It makes possible the identification of radium present in a substance in the proportion of io~ 5 But the radioactive reaction is still more sensitive; it makes possible than the identification of the radium when its concentration is no more .
12 io~~ .
The atomic weight
mean atomic weight
of radium, or the
of a mix-
radium and barium, can be determined, as for barium, with prethan 1000 cision. Although the radioactivity of the mixture is not less times that of uranium, its atomic weight differs only negligibly from that
ture of
of barium.
The method
,
used to
of radium, the purity of
make
this determination is as follows: chloride
which had been
certified
by
spectral analysis,
was
MASTERWQRKS OF SCIENCE
582
its water of crystallization at a temperature of about 150 C. carefully weighed in the state of an anhydrous salt. From a clear solution of this salt, the chlorine was precipitated as silver chloride, and
deprived of
and was
was weighed. From the relation of that second weight supposing that the formula for anhydrous chloride of radium is RaCl 2 by analogy with the formula BaCl 2 accepted for barium chloride and using the accepted atomic weights of chlorine and silver, the atomic weight of radium could be calculated. The details of this technique have been explained in special reports the silver chloride
to the
first,
,
(Marie Curie, E. Hoenigschmid). The quantities of the chloride of
dium used have
ra-
gm. to i.o gm., and the various determinations have resulted uniformly. Taking the atomic weight of silver as 107.88 and that of chlorine as 35.457, the atomic weight of radium is 226 varied from o.i
( Hoenigschmid ) .
To
isolate
radium
in its metallic state, the
amalgam
of
radium was
prepared by electrolyzing, with a cathode of mercury, a solution containing o.i gm. of pure radium chloride. The resulting liquid amalgam decomposes water and is modified by air. It was dried, placed in a vessel of pure iron, and distilled in an atmosphere of pure hydrogen obtained by osmosis through incandescent platinum. The amalgam solidified at about 400 C. The metal, cleared of mercury, melts at 700 C. and begins to volatilize. Radium is a white, shining metal which rapidly alters in air, and which decomposes water energetically. In accord with its atomic weight, radium has been placed in the periodic table of the elements as a higher homologue of barium, in the last line of the table; its atomic number is 88; its spectrum and its chemical properties accord with its position; similarly with its high-frequency
L^ and L 2 levels) (Maurice de Broglie). a resume of the chemical properties of the radium salts: the sulphate is insoluble~ in water and the common acids (solubility in water at 20 C. is i.4X IO 3 P er liter); the carbonate is insoluble in water and in solutions of alkaline carbonates; the chloride is soluble in water (at 20 C., 245 gm. of RaCl 2 per liter), insoluble in concentrated hydrochloric acid and in pure alcohol; the bromide behaves similarly (at 20 C., spectra (values of
Here
is
m
706 gm. of RaBr 2 per
liter); the hydrate and the sulphide are soluble. The separation of radium from barium by fractional crystallization depends upon the fact that the chloride and the bromide of radium are less soluble than the corresponding salts of barium (at 20 C., 357 gm. of BaCl 2 and
1041
gm. of BaBr2 per
liter of
water).
The Radio elements Each radioelement undergoes
a transformation consisting of the sucatoms, in accord with a law that half the number existing at a given moment are transformed in a time which is characteristic of the radioelement under consideration, and which is called cessive destruction of
all its
T
CURIE
RADIOACTIVITY
583
period. Measured by the magnitude of the period, radioelements have which is more or less long. Some, like uranium and thorium, which have survived several geological epochs in the ores which contain them> its
a
life
have a very long life. Others, such as radium, actinium, polonium, mesothorium, radiothorium, and so on, would have disappeared wholly from the ores if their decay had not been compensated for by their production from uranium, and thorium. These two primary elements form, therefore,, the heads of series or families to which belong all the other radioelements derivatives of the two, bound to one another by lines of descent. The quantities of the derived elements which exist in untreated ores are proportional to the quantities of the primary elements there, and to the periods of the derivatives. Each derived element with a life sufficiently long can be extracted from uranium and thorium ores, just as the primary
elements are; but sometimes it can be obtained by the decay of a more or less distantly related element which has already been extracted from the ore. For the radioelements of short life, only the latter method is. available. In this chapter are given descriptions of the radioelements in the order which they occupy in the several families. The chemical properties of uranium and of thorium have been described in treatises on chemistry, and will be omitted here. There exist at 9 least two isotopes of uranium, Ux (period of the order of io years) and derivative with in a a short small proportion along life, existing very Ujj, with r There is probably also a third isotope, AcU.
U
The
Derivatives of Uranium
A.
THE RADIUM BRANCH
Uranium X. The compounds of uranium emit alpha, beta, and gamma come from the uranium itself (Uj and U^);
rays; always, the alpha rays
the penetrating beta and gamma rays are emitted by a group of derivatives which together form Uranium X, discovered by Crookes. Experiments show that the alpha-radiating material cannot be separated from the uranium; but by various reactions, the material which emits the beta and gamma radiations can be separated from the uranium. The methods of operation most*employed are the following: fractional crystallization of uranium nitrate, extraction of the uranium from solution by the addition of ammonium carbonate in excess, and the treatment with ether of a
In the first process,, highly concentrated solution of uranium nitrate. is concentrated in the more soluble portions. In the second* uranium uranium passes into solution, and the uranium remains, with insoluble solution. In the third, two layers o impurities such as iron, in the alkaline the liquid form; the one richer in ether contains a solution of uranium, in excess. without uranium X; the on^ richer in water contains uranium The active material thus separated has a period of twenty-four days. is not simple, but is composed of several radioelements* Uranium
X
X
X
X
MASTERWORKS OF SCIENCE
584
substance with a period of twenty-four days, preparation of which has just been described, is an isotope of thorium (atomic number, 90), and is called uranium x ; it is produced by Up and it emits a group of
The
X
beta rays only mildly penetrative. Uranium "X^ gives rise to a derivative of very short
life, uranium X2 or brevium (Fajans and Goehring). Its period is 1.13 minutes; it is a higher homologue of tantalum (atomic number, 91); it emits a group of penefound in uranium X, in very small trating beta rays. Finally, there are uranium Y (Antonoff), an isotope radioelements: other two proportions, of thorium (atomic number, 90; period, 25 hours); and uranium Z
(Hahn) (atomic number,
91; period, 6.7 hours).
Ionium. Ionium, discovered by Boltwood, is the derivative of uranium which is transformed directly into radium. Its period is 83,000 years. Its chemical properties are exactly those of thorium, the two elements being isotopes (atomic number, 90). In the treatment of ores, ionium is found in the same portions as the thorium, and it is separated at the same time as that rare earth element. From the uranium ore, what is actually extracted is, therefore, a mixture of thorium-ionium; and though the proportion of ionium is generally smaller than that of thorium, it may be com-
parable to
it.
The spectrum
of
a thorium-ionium mixture
containing 30% of been taken as an argument that the spectra of isotopes are identical. Later researches into the isotopes of lead have shown, however, that the identity is not com-
ionium
is
identical with that of thorium. This fact has
plete; there are very
minute
differences.
Though ionium occurs in relatively important quantities in the uranium ores (perhaps 20 gm. per ton of uranium), it cannot be extracted as a pure
salt
The rays
because of
its
close association
radiation of ionium
accompanied by a weak
with thorium.
simple; it is composed principally of alpha gamma ray of little penetrative power.
is
its first derivatives. The chemical individuality of radium has already been given in earlier sections. Its period is 1600 years. By radioactive transformations, radium produces a series of short-lived radioelements by which it is generally accompanied. These are a radioactive * gas, or emanation from radium, called radon, and the components A,B,C,C',C" of the active deposit. The radiation of this group is complex,
Radium and
and
is
composed
of alpha, beta,
Radium D. Radium
and gamma
D
rays.
is an E. Radium isotope of lead (atomic number, 22 years). It emits a beta radiation of which the ionizing power is very small; its presence is revealed by the formation of derivatives. Of these derivatives, the first, radium E (isotope of bismuth; atomic number, 83; period, 5 days), has a beta radiation; the second, radium F, identical with polonium, has an alpha radiation. Radium D can be extracted from uranium ores at the same time as the lead which they con-
82; period,
CURIE
RADIOACTIVITY
585
and cannot be separated from
this lead. This radioactive lead or can be used as the primary material for the preparation of can also be obtained from radium, from which it polonium. Radium derives through the intermediary steps of radon and the materials of its tain,
radiolead
D
active deposit.
Polonium. Polonium
is the first radioactive element discovered by the of chemical analysis based on radioactivity. It is a derivative through the intermediary stage of radium. It is characterized
new method of uranium
by an alpha radiation, and by the absence of penetrating rays. Its presence was recognized in the sulphides precipitated in an acid solution of pitchblende, and, in the analysis of these sulphides, it particularly clung to the bismuth. By means of the fractional precipitation of the bismuth salts from water, the polonium can be concentrated in the less soluble portions. Later research has shown that this element occurs in the ores in a much smaller proportion than radium, and that it decays, with a period of 140 days. Marckwald has demonstrated that in certain of its chemical properties, polonium is analogous to tellurium. It is characterized also by the ease with which certain metals (iron, copper, silver) displace it from acid solutions. It can be prepared either from ores or from radiolead or from
radium.
The largest quantity of polonium hitherto prepared (Marie Curie and A. Debierne) consists of about o.i mg. mixed with several milligrams of foreign metals easily reducible. The radiation of that sample was comparable to that of 0.5 gm. of radium. Among the lines in the spark spectrum, there was one (4170.5 A) which seems to belong to polonium. More recently, there has been announced the existence of a line of 2450 (A.
A
Czapek), To polonium, in the periodic table, has been assigned a place, hitherto vacant, beside bismuth (atomic number, 84), as a higher -analogue of tellurium.
The
analogy which polonium presents in part with tellurium, in part
is explainable, apparently, on considerations of valency. For the compounds in which polonium is trivalent (sulphide), the analogy with bismuth is valid; for those in which it is tetravalent (chloride, hydroxide), the analogy with tellurium is valid (M. Guillot). Polonium is soluble in acid solutions and also in concentrated soda solutions. It can
with bismuth,
behave, then, like a metal, or it can enter, like tellurium, into an acid radical. In solutions almost neutral, its compounds undergo hydrolysis and the radioactive material is deposited on the walls of the container; this process is hastened by centrifugation. Polonium appears to be susof amceptible to linkage in certain complexes such as chloropoloniate
monia, an isomorph of the corresponding salts of iron, lead, strontium, platinum; or the diethylthiosulfocarbonate of polonium, an isomorph of the salt of cobalt having the same formula. Experiment in electrolysis points to ions of complex form. Polonium can be volatilized, and the distilled material can be caught
MASTERWQRKS OF SCIENCE
386
by a gas current. The purest preparation so far obtained upon a small according to numerical evaluations, to more than fifty molecular layers, superimposed; the color is gray or black, attributable to polonium or to one of its oxides. Some polonium compounds, such as the hydride and the polonium carbonyl have been reported to be par-
-surface corresponds,
ticularly volatile.
B.
THE ACTINIUM BRANCH
The elements
of the actinium family are, in all probability, derivauranium; but they are not of the same linked series as radium &nd its derivatives. It is supposed that the isotopes of uranium give rise "to two lines of derivatives, of which the radium family forms one and the actinium family the other. The first certainly known member of the latter -family is protoactinium. The connection between protoactinium and uratives of
nium
is
probably through the intermediary
UY.
Protoactinium (Hahn and Meitner, Soddy and Cranston). Protoactinium was discovered in the residue remaining from the treatment of pitchblende from St. Joachimstahl. It is the immediate parent of actinium. It emits alpha and beta rays, and it has a period of 30,000 years. In certain of its chemical properties it is analogous to tantalum, of which it is the higher homologue (atomic of Grosse, its oxide, behaves rather like a weak tional crystallization of the
ments
number, 91). But according to the experiinstead of having the properties of an acid, base. Grosse has perfected a method of frac-
chlorides of zirconium and of protoactinium, the latter concentrating in the solution, and has obtained several centigrams of the radioelement in a pure state. Protoactinium occurs in the ores of uranium in a proportion comparable to that of radium, and can be extracted in sufficient quantity to determine its atomic weight.
Like tantalum, protoactinium can easily be dissolved as an oxide or hydrate in hydrofluoric acid. The oxide (probable formula, Pa 2 O 5 ) is a white powder with a high fusion point; calcined, it is insoluble in hydrochloric, nitric, sulphuric acids. By fusion with NaSO 4 and recovery by water and sulphuric acid, it can be dissolved and separated from tantalum. After fusion with 3 CO 3 and recovery by water, protoactinium remains in the insoluble residue, whereas the tantalum dissolves. In a hydro-
K
chloric, nitric, or sulphuric solution, the protoactinium can be precipitated entirely by an excess of phosphoric acid.
