AMATEUR TELESCOPE M A K I N G ADVANCED (BOOK T W O )
A SeqfLel t 0 AMATETTR TELESCOYE ?I~AKIXG (BOOK ONE)
A ~ B E RG. T INGALLS' Editor Contributing Editor, Scientific American A eollection of contributionv to cclnateur preciaion opticv b y numerouv authorities
SCIEN'I'IFIC AMERTCAN, INC. 1952
.U7 rigltts ) . ~ s P I < I . P ~ Th? lti-lith o E Tr;iii~ltitioii: i 1 ~ , ri..-ri.\ ~ ( fl n r al1 l d ~ ~ z t i11(,111fIing ~ ~ i g ~ th? ~ ~ Sc;~~~diii:~vian Eiglitli l'rilitiiig 1 9 5 2
PRIXTED
IX
THE
ITNiTED STATPS
RIXGSPOIIT PI<EóS Ih<'.
OF
AYERICA
KlNCrYPOItT, T E N l h S S E E
CONTENTS H A V J N D T O DO W I T H THE C O S S T R I T C T I O N O F O P T I C A L INSTRUDIEA-TS PACE
Backwoods Philosophy-Everest
.......................................
3Iirror Making 'l'echnic
3
-
Sub-diameter Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Making and Using Metal 'Tools-Chrk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Metal Mirrurs aricl Flats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Astigmatism-Warner Prisms, Flats, Mirrors-Ferson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Sninll-scalr Prism Produetion
A Quantitative Optical Test for Telescope Mirrors-King
. . . . . . . . . . . . . . 104
Perforining tlie Ronclii Teat Qui~iiiiluti\ely
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 . The Hartmann Test-Caliler Flats-Selby . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 ... Notes on thc Opticnl Testing of Asplieric Surfaces-Selby . . . . . . . . . . . . . . 132 IIow t o Make Rouge-Selby . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Small 1,ens Wriril
.eco Lenses
A n Introduction to Srnall Lenses-Clarlr
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .247
31üiiil>- oii 11akiiig Byepieces
Oculars a t Smnll Cost-Patterson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .187 The Refractor-Met;~l Pnrts nnd Mounting-Triylor . . . . . . . . . . . . . . . . . . . . . .192 The Refracting Selescope-Principies of Operation and ConstructionHavilancl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212 1Iainly on tlie Objeetive Lens
Target Scopes-Kirlcliam
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .262 For thc Rifleman
Testing Convex Splierical Surfaces-King . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Collimatioii and Adjustrrient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 How t o M;il<e a Diagoiial for a xentoninn-Hindle . . . . . . . . . . . . . . . . . . 282 Making Srtting Circlrs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 . Tclescope 1)rives-1, ower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 . Drives for 1.arger Telescopes . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 319 Hand-Wound Spring Drivrs for Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321i She Sprin.gfielc1 Mouriting-Porter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 The Springfield Mounting-Pattern Making-Porter . . . . . . . . . . . . . . . . . . . . 339 With Principies of Yolding and Casting
Molding a n d Castiiig Springfield Mountiiig Parts-Ferson ...............3.1.i Moldirig and Casting a Fork-Mason . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i36l Sidelights on Molding and Casting
v
vi
CONTENTS PlOE
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Machining the Springfield 3lounting.Piirter Motor Drives, Coiiiiterweighting. Pier-Cpringfirl(1 Moiiiitiiip-Porter . . . . 371 'I'he Riiilding tif a 19-Inch lieflecting 'I'elescop<.-Yoiiiig . . . . . . . . . . . . . . . . . .376 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39.3 1 he Schinidt Carnera-Introductory-l<usht>ll Theory and Design of Aplanatic Heflectors Eiiiployirip ;i Correctirig 1.eiisWriglit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 Ineluding tlie S<.IiriiidtC;!iiirr;i Notes on the Construction of an F/1 Schrni
7
.
.
I'AllT HAVING TO
no
WITH
sonm
11
O F THE M O R E PRXCTICAL
ASIJE<'TS O F O B S E R V I N G
. Researches with Our Instriiments-Halb.ich . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 Definite, Systernütized Uses for Teleacopes The Dewing of Optical Siirfaces-Steav?nsori . . . . . . . . . . . . . . . . . . . . . . . . . .576 Limitations of Vision with u. Tclescol>e-Dall... . . . . . . . . . . . . . . . . . . . . . . . . . 579 Atmosphere, Te1escol)c arid Obierver-Douglass . . . . . . . . . . . . . . . . . . . . . . . . .565 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Heflrctors versus Refractors-Pickering U'oodin Tubes for Reflectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 6 Dealinp witli Spider Diflraction-Couder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 . . She Itichest-Field Telescope-Walkden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .623 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648 ..
H A V I N G TO DO WITH T H E CONSTHUCTTON OF OPTICAL INSTRUMENTS
By A . TI7. EI'LREST Pittsfield, 1\Iüssacliu\etts A
I'II~:UE
or
OI,ASS
He lahorrd late into tlie night, At rarly iiiorii' liis task rehulned, To f;~bhioii thus a < l i h ! i o£ glass Intu 2% sui~tleCUITT.C, not drep, But iiieasiired only by the slindes of light P'roin ;t uirnple yinholp me
N. J.
The first requirement in fiaurinp n mirror i s a rlear conception of how i t should :ippear on llie testing stand, sincc it is hy compnring wliot we see with ~v11:it we ciuglit t o ser tlint wc cleterniine \vliat t o do. Tliis :ippe:ir:ince, with tlie knife-edge in come intermediate positioii, 11:~s been snid t o resemble tlie an:ilogy is a good one, since, like arnateiir's t h a t of n doiigtinut-and mirrors, there are al1 kinds of douglinuts-roiigh ones, smootli ones, douglinuts witli lioles antl dougliniits mithout 'em. Well, whnt is t h r shape of tlie t r u e paraboloidal doi~glinut? Witli Porter a t the otlirr end of the continent, ahoul :ill we can do in tlie way of showirig this threc-dimensional appr:irance in two-dimensional space, is t o draw its cross-section only, nnd !e;~re it to the reader t o visualiee the surface of revolution this rrprcsriits. She calcu1;ition of ttiis cross-section is a simple niatter. I n f;ict, tlie cross-section of thr paraboloid, a.: it appears witli the lrnife-edge in nny iiscful position, may he covererl in :i single eclii;ttion. Let's figure ttie tiiing out under a lieading somewhat in keeping with thc method c f calculation.
F o r reacons w l i i c h will brcome cle,tr latcr on, the logical referrnce surface for our calculatioris will be a spliere whose center of curvature is a t 3
4
MIRROR MAKING
the point of ohservation, Le., where the knife edge cuts t l ~ econe of light. Further t o siinplify niatters, tliis refererice iphere mciy he inadc tangent to the paraboloid at i t i center, as in thc iipper par1 of Figure 1, mnking this point the origin of coordinates and therehy rliminating the constant of integration. In this example we have chosen n sphere whose center of curvature C prime is just outside of C , tlie center of curvature of the paraboloid's center zone. Starting a t the center, such ü sphere would lie outside the
Al1 drawings by the author FIGTRE1
paraboloid as f a r a s some zone X, bepond which it would lie within. Viewed froni its center of curvature, tliis reference sphere would appear flat, its apparent cross-section would be a straight line, and the apparent cross-section of the paraboloid would be a curve, somewhat as sliown in the lower p a r t of the same figure. A n expression f o r the deviation of the paraboloid frum this or any other reference sphere will involve the following t w o propositions, which will he stated with a degree of accuracy equivalcnt to that of r2/R without the tail end of the forrriula. This will permit t h e use of simple terms which will introduce no measurable error iñ the calculations for our telescope mirror; although, of coiirse, the error would be intolerable in similar calculations for a large searcliliglit reflector.