Actinium, Actinium (A. Debierne) belongs, according to properties, among the rare earth elements. Extracted time as the elements of this group, it can be
its
from ore
chemical
at the
same
separated only by laborious fractionations. Its presence is revealed by the radiation of its successive derivatives. These are formed so slowly that the activity of actinium freshly prepared increases for several months. The period of actinium
CURIE
RADIOACTIVITY
587
being about ten years, it forms with its derivatives a relatively stable group (actinium family) with a complex alpha, beta, gamma radiation. Like polonium and radium, actinium was first found in pitchblende. This generally contains, in a small proportion, rare earths, principally of the cerium group: cerium, lanthanum, neodymium, praseodymium, samarium; there are also always small quantities of thorium. In this mixture of substances with neighboring properties, thorium is the element most weakly basic, and lanthanum the one most strongly basic. Actinium is especially close to lanthanum and is even more strongly basic. Actinium is precipitated with thorium and with the rare earth elements in the state of hydrates, fluorides, or oxalates (the precipitation being relatively less complete than for lanthanum). It remains with the other rare earths when thorium and cerium are separated from them by the usual methods. The rare earths can be separated from one another by the methodical fractionation of their double ammoniacal nitrates in a nitric solution. The actinium comes out at the same time as the lanthanum, in the least soluble fractions. To enrich the actinium-bearing lanthanum in actinium, there has been used successfully the fractional precipitation of the oxalate in a nitric solution; the actinium concentrates in the solution to the ac(Marie Curie and collaborators). By applying* this method Katinium-bearing lanthanum extracted from uranium ore from Haut i to 2 milligrams of acthe of several oxide, containing grams tanga, in the ore tinium, have recently been obtained; this quantity corresponds to about ten tons of uranium. The isomorphism of the salts of actinium and lanthanum being demonstrated by the regularity of the fractional crystallizations, it can be supthat the chemical formulas of the actinium compounds are of the
<
^
posed
as the corresponding formulas for lanthanum. In the periodic table, there has been assigned to actinium a place,
same type
hitherto vacant, in the column of the trivalent elements, in the last line of the table (atomic number, 89).
Radio actinium. Actinium X. These substances are the first derivatives of actinium and are obtained by beginning with it. Radioactinium (Hahn) is an isotope of thorium (atomic number, 90), with a period of 18.9 days; it emits an alpha radiation and also weak beta and gamma radiations. It can be separated from actinium by the same methods used to separate thorium from lanthanum. It gives rise to the formation of actinium X a period of 11.2 days and a radiation like (Giesel, Godlewski), which has that of radioactinium. Actinium X is an isotope of radium (atomic numand acber, 88). From a solution containing actinium, radioactinium, amwith them be can two first the tinium X, separated by precipitating X gives birth to monia; the actinium X remains in solution. Actinium which produces an active deposit from radioactive actinon (a
gas),
actinium composed of a number of constituents.
MASTERWORKS OF SCIENCE
588
The
Derivatives of
Thorium
Mesothorium /. This substance, discovered by O. Hahn, accompanies the radium extracted from ores which contain uranium and thorium (thorianite, monazite). The beta and gamma radiations which it appears to give really come from a short-lived derivative of it, mesothorium 2. The latter can be separated from the former by precipitation by ammonia, and it immediately re-forms. Mesothorium i gives off no measurable radiation. It has not been separated from radium, of which it is an isotope (atomic number, 88); its period is 6.7 years. Its use in medicine is analogous to that of radium, and it has been industrially extracted as a by-product of the preparation of thorium in the incandescent-mantle industry. Mesothorium 2 is an isotope of actinium (atomic number, 89), and though its period is only 6.2 hours, it has nevertheless been possible to study its chemical properties (Yovanovitch). Thence has been learned
much about
the chemical properties o actinium, the study of which, as has been observed, involves great delays. This is an example of the method of radioactive indicators. To separate mesothorium 2 from mesothorium i, the method is currently used of crystallization in a strongly acid hydrochloric solution in the presence o barium. This operation leaves mesothorium 2 in solution while the chloride of mesothorium i crystallizes with the barium-chloride. Mesothorium is a source of radiothorium. After the solution has been for some time undisturbed, that substance accumulates, and can be separated by 3 after the addition of several milligrams of another reagent. In the crystallization hitherto described, radiothorium accumulates in the solution with mesothorium i; but if the operation is repeated several times at intervals of a day, finally mesothorium 2 quite free of radiothorium collects, the speed of formation of these two being different,
NH
Radiothorium. Thorium X. Radiothorium was found by O. Hahn in thorianite from Ceylon of which some hundreds of kilos had been submitted to treatment for the extraction of radium. This ore is composed chiefly of thorium oxide, but contains also some uranium oxide, and, consequently, some radium. When the chloride of radium-bearing barium coming from this mineral was submitted to fractional crystallization, it was remarked that at the same time that the radium concentrated in the less soluble portions, another radioactive substance concentrated in the more soluble portions. This material had the radioactive properties of thorium, but in a heightened degree; in particular, it gave off in great quantities the radioactive gas which is obtained from thorium compounds and which is called thoron t or thorium emanation. The new radioelement responsible for this release of gas has been called radiothorium. It is now known- that it is present in the compounds of thorium as a derivative. Radiothorium
has also been discovered in the deposits of some hot springs in Savoy
CURIE
RADIOACTIVITY
589
(Blanc). Radiothorium is an isotope of thorium (atomic number, 90); its period is 1.9 years. Its radiation is made up chiefly of alpha rays, but it also feebly gives off beta rays. It produces a short-lived derivative, thorium
X
(Rutherford, Soddy) (isotope of radium, period of 3.64 days, alpha and radiation), which is used in medicine. It can be separated from a solution of radiothorium by precipitating the latter with ammonia or with oxygenated water; thorium remains in solution. Thorium is the direct parent of thoron, from which come other derivatives forming
weak beta
X
its
X
active deposit.
THE RADIOACTIVE ORES AND THE EXTRACTION OF THE RADIOELEMENTS The Radioactive Ores THESE ORES, of which a large number are known, are all ores of uranium and thorium, containing these two elements in varying proportions, in association with inactive elements. Sought for more actively since the discovery of radium, they have been found in different parts of the globe. radioelements, derivatives of uranium or of thorium, occur in the ores in quantities proportional to those of the primary substances, respectively. Among the exploitable ores of uranium, some are almost free of thorium and contain only the series of derivatives which begin with uranium; the radium which is extracted from them is free of mesothorium. On the contrary, the commercial ores of thorium contain an appreciable quantity of uranium; with the descendants of thorium there are also present those of uranium. The mesothorium obtained in industry is therefore always accompanied by radium. For equivalent radiation, such a mixture is less valuable than radium, for mesothorium decays in accord with its
The
period of 6.7 years, whereas radium is practically constant, its period being 1600 years. The radioactive ores occur sometimes in a concentrated form, but more frequently in a dispersed form. In the first case, they form crystals of considerable volume, or compact masses which are found as threads or
beads embedded in massive rock. In the second case, they are intimately mixed through rock or soil which they impregnate wholly, or through which they are disseminated in the form of extremely tiny crystals. Indusores containing 50 milligrams or more of ratrially, not only the rich dium per ton but also the poorer ores containing only a few milligrams of radium per ton have been successfully used. In the ores, the relation between the quantity of radium and that of uranium has a constant value 7 of 3.4Xio~ . Consequently, no ore can possibly contain more than 340 milligrams of radium per ton of uranium. To recognize that an ore is radioactive, two simple processes are available: is
i.
A
piece of the ore
is
placed
on a photographic
kept entirely in darkness for a day before
it is
plate
which
developed. In the image
MASTERWORKS OF SCIENCE
590
obtained, the dark portions correspond to the active portions of the specipiece of the ore light portions to the inactive parts, 2. may be pulverized, the powder so obtained placed upon a plate, and the
A
men, and the
ionization produced by the specimen measured in an electrical apparatus. Both processes are used in prospecting, and for that purpose there is available a portable electroscope. The primary, compact ores of uranium, com-
posed of uranium oxide more or less pure, are black and dense; those in which the uranium is accompanied by acids tantalic, niobic, titanic are similarly black or dark brown. But there (samarskite, betafite, etc.) are also uranium ores of more recent origin, the result of the alteration of primary ores (autunite, chalcolite, curite, etc.) which are vividly colored. The thorium ores are generally of a more or less dark brown (thorite, orangite, thorianite, monazite, etc.). Below is given a table showing a certain
number of the ores, and later are recited the principal points in the treatment of first the uranium ores and then the uranium and thorium ores, A. Ores of the oxides of uranium or of uranium and thorium: Pitchblende (uraninite), possibly containing 30% to 80% of uranium in the form of the oxides UOa and UOs, with little or almost no thorium, but with a great number of other materials in small quantities: SiOs, Fe, Ca, Ba, Sb, Cu, Pb, Bi, etc. Compact or cryptocrystalline structure (St. Joachimstahl, England, United States, Belgian Congo, Canada). Broggerite, cleveite, etc. Ores of crystallized uranium oxide, possibly containing thorium oxide, ThOa, in varying proportions (Norway, United States).
Thorianite, an ore of the crystalline oxide of uranium and thorium with a great predominance of thorium (e.g., Th, 65%, U, 10%) (Ceylon). B. Ores of hydrated deterioration:
Bccquerelite (UOs 2HaO), 72% U (Belgian Congo). Curite (zPbO 5UOa 4HaO), lead uranate, 55% uranium (Belgian Congo). Kasolite (s?bO sUOs 3SiOa 4HaO), 40% uranium, silicouranate of lead (Belgian Congo). C. Hydrated silicates: Soddite (i2UOa 5SiOa i4HaO), 72% uranium (Belgian Congo). Qrangite, 66% thorium, i% uranium (Norway). Thorite, 45%-65% thorium, 9% uranium (Norway). D. Phosphates: Autunite (Ca 2UO* 2PO* 8HaO), phosphate of calcium and uranyl, about uranium, in green crystalline spangles (Portugal, Tonkin). Chalcolite, torbernite (Cu zUOa 2PO* 8HaO), phosphate of copper and uranyl, about 50% uranium, in green crystals (Cornwall, England; Portugal). Monazite, phosphate of rare earths, principally eerie (CePO*), containing thorium (of the order of 10%) and a little uranium (of the order of i%) (Brazil, United States, India). E. Vanadates: Carnotite, vanadate of UOa and hydrated K, about 50% uranium, in yellow
50%
crystalline
powder (United
States).
Ferghanite, Tuyamunite, composed of (Turkestan).
UOa and
VaOs, about
50% uranium
CURIE
RADIOACTIVITY
591
^
F. Niobates, tantalates, titanates: Samars'kite, niobate and tantalate of rare earths (especially the yttrium to 15% uranium, thorium (Russia, United States, India, group),
3%
Madagascar)
4%
.
niobate and
Euxenite,
titanate
of rare earths
3%
(yttrium),
to
15%
6%
thorium (Norway, United States, Madagascar). Betafite, titanoniobate and tantalate of uranium, crystallized, 25% uranium, i% thorium (Madagascar). uranium,
Uranium Ores Containing a
little
Thorium. Treatment of Pitchblende
The principal ores which the radium industry has used are pitchblende, autunite, carnotite, betafite. Some of these contain so little thorium that the Th/U ratio is of the order of io~ 5 (pitchblendes from St. Joachimstahl and from Haut Katanga). In betafite, the ratio is higher, i to 4%. The St. Joachimstahl pitchblende is the ore in which were discovered polonium and radium; exploited first for uranium, it was later exploited for radium. It occurs in association with dolomite and quartz in veins located at great depths (500 meters and more) in the granite mass of the region. Its composition is complex and variable; here is an ex-
ample: UsOs
76.82
FsOs
4.0
PbO
4.63
BiaOa
.67
ASaOs
82
ZnO
22
MnO
04
SiOa
5.07
CaO
245
MgO
19
KsO NasO
.28
Rare earths
HsO
1.19
52 3-25
S
Thorium
1-15 traces
The pitchblende from the Belgian Congo (Haut Katanga) occurs in ores resulting nuggets within sedimentary rocks; it is accompanied by from the alteration of pitchblende under the action of various physical and chemical agents: chalcolite, kasolite, etc. These ores are treated in the and actually provide the chief source of radium. in Oolen plant
Belgium
In Canada, pitchblende has been found in lengthy veins, in ancient sedimentary rock near the Arctic Circle.
The principal phases in the extraction of radium are the following: Reduction of the ore to which has been added previously a proper amount of barium to serve as a radium capturer. 2. Separation of the i.
MASTERWORKS OF SCIENCE
592
^
crude sulphates containing the radium-bearing barium. 3. Purification of the crude sulphates and transformation of the radium-bearing barium into a chloride. 4. Fractional crystallization of the chloride to obtain a salt enriched in radium. 5. Purification of the enriched chloride and final fractional crystallization of the chlorides or bromides. are represented in the accompanying table These
with an operations indication of the products of the treatment in which certain radioelements are concentrated. It must be observed that this treatment is adapted the extraction of radium and of uranium. The its principal objective other radioelements, of which less accurate account is given, are dispersed in the course of the operations. (See Table I.)
to
TABLE
I
+
Pitchblende
I
I
residue (Ra, RaD, Pa) -f- hot solution NaCl
solution
lo,
Ac, Po)
4. Na-jCOa
~I .[ residue hot solution Na 2CO 3
U, Fe(Pa,
I
1
solution
precipitated
solution
treated with
Fc
U
NasCOa residue solution
precipitated
HC1
-f
1
I
residue silica,
solution
Pa
Ba
-f-
impure Ra
coarse fractional crystallization I
I
less soluble fraction
more
treatment with HaS
precipitated -j-
Pb
RaD
Pb
soluble fraction, lo.
Ac
solution
RaD, Po
peroxidized -f
hydrates Ac. lo
NHa solution precipitated
(NH<)*
by
C0a
precipitated. dissolved HBr fine fractional crystallization
less soluble fraction
Ra
Pitchblende is generally reduced by the use of weak sulphuric acid; but that operation must sometimes be preceded by a preliminary treatment such as the roasting of the ore finely ground and mixed with carbonate of soda.
CURIE The
RADIOACTIVITY
fractional crystallization of the chlorides (the
593
.
method
originated
by Marie Curie) is a fundamental step in the treatment. It is accomplished at first in an aqueous solution. As the extraction of the radium salt advances,
it is
desirable to crystallize it in a solution of increasing acidity, its solubility, partly to aid in the elimination of various
partly to decrease
impurities (iron, calcium, rare earth elements). Generally, the fractional crystallization is not continued until a pure radium salt is obtained, but is stopped when a concentration fixed by the use to which the product is to be put (50% to 90%) has been reached. To enrich the concentrated products,
fractional
crystallization
of bromides replaces that of chlorides
(Giesel).
The method of treating pitchblende in order to obtain polonium, used in some attempts in that direction, is given in an accompanying table. The separation of polonium with lead, bismuth, and other easily reducible metals is accomplished by making use of the chemical and electrochemical properties of polonium described earlier. (See Table II.)
TABLE Pitchblende
+
II
hot solution of
HCl I
I
solution
residue to be treated for
extraction of
+
HaS
I
radium
precipitate
dissolved in
HNOs
+
HCl
Solution precipitated by
+ NHa I
I
hydrates Pb, Bi, Po treated to concentrate Po
solution
Cu
+
From Table I, it is clear that radiolead (lead RaD) is a by-product in the preparation of radium; its separation from the ore is generally is greater as the sufficiently complete, and the concentration in Radium ore contains less inactive lead. This radiolead may be conserved for the
D
The method
of concentration involves the folof lead in a nitric solution by concenprecipitation lowing steps: trated hydrochloric acid, leaving the polonium in solution; 2. The deposit electrochemical means upon copper or silver leaves of
preparation of polonium. i.
The
polonium by plunged into the solution of radiolead;
of polonium with a 3. The capture ferric hydrate. colloidal of precipitate Among the other by-products in the preparation of radium, protoactinium occurs either with the final residue of the reduction composed or in the sulphuric solution of uranium. Ionium and principally of silica in part in that same solution, in part in the insoluble occur also actinium to extract The accompanying table records the method used sulphates. that material, on one hand the mixture thorium-ionium, on the other, actinium associated with lanthanum. In this treatment, hydrofluoric acid
may
be substituted for the oxalic acid. (See Table
III.)
MASTERWORKS OF SCIENCE
594
TABLE More resulting
III
soluble fraction o
solution
from the coarse fractional crystallization of radium (Ba, lo, Ac) treated by H*S 1
|
pcroxidizcd solution
sulphides y
solution
hydrates dissolved in oxalic acid HCl
Ba
+
solution
oxalates
4- hot solution
Fe
NaOH
I
hydrates dissolved in HCl, treatment with NaaCOs 1
I
solution Th. To
precipitates
Ac
-f La,
Nd,
Pr, Cc, etc.
separation or Ce then fractional precipitation of the oxalates in a nitric solution
Only a few indications of the treatment used for other ores which have been exploited industrially are given here. The principal phases of the treatment are the same as for pitchblende, but the processes employed for the reduction of the ore and the obtaining of the crude sulphates may vary from one ore to another. Carnotite a vanadate of uranium found principally in the United States and autunite a phosphate of uranium and lime which has been mined principally in Portugal can both, in certain cases, be treated with weak, hot hydrochloric acid; from that solution, the crude sulphates are In other cases there is an advantage in treating the ore with precipitated. carbonate of soda prior to dissolving it in acid. Betafite an ore from Madagascar which contains bic, titanic,
and
tantalic acids
is
uranium with nioreduced by fusion with soda and car-
bonate of soda in order to cause the rare acids to pass into solution. The reduction can also be accomplished with bisulphate of soda and reclamation with water; the sulphate of radium-bearing barium then remains in the residue with the rare acids. These latter can be separated by treatment with soda or with weak hydrofluoric acid.
Ores of Thorium and Uranium ores of thorium are poor in uranium, and consequently have a from the fact that they contain almost solely the derivatives of thorium; this is the situation with certain thorites. But in the
Some
scientific interest
CURIE
RADIOACTIVITY
595
which have been exploited (thorianite, monazite) the proportion of uranium to thorium is sufficiently large for the derivatives of these two
ores
elements to be represented by comparable radiations. Thorianite is an ore rich in thorium, found in the island of Ceylon in the form of small crystal cubes. By the treatment of several hundred kilo-
grams of that
ore,
mesothorium and radio thorium were discovered. The
proportion of thorium in this ore runs as high as 60 to 80%; that of uranium, 10 to 20%. Monazite, though it is less rich in thorium, is nevertheless regularly exploited for the incandescent-mantle industry, because it is found in great quantities in the so-called monazite sands of the
United States and of Brazil. Monazite is a rare-earth phosphate, crystallized, containing generally 6 to 12% of thorium. It is reduced with hot sulphuric acid, and all the soluble sulphates are extracted; in the insoluble sulphates, along with barium, radium and mesothorium i occur. The latter treatment of these crude sulphates does not differ in principle from that already described. The fractional crystallization is undertaken to separate in the less soluble in the more soluble portions the radium and the mesothorium i and, of mesothorium. portions, the radiothorium a disintegration product The fractional crystallization can be continued until there is obtained a chloride or a bromide of radium quite free of barium and containing a continued fractional crystalnegligible amount of mesothorium. After that, lization does not alter the product thus obtained. The effect of the mesothorium is, however, so important that in certain products a month old it is estimated that about 75% of the most penetrating gamma rays are due to the mesothorium (through its derivative MThll) and about 25% of the most penetrating gamma rays to the radium (through its derivative RaC). The gamma radiation increases constantly for about three years because of the formation of radiothorium and its later derivatives. Having passed it lessens because of the destruction of the meso thorium^ i; about fifty years, the radiation is due almost solely to radium, with a diminution of about 2% of the original quantity of radiation.
a
maximum,
after
THE SPECIAL AND GENERAL THEORY
RELATIVITY:
by
ALBERT EINSTEIN
CONTENTS Relativity:
Part One: I.
II.
The
Special
and General Theory
The Special Theory of Relativity Physical Meaning of Geometrical Propositions The System of Co-ordinates
Space and Time in Classical Mechanics The Galileian System of Co-ordinates V. The Principle of Relativity (in the Restricted Sense) VI. The Theorem of the Addition of Velocities Employed III.
IV.
in Classical
Mechanics VII,
The Apparent
Incompatibility of the
Law
of Propagation of Light
with the Principle of Relativity VIII.
IX.
On
the Idea of
The
Time
in Physics
Relativity of Simultaneity
X* On the Relativity of the Conception XL The Lorentz Transformation XII. XIII.
XIV.
XV. XVI. XVII.
of Distance
The Behaviour of Measuring Rods and Clocks in Motion Theorem of the Addition of Velocities. The Experiment of Fizeau The Heuristic Value of the Theory of Relativity General Results of the Theory Expedience and the Special Theory of Relativity Minkowski's Four-dimensional Space
Two: The General Theory of Relativity XVIIL Special and General Principle of Relativity XIX. The Gravitational Field XX. The Equality of Inertial and Gravitational Mass
Part
XXI. XXII. XXIII.
XXIV.
XXV. XXVI. XXVII.
XXVIIL XXIX.
as
an Argument for
the General Postulate of Relativity In What Respects Are the Foundations of Classical Mechanics and of the Special Theory of Relativity Unsatisfactory? Few Inferences from the General Theory of Relativity Behaviour of Clocks and Measuring Rods on a Rotating Body of Reference Euclidean and Non-Euclidean Continuum Gaussian Co-ordinates The Space-time Continuum of the- Special Theory of Relativity Considered as a Euclidean Continuum The Space-time Continuum of the General Theory of Relativity Is Not a Euclidean Continuum Exact Formulation of the General Principle of Relativity The Solution of the Problem of Gravitation on the Basis of the General Principle of Relativity
A
Part Three: Considerations on the Universe as a Whole XXX. Cosmological Difficulties of Newton's Theory XXXI. The Possibility of a "Finite" and yet "Unbounded" Universe XXXIL The Structure o Space according to the General Theory of
Relativity
ALBERT EINSTEIN 1879-
is undoubtedly the best known of contemporary names. His love of music and his skill as a violinist forgotten, his devotion to philanthropic causes and his services to international order neglected, he has come to be regarded as the type of the scientist who lives in an intellectual atmosphere so rarefied that the layman dare not enter it. He is widely believed to have made science so abstruse and complicated that it retreats ever farther from the ambitious grasp. Yet he himself considers his object to be the increase of scienr
EINSTEIN'S scientists*
tific clarity
and
simplicity.
Einstein was born in 1879 in Ulm, Wiirttemberg, where his father owned a small electric-technical plant. In Munich he attended the Luitpold Gymnasium until 1894; then his family moved to Milan, and he entered the Cantonal School at Aarau, Switzerland., Two years later he began to attend lectures at the Technical Academy in Zurich, and shortly afterward, while still a student, he taught mathematics and physics in the same school. In 1901 he became a Swiss citizen, *thus qualifying for a post as examiner of patents in Berne. He held this position for eight years. Meantime he married a fellow student, a Serbian girl; he served as an unsalaried lecturer in the University of Berne; and he began publishing his first important papers. An early believer in Planck's quantum theory (1900), in these early papers Einstein treated problems which invited application of quantum mechanics. In one series (1905-09), on the assumption that propagated radiation has a "quantumlike" structure, he developed the light-quantum hypothesis, and a law of photoelectric effects. He made the first real extension of Planck's fundamental hypothesis in a paper (1907) on the variation of specific heat with temperature. Using the generalized Bohr atom rather tjian Planck's linear oscillator as
MASTERWQRKS OF SCIENCE
600
his basic concept, he developed his Law of Radiation. Much earlier he had exhaustively studied the Brownian Movements
those erratic motions of microscopic particles of insoluble matter in still water. Though these movements observably demonstrated the kinetic theory of matter, they had puzzled physicists for eighty years. Now Einstein published a complete theory and working formulas to explain them. six,
Discussing the Brownian Movements when he was twentyEinstein wrote that "rest and equilibrium can only be an
outward semblance which marks a state of disorder and unrest and prepares us for a profound alteration in the aspect of the universe as soon as we alter the scale of our observations. Nature is such that it is impossible to determine absolute motion by any experiment whatever." He was challenging the three-century-long reign of Newton's concept of the universe, signalizing the revolution in scientific thought which has transferred the study of the inner workings of nature from the .
.
.
engineering scientist to the mathematician. The readers of these early papers recognized in them the scope of imagination and the boldness of deduction of a new master. In 1909 the University of Zurich, where shortly before he had earned his doctoral degree, made him professor extraordinary of theoretical physics; two years later he was named professor of physics at the University of Prague; the next year he returned to Zurich as professor of physics in the Technical Academy; and in 1913, after becoming once more a German citizen, he was named director of the Kaiser-
Wilhelm Physical Institute in Berlin. He had now a stipend enough to allow him to devote all his time, free of
large
routine duties, to research; and he published constantly in the learned journals of Germany, Russia, Switzerland. The Academies of Copenhagen and of Amsterdam and the Royal Society elected him to membership. In 1921, for his work on the photochemical equivalent, the Nobel Prize was conferred upon him. Six years prior to the award of the Nobel Prize, Einstein
had published his generalized theory of relativity, and ten years before that, his restricted theory, with an account of its consequences. The restricted theory had been generally accepted in Germany as early as 1912; but elsewhere it was skeptically. The complete theory made its way slowly, only gradually winning British scientists. By their vote Einstein was awarded the Copley Medal of the Royal Society in 1925, and the Davy Medal in the following year. Both awards were for the relativity theory.
viewed
growing fame brought him urgent invitations He had lectured in France in the early eager to further friendliness between French and Ger-
Einstein's
to visit other countries. 19208,
EINSTEIN man
scientists.
Now
RELATIVITY
he traveled to India,
to
China, Japan, to Latin
where he seconded Zionist ambition America, England, the United States. Everywhere
Palestine
his vast learning, his modesty, his humanity, his intellectual honesty impressed his hearers. Universities everywhere conferred honor-
degrees upon him, and learned societies everywhere pressed him for contributions to their journals. While he was on the Pacific Coast in 1932, Hitler came to power in Germany. When a "German physics" was promulgated, Einstein resigned his directorship of the Institute in Berlin. Almost im-
ary
mediately he became professor of mathematics in the Institute for Advanced Study of Princeton University. In Princeton an American citizen since 1940 he now resides. Einstein's theory of relativity grew out of his supposition that the identity in our world of inertial mass as measured by Galileo and of gravitational mass as measured by Newton is not accidental. If it is not, the Newtonian physics does not explain as wide a range of physical phenomena as is desirable. Classical, or Galilean-Newtonian, physics had explained many natural phenomena in terms of simple forces acting along
had triumphantly developed astronomy, and, mechanical "ether," had applied its principles a by assuming to problems apparently not mechanical. But the MichelsonMorley experiment on the velocity of light propagation provided sound reasons for denying the existence of an "ether"; the planet Mercury did not behave quite according to the straight lines,
predictions of Newtonian astronomy; electro-magnetic phenomena could not be wholly explained in terms of simple forces. Einstein weighed these difficulties, restudied the fundamental assumptions of physical science, and produced the special theory of relativity.
The special theory makes it possible, by use of the Lorentz transformation, to translate the phenomena of any given inertial system into terms of any other similar system. But Einstein was able to imagine a system not inertial in fact, to question whether an inertial system could really exist. In 1913, during a walking tour in the Engadine with a party which included Mme. Curie one of the few mathematicians in Europe sufficiently skilled to discuss his ideas with him he remarked to her, "What I need to know is what happens to the passengers in an elevator when it falls into emptiness." This problem is not susceptible to experimental solution. But Einstein is a mathematician, not an experimentalist. He did solve the problem, and the answer is the general theory of relativity. This theory requires that energy and mass being interchangeable and similar in properties, energy in the form of must have weight. It will, therefore, be light, for example
601
MASTERWORKS OF SCIENCE
602
the eclipse of deflected in a strong gravitational field. During the sun in 1919, observation startlingly confirmed ^the theory. stars was deflected in the neighborhood Light from the fixed the amount of the sun, and exactly in the direction and to
which Einstein had computed. The theory
also satisfactorily
in the path of Mercury; using the explained the aberration Maxwell equations, it accounted for the phenomena of electroatomic fission and the transmagnetism. Further, it foretold mutation of one element into another, ideas which later skilled experimentation confirmed. These triumphant demonstrations have led to general acof relativity, and thus to modern ceptance of the theory
physics.