MIRROR MAKING
6
Proposition. 1 : For the condition shown in Figure 2, the deviation of paraboloid from sphere varies as the fourth power of its radius r , and inversely as the cube of its radius of curvature R. I n mathemi~ticalterms we woul
y =
-
k- x4 R3
The minus sign is inserted t o indicate t h a t the curve bends away from the ohserver. E'or the slope a t any poiiit, the first theorem in elementary caiculus (about al1 we remcmher) tells lis,
Proposition 2 : When observed from first one and then the other, of two points aloiig tlie axis iiear the center of curvature, the slope of any
zone changes in proportion t o the radius x of the zone, in proportion t o tlie distance L) between the two points of observation, and in inverse proportion t o R. F o r the slope in one position compared with that in the other we may write, wlience,
* dx
=
KD-2
R
y = KD-
2R
(4)
A useful example of this would be a spherical mirror examined first from its centcr of curvature, whcn i t would appear flat and its apparent crosssection would be the straight line shown in Figure 3. If now the knife-edge be moved a short distance D toward the obberver, the surface will a p p e a r concave, y varying in proportion t o $2 as shown. W e may now investigate what would happen t o the curve shown in Figure 2 if the knife-edge is moved toward the ohsrrver. The slope of each zone would change in accordance with the law given in the preceding paragrnph, which means t h a t certain sets of y values determined by Prop. 2 would b e added t o those determined by Prop. 1. F o r example, Figure 4 shows the re-
sult of adtling the zictual !/ va1ut.i of Figure 3 t o thosr of Figure 2. As a useful prol>osition, liowrrir, tlie riirrc :i
x2
2R
24
- kR3
(5)
woiild mean notliing until wr rspress T< i i i tcrrn.; of k. To do this me tn;iy consider tliat ?/ is to reticli its riliis iiii~xiiriiiiii ;rt tlic point \vlirrt* tlic rurve, surh us tlie onr sliown iri Figiire 1, iit Iiottom, or tli' oric hlioxvri iir Figiire .1., bec~iniesflat a t the crest. l'liis will be xvhen tlie slol>cs re~~reheritc.tl by tlie
* dx
I"rc,unr: 3
values of Propositions 1 and 2 cancr! each other, L e . , where
alrence,
K
=
x2
&kDR2
F o r tliis point iri tlie curvr,
D
x2 R
= -
Subslitutirig this valur of D in equation ( 6 ) , -.
and substituting this value of
in cquntion ( S ) ,
MIRROR MAKING
7
where D is the distance of the knife-edge from the eenter of curvature o € the center zorie. For tlie actu;il deriation of paraboloid from rcference spliere, k would be 0.125, tlnd the wliole expression would represent a n amount too small t o be seen. IlzrtThe coiiil>ination of tin can and razor blade forms a telescope magnifying, roughly, one Iiundred thousnnd tinws; the exact amount varying directly with the foca1 lenpth nnd depending somewhat iipon the sensitivity of the arrangement and individual interpretation. The amount stated is ahout right for a n f/8, 10" mirror, hased on tlie opinions of a riumher of experienced amateurs, using the testing arrangement t o be described. Any error here is
immaterial, since i t will have no eflect whatsoevcr upon the characteristics of the curve which are t o be considered. Compared with the more familiar telescope, this one has the peculiarity that its tremendouc magnification is in d ~ p t honly, that is, the mirror is seen with actual diameter, but with evcry deriation from reference sphere magnified by t h e above amount. F o r example, our 10" paraboloid, exainined with ihis apparatus froin the center of curvature of the ccnter zone, appears t o deviate about 2" from flatness a t the marginal zone, although in reality this deviation is only aboiit 20 millionths of a n inch. Likewise, thc apparent deviations of al1 intermcdiate zones bear the same relation t o the real. Assuiiiing a magnification of 100,000, or 625R, t o be correct for the 10" mirror, k becomes about SOR, a n d equation ( 7 ) changcs to,
8
MIRROR MAKING
This is our final "Equation of the Doughnut," from which the values of y may he stated in terrns of the niarkings on a 6" scale. Selecting values of l3 from zero to r"R in 10 percent steps, we may calculate coordinates for our 10" mirror and then put these in curve form, as shown in Figure 5. The top curve hhows the apparent cross-section of the mirror as it should appear with the knife-edge a t the center of curvature of the center zone. The bottoiii curve shows how it should appear with the knife-edge ut the center of curvature of the marginal zone. The heavy curve
half way down shows how i t should appear with the knife-edge cxactly half way between the above two positions. W e cal1 thiq tlie "lialf-way" or 50 percent curte. Starting a t the top, the light curre5,drawn in betweeri the three heavy onps represent the apparent cross-sections corresponding to knife-edge positions of 10, 20, 30, 40, and 60, 70, 80 and 90 percent of ??/R. The curvcs have heen drawn with sufficient accuracy t o bring out their fixed characteristici, that is, those landmarks whicli remain unchanged regardless of the values of k, r, or R we may select. First, note that al1 the curves are smooth. There is no sudden change in slope at any point. Next, starting with the top curve and examining tlie whole serie; in order, note how the crest spreads from center t o end; in large
MIRROR MAKING
9
jiimps for thc first step or two, and then with s m a l l ~ rand smaller hops with each succeeding curve. A simple transposition of the +/It formula tells us that tlie location of the crest should be as follows. Knife-edge position of +/R
00 percent 10 " 20 " 30 " 40 " 50 " 60 '' 70 " 80 90 " 100 '<
"
"
"
"
'' '' ''
'' '' '' ''
"
"
"
'<
"
"
"
'S
"
Location of crest Center 31.6 percent of "r"
44.7 54.8 63.3 70.7 77.5 83.7 89.5 94.9 100.0
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
"
'6
i&
"
"
"
"
"
"
A trial with straiglitedge and scale will show the curves to be in agreement with tlie above. Note, however, the flatness of crests near the center and the reiulting difficulty of determining their exact location cornpared with those fartlier o u t Note especially the flatness of the crest in the first curve which, of course, is a t the center of the mirror. P a y particular attention to the distance this flatness extends from the center before there is any perceptible deviation from a straight line. Now t r y t o locate the regions of greatest slope in the central deprewions, Le., where the curves reverse. This will be more difficult to decide, and impossible with the first two or three curles. But, as nearly as can be judged, these regions of greatest slope will be found t o extrnd from 50 percent t o 70 percent of the distance from center to crest for any of the curves. A solution for tlie maxirnum plus value of the expression
2
22
= &k,(~
22
),
-
[derived frorn equations (2) and (3)], would slioa
an intermediate point of slightly greater slope than the rest. B u t let's not introduce this typesetter's nightmare into the discussion, as no differeiice could possihly be detected by visual inspection. We are interested only in the practica1 result, which is shown in Figure 4 and will be discussed in more detail later on. Other landmarks: The depth a t the end of the first curve is the same as the depth at the center of the Iast one. The depth of thc lialf-wny curve is one-quarter of the abore. The center and end of the half-way curve are of the same depth, and this is the only curve for mhich this is true. I n the 70 perceiit curve (the eighth one down), the greatest slope in the central depression is the same as that nt the end. There is only one shape of dozcghnut, just as there is orily one shape of
10
MIRROR MAKING
par:rhola. This i.; sliown in Figure 6, where we have superirnposerl the halfway curves for three paraboloid5 of the same diamrter biit different foca1 ratios. All have exactly the sairie r1i;tracteristics iii regard to tlie relation between progressive values of y and dy/dx. The only difiereiice is in tlie intensity of the "bulge." A glance a t the douglinut farnily will show how the intensity of curvat u r e v;rries f a r out of proportion t o the diameter of the mirror. F o r any of the curves after the first one, the portioii incide tlie crests niny be used t o represent the 100 percent curve for a mirror of tliat diaiiieter. F o r tlie second curve, this dinmeter would be 31.6 ~ i r r c e n tof the last one, but blie depth i\ hardly discernible in comparison- actually 1 pcrccnt. A ~ i dnow tliat we l i ; ~ \ ecornpleted soine p
forget i t and just form a clear mental picture of the curves, especially the three heavy ones, and the surfaces of revolution they represent. The squared background of the graph paper on which the curves were originally drawn has been purposely omitted from the reproductions, since there will be no such thing t o guide us in tlie knife-edge test. Outside of a few zona1 measnrements, when figuring our shallow rnirrors, we must be guided entircly by appearance, in deciding when the goal has been reached.