But modern physics
differs radically
from Newtonian
it provides a wholly new concept of the physiphysics. Indeed, in which a mechanical ether does not exist, one cal universe
which mass and energy are interchangeable, in which absolute rest is impossible, and in which absolute time is unrecogthe twentieth century may claim to add to the nized. in
Properly
of builders of world concepts Newton one more: Einstein.
list
What The
follow!
is
Pythagoras, Copernicus,
a condensation of Einstein's Relativity:
written while he was Special and General Theory,
sor of physics in the University of Berlin.
profes-
RELATIVITY PART ONE: THE SPECIAL THEORY OF RELATIVITY I.
PHYSICAL MEANING OF GEOMETRICAL PROPOSITIONS
GEOMETRY
sets
out from certain conceptions such as "plane," "point," and
with which we are able to associate more or less definite and from certain simple propositions (axioms) which, in virtue of these ideas, we are inclined to accept as "true." Then, on the basis of a logical process, the justification of which we feel ourselves compelled to admit, all remaining propositions are shown to follow from those axioms, "straight line," ideas,
/.
they are proven.
If, in pursuance of our habit of thought, we now supplement the propositions of Euclidean geometry by the single proposition that two points on a practically rigid body always correspond to the same distance (line-interval), independently of any changes in position to which we may subject the body, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative position of practically rigid bodies. Geometry which has been supplemented in this way is then can now legitimately ask as to the to be treated as a branch of physics.
We
"truth" of geometrical propositions interpreted in this way.
//.
THE SYSTEM OF CO-ORDINATES
EVERY DESCRIPTION of the scene of an event or of the position of an object in space is based on the specification of the point on a rigid body (body of reference) with which that event or object coincides. This applies not only to scientific description, but also to everyday life. If I analyse the I arrive at the following place specification "Trafalgar Square, London," result. The earth is the rigid body to which the specification of place refers; "Trafalgar Square, London" is a well-defined point, to which a name has been assigned, and with which the event coincides in space. If a cloud is hovering over Trafalgar Square, then we can determine its a pole perpendicuposition relative to the surface of the earth by erecting cloud. The length of the pole larly on the Square, so that it reaches the measured with the standard measuring rod, combined with the specifi-
MASTERWORKS OF SCIENCE
604
cation of the position of the foot of the pole, supplies us with a complete place specification.
We
imagine the rigid body, to which the place specification is supplemented in such a manner that the object whose position we require is reached by the completed rigid body. (a)
referred,
() In locating the position of the object, we make use of a number (here the length of the pole measured with the measuring rod) instead of designated points of reference. (c) speak of the height of the cloud even when the pole which reaches the cloud has not been erected. By means of optical observations of the cloud from different positions on the ground, and taking into account the properties of the propagation of light, we determine the length of the pole we should have required in order to reach the cloud.
We
From this consideration we see that it will be advantageous if, in the description of position, it should be possible by means of numerical measures to make ourselves independent of the existence of marked positions (possessing names) on the rigid body of reference. In the physics of
measurement
this is attained
by the application of the Cartesian system
of co-ordinates.
This consists of three plane surfaces perpendicular to each other and rigidly attached to a rigid body. Referred to a system of co-ordinates, the scene of any event will be determined (for the main part) by the specifi-
cation of the lengths of the three perpendiculars or co-ordinates (x, y, z) to those three plane
which can be dropped from the scene of the event surfaces.
We
thus obtain the following result: Every description of events in the use of a rigid body to which such events have to be involves space referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for "distances," the "distance" being represented physically by means of the convention of two marks on a rigid body.
///.
SPACE
AND TIME
"THE PURPOSE of mechanics
is
IN CLASSICAL MECHANICS
to describe
how bodies change
their position
in space with time."
not clear what
is to be understood here by "position" and stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. pedestrian who observes the misdeed from that the stone falls to earth in a parabolic curve. I athe footpath notices now ask: Do the "positions" traversed by the stone lie "in reality" on a straight line or on a parabola? Moreover, what is meant here by motion "in space"? From the considerations of the previous chapter the answer is self-evident. In the first place, we entirely shun the vague word "space,"
It
is
"space."
I
A
of which,
we must
honestly acknowledge,
we
cannot form the slightest
EINSTEIN
RELATIVITY
605
we replace it by "motion relative to a practically rigidreference." If instead of "body of reference" we insert "system of co-ordinates/' which is a useful idea for mathematical description, we are in a position to say: The stone traverses a straight line relative to a system of co-ordinates rigidly attached to the carriage, but relative to a system of co-ordinates rigidly attached to the ground (embankment) it describes a parabola. With the aid of this example it is clearly seen that there is no conception, and
body of
such thing as an independently existing trajectory (lit. "path-curve"), but only a trajectory relative to a particular body of reference. In order to have a complete description of the motion, we must specify how the body alters its position with time; i.e. for every point on the trajectory it must be stated at what time the is situated there.
body These data must be supplemented by such a definition of time that, in virtue of this definition, these time-values can be regarded essentially as magnitudes (results of measurements) capable of observation. If we take our stand on the ground of classical mechanics, we can satisfy this requirement for our illustration in the following manner. We imagine two clocks of identical construction; the man at the railway-carriage window is holding one of them, and the man on the footpath the other. Each of the observers determines the position on his own
reference-body occupied by the stone at each tick of the clock he is holding in his hand. In this connection we have, not taken account of the inaccuracy involved by the finiteness of the velocity of propagation of light.
IV.
THE GAL1LE1AN SYSTEM OF CO-ORDINATES
As is WELL KNOWN, the fundamental law of the mechanics of GalileiNewton, which is known as the law of inertia, can be stated thus: A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line. This law not only says something about the motion of the bodies, but it also indicates the reference-bodies or systems of co-ordinates, permissible in mechanics, which can be used in mechanical description. The visible fixed stars are bodies for which the law of inertia certainly holds to a high degree of approximation. Now if we use a system of co-ordinates which is rigidly attached to the earth, then, relative to this sytem, every fixed star describes a circle of immense radius in the course of an astronomical day, a result which is opposed to the statement of the law of inertia. So that if we adhere to this law we refer these motions only to systems of co-ordinates relative to which
must
A
the fixed stars do not move in a circle. system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a "Galileian system of co-ordinates." The laws of the mechanics of
Galilei-Newton can be regarded co-ordinates.
as valid only for
a Galileian system of
MASTERWORKS OF SCIENCE
606
V.
THE PRINCIPLE OF RELATIVITY
(IN
THE
RESTRICTED SENSE) IN ORDER TO ATTAIN the greatest possible clearness, let us return to our example of the railway carriage supposed to be travelling uniformly. We call its motion a uniform translation ("uniform" because it is of constant velocity and direction, "translation" because although the carriage changes its position relative to the embankment yet it does not rotate in so doing). Let us imagine a raven flying through the air in such a manner that its motion, as observed from the embankment, is uniform and in a straight line. If we were to observe the flying raven from the moving railway carriage, we should find that the motion of the raven would be one of different velocity and direction, but that it would still be uniform and in a straight line. Expressed in an abstract manner, we may say: If a mass m is moving uniformly in a straight line with respect to a co-ordinate system K, then it will also be moving uniformly and in a straight line relative r to a second co-ordinate system , provided that the latter is executing a uniform translatory motion with respect to K. In accordance with the
K
discussion contained in the preceding section, it follows that: If, relative to K, is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K? according to
K
same general laws as with respect to K. This statement is called the principle of relativity (in the restricted sense). As long as one was convinced that all natural phenomena were capable of representation with the help of classical mechanics, there was no need to doubt the validity of this principle of relativity. But in view of the more recent development of electrodynamics and optics it became more and more evident that classical mechanics affords an insufficient foundation for the physical description of all natural phenomena. At this juncture the question of the validity of the principle of relativity became ripe for discussion. exactly the
There are two general facts which at the outset speak very much in favour of the validity of the principle of relativity. It supplies us with the actual motions of the heavenly bodies with a delicacy of detail little short of wonderful. The principle of relativity must therefore apply with great accuracy in the domain of mechanics. But that a principle of such broad generality should hold with such exactness in one domain of phenomena, and yet should be invalid for another, is a priori not very probable. now proceed to the second argument. If the principle of relativity (in the restricted sense) does not hold, we should be constrained to believe that natural laws are capable of being formulated in a particularly, simple manner, and of course only on condition that, from amongst all possible Galileian co-ordinate systems, we should have chosen one (K a ) of a particular state of motion as our body of reference. should then be justified in calling this system "absolutely at rest/' and all other Galileian
We
We
EINSTEIN
RELATIVITY
607
K
"in motion." If, for instance, our embankment were the system systems then our railway carriage would be a system t relative to which less 0f This diminished simsimple laws would hold than with respect to would be due the to fact that the would be in motion plicity carriage In the general laws of nature which have (i.e. "really") with respect to been formulated with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part. Now in virtue of its motion in an orbit round the sun, our earth is comparable with a railway carriage travelling with a velocity of about 30 kilometres per second. If the principle of relativity were not valid we should therefore expect that the direction of motion of the earth at any moment would enter into the laws of nature, and also that physical systems in their behaviour would be dependent on the orientation in space with respect to the earth. For owing to the alteration in direction of the velocity of revolution of the earth in the course of a year, the earth cannot be at rest relative to the hypothetical system throughout the whole year. However, the most careful observations have never revealed such anisotropic properties in terrestrial physical space, Le. a physical non-equivalence of different directions. This is a very powerful argument in favour of the principle of relativity.
K
K K K .
K
.
K
VI.
THE THEOREM OF THE ADDITION OF VELOCITIES EMPLOYED IN CLASSICAL MECHANICS
LET us SUPPOSE our
old friend the railway carriage to be travelling along the rails with a constant velocity v, and that a man traverses the length of the carriage in the direction of travel with a velocity w. With what does the man advance relative to the embankment during the velocity the man were to stand still for a second, he would advance If process? relative to the embankment through a distance v equal numerically to the
W
velocity of the carriage. As a consequence of his walking, however, he traverses an additional distance u> relative to the carriage, and hence also relative to the embankment, in this second, the distance being numeri-
w
equal to the velocity with which he is walking. Thus in total hecovers the distance v-\-w relative to the embankment in the second considered.
cally
VII.
THERE
W
THE APPARENT INCOMPATIBILITY OF THE LAW OF PROPAGATION OF LIGHT WITH THE PRINCIPLE OF RELATIVITY is
HARDLY a simpler law
in physics than that according to which:
at school knows, or light is propagated in empty space. Every child believes he knows, that this propagation takes place in straight lines with
=
a velocity c 300,000 km./sec. Of course we must refer the process of the propagation of light (and indeed every other process) to a rigid reference-body (co-ordinate system)*
MASTERWORKS OF SCIENCE
608
As such
embankment. We shall imagine have been removed. If a ray of light be sent along the see from the above that the tip of the ray will be trans-
a system let us again choose our
the air above
it
to
embankment, we
mitted with the velocity c relative to the embankment. Now let us suppose that our railway carriage is again travelling along the railway lines with the velocity v f and that its direction is the same as that of the ray of light, but its velocity of course much less. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage, w is the required velocity of light with respect to the carriage, and we have u>
The
=c
v.
velocity of propagation of a ray of light relative to the carriage thus
comes out smaller than c. But this result comes into
conflict with the principle of relativity set forth in Chapter V. For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway carriage as reference-body as when the rails are the body of reference. But if every ray of light is propagated relative to the embankment with the velocity c, then for this reason it
would appear that another law of propagation of light must necessarily hold with respect to the carriage a result contradictory to the principle of relativity. In view of this
dilemma there appears
to
be nothing else for
it
than
abandon
either the principle of relativity or the simple law of the propagation of light in vacuo. The epoch-making theoretical investigations of H. A. Lorentz on the electrodynamical and optical phenomena
to
connected with moving bodies lead conclusively to a theory of electromagnetic phenomena, of which the law of the constancy of the velocity of light in vacuo is a necessary consequence. Prominent theoretical physicists
were therefore more inclined to reject the principle of relativity. At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became not the least incompatibility between the of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has. been called the special theory of relaevident that in reality there
principle of relativity
is
and the law
tivity.
VIII.
ON THE IDEA OF TIME IN PHYSICS
LIGHTNING has struck the rails on our railway embankment at two places A and B far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously. If I now approach you with the request to explain to me the sense of the statement more precisely, you find after some consideration that the answer to this question
is
not so easy as
it
appears at
first sight.
EINSTEIN
RELATIVITY
609
After thinking the matter over for some time you offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured and an observer placed at of the distance AB. This observer should be supplied the mid-point with an arrangement (e.g. two mirrors inclined at 90) which allows him and B at the same time. If the observer visually to observe both places perceives the two flashes of lightning at the same time, then they are simultaneous.