I n speaking of a shadow. we refer t o the dioision between ligl~tand shade, not t o a whole area of shade. I n locatiiig a shadow, we refer t o the point where it crosses the horizontal diameter of the mirror, since this is the point where any mcasurement will be taken. A n area of shade which does not extend to the rim of the mirror will, of course, be snrrounded b y one continuous shadow; but since this shadow will cross the horizontal diametrr a t two different points, we shall speak of this area as hounded by trero shadows, one on the left and one on the right. If we imaginc the mirror t o be divided in half vertically, zones which have any appreciable slope will be illuminated in one half and dark in the other, when the knife-edge is in tlie correct position t o hring out the grazing
MIRROR MAKING
11
incidente cffect. I n Figure 7, for example, the outer zone will be illuminated in the right half ancl dark ir1 ttie left. I n ttir central zone the illumination will be ju\t tlir. rexerw. 111 this illustration wc sce three shadows as defined above which, for reference purpoics, will be numbered 1, 2 and 3, as shown. It is evident from the law of reflection that sliadowi will niove in the
same direction as the knife-edge in zones which appear convex townrd the observer, and in the opposite direction in zones tvhich appear concave. In Figure 8, a t left, the mirror is convex from center to rim, in spite of the fact that i t has a central depression. Thereforr, shadows 1 and 3 would move in the same direction as the knife-edge across their respective halves of the
mirror. (Shadow 2 in this case would remain stationary a t the center.) I n Figure 8, a t right, which represents the same surface as it would appear with the knife-edge just oiitside the center of curvature of the marginal zone, the shadows would still move in the same direction. For the zone inside the crcst in Figure 8, left, and for the wliole surface in Figure 8, right, the direction in which the sliadows mobe contradicts the old r i i l ~that "the shadow will move in the opposite direction wlien the knife-edge is outside
12
MIKROK MAKING
thc center of eurvature." Strictl) spedkirig, thi5 rule applies to sphcrical mirrors alorle, tina, for p e n e r ~ l applictition, should he restated '1s at the beginning of this parsgraph. Assurning a uniform spced of the knifc-edge ds it cutc througli the conc
'
,,EArnR,,,, EVEIVLY ALL OVER SHAüOW
SXADOW
3
2
FI(:cR~ 9:
of light, the speed of a shadow will he an inverse function of the rate of change of slope. Iri other ~vorcls,tlir ihadow a i l l rIiore slo~vlyacross zones of prnnounced currature, and comy>arntively fast across zones Iinving little change in slope. I n Figure 9, shadow 1 would move slowly to the rreat aiid
then move faster and faqter as it approached L. where the curre flattenc out at the beginning of the zone of greatest slope in tlie central depression. I n zones where there i i no cliarige in apparent slopc with a gixen knifeedge settitig, there will be no shadolv motion. Such zonei; will darken evenly al1 over. Heferring back t o Figure 4, we see that, in the true paraboloidal figure, such a zone alwajs exists in the central depression exteriding frorn
RlIRROR M A K I N G
13
about 50 percent t o 70 percent of tlie distnrice from center t o crest. W e are particulurly interested in the 70 percent point, L, whicli we may cal1 "the shadciw limit," since tliii is thr point beyond nhicli no motion of shadow 1 can be deterted. Picking u p this sliadow ngiiiii frorii Tvhere we left off in the preceding pdrapraph, wlieii i t renches the sliadow limit, tlie zone of
greatest slope mil1 have just finished darkeiiirig, and the two effects will bleiid in witli eacli other. n u r i n g al1 tliis procedure, shadow 2 will have been approachiiig shadow 1 across tlie concave p a r t of tlie central depression and will hlend in about the snme manner, except, of course, from the opposite direction. I n interpretirig shadowc, wc imagine them t o be caused by the light source beiiig off somewhere t o the right of the mirror rather tlian by the kiiife-edge qhutting off thc light. For a shadolv t o exist under this condition, i t follows that the incident light path must be imagincd to be tangent
And, since shadows move as discussed above, it folloms again that the light source must be imagined as moving amay from the observer in n. direction parallel t o the axis of the mirror. I n Figure 10, from the time when shadow 1 enters the left side of the mirror until the time shadow 3 disappears off the right, the light 5ource must be iniapined t o llave traveled from A t o 2. Bumps, raised zones, etc., will not cast 5hadows on adjoining parts of the mirror. This is due, of course, to the fact thnt the actual direction of the light path is parallel t o the axis of the rnirror. In Figure 11, wlien the
t o the surface at the point where tlie sliadow liappens t o be.
MIRKOH MAKPNG
1A
surprisingly consistent. 1\11 stntcd thnt tlie (liffraction around the ares hnd a blinding effect on irliat tlicy ivcre tryiiig t o sce. Hence, tlie stop wtis replaced ivitli n c1u;irter-incli strip of mood íicross t h r liorizont;il diariieter of the mirror, ~ r i t l itivi.« sliort pirceh of piri (lrireri into tlie stick to iiidicnte tlie exact locntion of tlie zorie. Tlic trst tliis tiriie w;is to sre liow ftir tlir knifeedge coiild he riio\,ecl nnd still litive sliado~i~s 1 :rii(l :1 nI)pc:ir to rr:ic.li tlic,ir respective pins :it tlie sorne insttliit. Tlie average iriiiiie~lititely c:inie down t o sliglitly less tlian .0lV,tlie rn:iiii
knife-edge could be movecl aboiit .O&'' urithoiit cletecting any motion of tlie sli¿id»w whrn uiiiig tlie \tul), or seeiiig titi)- deriation from apparent flatiiess at tlie ceiitcr ii-itliout tlie stop. 111 tliese testa, Tve were snealiing u p from botli iides, so t o sprak, so tliat the iiiasirriurii dis~)loceiiieiit of l
MIRROR MAKING
16
the two sides, tlie same will liold true for error uf observation involre\ ti iniiiute fixecl radius of the zone. We s:lw in Doughnut cliaiige in slope of a zoiie, resulting from along the axis, mas reprrsented
the otlier. I n other words, tlie value of slope, regilrdle?ih of tlie hlatliematics, Prop. 2 , tliat any a movement of the knife-edge
by tlie evpression
d?l = KD?. dx R
And
since, here, dy/d.e has a fixed ralue, as stated abore, \ve may combine the constants and relvrite the expression, K
=
DA R
whence, D
=
K-.R
x
(8)
Figure 15 s h o ~ r sanother way t o approntli tlie 1irohlrm. Here we h a r e two mirrors of different foeiil leiigth, but tlie s,tme focal point f , being tested
for zones $1-M' and m - n ~ ' of tlic w m e aperture rtitio, R/r. If the knifeedge cuts througli the corie of liglit a t sonir cli,ttiricr E from f, but just close enoupli so tlitrt no ditiereiice in tlie tixxie uf (1,irkening uf ,11 aiid X' can be detected, the harne will Iiold true for i n and m'. I n othcr ñords, the error of observation is a direct functiori of the focal ratio, for ~vhicliwe may write,
E
=
k-.R r
This, of course, is tlie same tliing as equation (8) with
Solring for k, by using the value of E determined f o r either the 1" or the 4" zone of the 10" mirror, the equation for the error of observation be come^, a change of characters.
MIRROR RlAKING
17
The answer t o the question, "How accurate is the knife-edge test?" depends upon which class of errors is under considertition-those which can be measured but not seen, or those whicli can be seen but not meaxured. Strange as it may sound, the latter can be detected much the closer of the two, in terms of thickness of glass t o be removed. Heferring back t o Figure 6, a n d assuming t h a t the three curves represent different intensities of figure on one and tlie snme mirror, it woulrl be impossible to te11 from visual inspection under tlie knifc-edge test, which one was correct. Zona1 measurenient for rarlius of cur\r:itiire would be required. I n Figure 16, homever, sucli measurement would be impossible; i t would be necess;iry t o estirnate the intensity of tliese vtlrious protu1)er;iiiczs by visual inspection alone. The measurable errors, then, a r e those in over-al1 correction, and the
accuracy obtained depends upon the zones <electeil f o r test. Theoreticnlly, the esact ceiiter of ;i rriirror ci~riiiotbe tcstcd for r;i
percent error
9/8R3
r?/R
knifeedge error
error in millionths of an inch
.075" .125" .2001'
.008" .008" .005"
10.7 6.4 2.5
.O0001 14" .0000191'/ .O00078lr'
1.2 1.2 2.0
80 percent of j / 8 SIr f/8 10" j / 5 10"
The above sliows t h a t mensiirements clown t o 1 rnilliontli of nn incli i i i thicliness c:rririot be made iritli :iiiy clepree of cert:iinty. I3ot i t ivill be w r n . hy referring t o "Acciir:icy in P:rrnholi.~irig," i r i "rl.l'.>I.," tliat t h ~prohnhlc e r r o r of observntiori is ~ v c l lvitliiii tlie toler;irice givcii-:ill of wliicli 1iie:iric tliztt, if n mirror ir figureti t o this clegrce of acciirncy, bri1li:iiit ~,erforninnce triny he expected, provicled tlie ri~imcrousotlier conclitions necessary for tliis perforrii?ince ;ire corrcct. 'I'lie otlicr cliiss of errors incl~iclcs close zonnl irregulnrities, dog-hisciiit, lemoii peel, buiiilis, etc. One illustrtitioii witli tlie 10" iiiirror will serve t u
sliow h o a closc.ly tlir thiclinrss of tlicsc ~irotiihc~r;inces m:iy he e.;tim:itecl 1)'. visual irialiectioii, :iltlioiip~iit is irnpossil~lr:ictii;illy ti1 irics:isure it. Figiire 17 sliows tlic al)li?irciit cross-sertion iritli tlic Icriife-edpe a t tlie Iialf-\\-ay 1)o~itioti, hriiigiiig tlie c r e d ut 7U pisrcerit of tlic t1ist:iiice froiri ceiit(ar to riiri. Referring t o 1i;ige 9, it will h r sccm tlint tlie t1evi:rtioii of tlii\ crest f l ~ ) l i i the refcrerice splicrc is oiie qu;irtcr of 1-~/8liZ.o r :ihout 5 millioiitlis of ;in inch. Se\.er;il iliglit firotiihri.:~riccs I i ~ i r r1)ccii l)l;ice
I,ct this he sirriplr t ~ i i tsiilist;inti;il. .\Ii<.rorncter screwh :irc unnecess;iry, aiid if tlir outfit is riiiiiiiitc(l oii ;tnytliing less' rigitl tli;rii n solid concrrte foundatioii, tliey elre iihrlcii. I f tlie mirror nricl Iíriife-cdpe a r e mounted «n separate siipports, ;L aliglit pressiire of tlie í71igi.r ti[>&ori tlie sicle of tlie hc.ncli lioldiiig tlie knifr-etlpc* xrill gire morc. sensiti\pc coritrol of tlie shntlom tlian iiny rnicrolnrter ;irroiigeii~ciittlie ani:lteiir IG-ill bc liltcly t o rn;ilie. Tlie only c a r e nececsuiy is tu sce tliat this prrassure x-ill reiult in rnotion at riglit anples t o tlie ~nirror'h asih :iloiir. Aiicl the iiiore solid tlie bencli, tlie hettcr tliis will work.
MIRROR MAKING
19
If tliere a r e any perceptible air currents betaeen tlie knife-edge and mirror, a testing tunnel will be required for close readinp. This may be a simple wooden framcwork covered with lieavy cloth, arid htiviiig a crosssection about 50 percent greater than the diameter of tlie mirror. The cloth may Iiang down a t one side, in the form of a flap wliich niay be raised t o insert tlie mirror. Provide the mirror support with some means of adjiisting t o bring the light rays back to the proper point a h e n the mirror is in position. Three wooden wedpes will serve the purpose. After the ad,justnient is once made, screw or clamp the support t o the bencli. If the front and back of the mirror are not partillel, paint an index mark on the edge, and always have
KE
BLOCK
BASE BOARD
this mark in tlie same position when the rnirror is on the rack. The abore will save tinie getting lined u p for those frequent tests during the final stages of figuring. The light sourcr tnay be a an inside-frosted incandescent lamp bulb inside a striall tooth powder can, in one side of which a 3/s" square or circular opening has beeii made: Thr slit may be two safety razor blades clipped between t ~ spring o paper clips, as shown in Figure 18, a t left, 114th the opening betweeti tlie blades set t o about the thickness of ten sheets of typewriter paper. Aii extreniely n:lrrolv slit is not advisable when used witli the knife-edge, due t o the diffraction effects which result. Sensitivity depends on par;illelism of Iinife-edpe and slit. True, mlien the mirror is just beginninp to darlíen, there will he a rnarlied reduction in contrast hetween light nncl slindr ~ v i t h the witle slit, muliiiig the over-al1 slinpe much easier to see or photograpli. nlit tire actual shadow, as (lefinetl ahove, will be as sliarply definrd :is if procluced hy an infinitely nnrrow slit. I n fact i t iz producetl by just siich a n a r r o a strip of light, bounded o11 one side by tlie right edgc of tlir iriiage
20
MIRROR MAKING
of the slit and on the other side by the knife-edge itself. F o r the same rmson, the wide slit will he ,just as effective as the narrow one in detecting close zona1 irregularitirs jiist before the mirror comple'tely darkens. A n d for comparative freedom from diffraction effects in the vicinity of the shadow, the wide slit is easily the choice. Also the rectangular iiperture of the slit is the only liglit source which will illuminate the various zones of the mirror in direct proportion t o their slopes, giving the correct appearance t o tlie curve. I t is essential t h a t knife-edge and slit hoth be a t right angles t o the axis, otherwise a marked reduction in sensitivity will result.
Remember that the pupil of the eyr is well dilated nhen testing and takes in considerable of the knifc-edge and image of the slit. For Ronchi testing, tlie slit niust be closed down t o tlie thickness of one o r two sheets of paper. For example, if gasolene screen is used for the grating, the slit must be sorriewhat narrower than the thickness of the wires in the screen, t o get good d e h i t i o n of the lines. F o r quick exchange from razcir blade t o screen, a spring clothes pin may be cemented t o one end of the knife-edge block, as shomn in Figure 18, üt right. Tliis will also permit rotation of either one around the mirror's axis, t o pet parallelism with the slit. S o get the knife-edge parallel, pusli it about 1" inside the center of curvature, bring the shadow in t o tlie center of the mirror, and then rotate the knife-edge one way or the other until the point is found where the shadow doesn't move sidewise when the head is bobhed u p and donn. Witli tlie Ronchi grating, do the sarne thing until the lines will stand still. The reconirnended length of slit, or even longer, will be found a decided advantage in getting accurate parallelism by this s i r r ~ l e method. The knife-edge block should slide freely on its base boiird. I t is rather difficult to construct parallel ways for the block t o slide between with the necessary freedom, so it is better for the amateur's purpose to provide just
MIRROR MAKING
21
one cleat, a s shown in the illustration, using a little side pressure when moving the block, iii order t o keep it a p i n t this cleat. The measuring devices will include a scale ori tlie knife-edge base board, iind a measuring stick hung trcross the horizontal diameter of the mirror. Tlie scale wr prefer, becaiise of its simplicity and ense of reading, is hliown in Figure 19. This is a flat plitte of brass screwed to the base board, with parallel cross lines a t tenth-inch intervals, and diagonal and vertical lines as chown; al1 accurately scribed with a fine, sharp engraver's tool. The in~iicator is another piece of brass screwed t o the under side of the knifeedge block, a s shown in Figure 18. With this device, the nearest half of a hundredth inch may be easily seen, which is about as accurately as we may expect t o read. The measuring stick is a quarter-inch-square stick of wood with a loop of wire t o hang it across the horizontal diameter of the mirror, as shown in Figure 20. Our preferente for the spacing of the pins is t o
locate the zones given in the tahle on page 9, those a t the center and a t the 70 percent points being slightly longer than the rest. Others, depending upon how their mental processes work, may prefer t o place them at S'' intervals. F o r the reasons given in "The E r r o r of Observation," stops a r e taboo for testing parabolic mirrors in a t least one outfit we can name. They are used only for finisliing spherical mirrors nnd flats, where sliadows are lacking t o test both sides of a zone. And we a r e not so sure that even here we cannot see al1 there is t o see without them on smail surfaces. R h e n used, the openings a r e made 1" wide.
The tests for a true parabolic curve will include the following routine. 1. 1,ook f o r the diffraction effect a t the rdge, as explained in "A.T.M." T l ~ e o r e t i c a l l ~the , left edge sliould be a s bright as the right, but in practice this will seldorn be obtained. However, a clean hair-line of liglit shoi~ld
follow the left edge of the mirror, and the illumination nt the riglit side sliould not persiht to aiiy noticetible extent longrr tli:~ntlie diffractioii tiround tlic edges of a screw driver or similar object placcd vertically before the mirror. 2. Inspect the surface as a whole for zona1 irregiilarities, tlitit l~iimpiness called dop-biscuit, lenion peel, etc. If thrse are :ibscnt nnd tlie surf:ice üpI)r;lrs velvety srnooth, it has soinethiiig greatly to he desired, or in more highbrow terms, i t is an optirnl yurface. 3. Set tlie knife-edpe a t tlie 90 percent position on the scale, and then slide the wliole assembly including the base board along tlie hcnch until the point is found wliere shadows 1 :ind 3 reach the 95 percerit zones together. Here is where the volue of the recommcnded spacing of t h r ~iiiis on the nieasiiriiig stick will be seen-tliey leave nothing t o guess~vork. Take a squint d o n g tlir hidr* of thc cleat to see that it is pointing a t tlie center of tlie niirror, since this is tlir kcy setting for tlie wliole test. If itccurately lined up, the knife-edge niay be puslied towaird tlie rnirror, cauiing the crest t o rol1 iii towatrd the centrr withoot tlie illurnination otlicrwisc dying out, or the mirror becoming wliolly illiiniinated. After makiiig ciny ;~d,justrnent necessary to produce this effect, clieclr the 90 percent positioii agtrinst Ilie 95 prrcrnt zoiic once niore tind thcn leave the hice bottrcl in tliis position. Before lcaving tliis zone, clieclr tlie sliadow liriiit, which should be a t 70 percent of tlie 9.5 percent. No guicling pin will be foiind lirrr, but tlie point may be estirri:ited closely enough froiii the pins tit eithrr side. And doii't forget tliat liomely metliocl of pusliirig lightly on one side or the otlier of the bench t o bring the slirdo~vsextictly urliere wt~nted. Also decide right hcre whnt you arc going t o cal1 tlie sliadow; probably the poirit wliere none of the remaining s ~ i i ~ l r r w r hof s liglit cross tlie piri. 4. Push the knife-edge in t o the 50 percent position and test as nbove on the 70 percent zone, first seeing tlitit shadows 1 t~ncl3 reach tlieir respective pins a t tlie same tiiiie, niir1 then tliat tlic. sliadow liiriit for sliatlow 1 is lialf way from center t o rim. Also note, while tlie iriirror is only partially darkened, t h a t the d c p t h at the center appears t o be thc saitie as that a t tlie rirn. 5 . Pusli tlie knife-edpe t o the 10 percent position ancl test tlie 32 percent zone. Shis time there \vil1 be sorrie difficulty in cirtermining just when the shadows reach thcir respective pins, due t o the flxtness of thc crest. The general appearance of the nhole central iireti of the niirror inust he taken into coiisideration, based on the 10 percent curve of the douglinut family. There should be just a slight resemblance of a depression inside the zone, coming t o a crrst a t the 32 percent point, as riearly as can be decided. I f no slope can be detected une way or the other a t this zone, i t will never scatter light in :i star image. 6 . Pusli the I
BIIRROR M A K I N G
23
half way in from tlie lcft etlge to center. Thc slinrlo~r.'