M
A
I am very pleased with this suggestion. You declare: "There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled. That light re>M as for the path quires the same time to traverse the path A >M is in reality neither a supposition nor a hypothesis about the B physical nature of light, but a stipulation!' It is clear that this definition can be used to give an exact meaning not only to two events, but to as many events as we care to choose, and independently of the positions of the scenes of the events with respect
We
are thus to the body of reference (here the railway embankment). led also to a definition of "time" in physics. For this purpose we suppose that clocks of identical construction are placed at the points A, B and C of the railway line (co-ordinate system), and that they are set in such a
manner
that the positions of their pointers are simultaneously (in the
above sense) the same. Under these conditions we understand by the "time" of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.
IX.
WE
THE RELATIVITY OF SIMULTANEITY
rails with the constant in v and direction indicated in the velocity Fig. i. People travelling in this train will with advantage use the train as a rigid reference-body (co-
SUPPOSE a very long train travelling along the
^
^f
u
A
M FIG.
E,
/
3rai-7*'
J3 i.
ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. * and B) which Are two events (e.g. the two strokes of lightning are simultaneous with reference to the railway embankment also simultaneous relatively to the train?
A
MASTERWORKS OF SCIENCE
610
When we
say that the lightning strokes
A
and
B
are simultaneous
with respect to the embankment, we mean: the rays of light emitted at the meet each other at the midplaces A and B, where the lightning occurs, of the embankment. But the events A >B A of the length point and B also correspond to positions A and B on the train. Let M' be the >J? on the travelling train. Just when the mid-point of the distance A f flashes of lightning occur, this point naturally coincides with the point M, but it moves towards the right in the diagramf with the velocity v in the train did not of the train. If an observer sitting in the position remain he would then this permanently at M, and the velocity, possess
M
M
M
flashes of lightning A and B would reach him they would meet just where he is situated. Now in reference to the railway embankment) he is reality (considered with hastening towards the beam of light coming from B f whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took thus arrive at the important place earlier than the lightning flash A.
light rays emitted
simultaneously,
by the
i.e.
We
result:
Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an
event.
We
concluded that the man in the carriage, who traverses the disper second relative to the carriage, traverses the same distance also with respect to the embankment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to tance
tv
the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance tv relative to the railway line in a time which is equal to one second as judged from the embankment.
X.
ON THE RELATIVITY OF THE CONCEPTION OF DISTANCE
LET us CONSIDER two particular points on the embankment with the velocity v, and inquire
train travelling along the as to their distance apart.
It is the simplest plan to use the train itself as the reference-body (coordinate system). An observer in the train measures the interval by marking off his measuring rod in a straight line (e.g. along the floor of the carriage) as many times as is necessary to take him* from the one marked point to the other. It is a different matter when the distance has to be judged from the
EINSTEIN A
f
RELATIVITY
6H
r
and B the two points on the train whose disrailway line. If we call tance apart is required, then both of these points are moving with the velocity v along the embankment. In the first place we require to deter-
mine the points A and B of the embankment which are just being passed by the two points A' and #' at a particular time t judged from the embankment. These points A and B of the embankment can be determined by applying the definition of time given in Chapter VIIL The distance between these points A and B is then measured by repeated application of the measuring rod along the embankment. A priori it is by no means certain that this last measurement will supply us with the same result as the first. Thus the length of the train as measured from the embankment may be different from that obtained by measuring in the train itself. This circumstance leads us to a second objection which must be raised against the apparently obvious consideration of Chapter VI. Namely, if the man in the carriage covers the distance w in a unit of time measured from the train then this distance as measured from the embankment is not necessarily also equal to w.
XL THE LORENTZ TRANSFORMATION THE
RESULTS of the last three chapters show that the apparent incompatilaw of propagation of light with the principle of relativity (Chapter VII) has been derived by means of a consideration which bor-
bility of the
rowed two
unjustifiable hypotheses
from
classical
mechanics; these are
as follows:
(1)
The
time-interval (tirne)
between two events
is
independent of
the condition of motion of the
body of reference. (2) The space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference.
we drop
these hypotheses, then the dilemma of Chapter VII disbecause the theorem of the addition of velocities derived in appears, Chapter VI becomes invalid. The possibility presents itself that the law of the propagation of light in vacua may be compatible with the principle of relativity. In the discussion of Chapter VI we have to do with places and times relative both to the train and to the embankment. Can we conceive of a relation between place and time of the individual events relative to both reference-bodies, such that every ray of light possesses the velocity of transmission c relative to the embankment and relative to the If
train?
Up to the present we have only considered events taking place along the embankment, which had mathematically to assume the function of a straight line. In the manner indicated in Chapter II we can imagine this reference-body supplemented laterally and in a vertical direction by means of a framework of rods, so that an event which takes place any-
MASTERWORKS OF SCIENCE
612
localised with reference to this framework. Similarly, we train travelling with the velocity v to be continued across the can imagine how far off it may be, the whole of space, so that every event, no matter framework. In every second the to with localised respect could also be three surfaces perpendicular to each other framework we
where can be
imagine and designated
such
marked
out,
as "co-ordinate planes"
("co-ordinate sys-
K
then, corresponds to tjie embankment, and co-ordinate system An event, wherever it may have taken train. the to K' a co-ordinate system fixed in space with respect to be by the three perpendicuwould place, with regard to time by a timelars x, y, * on the co-ordinate planes, and event would be fixed in respect of space , the same value /. Relative to f f values x f y , zf, t', which o course are not time
tem"). A
K
K
and
by corresponding identical with x,y,z,t.. What are the values yf /,
the magnitudes
The
relations
K
of an event with respect to , when are given? of the same event with respect to be so chosen that the law of the transmission of light ,
f
sf, t
K
x, y, z, t
must
-JT' "JC
FIG. 2.
one and the same ray of light (and of course for f For the relative orientation in space and the diagram (Fig. 2), this problem in indicated of the co-ordinate systems
in vacuo
is
satisfied for
every ray) with respect is
solved by
to
K
K
means of the equations: / ,_.
This system of equations If in
.
known
as the
vt
"Lorentz transformation."
law of transmission of light we had taken as our the absolute assumptions of the older mechanics as to
place of the
basis the tacit
is
x
_
RELATIVITY
EINSTEIN-
_
character of times and lengths, then instead of the above obtained the following equations:
=x
This system of equations
The
is
615
we
should have
Vt
often termed the "Galilei transformation."'
from the Lorentz transformation by substituting an infinitely large value for the velocity of light c in the latter transformation. Galilei transformation can be obtained
XII.
THE BEHAVIOUR OF MEASURING RODS AND CLOCKS IN MOTION
K
f
#'-axis of in such a manner that one end o, whilst the other end (the beginning) coincides with the point yf f i. What is the (the end of the rod) coincides with the point x length of the metre-rod relatively to the system K? In order to learn this, we need only ask where the beginning of the rod and the end of the rod lie with respect to at a particular time t of the system K. By means of I
PLACE a metre-rod in the
=
=
K
equation of the Lorentz transformation the values of these two* -o can be shown to be points at the time t the
first
=
^(beginning of rod)
r(end of rod)
= o.^ =
/
i.J
fL
x
I
_*
the distance between the points being
%/
i
-.
But the metre-rod
is moving with the velocity v relative to K. It therefore follows that thelength of a rigid metre-rod moving in the direction of its length with a 2 v^/c of a metre. The rigid rod is thus shorter when velocity v is \/ i in motion than when at rest, and the more quickly it is moving, the*
=
=
2 the rod. For the velocity v c we should have >/ i t^/c o,. velocities the root becomes greater square imaginary. From this we conclude that in the theory of relativity the velocity c plays the part, of a limiting velocity, which can neither be reached nor exceeded by any real body. If, on the contrary, we had considered a metre-rod at rest in the #-axis with respect to K, then we should have found that the length of shorter
and for
is
still
2 the rod as judged from K! would have been \J i tfi/c ; this is, quite in accordance with the principle of relativity which forms the basis of our
MASTERWORKS OF SCIENCE
614
we had based our considerations on the Galilei transshould not have obtained a contraction of the rod as a consequence of its motion. Let us now consider a seconds clock which is permanently situated o and / i are two successive ticks of at the origin (x' o) of Kf; t' this clock. The first and fourth equations of the Lorentz transformation considerations. If
formation
we
=
=
=
give for these two ticks: t
=o
and
As judged from from
K
f
the clock
is
is moving with the velocity v; as judged time which elapses between two strokes of
the clock
this reference-body, the
not one second, but
\
,
-:
pr
\'
seconds,
/.
e.
a
somewhat
?
larger time. As a consequence of its motion the clock goes more slowly than when at rest. Here also the velocity c plays the part of an unattain-
able limiting velocity.
XIIL
THEOREM OF THE ADDITION OF VELOCITIES. THE EXPERIMENT OF FIZEAU
IN Chapter VI we derived the theorem of the addition of velocities in one direction in the form which also results from the hypotheses of classical mechanics. This theorem can also be deduced readily from the Galilei transformation (Chapter XI). In place of the man walking inside the carriage, we introduce a point moving relatively to the co-ordinate
system K' in accordance with the equation yf
By means
we
of the
first
can express x' and
- wf.
and fourth equations of the Galilei transformation / in terms of x and t, and we then obtain
x
= (v-\-w}t.
This equation expresses nothing else than the law of motion of the point with reference to the system (of the man with reference to the emand we then bankment). We denote this velocity by the symbol f
K
obtain, as in Chapter VI,
W= v+w
W
(A).
EINSTEIN
^
RELATIVITY
615
But we can carry out this consideration just as well on the basis of the theory of relativity. In the equation y?
= wf
f
we must
then express x and / in terms of x and t, making use of the and fourth equations of the Lorentz transformation. Instead of the equation (A) we then obtain the equation
first
(B),
which corresponds
to the theorem of addition for velocities in one direction according to the theory of relativity. The question now arises as to which of these two theorems is the better in accord with experience. On
we
most important experiment which the Fizeau performed more than half a century ago. The experiment is concerned with the following question. Light travels in a motionless liquid with a particular velocity w. How quickly does it travel in the direction of the arrow in the tube T (see the accompanying diagram. Fig. 3) when the liquid above mentioned is flowing through the tube with a velocity v? In accordance with the principle of relativity we shall certainly have to take for granted that the propagation of light always takes place with the same velocity w with respect to the liquid, whether the latter is in motion with reference to other bodies or not. The velocity of light relative to the liquid and the velocity of the latter relative to the tube are this
point
are enlightened by a
brilliant physicist
thus
known, and we require
the velocity of light relative to the tube.
/
T
FIG. 3.
If
we
denote the velocity of the light relative to the tube by
W
f
then
given by the equation (A) or (B), according as the Galilei transformation or the Lorentz transformation corresponds to the facts. Experiment decides in favour of equation (B) derived from the theory of relativity, and the agreement is, indeed, very exact. this is
XIV.
THE HEURISTIC VALUE OF THE THEORY OF RELATIVITY
OUR TRAIN OF THOUGHT in the foregoing pages can be epitomised in the following manner.
MASTERWORKS OF SCIENCE
616
Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-
K
x, y, z, t of the original co-ordinate system f we introduce f f space-time variables xf, y , z , tf of a co-ordinate system K'. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations. This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then
time variables
new
at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.
XV. IT
GENERAL RESULTS OF THE THEORY
CLEAR from our previous considerations that the (special) theory of grown out of electrodynamics and optics. In these fields it not appreciably altered the predictions of theory, but it has consider-
is
relativity has lias
ably simplified the theoretical structure,
i.e.
the derivation of laws, and
what is incomparably more important it has considerably reduced the number of independent hypotheses forming the basis of theory. Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in which the velocities of matter v are not very small as compared with the velocity of light. We have experience of such rapid motions only in the case of electrons and ions; for other motions the variations from the laws of classical mechanics are too small to make themselves evident in practice. In accordance
with the theory of
kinetic energy of a material point of mass
m
is
relativity the
no longer given by the
well-known expression v*
.
m-
9
but by the expression
me2
This expression approaches ever great
infinity as the velocity
v approaches the veloc-
The velocity must therefore always remain less than c, howmay be the energies used to produce the acceleration. If we
ity of light c.
EINSTEIN
RELATIVITY
617
develop the expression for the kinetic energy in the form of a series, obtain
we
r\r\i-rt IT*
_ When
V* -g-
.
is
small
compared with
unity, the third of these terms
is
always small in comparison with the second, which last is alone considered in classical mechanics. The first term me2 does not contain the velocity, and requires no consideration if we are only dealing with the question as to how the energy of a point-mass depends on the velocity. Before the advent of relativity, physics recognised two conservation laws of fundamental importance, namely, the law of the conservation of
energy and the law of the .conservation of mass;, these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law.
The principle of relativity requires that the law of the conservation of energy should hold not only with reference to a co-ordinate system K, but also with respect to every co-ordinate system Kf which is in a state of uniform motion of translation relative to K, or, briefly, relative to every "Galileian" system of co-ordinates. In contrast to classical mechanics, the Lorentz transformation isjie deciding factor in the transition from one
such system to another. By means of comparatively simple considerations
we are led to draw the following conclusion from these premises, in conjunction with the fundamental equations o the electrodynamics of Maxwell: body moving with the velocity v, which absorbs an amount of energy EQ in the form of radiation without suffering an alteration in velocity in the process, has, as a consequence, its energy increased by an amount
A
In consideration of the expression given above for the kinetic energy of the body, the required energy of the body comes out to be
~
(*+!> Thus
the body has the same energy as a bo'dy of mass
moving with the amount
of energy
velocity v.