ings, nncl t o tlie nrcessity of seeinp snnicstliinp Ii;rl)l)<*ii;:1 two clifferent 1)l;tces at one tiriie. 'I'lirsr troiii)lcs tire not 1)rt.sciit witli creht reaciinp. Tíie diffraiction t i t tlic pins is just siificieiit t o entible tlierri t o be readily seen. Shadow 1 is brougtit to its pin aiid s l o p p r d t h ~ r c ,so tliat \ve iii:iy talte al1 tlie time me wish, t o see wlietlier sh;idom 3 hats jiist renclied the correct point. If botli are wliere tliey brlong for the various settings of the knifeedpe, tliey jii.;t cari't be nnywliere else-tlint is, xvitliin the limits of the error of óbservation. By no" we can sec the ndvantapes of testing in eyual steps of linife-edpe position ratlicr tlian iri Cc~u;ilsteps of the rndius of the mirror. Each eone may be measuretl witli tlie stime drgtee of certainty, nnd iill are of cclu;rl iniportaince, since cacli involvrs tlir snme arca of the mirror. Wcll, we liavc tested n poo
the same for al1 threr mirrors, nnd if tliesr were the onlp tests mnde, any one of tlie tliree mirrors nould be proiiourice~l corrcct. Yet it is obvious that the upper rurve reprrst.rits nhout 50 percent over-correcticin, aricl tlie lower one nbout tlie siime tirriount under. While i t is true tli:it tlie liglit reflected from tliese three zones could be broiight t o a fociis, tlic waves arriving from the 70 prrcerit zone nould be somewhnt out of pliase with those from the otlier two zones, resulting in aii actual 10.~8 of lipht. Tlie best means of detectiny tlicse errors \vil1 depend on tlie size of tlit. inirror
( T h e lnirror ori tlir l e i t zimrrri n o t nirrJr hji t h e fc<.hnic rleseribr<E iri t h i s c h a p t e r or b y i t r n u f h o r , biit tlir onp o n t h e righr zrnx n i a d r i n its e n t i r e t y b y Mar?/ A'. E L . ~ T P Rt k~e, iuife of t h e airthoi., ! L I L rlrtrd. I t uins i ~ o l i s h e d a n d figirrerl i n t h i s conrlition, a f t e r wlrich t h e p l u g wiis linocked o u t b y t a p l ~ i n g liglitly o n i f s f n c e w i t h a h a n i m e r . D u r i n g t h e polishing thi.7 r h g . ]A0'' t l i i c k , could n o t di.s.si/>ate i t s h r n t a s rnpirlly nx t h e r r m n i n d e r o f f h r s u r j a c e . A s a rrnirlt. t h e r i n q w a s szcolle~i o u t , polislied o f a n d , a f t e r coniing t o ~ q ~ c i l i b r i u r nb,e c a m e a d e p r ~ ~z o~r ~~e . d
and the deptli of the curve. For 5hallow mirrbr.;, which nill inclurle most amateur sizes of f/8 or thereaboutq, the general appearance of the doughnut will tell the story. For the upper curre, t h r crest will nppear too sharp, a s in Figure 22, a t the left, nnd for t h r lower siirve, it will nppe:ir too flat. The correct appearance will be about as in the same figure, a t the ripht. F o r mirrors of more pronounced c u n a t u r e , wliere the depth of tlie shading makes it difficult to see the over-al1 correction a t a single view, the shadow limit will spot the trouble. F o r the upper curve, the sliadow limit will be
MIRROR MAKING
25
toa near the crest; for the lower onr, too f;ir awa7. And if we have developed a sensitire touch in pressing on the side of tlie bench, the shadows for the upper curve \vil1 slow (lown tao iiiucli a t tlie crest; for the lower curve, they will junip across too ftist. F o r still larger mirrors, wliicli t t k e s u s u p out of the amateur cltiss, actual measureinent for center of curvature of successire zones, in not over ten percent steps, is required to determine the figure with tlie necessiiry degree of accuracy. A frequent error in amateur mirrors litiving the correct difference between inside anrl outside centers of curvature, is misplaced crest when the knife-edge is in tlie 50 ~ ) r r c e n tposition. Tlie crest is ton f a r in or too f a r out. These a r e sliown by tlie rlotted lines in Figure 23. With tlie cxceptiori of the final test t o prove the perfection of figure, the
purpose of al1 testing is to determine the comparative tliickness and radial location of tlie surplus material which is t o be removed. Iii rriost cases this may be estimated a t a glance, with the aid of the rneasuring stick. In other cases, after measuring up, it map be adrisable to drtrw on a. piece of paper the cross-section of the surfcice seen, supeririiposing tliis curve upori the curve of nearest fit from the doughnut family. Then the aren between the two curves will represent the material to be removed. F o r the upper curve in Figure 21, i t can be seen a t a glance t h a t the greirtest thickness of surplus material is a t the crest, gradually tapering off into the adjoining zones. F o r the lower curve, however, i t might be advisable t o d r z w underneath a t r u e 50 percent curve, such a s the one shown in the dougliniit family, but a i t h the y values c u t down t o get a closer fit. Removing the material indicated would brirlg the surface t o a t r u e paraboloidal shnpe, but under-corrected, nfter which the. crest could be brought u p by regular parabolizing methods. A similar process is indicated for both cases in Figure 23, reducing tlie figures tu the correct shape, but undercorrected. With a little experience, this process of superimposing the surface seen on thc correct surface, will generally be a mental one. For the medium deep curves, we can get along in similar fashion. But, f o r the big fellows, where al1 but the crest is so hrightly illurriiiiated or so deep in sli~idetliat the orer-al1 figure cannot be seen under any conditions, complete zona1 measurement in not over ten percent steps is requlred, after which some laborious graphical work based on these measurements is necesSary in order t o determine the exact condition of the figure.