E09
Hence we can
say: If a
I
m +"~3
1
body takes up an
E
then
the inertial mass of a body
its inertial is
mass increases by an amount -5;
not a constant, but varies according to the
MASTERWORKS OF SCIENCE
618
inertial mass of a system of bodies change in the energy of the body. The can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form
we
term me2 is nothing else than the energy possessed by the absorbed the energy E Q direct comparison of this relation with experiment is not possible
see that the
body before
A
it
.
at the present time, owing to the fact that the changes in energy E to which we can subject a system are not large enough to make themselves 77
perceptible as a change in the inertial mass of the system.
|
is
too
small in comparison with the mass m, which was present before the alteration of the energy. It is owing to this circumstance that classical mechanics was able to establish successfully the conservation of mass as a
law of independent
validity.
XVL EXPERIENCE AND THE SPECIAL THEORY OF RELATIVITY is KNOWN that cathode rays and the so-called /?-rays emitted by radioactive substances consist of negatively electrified particles (electrons) of very small inertia and large velocity. By examining the deflection of these
IT
under the influence of electric and magnetic law of motion of these particles very exactly.
rays
fields,
we
can study the
In the theoretical treatment of these electrons, we are faced with the electrodynamic theory of itself is unable to give an account of their nature. For since electrical masses of one sign repel each other, the negative electrical masses constituting the electron would necessarily be scattered under the influence of their mutual repulsions, unless there are forces of another kind operating between them, the nature of which difficulty that
has hitherto remained obscure to us. If we now assume that the relative distances between the electrical masses constituting the electron remain unchanged during the motion of the electron (rigid connection in the sense of classical mechanics), we arrive at a law of motion of the electron which does not agree with experience. Guided by purely formal points of view, H. A. Lorentz was the first to introduce the hypothesis that the particles constituting the electron experience a contraction in the direction of motion in consequence of that motion, the amount of this contraction being proportional to the expression *
/
i
-5 .
This hypothesis,
EINSTEIN
RELATIVITY
619
which
is not justifiable by any electrodynatnical facts, supplies us then with that particular law of motion which has been confirmed with great
precision in recent years. The theory of relativity leads to the same law of motion, without requiring any special hypothesis whatsoever as to the structure and the behaviour of the electron.
XVII. SPACE
is
MINKOWSKTS FOUR-DIMENSIONAL SPACE
a three-dimensional continuum.
By
this
we mean
that
it is
pos-
sible to describe the position of a point (at rest)
by means of three numbers (co-ordinates) x, y, z, and that there is an indefinite number of points in the neighbourhood of this one, the position of which can be described by co-ordinates such as x l9 y v z v which may be as near as we choose to the respective values of the co-ordinates x, yf z of the first point. In virtue of the latter property we speak of a "continuum," and
owing
to the fact that there are three co-ordinates
we
speak of
it
as being
"three-dimensional." Similarly, the world of physical phenomena which was briefly called "world" by Minkowski is naturally four-dimensional in the space-time sense. For it is composed of individual events, each of which is described by four numbers, namely, three space co-ordinates x, y, z and a time coordinate, the time-value t. The "world" is in this sense also a continuum; for to every event there are as
many "neighbouring"
events (realised or
at least thinkable) as we care to choose, the co-ordinates x^ 9 y i9 z^ t of which differ by an indefinitely small amount from those of the event
xt y, zt t originally considered. As a matter of fact, according to classical mechanics, time is absolute, /.
=
to give
due prominence
however, we must replace i. ct proby an imaginary magnitude \/
to this relationship,
the usual time co-ordinate
/
portional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same role as the three
space co-ordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean geometry. It must be clear even to the non-mathematician that, as a consequence of this purely
MASTERWORKS OF SCIENCE
620
formal addition to our knowledge, the theory perforce gained clearness in no mean measure.
PART TWO: THE GENERAL THEORY OF RELATIVITY XVI1L
SPECIAL
AND GENERAL
PRINCIPLE OF RELATIVITY
THE
BASAL PRINCIPLE, which was the pivot of all our previous considerawas the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion. The principle we have made use of not only maintains that we may equally well choose the carriage or the embankment as our reference-body tions,
for the description of any event. Our principle rather asserts what follows: If we formulate the general laws of nature as they are obtained from experience, by making use of (a) the embankment as reference-body, (&) the railway carriage as reference-body, then these general laws of nature (e.g. the laws of mechanics or the law of the propagation of light in vacuo) have exactly the same form in both cases. This can also be expressed as follows: For the physical description of natural processes, neither of the reference-bodies K, Kf is unique (lit. "specially marked out") as compared with the other. Unlike the first, this latter statement need not of necessity hold a priori; it is not contained in the conceptions of "motion" and "reference-body" and derivable from
them; only experience can decide as to its correctness or incorrectness. We started out from the assumption that there exists a referencebody K, whose condition of motion is such that the Galileian law holds" with respect to it: A particle left to itself and sufficiently far removed
from
other particles moves uniformly in a straight line. With refer(Galileian reference-body) the laws of nature were to be as simple as possible. But in addition to K, all bodies of reference K! should be given preference in this sense, and they should be exactly equivalent to for the formulation of natural laws, provided that they are in a state of uniform rectilinear and non-rotary motion with respect to K; all these all
ence to
K
K
bodies of reference are to be regarded as Galileian reference-bodies.
The
validity of the principle of relativity was assumed only for these referencebodies, but not for others (e.g. those possessing motion of a different
kind). In this sense
we
speak of the special principle of
special theory of relativity. In contrast to this we
relativity, or
wish to understand by the "general principle of relativity" the following statement: All bodies of reference K, K', etc., are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion. Let us imagine ourselves transferred to our old friend the railway carriage, which is travelling at a uniform rate. As long as it is moving uniformly, the occupant of the carriage is not sensible of its motion, and it
EINSTEIN
RELATIVITY
621
for this reason that he can without reluctance interpret the facts of the case as indicating that the carriage is at rest, but the embankment in motion. Moreover, according to the special principle of relativity, this interpretation is quite justified also from a physical point of view. If the motion of the carriage is now changed into a non-uniform is
motion, as for instance by a powerful application of the brakes, then the occupant of the carriage experiences a correspondingly powerful jerk forwards. It is clear that the Galileian law does not hold with respect to the non-uniformly moving carriage. Because of this, we feel compelled at the present juncture to grant a kind of absolute physical reality to non-uni-
form motion, in opposition XIX.
to the general principle of relativity.
THE GRAVITATIONAL FIELD
WE
PICK UP a stone and then let it go, why does it fall to the ground?" usual answer to this question is: "Because it is attractecl by the earth." Modern physics formulates the answer rather differently for the following reason. As a result of the more careful study of electromagnetic phenomena, we have come to regard action at a distance as a process impossible without the intervention of some intermediary medium. If, for instance, a magnet attracts a piece of iron, we cannot be content to regard this as meaning that the magnet acts directly on the iron through the intermediate empty space, but we are constrained to imagine after the manner of Faraday that the magnet always calls into being something physically real in the space around it, that something being what we call a "magnetic field." In its turn this magnetic field operates on the piece of iron, so that the latter strives to move towards the magnet. "!F
The
The
action of the earth
on the stone takes place
indirectly.
The
earth
produces in its surroundings a gravitational field, which acts on the stone and produces its motion of fall. As we know from experience, the intensity of the action on a body diminishes according to a quite definite law, as we proceed farther and farther away from the earth. From our point of view this means: The body (e.g. the earth) produces a field ia its immediate neighbourhood directly; the intensity and direction of the field at points farther removed from the body are thence determined by the law which governs the properties in space of the gravitational fields themselves. In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body. This
law, which holds most accurately, can be expressed in a different form in the light of the following consideration. According to Newton's law of motion, we have
(Force)
= (inertial
mass)
X (acceleration),
MASTERWORKS OF SCIENCE
622
where the body.
If
"inertial
now
mass"
gravitation
(Force)
a characteristic constant of the accelerated the cause of the acceleration, we then have
is
is
= (gravitational
X (intensity
mass)
of the
gravitational field),
where the "gravitational mass" is likewise a the body. From these two relations follows: /
.
,
v
(acceleration)' v
(gravitational = ^-r-. n (inertial
characteristic constant for
mass) vv/ r
mass)
.
.
~X (intensity v
7
f
,
of the
gravitational field).
we
from experience, the acceleration is to be indenow, pendent of the nature and the condition of the body and always the same as
If
find
for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable
We
then have choice of units we can thus make this ratio equal to unity. the following law: The gravitational mass of a body is equal to its Inertial mass. It is true that this important law had hitherto been recorded in me-
chanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as "inertia" or as
"weight"
XX.
(lit,
"heaviness").
THE EQUALITY OF INERTIAL AND GRAVITATIONAL MASS AS AN ARGUMENT FOR THE GENERAL POSTULATE OF RELATIVITY
WE IMAGINE a large portion of empty
space, so far
removed from
stars
and
other appreciable masses that we have before us approximately the conditions required by the fundamental law of Galilei. As reference-body, let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus. Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room. To the middle of the lid of the chest is fixed externally a hook with
rope attached, and now a "being" (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begins to move "upwards" with a uniformly accelerated motion. In course of time its velocity will reach unheard-of values provided that we are viewing all this from another reference-body which is not being pulled with a rope. But how does the man in the chest regard the process? The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. If he release a body which he previously had in his hand,
EINSTEIN the acceleration of the chest will for this reason the body will accelerated relative motion. The that the acceleration of the body of the same magnitude, whatever the experiment.
and
RELATIVITY
623
no longer be transmitted to this body, approach the floor of the chest with an observer will further convince himself towards the floor of the chest is always tynd of body he may happen to use for
Relying on his knowledge of the gravitational field (as it was discussed in the preceding chapter), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field. Even though it is being accelerated with respect to the "Galileian space" first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a general-
ised postulate of relativity. Suppose that the man in the chest fixes a rope to the inner side of the lid, and that he attaches a body to the free end of the rope. The result of this will
wards.
If
be to stretch the rope so that it will hang "vertically" downwe ask for an opinion of the cause of tension in the rope, the
in the chest will say: "The suspended body experiences a downward force in the gravitational field, and this is neutralised by the tension of the rope; what determines the magnitude of the tension of the rope is the gravitational mass of the suspended body." On the other hand, -an observer who is poised freely in space will interpret the condition of
man
things thus: "The rope must perforce take part in the accelerated motion of the chest, and it transmits this motion to the body attached to it. The tension of the rope is just large enough to effect the acceleration of the body. That which determines the magnitude of the tension of the rope is the inertial mass of the body." Guided by this example, we see that our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass. Thus we have obtained a
physical interpretation of this law. can now appreciate why that argument is not convincing which we brought forward against the general principle of relativity at the end of Chapter XVIII. It is certainly true that the observer in the railway the application of the carriage experiences a jerk forwards as a result of brake, and that he recognises in this the non-uniformity of motion (re-
We
refer this tardation) of the carriage. But he is compelled by nobody to also He the of acceleration "real" a to might carriage. (retardation) jerk of reference (the carriage) reinterpret his experience thus: "My body at rest. With reference to it, however, there exists mains
permanently a gravitational (during the period of application of the brakes)
field
MASTERWQRKS OF SCIENCE
624
which is directed forwards and which is variable with respect to time* Under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards direction
XXI.
is
continuously reduced."
IN WHAT RESPECTS ARE THE FOUNDATIONS OF CLASSICAL MECHANICS AND OF THE SPECIAL THEORY
OF RELATIVITY UNSATISFACTORY?
WE HAVE ALREADY STATED several times that classical mechanics starts out from the following law: Material particles sufficiently far removed from other material particles continue to move uniformly in a straight line or continue in a state of rest. have also repeatedly emphasised that this
We
K
fundamental law can only be valid for bodies of reference which possess certain unique states of motion, and which are in uniform translational motion relative to each other. Relative to other reference-bodies the law is not valid. Both in classical mechanics and in the special theory of relativity we therefore differentiate between reference-bodies relative to which the recognised "laws of nature" can be said to hold and reference-bodies relative to which these laws do not hold. But no person whose mode of thought is logical can rest satisfied with this condition of things. He asks: "How does it come that certain
K
K
K
reference-bodies (or their states of motion) are given priority over other reference-bodies (or their states of motion) ? What is the reason -for
Ms
preference?" I seek in vain for a real something in classical mechanics (or in the special theory of relativity) to which I can attribute the different behaviour of bodies considered with respect to the reference-systems and
K
Kf.
Newton saw
this objection
and attempted
to invalidate
but without success. It can only be got rid of by means of a physics which is conformable to the general principle of relativity, since the equations of such a theory hold for every body of reference, whatever may be its state of motion.
XXII.
it,
A FEW INFERENCES FROM THE GENERAL THEORY OF RELATIVITY
THE
XX
CONSIDERATIONS of Chapter show that the general theory of relaputs us in a position to derive properties of the gravitational field in a purely theoretical manner. Let us suppose, for instance, that we know the space-time "course" for any natural process whatsoever, as regards the manner in which it takes place in the Galileian domain relative to a Galileian body of reference K. By means of purely theoretical operations (i.e, simply by calculation) we are then able to find how this known natural process appears, as seen from a reference-body K? which is accelerated tivity
EINSTEIN relatively to
new body
RELATIVITY
625
K. But since a gravitational
of reference
K
',
field exists with respect to this our consideration also teaches us how the
gravitational field influences the process studied. For example, we learn that a body which is in a state of uniform rectilinear motion with respect to (in accordance with the law of
K
executing an accelerated and in general curvilinear motion with respect to the accelerated reference-body K? (chest). This acceleration or curvature corresponds to the influence on the moving body of the gravitational field prevailing relatively to K. It is known that a gravitational field influences the movement of bodies in this way, so that our consideration supplies us with nothing essentially new. However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body K, such a ray of light is transmitted rectilinearly with the velocity c. It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest (reference-body K'). From this we conclude that, in general, rays of light are propagated curvilinearly in graviGalilei)
is
tational fields.