26
MIILROR M A K I N G h o n r ONE T N
TO
ANOTHER
,4s the reader has prohably surmiseel by non. tliis paper ic being written bnckwtird, so that it will lirie u p witli "A.T.JI." * Pitch: This, :is f a r as thc optical worker i conceriiecl, is nriy rri:itrrial whicli will gradually yield or Aow, and t:ilie on prrmanent deforrn~itioniindcr pressure. If it fulfills tliese requirenirnts, tliv rn:tin tliirlg we tire interested in is its "temper," whic-h, for clarity, we mny define :LC tlie iiurnber of seconds requirctl t o producc n qiitirtt,r-incli clcnt in its siirf;icc witli one pounil pressure of the tliunibn~iil. Thiis we mtiy spcak of 5-second pitch, 20-second pitch, etc. Tlie proper tvinper is seciiriil by l~oiling to make harcler, or melting and thorougtily stirring in turpentine t o nitike softer, and then giving tlie thumbnail test on a snmple teaspoonful wliich has heen suhrnerged in water (it tlie working tenipernturi. for :it least ten minutes. Optical workers use everytliing frorn the hiphly rcfined wood pitches of verioiis t r ~ i d enzimes sold by tlie denlers, dolvn to ordiii;iry roact t:ir. I t is s:ii(l tli:it tlie riiiiier~ilpitclies 1i:ire :L miich witier 1;~titiidein iisefiil workiiig trmperature, and this is certtiinly ilesirnble. IVr mrre broiiglit u p on corrirnnii h;irdwarr store rosin tind tiirpentine, probably tlie most cussed of tlie cussed, hiit we a r e still thriring on it, and are in no position t o recomniend a selection from tlie others. .Ibrrrxiz*rs: Jlost tyros st;irt oiit with tlie ide;i tliat grinding will result from the use of C:rrborundum, :ind polisliing will result from tlie use of rouge. Tliat's wrong. 130th are excellent abrasires, ;ind either may he rnaclr to grind or polisli a t will, deperidirig iilioii hom it is ~ i s e d . Two pieccs of flot pltite plass will soon brcome fine ground if riibbed together witli rouge mixt u r e between. On the other htind, o pitch tool, properly charged with finest Carborunclum, will procluce cliiite :i respectabl<. polish, coinp:ired with wli;it niiplit t>c c.xprctrd. So Iiere's the riile. Iiollirip :ibr:isires priiiil, dile ti) ti chipping ;icticiri o11 tlie brittle siirf;ices betwreri wlii<,h they roll. St:itionnry abrasires o11 one siirf;ice polish tlie otlier, tlie kiction this time being ;L firie scraping or smooth wr:~ring ti\tTay. 1 . 1 1 ~s p i t t e s t : 'rliis roiigli :ind rrtidy procedurc Eor keepirig track of tlic radius of curvature (liiring the rougliing out, has stood tlie test of tiriie. Tlie routinr is :is follows: Provide :i mirror rack in sonie corner of tlie cellar, t o bv uiecl only for tliis purpose. Place ihe mirror in pohition nnd drop n pliin111 line from itc; fiice ti) the floor. Malíe a chalk rn~irlr oii tlie floor nt tiiis point, mcasure hnck t o wliere the clesired center of ciirv:lture sIioul(1 he, :iiid rnxrlc tliis point i11so on tlie floor. 'I'o test tlie riiirror, wahli oti tlie grit mil, while tlie surftice is still ivet, p1;ice tlie rriirror nri tlie rack. liold a liglitecl c;indIe close to tlie side of tlie observing eye, find the irnage in tlie wet surfacr, uralk haclc ti11 ttie mirror filli witli liplit, and drop a gob of spit. Conip~ire tliis ~vitli tlic cli~ilk rnarli tind there's the answcr. One T N ' s wife added a can of cliloride of lime t o the technic. Son-eraporating iiquidi siicli'as tliin oil or glycerine are unnccess;iry for * Let the r e n d e r jiidze mlietlier tiir autlior's hacliwnrd ~vritinx 2nd nrriiiigrsrrirnt ar.. i n ;i cln-q ~vr-itlithv trilile-coiii~)ouri
MIRROR MAKISG
27
thirs kreping track of tlie radius of curvature since, witli a few trials, this rnetliohcd ir/' ctnd (Ioz~n,,causirig the sliadow t o more vertically betmeen tlie stre;il<s, tirid ni;iking it c:isizr t o rcail. After tlic first stage of fine grinding, the siirface will be srnooth enough t o perniit tlic ¿ictii:il figure oii tlie iiiirror t o be seen, tlie iris of tlic rye arting as a knife-eclpe. lliis cffcct, of course, will show u p unly wheri tlir rye is crt a very critica1 point very nrnr tlie rxact crnter of currature, m;ikirip tlie test :it tliis st;ipr ;~cci~r;ite to a fraction of nn inch. Xeedlrss t o say, tlie spit rnust I)c allowed to drop straight down, and not be ejected iri :i p;ir;ibolic psth. 7'001 ~ , f í , c t : This term refers t o the more rapid grindinp (ir poliihirig which ;il\v:iys occrirs in tlint zone of tlic mirror ~vliich is at tlir edpc of tlie tool n t tlie en(] of tlie stroke, provided t h r edge of the tool is in rontact. Tlir c:iiise is oh\i«ue. A t thc enrl of :i stroke, tlie iinsiipportecl :ire;i of the mirror p;irti;illy coiinterba1:inces tlic o1)posite side, relicving t h r ressi sir re tliere, so tliat tlie grc;itest pressiire is ;it the edge of tlie tool nc.arrst tlie unsupl>«rtc-il inrea. 'ihe net effect is, t o a mirior clegree, tlie s;imc. :is with tlie ovcrli;ing stroke made p;~r;illel t o this edge of tlie tool, excvpt hlendt-d out more iiito tlie nd,i;tcent zories. If tlie edge of tlie tool htis hren proiriid down excessively, or ttie edge of tlie pitcli Inp has been puslie(1 cln\rn. tlie cause in citlier c:i<e linving hren lorig strokes or overliiing, tlie tool effect will, with sliorter strokes, he soine~vliat f:irtlirr in wlirre actual rorit;ict eiiíls. A rcltited t.tfrct is present \vlirn gririding or polishing face u p xvith rirc,itl«.r sub-r1i;inictcr tools, unless tliere is a frrcluent cliange in the chord of the rnirror ovcr \\,liicli tlir stroke is directed. l'Iierv,nl c ~ f e r t :Tliis is distortiori of the niirror's surftice clue t o 1oc;ilized heat or cold, c:iuied by the hetit uf poliihing friction, or tlie tcniprriitiire drop of ev;!l~or:itiori frurii :trr;is of tlie tool zinc1 nijrror exposecl during the .itrolte; :ind since glahs lias a corficient uf rxpansiori runriirig into sigiiific;int figures, tlir Iiot spots \vil1 teiid t o swell oiit ;ind the cliillcd :irr;is slirinlc awny. If tlie bit11 of tlie tliiiiiit) is Iield :ig;iiiist tlie facc of the niirror for a momeiit, arici tlic rriirror is tlirn placrcl on tlie tcctirig stand, a pronounred tliermal hurnp \vil1 he heen. I n fnct, ~ r i t l ia little exlierience nn(1 our linowledge of tlic amouiit of ni:ignification of tlie teít. me muy rstiinate approximately how ninriy rnilliontlis of nn incli tlie hiimp protriides. If polisliiiip is re~iiirir(1before the hump has reccdc.ti, tlie first effect wiIl be a rriore proiioiincrd cweiiing of tIie l~urnp,since it wiil rrrrive more frictli;tri t h r srirroiiii~1irig tire;\. I)iit, clue t o tliis adi1ition:il fricttion, tlie burnp w i ~ ialsu b(: poiisIiing fastcr iip t o the point wliere its excess iieat is ~lissipated ;is fast as ~>rocliiced,whcii thc burnp mil1 sucldenly sliririk baCk
28
MIRROR MAKING
and he replaced by a hole. This iaperiment may be readily performed with ordinary glass, and aeems t o explain tlie cau\e of tlie dog-tiisruit aurface siicli as shown in Figure 24. Tlie protrutling iLre;ii ivill behave in exactlp the ' ~;f t e ri~ little polisliing they will recede and same manner aa the tiiuriib ~ i i ~ i r k the valleys iviil become the burnps. Tfiis would indicate tliat the whole surface of a mirror is in a constant state of slow, irregular oscillation during polishinp, if tlie polisliirip speed exceetlc. a crrt:iin limit. 'rlierefore, there is a defiriite limit to the speed ivith wliich fine optical work may be performed, this lirriit beconiirig a m:itter of iristinct if tlie worker is alert t o what is going 011. l'he greater tlie polisliing drag, the ilower the stroke must be,
so that the result of the two will not exceed the alloivable heat of friction per square inch. Here the hand worlcer has the advantage over tliose working with machines, since he can te11 tlie ainourit of drng mucli hpttrr by the "feel" thaii he can by tlie groans of a macliine. This is probably offset, tliough, by the fact t h a t the macliine worker is generally content t o take several times as long to polish as by the hand mcthod, since he doesn't have to work. Assuming that he keeps out of this dog-biscuit mess, as is quite likely if Pyrex is used, there are still two general thermal effects which must always be considerecl, since they are present in al1 polishing operations, arid particularly witli tlie usual amateur practice of polishing face down ori a full-sized tool. One of them is also present during the grinding operation, if water is used as the ahrasive vehicle. These will be given separatc: hend: ings for easy referrnce later on.
polisliing Inps tire rn:idc. I%ut Iiere \ve sliall íind an offscttirig f:ictor, a s f a r as tlie edpe is coiiceriicd. Friction ~ f f ~ c Froiii l : oiir ronsitlcratioii of tlie tool rticct, it i\ cvidcnt that tlir Iieat geiieratthd by polisliini: friction fr«rri oiir-tliirlit~roi
swell iip, nnd elrcii thoi~pliwe ~>olisliecloff miich of its surfncr, we cannot see tliis irnrnrperied, \ve rnay place it b;ick on the lap :ind sc~rii\>:I littlu hürcler ;it thut central tLrcti. Perhiips, : i ~ : i i r i , no results are sccri. Iliit tiftcr sevcr:il such attenipts, tlle lniinp will sucldenly stiirt t o shririk bnclí as wr watcli, ~viiidingu p iii :i deci
MIRROR MAKING
31
currence after a sprll of polisliirig. Sliis w;is iictiinlly clirckrtl hy n tlicrrnocouple sealed in tlie bottoiri of a liole drilled ne:irly througli a mirror. Al1 of which riiesris tliat, as fiir as tlic edge is conccrrie(1, the frictiori effect may, with luck, just offset tlic erapor:ition effrct, s o tliat thr extrrnie cdgr stays clean-cut. Ancl for tliose 1vi.110a r e crztnks on getting ;L
sinking spectl nf tlir facets of .Ola" pt.r Iioiir, ancl 60 strolres per miniitr, tlie l:i11 will be sinking tliree milliontlis of :iii iiicli 1)r.r ztrokc.. No sinkiiig occiirs a t tlie eclpe w-hile it is uncorered diiririg Iialf cif tlie strokc, brit wlien tlie mirror is slid bnck across tliis areti, its eclge iviil plom into tlii\ sliglitlp higlier pitch :lbout tlie snme as slicliiig tlie foot si
t o be the face of a clock. JInke tlie first stroke t o 12 o'clock ancl hack t o 6, next to 1 nnd back to 7, then to 2 anti orer to 8, and so on around the dial. As tlie strokes tire made, rotate tlie mirror very slomly in a counter-clockwise direction, rriakirig from '4 t o not over ?i revalutiori of tlie mirror for each cycle of strokes. Iiutating tlic niirror in the same direction as t h a t in whicli tlie strokes progress miglit result in tlie sarne side of the mirror getting most of tlie polisliirig for a long successiori of strokes, making the surface lop-sided and no longer a figure of revolution. \Vilile getting accustomed to tlie "feel" of this stroke, t r y placing a sxnall piece of paper, wet t o make it stick, near the edge of the niirror, and see lionr slowly but uniformiy it can be made to go around. Nerer allow tlic rnirror t o be turning a t the end of a stroke. J u s t ti sliglit turning shoulrl take place dicring the stroke. In normal grinding and polisliirig the action sliould come frorn tlie stroke, and not froiii the rotation of tlie mirror. Tliis will give the niost zone-free and blended results of tlie rarious tool ancl tem1ier:iture effects. Tiie blenrling ozsrrhnng stroke: Except to ,remove a narrow raised zonc, the orerlianging stroke sliould always be perforniecl as slioxrn in Figure 28, :it left, where tlic zigztig line shoxs tlie patli of the ceiiter of tlie mirror arouiid the lap. This blends the action from tiie edge o£ the lüp over a rather wide
* T ~ aiithor's P niore
tanical
a c c u r n t r Inngiiage h s i l t o bt. \lirlitlg niodified. as old kiI1,iog-, Aunt S o p h r o ~ i y ,sufferrd ;i syasiii.->;d.
that
puri-
M I R R O R MAICIBG
33
zone of the mirror, instettd of prodiicing n n:irrow depressrd aone. Tlie direction iri whirli tlie strokes progress :irouncl tlie Iap, and the rotation of the mirror, sliould be as siiri~vn,for the hmne reasons stated iii tiie preceding paragrapli. Tlie effects of tliis stroke tire piirticul;irly notice:iiilc tvlien \vorl the surf:ice of tlie lap somrwliat coiiiplerneritary to tlie surface of the mirror. It is per-
formed b y sliding the mirror u p to 12 o'clock and back to center, then to 1 ancl bark, 2 ;ind back, tind so on :tround. Tliis brings tlie mirror t o rest a t the ceritcr of tlie lap as niiicli as a t tlie edge, so thnt tlie central area sinks as fast as tlie rirri, maintuining uniforrii pressiire of al1 facets throughout the stroke. Ari alternatire tli:rt is riot su tedious, perhaps, is tapered pressing a t tlie cornpletion of cticli cycle of full strokes, starting with about 20 pounds additional pressure from tlie Iitinds of ttie o p r a t o r , nnd tapering down t o zeru pressure a t the encl of about 15 seconds, xvlirn tlie strokes are resumed. Except f«r rough grinding wnd zonnl correction with small polisliers, the abore threr strokes, of rarious lengtlis as the occasion demands, will meet the requirernents of amateur mirrors.
The hnndle: L s e n hnrdwood handlc, turned with vertical grnin and a flange just large enoiigh t o permit a comfortable grip with tlie finger tips
and tlir halls of tlie thiiml)~. Tiie diminsioris in Figiire 28, a t right, a r e gootl. Cerneiit the lianclí tliis iiir;lsiirernrnt :it tlir hrpiniiitip of r:icli "spell." If founcl sliglitly out of positioii, loop a stoiit cord :irouri
not quite toucliinp the mirror. A higli grip will agprnvate tool plowing arid turn the edpe. Duririg griridirig, :i
MIRROR MAKING
35
diameter of the tool, :irid the grinding sliould have just renched the center of the tool, tibout $5 strokes Iiariiig beeri nri:iintaineci tliroughout. Cse al1 tlie prehsure desired iri tlie rougli grindirig. The more pressure, the quicker tlie results. A d d fresli abrasive as often as necessary t o maintain n loud grinding sound. This will be rather frequent, a t the start, as the mirror will pus11 tlie grains off the edge of the tool nearly as fast a s applied. E u t as soon as tlie concavity is a e l l started, tlie abrasive will come t o reason; :ind, of course, whatever is pushed over the side may be reclaimed. Just scrape it up, drop i t in a glnss of water, stir tliorouglily and imrncdi;ltely pour off the gunk. 'l'he useful grains will be left in the bottom. If a t any time the ciirre gets too deep, as indicated by the spit test, use strokes over chords n little Iiearer the ccnter of the tool; if too shnllow, stay :a little f a r t h r r out. Frequent spit testing nhile wiping the swent off the brow, will indictite wliat to dil. If a tool is ;ivt~ilablewliich already has the desired radius of curvature,
so much the better. Use it. I n tliis case, forget wlint is liappening t o the mirror x-hile working, and t r y t o we:ir tlie tool iinifor~nlyal1 over, starting with tlie strolces shotvn in Figiire 30, left. As tlie coiicavity in tlie rriirror spreadi, sliorteri tlie strokes a little, arid as it npproiiclies the edge of the mirror, g r a d u a l l ~ -bbleiid into tlie regu1:ir i/i: straigtit diametrical stroke. Spit test often, 21s before. If the curve brcorries a little sli;illow, xvork a littlr more to tlie outside of the tool, as shown in Figure 30, center; if too deep as in Figure 30, right. Of coiirie, noiie of these corrcctive measures npply t o a c u r r e which is founcl too cleep n f t e r it /las ~ ~ c r c h e tthe l e d g e . With any care, this will not happen. Tiiit if i t does, it menns reversing tlie toiil : ~ n dniirror. Botli of tlie above nietliod.; of rougli grindinfi tire easiest performed ori tlie barrel, and either inay be depen(lec1 upon to t~ririgthe riiirror tliroiigli very ne:irlg- spliirical. But test, in orrler t o iii;ike 5iirc. If not expcrienced rnough t o see tlie figure as explained unis a loiig stroke is itsed t o 1,rilig tliern oiit to thc e d ~ eof tlie rnirror. If tliey remain unc1i:ingecl ir1 \he, tlie mirror is rie:ir enoupli t o spherical for tliis stage. Watcli t t t tlie edge i ~ particular. i I f 'he bubbles be-