Although a detailed examination of the question shows that the curvature of light rays required by the general theory of relativity is only exceedingly small for the gravitational fields at our disposal in practice, its estimated magnitude for light rays passing the sun at grazing incidence is nevertheless 1.7 seconds of arc. This ought to manifest itself in the following way: As seen from the earth, certain fixed stars appear to be in the neighbourhood of the sun, and are thus capable of observation during a total eclipse of the sun. At such times, these stars ought to appear to be displaced outwards from the sun by an amount indicated above, as compared with their apparent position in the sky when the sun is situated at another part of the heavens. The examination of the correctness or otherwise of this deduction is a problem of the greatest importance, the early 1 solution of which is to be expected of astronomers. In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we ferred, cannot claim any unlimited validity.
have already frequently
re-
A
curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid can only conclude that in the dust. But in reality this is not the case. the special theory of relativity cannot claim an unlimited domain of
We
validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light). a By means of the star photographs of two expeditions equipped by a Joint Committee of the Royal and Royal Astronomical Societies, the existence of the deflection of light demanded by theory was confirmed during the solar eclipse of May 29, 1919.
MASTERWORKS OF SCIENCE
626
attractive problem, to the solution of which the general of relativity supplies the key, concerns the investigation of the theory laws satisfied by the gravitational field itself. Let us consider this for a
The most
moment.
We are acquainted with space-time domains which behave (approximately) in a "Galileian" fashion under suitable choice of reference-body, i.e. domains in which gravitational fields are absent. If we now refer such a domain to a reference-body K? possessing any kind of motion, then relative to K' there exists a gravitational field which is variable with rethe general theory of relativity, spect to space and time. According to the general law of the gravitational field must be satisfied for all gravitational fields obtainable in this way. XXIII.
BEHAVIOUR OF CLOCKS AND MEASURING RODS ON A ROTATING BODY OF REFERENCE
WE
START OFF AGAIN from quite special cases, which we have frequently used before. Let us consider a space-time domain in which no gravitawhose state of motion has tional field exists relative to a reference-body is then a Galileian reference-body as regards the been suitably chosen. domain considered, and the results of the special theory of relativity hold relative to K. Let us suppose the same domain referred to a second body which is rotating uniformly with respect to K. In order of reference to fix our ideas, we shall imagine K' to be in the form of a plane circular disc, which rotates uniformly in its own plane about its centre. An observer who is sitting eccentrically on the disc K' is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body K. But the observer on
K
K
K
',
the disc
may
regard his disc'as a reference-body which
is
"at
rest.'*
The
force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field.
The
observer performs experiments on his circular disc with clocks so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to f the circular disc , these definitions being based on his observations. To start with, he places one of two identically constructed clocks at the centre of the circular disc, and the other on the edge, of the disc, so that they are at rest relative to it. As judged from this body, the clock at the centre of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to in consequence of the rotation. According to a result obtained in Chapter XII, it follows that the latter clock goes at a rate permanently slower than that of the clock at the centre of the circular disc, i.e. as observed from K. Thus on our circular disc, or, to make the case more general, in every gravitational field, a clock will go more quickly or less quickly, according to the position in which the
and measuring rods. In doing
K
K
EINSTEIN
RELATIVITY
627
clock is situated (at rest). For this reason it is not possible to obtain a reasonable definition of time with the aid of clocks which are arranged at rest with respect to the body of reference. If the observer applies his standard measuring rod (a rod which is short as compared with the radius of the disc) tangentially to the edge of the disc, then, as judged from the Galileian system, the length of this rod will be less than i, since, according to Chapter XII, moving bodies suffer a shortening in the direction of the motion. On the other hand, the from measuring rod will not experience a shortening in length, as
judged
K,
applied to the disc in the direction of the radius. If, then, the observer first measures the circumference of the disc with his measuring rod and then the diameter of the disc, on dividing the one by the other, he will not obtain as quotient the familiar number TT . but 3.14 a larger number, whereas of course, for a disc which is at rest with reif it is
=
.
.
,
spect to K, this operation would yield TT exactly. This proves that the propositions of Euclidean geometry cannot hold exactly on the rotating disc, nor in general in a gravitational field, at least if we attribute the length i to the rod in all positions and in every orientation. Hence the idea of a straight line also loses its meaning. are therefore not in a position to define exactly the co-ordinates x, y, z relative to the disc by means of the method used in discussing the special theory, and as long as the co-ordinates and times of events have not been defined we cannot assign an exact meaning to the natural laws in which these occur.
We
XXIV.
EUCLIDEAN AND NON-EUCLIDEAN CONTINUUM
THE
SURFACE of a marble table is spread out in front of me. I can get from any one point on this table to any other point by passing continuously from one point to a "neighbouring" one, and repeating this process a (large) number of times, or, in other words, by going from point to point without executing "jumps." We express this property of the surface by describing the latter as a continuum. Let us now imagine that a large number of little rods of equal length have been made, their lengths being small compared with the dimensions of the marble slab. We next lay four of these little rods on the marble slab so that they constitute a quadrilateral figure (a square), the diagonals of which are equally long. To this square we add similar ones, each of which has one rod in common with the first. proceed in like man-
We
ner with each of these squares until finally the whole marble slab is laid out with squares. If everything has really gone smoothly, then I say that the points of the marble slab constitute a Euclidean continuum with respect to the little rod, which has been used as a "distance" (line-interval). By choosing one corner of a square as "origin," I can characterise every other corner of a square with reference to this origin by means of two numbers. I only need state how many rods I must pass over when, starting from the
MASTERWORKS OF SCIENCE
628
origin, I proceed towards the "right" and then "upwards," in order to arrive at the corner of the square under consideration. These two num-
bers are then the "Cartesian co-ordinates" of this corner with reference to the "Cartesian co-ordinate system" which is determined by the ar-
rangement of
little
rods.
We
recognise that there must also be cases in which the experiment would be unsuccessful. shall suppose that the rods "expand" by an amount proportional to the increase of temperature. heat the central part of the marble slab, but not the periphery, in which case two of our little rods can still be brought into coincidence at every position on the
We
We
table. But our construction of squares must necessarily come into disorder during the heating, because the little rods on the central region of the table expand, whereas those on the outer part do not. With reference to our little rods defined as unit lengths the is no longer a Euclidean continuum, and we are also no longer in the position of defining Cartesian co-ordinates directly with their aid, since the above construction can no longer be carried out.
marble slab
rods of every kind (i.e. of every material) were to behave in the as regards the influence of temperature when they are on the variably heated marble slab, and if we had no other means of detecting the effect of temperature than the geometrical behaviour of our rods in experiments analogous to the one described here, then our best plan would be to assign the distance one to two points on the slab, provided that the ends of one of our rods could be made to coincide with these If
same way
two
points.
The method
of Cartesian co-ordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies. The reader will notice that the situation depicted here corresponds to the one brought about by the general postulate of relativity.
XXV. GAUSSIAN CO-ORDINATES ACCORDING TO Gauss, this combined analytical and geometrical mode of handling the problem can be arrived at in the following way. We imagine a system of arbitrary curves (see Fig. 4) drawn on the surface of the table. These we designate as ^-curves, and we indicate each of them = 2, and u = 3 are drawn in by means of a number. The curves u i, u the diagram. Between the curves u i and u = 2 we must imagine an infinitely large number to be drawn, all of which correspond to real numbers lying between i and 2. We have then a system of ^-curves, and this "infinitely dense" system covers the whole surface of the table. These w-curves must not intersect each other, and through each point of the surface one and only one curve must pass. Thus a perfectly definite value of u belongs to every point on the surface of the marble slab. In like manner we imagine a system of ^-curves drawn on the surface. These satisfy
= =
EINSTEIN
RELATIVITY
629
the same conditions as the w-curves, they are provided with numbers in a corresponding manner, and they may likewise be of arbitrary shape. It follows that a value of u and a value of v belong to every point on the surface of the table. For example, the point P in the diagram has the
on
=
=
i. Two 3, v neighbouring points the surface then correspond to the co-ordinates
Gaussian co-ordinates u P:
u, v
P':
u
P
and P'
+ du, v + dv,
where du and dv
signify very small numbers. In a similar manner we may Indicate the distance" (line-interval) between P and P', as measured with a little rod, by means of the very small number ds. Then according to
Gauss we have ds*
= U
du 2
+2
12
du dv
+
22 dv*,
where g119 gi29 g22 are magnitudes which depend in a perfectly definite way on u and v. The magnitudes g n glZ9 and g22 determine the be,
haviour of the rods relative to the w-curves and ^-curves, and thus also relative to the surface of the table.
For the case in which the points of the surface considered form a Euclidean continuum with reference to the measuring rods, but only in this case, it is possible to draw the ^-curves and ^-curves and to attach numbers to them, in such a manner, that we simply have:
Under
these conditions, the ^-curves and ^-curves are straight lines
m
the sense of Euclidean geometry, and they are perpendicular to each other. Here the Gaussian co-ordinates are simply Cartesian ones. It is clear that Gauss co-ordinates are nothing more than an association of two sets of numbers with the points of the surface considered, of such a nature that numerical values differing very slightly from each other are associated with neighbouring points "in space." So far, these considerations hold for a continuum of two dimensions. But the Gaussian method can be applied also to a continuum of three, four, or more dimensions. If, for instance, a continuum of four dimensions be supposed available, we may represent it in the following way. With every point of the continuum we associate arbitrarily four numbers,
MASTERWORKS OF SCIENCE
630
X B> xv w hi cn are known as "co-ordinates." Adjacent points correspond to adjacent values o the co-ordinates. If a distance ds is associated with the adjacent points P and P', this distance being measurable and well-defined from a physical point of view, then the following formula *i> *2>
holds:
d?
=
2 11 <**i
+2
where the magnitudes g ll9 in the continuum.
i2
etc.,
dx dxz
"
*+Sii dx
*
'
-L
*>
have values which vary with the position
We can sum this up as follows: Gauss invented a method for the mathematical treatment of continua in general, in which "size-relations"" between neighbouring points) are defined. To every point continuum are assigned as many numbers (Gaussian co-ordinates) as the continuum has dimensions. This is done in such a way that only one meaning can be attached to the assignment and -that numbers (Gaussian co-ordinates) which differ by an indefinitely small amount are assigned ("distances'*
of a
to adjacent points.
The Gaussian
co-ordinate system
is a logical generalialso applicable to nonrespect to the defined "size" or
sation of the Cartesian co-ordinate system. It
Euclidean continua, but only when, with "distance,"
more nearly
is
small parts of the continuum under consideration behave like a Euclidean system, the smaller the part of the continuum
under our notice.
XXVI.
THE SPACE-TIME CONTINUUM OF THE SPECIAL THEORY OF RELATIVITY CONSIDERED AS A EUCLIDEAN CONTINUUM
Galileian system to another, which is moving uniformly with reference to the first, the equations of the Lorentz transformation are valid. These last form the basis for the derivation of deductions from the special theory of relativity, and in themselves they are nothing more than the expression of the universal validity of the law of transmission of light for all Galileian systems of reference. Minkowski found that the Lorentz transformations satisfy the following simple conditions. Let us consider two neighbouring events, the relative position of which in the four-dimensional continuum is given with respect to a Galileian reference-body by the space co-ordinate
FOR THE TRANSITION from one
K
differences dx, dy f dz and the time-difference dt. With reference to a second Galileian system we shall suppose that the corresponding differf f ences for these two events are dx' t dy , dz , dt'. The magnitude
d?
= dx* + dy2 + da? m
2
dt? 9
two adjacent points of the four-dimensional space-time continuum, has the same value for all selected (Galileian) referencebodies. If we replace x, y, z f \/ i ct, by xv x2> XB) #4 , we also obtain the
which belongs
result that
to
EINSTEIN
RELATIVITY
631
is independent of the choice of the body of reference. We call the magnitude ds the "distance" apart of the two events or four-dimensional points.
Thus, if we choose as time-variable the imaginary variable \/-i ct instead of the real quantity /, we can regard the space-time continuum in accordance with the special theory of relativity as a "Euclidean" fourdimensional continuum.
THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT A EUCLIDEAN CONTINUUM
XXVII.
IN THE FIRST PART of this book we were able to make use of space-time co-ordinates which allowed of a simple and direct physical interpretation, and which, according to Chapter XXVI, can be regarded as four-dimensional Cartesian co-ordinates. This was possible on the basis of the law of the constancy of the velocity of light. But according to Chapter XXI, the general theory of relativity cannot retain this law. On the contrary,
we
arrived at the result that according to this latter theory the velocity must always depend on the co-ordinates when a gravitational field is present. In connection -with a specific illustration in Chapter XXIII, we found that the presence of a gravitational field invalidates the definition of the co-ordinates and the time, which led us to our objective in the of light
special theory of relativity. are led to the conviction that, according to the general principle of relativity, the space-time continuum cannot be regarded as a Euclidean one, but that here we have the general case, corresponding to the marble slab with local variations of temperature. Just as it was there impossible to
We
construct a Cartesian co-ordinate system from equal rods, so here it is impossible to build up a system (reference-body) from rigid bodies and clocks, which shall be of such a nature that measuring rods and clocks, arranged rigidly with respect to one another, shall indicate position and
time directly.
But the considerations of Chapter XXV and XXVI show us the way surmount this difficulty. We refer the four-dimensional space-time continuum in an arbitrary manner to Gauss co-ordinates. We assign to every point of the continuum (event) four numbers, x v x2 XB , x4 (coordinates), which have not the least direct physical significance, but only serve the purpose of numbering the points of the continuum in a definite but arbitrary manner. This arrangement does not even need to be of such a kind that we must regard x v x2) x z as "space" co-ordinates and x to
,
as a
"time" co-ordinate.
The
only statements having regard to these points which can claim
a physical existence are in reality the statements about their encounters. In our mathematical treatment, such an encounter is expressed in the fact
two lines which represent the motions of the points in question have a particular system of co-ordinate values, x ly x2 #3 , #4 in common. that the
,
,
MASTERWQRKS OF SCIENCE
632
After mature consideration the reader will doubtless admit that in reality such encounters constitute the only actual evidence of a time-space nature
with which we meet in physical statements. The following statements hold generally: Every physical description resolves itself into a number of statements, each of which refers to the coincidence of two events A and B. In terms of Gaussian cospace-time
ordinates, every such statement is expressed by the agreement of their four co-ordinates x I9 x2 #3 , #4 . Thus, in reality, the description of the co-ordinates completely replaces time-space continuum by means of Gauss ,
the description with the aid of a body of reference, without suffering from the defects of the latter mode of description; it is ndt tied down to the Euclidean character of the continuum which has to be represented.
XXVIII.
EXACT FORMULATION OF THE GENERAL PRINCIPLE OF RELATIVITY
THE FOLLOWING STATEMENT
corresponds to the fundamental idea of the
"All Gaussian co-ordinate systems are general principle of relativity: the general laws of nature." essentially equivalent for the formulation of If we desire to adhere to our "old-time" three-dimensional view of
which is being underthings, then we can characterise the development of the idea of fundamental the relativity as follows: theory general gone by The special theory of relativity has reference to Galileian domains, i.e. to those in which no gravitational field exists. In this connection a Galileian of reference-body serves as body of reference, i.e. a rigid body the state motion of which is so chosen that the Galileian law of the uniform recmotion of "isolated" material points holds relatively to it. In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no
tilinear
avail in the general theory of relativity.
The motion
of clocks
is
also
influenced by gravitational fields, and in such a way that a physical definition of time which is made directly with the aid of clocks has by no means the same degree of plausibility as in the special theory of relativity. For this reason non-rigid reference-bodies are used which are as a
whole not only moving in any way whatsoever, but which also suffer alterations in form ad lib. during their motion. Clocks, for which the law of motion is of any kind, however irregular, serve for the definition of time. We have to imagine each of these clocks fixed at a point on the non-rigid reference-body. These clocks satisfy only the one condition, that the "readings" which are observed simultaneously on adjacent clocks (in space) differ from each other by an indefinitely small amount. This nonrigid reference-body,, which might appropriately be termed a "referencemollusk," is in the main equivalent to a Gaussian four-dimensional coordinate system chosen arbitrarily. Every point on the mollusk is treated as a space-point, and every material point which is at rest relatively to it as at rest, so long as the mollusk is considered as reference-body. The
EINSTEIN
RELATIVITY
633
general principle of relativity requires that all these mollusks can be used as reference-bodies with equal right and equal success in the formulation of the general laws of nature; the laws themselves must be quite independent of the choice of mollusk. The great power possessed by the general principle of relativity lies
which is imposed on the laws of nature what we have seen above.
in the comprehensive limitation in consequence of
XXIX.
THE SOLUTION OF THE PROBLEM OF GRAVITATION ON THE BASIS OF THE GENERAL PRINCIPLE OF RELATIVITY
FINALLY, the general principle of relativity permits us to determine the influence of the gravitational field on the course of all those processes which take place according to known laws when a gravitational field is absent, i.e. which have already been fitted into the frame of the special
theory of relativity; it has also already explained a result of observation in astronomy, against which classical mechanics is powerless. According to Newton's theory, a planet moves round the sun in an ellipse, which would permanently maintain its position with respect to the fixed stars, if we could disregard the motion of the fixed stars themselves and the
action of the other planets under consideration. Thus, if we correct the observed motion of the planets for these two influences, and if Newton's theory be strictly correct, we ought to obtain for the orbit of the planet an ellipse, which is fixed with reference to the fixed stars. This deduction, which can be tested with great accuracy, has been confirmed for all the planets save one. The sole exception is Mercury, the planet which lies nearest the sun. Since the time of Leverrier, it has been known that the ellipse corresponding to the orbit of Mercury, after it has been corrected for the influences mentioned above, is not stationary with respect to the fixed stars, but that it rotates exceedingly slowly in the plane of the orbit and in the sense of the orbital motion. The value obtained for this rotary movement of the orbital ellipse was 43 seconds of arc per century, an amount ensured to be correct to within a few seconds of arc. This effect can be explained by means of classical mechanics only on the assumption of hypotheses which have little probability and which were devised solely for this purpose. On the basis of the general theory of relativity, it is found that the ellipse of every planet round the sun must necessarily rotate in the manner indicated above; that for all the planets, with the exception of
Mercury, this rotation is too small to be detected with the delicacy of observation possible at the present time; but that in the case of Mercury it must amount to 43 seconds of arc per century, a result which is strictly in agreement with observation. Apart from this one, it has hitherto been possible to make only two deductions from the theory which admit of being tested by observation,
MASTERWORKS OF SCIENCE
6 34
by the gravitational field of the sun, of light reaching us from large the of a and spectral lines displacement with the corresponding lines for light produced in an stars, as compared manner by the same kind of molecule). to wit, the curvature of light rays
terrestrially
analogous
(*'.*.
PART THREE: CONSIDERATIONS ON THE UNIVERSE AS A
WHOLE
XXX COSMOLOGICAL DIFFICULTIES OF NEWTON'S THEORY over the question as to how the universe, that suggests itself to us is be regarded, the first answer whole, universe is infinite. There the surely this: As regards space (and time) variable are stars everywhere, so that the density of matter, although very same. the the in detail, is nevertheless on average everywhere This view is not in harmony with the theory of Newton. The latter that the universe should have a kind of centre in rather IF
considered as a
WE PONDER is
theory
to
requires
which the density of the stars is a maximum, and that as we proceed outwards from this centre the group-density of the stars should diminish, of until finally, at great distances, it is succeeded by an infinite region The- stellar universe ought to be a finite island in the infinite emptiness. ocean of space.
This conception is in itself not very satisfactory. It is still less satisto the result that the light emitted by the stars factory because it leads and also individual stars of the stellar system are perpetually passing out into into infinite space, never to return, and without ever again coming universe interaction with other objects of nature. Such a finite material would be destined to become gradually but systematically impoverished. In order to escape this dilemma, Seeliger suggested a modification of Newton's law, in which he assumes that for great distances the force of attraction between two masses diminishes more rapidly than would result this way it is possible for the mean density of matter to be constant everywhere, even to infinity, without infinitely
from the inverse-square law. In
fields being produced. large gravitational
XXXI THE POSSIBILITY OF A "FINITE" AND YET "UNBOUNDED'' UNIVERSE BUT SPECULATIONS on the structure of the universe also move in quite another direction. The development of non-Euclidean geometry led to the recognition of the fact that we can cast doubt on the infiniteness of our space without coming into conflict with the laws of thought or with experience (Riemann, Helmholtz). In the first place, we imagine an existence in two-dimensional space.
EINSTEIN
RELATIVITY
635
Flat beings with flat implements, and in particular flat rigid measuring rods, are free to move in a plane. For them nothing exists outside of this plane: that which they observe to happen to themselves and to their flat is the all-inclusive reality of their plane. In particular, the constructions of plane Euclidean geometry can be carried out by means of the rods, e.g. the lattice construction, considered in Chapter XXIV. In
"things"
contrast to ours, the universe of these beings is two-dimensional; but, like it extends to infinity. In their universe there is room for an infinite number of identical squares made up of rods, i.e. its volume (surface)
ours,
is infinite. If these beings say their universe is "plane," there is sense in the statement, because they mean that they can perform the constructions of plane Euclidean geometry with their rods. In this connection the individual rods always represent the same distance, independently of their
position.
Let us consider now a second two-dimensional existence, but this time on a spherical surface instead of on a plane. The flat beings with their measuring rods and other objects fit exactly on this surface and they are unable to leave it. Their whole universe of observation extends exclusively over the surface of the sphere. Are these beings able to regard the geometry of their universe as being plane geometry and their rods withal as the realisation of "distance"? They cannot do this. For if they realise a straight line, they will obtain a curve, which we "three-dimensional beings" designate as a great circle, i.e. a self-contained line of definite finite length, which can be measured up by means of a measuring rod. Similarly, this universe has a finite area that can be compared with the area of a square constructed with rods. The great charm resulting from this consideration lies in the recognition of the fact that the universe of these beings is finite and yet has no limits. But the spherical-surface beings do not need to go on a world tour in order to perceive that they are not living in a Euclidean universe. They can convince themselves of this on every part of their "world," provided they do not use too small a piece of it. Starting from a point, they draw "straight lines" (arcs of circles as judged in three-dimensional space) of equal length in all directions. They will call the line joining the free ends of these lines a "circle." For a plane surface, the ratio of the circumference of a circle to its diameter, both lengths being measured with the same rod, is, according to Euclidean geometry of the plane, equal to a constant value TT, which is independent of the diameter of the circle. On their spherical surface our flat beings would find for this ratio the value
attempt to
sin/
]
\R) 7T
a smaller value than TT, the difference being the more considerable, the greater is the radius of the circle in comparison with the radius R of
i.e.
MASTERWORKS OF SCIENCE
636
the "world-sphere." By means of this relation the spherical beings can determine the radius of their universe ("world"), even when only a is available for their measurerelatively small part of their world-sphere ments.
Thus if the spherical-surface beings are living on a planet of which the solar system occupies only a negligibly small part of the spherical whether they are living _ universe, they have no means of determining a finite or in an infinite universe, because the "piece of universe" to which they have access is in both cases practically plane, or Euclidt *i. from this discussion that for our sphere-beings the It follows directly
circumference of a circle first increases with the radius until the "circumference of the universe" 'is reached, and that it thenceforward gradually decreases to zero for still further increasing values of the radius. During this process the area of the circle continues to increase more and more, until finally it becomes equal to the total area of the whole "worldsphere."
Perhaps the reader will wonder why we have placed our "beings" on a sphere rather than on another closed surface. But this choice has" its of all closed surfaces, the sphere is unique justification in the fact that, the property that all points on it are equivalent. I admit in possessing
that the ratio of the circumference c of a circle to its radius r depends on r, but for a given value of r it is the same for all points of the "worldis a "surface of constant sphere"; in other words, the "world-sphere" curvature." To this two-dimensional sphere-universe there is a three-dimensional
which was disanalogy, namely, the three-dimensional spherical space covered by Biernann. Its points are likewise all equivalent. It possesses a 3 finite volume, which is determined by its "radius" (zi^R ). Suppose we draw lines or stretch strings in all directions from a r with a measuring point, and mark off from each of these the distance
We
rod. All the free end-points of these lengths lie on a spherical surface. can specially measure up the area (JP) of this surface by means of a square
made up if it is
of rt
F
of
measuring rods.
If
the universe
F
is
Euclidean, then
F=
2
4?rr
;
2
With increasing values is always less than spherical, then increases from zero up to a maximum value which is determined
^r
.
still further increasing values of r, the area gradually diminishes to zero. At first the straight lines which radiate from the starting point diverge farther and farther from one another, but later they approach each other, and finally they run together again at a "counter-point" to the starting point. Under such conditions they have
by the "world-radius," but for
is easily seen that the three-dimensional spherical space is quite analogous to the two-dimensional spherical surface. It is finite (i.e. of finite volume), and has no bounds.
traversed the whole spherical space. It
It follows, from what has been said, that closed spaces without limits are conceivable. From amongst these, the spherical space (and the elliptiAs a cal) excels in its simplicity, since all points on it are equivalent.
result of this
discusion ? a most interesting question arises for astrono-
EINSTEIN mers and
physicists, infinite or whether
and that
is
is finite
it
RELATIVITY
637
whether the universe in which we in the
manner of the
Our experience
live is
spherical universe.
is far from being sufficient to enable us to answer this question. But the general theory of relativity permits of our answering it with a moderate degree of certainty.
i:;
THE STRUCTURE OF SPACE ACCORDING TO THE GENERAL THEORY OF RELATIVITY
XXXII.
ACCORDING TO the general theory of
the
relativity, geometrical properties of space are not independent, but they are determined by matter. Thus we can draw conclusions about the geometrical structure of the universe
only if we base our considerations on the state of the matter as being something that is known. We know from experience that, for a suitably chosen co-ordinate system, the velocities of the stars are small as compared with the velocity of transmission of light. We can thus as a rough approximation arrive at a conclusion as to the nature of the universe as
a whole,
if
We
we
treat the
matter as being at
rest.
already know from our previous discussion that the behaviour of measuring rods and clocks is influenced by gravitational fields, i.e. by the distribution of matter. This in itself is sufficient to exclude the possibility of the exact validity of Euclidean geometry in our universe. But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the that the metrics of surrounding
more probable, since calculations show space is influenced only to an exceedingly small extent by masses even of the magnitude of our sun. might imagine that, as regards geometry, our universe behaves analogously to a surface which is irregularly curved in its individual parts, but which
We
nowhere departs appreciably from a plane: something like the rippled surface of a lake. Such a universe might fittingly be called a quasi-Euclidean universe. As regards its space it would be infinite. But calculation shows that in a quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be inhabited by matter everywhere; it would present to us that unsatisfactory picture which we portrayed in Chapter XXX. If
differs
we
are to have in the universe an average density of matter which from zero, however small may be that difference, then the universe
cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical). Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in indi-
vidual parts from the spherical,
i.e. the universe will be quasi-spherical. be necessarily finite. In fact, the theory supplies us with a simple connection between the space-expanse of the universe and the average density of matter in it.
But
it
will