come smaller as they pass out under tlie edge, the edge is turned. If the mirror is not spherical, continue ~vitlitlie coarse abrasivc until it is, using 7/3 or slightly shorter diarnetrical strokes. The worst form of tiirned edge and slow edpe polisliing i.5 i~ hanp-over frorn tliis s t ; ~ g e . Fine grinding: For tlie f:isteht action, the fin? grinding stages should be used only for the purpose for whicli they are suited-remoring tlie pits of the previous stage. If the fine grinding sttigrs a r e deliherately used t o deepen tlie curve, this not only is n vcry slow process, but it tnkes several times longer than neccssary t o pet sufficient grinding a t tlie edge of the mirror, since most of it is occurring a t tlie ceriter. H e r e tlie professiorial, with his channeled cast iron tools wliicli hold their sliape and spread tlie abrasive ir) a uniform manuer, has a decided advantage over the amiiteur with his glass tool which chaiiges shape a< easily :is the mirror, zinc1 wliicli cannot safely be clianneled due t o the liability of cliipping iind scriltcliing tlie mirror. Two metliocls are open t o the amateur for petting as fast grinding down tlie stroke t o a n incli or less, a t the edge as :it tlie center-sliorteniiig or using the regular $5 stroke ;ind reversing tool tind iiiirror in the riiicldle of eacli stage. For ex:iniple, with ten wrts per st:ige, prind for fivr 1vet.i with the rnirror on top and then rcverse for the other Are. 1,e;ive in tliis position for tlie first five wcts of the next stage, and tlien reverse tigaiii And so oii witli enrh successive grade of i~hrasive. Sliis riiet1i~)rlis a little niussy and rrqiiires sonie special equipnient, and so, :~ltliougli it is a surefire method of finishing u p with a splierieal surface, we sliall probably c h o o ~ t o stay on top. Even tlie reeommended short strokes %vil1sliorten the radiiis of curvature a sliglit :iniouiit, and iin iricli or so sliould be left for this piirpose after tlie rough grinding is completed. From a practica1 point of view, Iiowever, the edpe may be considered to be grinding as fast as the center, and tlie grinding time per stage may be cut in liulf if the speed of the strokes is increased t o ofTset sliorteiiiiig them (lown. A s soon a s tlie noise of grindirig dies duwn, acid fresh material, first washing out tlie "inud" if aiiy appreciable ainount of tliis is present. Mud forms a support for the coarser gr:ii~isof abrasive, sloaiiig down tlieir action t o a marlíed extent. ?'o w:isli out the rnud, slide o@ the iiiirror, throw on a tablespoonful of water, replace tlie mirror and make tlie regular strokes t o squeeze it out. One wet of this is sufficient. F o r the last two or three grarles of abrasive, use kerosene for the mixture, for the reason explained uiider "Evaporation effect." Also, during tliese later stages, be careful when adding fresh abrasive. Add tlie required amount t o the center of the tool, plus tliree tlrops about 120° a p a r t near tlie rini, for "balancers," lower the mirror carefully And parallel t o tlie tool, so t h a t when i t touches the abrasive mixture this will be spread out evenly in al1 directions. Work the mirror very slowly, and :tctually hold u p on tlie handle a bit so that it will take 10 or 15 seconds before the abrasive tnkes hold. Listrri for the first sound of the coarser grains and let tliese take tlieir time cru\hing down iintil tlie sound indicates a uniform grinding al1 over. Tlien take a few seconds more in gradually applyirig whatever pressure
is t o be used. A little care like this will greatly reduce the liability of scratches, wliicli generally occur when the mirror is first placed on the tool. Even an extra large grain will crush u p without more tlian a pit or two, if the pres5ui-e is gradually applied as above. Of course, if the sound inciicates a chunk of concrete between the surfaces, the mirror should be l i f t e d off a t once, and both surfaces flushed. And it a d d i :I feeling of security, even with the sealed commercial grades, t o settle them first in the water or kero5ene, and use only the upper two-thirdq. With regard t o pressure, i t is safest t o taper off t o practically zero for tlie lnst g r d t t . If the mirror has a weak diameter, any appreciable pressure here will result in an astigmatic surface. The l a p : If the addition of turpentine is nrcrssary, stir tlioroughly, nnd tben stir sonie more. A n egg beater is good. Variation in tlie temper among the tool facets, resulting from insufficient mixing of the pitch a n d
turpentine, will cause come of them t o resist the pressure of the mirror more than others, and the action of such a tool cannot he depended iipon. The stirring sliould be done just below the boiling point, so that the buhbles caused by stirring will rise t o tlie surface after the stirring is completed. Rubbles d o no harm after the l a p is pressed, or while i t is in use. Rilt during use, when the pitch is under pressure and seeking an escape, the air in the bubbles is compressed; and during a n over-night period of rest, the bubbles will swell out again, warping the surface of the facets. This makes longer cold-pressing necessary before polishing may be resiimed. If wellstirred a n d buhble-free pitch is used, the lap will Iiold its shape for many days, a n d require only a few moments' eold-pressing a t the end of that period. In cutting the channels, a carpenter's r i p saw with plenty of soap suds is a fast worker, after which tliey may be easily widened into the usual "V" section with a sharp knife. A rubber grid, rii;ide as shown in Figure 31, will save some time and eliminate most of those chips which fly around the piace. H e a t the tool t o about 30" F. above working ternperature, pour anu
form the pitch in tlie regular maniier t o :~l)oiitthe thicltness of t h r mat, lay on the mat with tlir central facet properly locateel, nnd piisli it down into the pitcli witb the iriirror and plenty of warni soapsii(li iiiitil :iII hiit tlie marginal facets coriir up into cont;~ct. If tlie Inp chills before tlie m:~t gets down t o sufficient drptli, rciiio\-c. tlie mirror tind reheat the la11 in a pan of warm water. A f t e r the proper deptli has heen reached, chill the Inp iinder tlie colcl water ttip, reriiovc thc rri:it hy piilling u p a t s corner, rinse off nll tr:ices of sotip, d r y the siirf;icc witli zin old piece of linen, paint liot pitch on the marginal facrti tu briiig tlirrri iip to the lerel of tlie rest, and tlien repress for coniplete coiit:ict :i11 ovcr. S h e sinkirig spcctl of tlic 1:~p (lciervei a l i t t l ~thought. Tliis refers t o the speed with wliicli the fnccts rediice in tliickness from tlie pressure of polishing. The lou-cst possible sinliing spred will iiiiure freedom from eclge trouhles. Tliis involrcs pitcti trriiper, he;it of polishing and tlie rrsulting softc.iiirig of the pitcli. prt,h,iire used, c1i;imrtir :irid tliiclíness of tlic f:icets. Pitcli 1i;irdiiess is liriiitrcl to tlie point wliere ileeks are likcly t o result. With fine optical rouge, 20 sec. pitcli for plate glass ;ind 40 sec. for Pyrex ieem t o I)e íil)out the maximum safe limits. Witli cnre in washing the roiige and applying it t o the l;iy:, tliese limits may be e x c e d e d by experienced worlcers. Hut, for safety a i t l i super-hard laph, it is good insurcince t o piiint on the tliiriiiest possible laminkition of aboiit 10 sec. pitch, not over a few thous:~tidttis of an inch iri tliickness. O r scrubbing the surface with t u r pentine, nnd letting i t air-dry, will generiilly soften the surface enoirgli to remedy a l a p which has a tendency t o sleek. The lieat of polisliing w:is incritioncd a few piiges back. A lap of 5 t o 10 sec. pitch will beliave fnirly me11 for the first 10 or 15 minutes. But after the heat gets well down into tlie pitch, it ~vill soften enough to c:iuse tool ploming and a r;ipid closing in of the channels. Vse of tlie iri:ixirriurn safe h;~rclnessof the pitcii, as huggrsted above, mil1 grri<.rülly prevent tlie trouhle. If it doesn't, the pressure sliould be relieved, ancl tlie proper polisliinp d r a g secured by corre<+. adjustment of the roiige mixture. To deteriiiirie tliis, s t a r t witli a niixtiire Iinving tlie consistency of tliick crr:im. Witli tliis the rouge granules will : ~ c tlike so m:iny h;ill benrings, allowing the mirror to slide eti5ily orer tlir Izip nnd making tlie facets inviiible tlirciugh the mirror. This, of coiirse is not a true polisliing action. Graclunlly add water, a few drops a t a time t o exposed areas of tlie 1x11, iiotirig Iiow tlie d r a g grndually increnses as tlie oiitlines of tlie facets begiri t o appear. Continue until the facets are just pl:iiiily visíl)le, witli ari ereri red cast, and the lap has a heavy but .sn~oolli drng. With further additious of water, t h r facets will rapidly 1)ecorrie dark tirid tlie mirror stnrt to grah from gltiss-to-pitch frictiori. Tlie beit point is where the facets harc tlie clear red c;ist, or just before, arid tlie rouge misture slioiild be adlustcd t o produce tliis efiect. No set ratio of rouge to water can l)e giren, as tliis varies witli tlie grade of rouge nnd teiriper of the pitch. She size of tlie facets is limited from about 1" for 6" and 8" niirrors, to :il)oiit 1';" for 10" or 12" mirrors. 1,arger facets llave a tendencj- to produce zoiies. Regnrdless of tvtiere tlie
center facet is placed, there is never a uniform distribution of facets in al1 directions from the center of tlie lap. Witli too large facets tliere will be insufficient overlapping of the facet action to prevent zones. Tlie danger is increased by thc ftict tliat thc pressure of a fkicet is greatest a t tlie center, tapering to zero :it tlie edge wliere there is free escape for the pitch. This mtiy be demonstrated by polishing for a few moments witliout rotating the mirror, kreping the strokes p:irallel to one set of channels. Tlie surface, when tested, will appear as in Figure 32 a t .tlie left, not as shown a t tlie right, same figure. F o r sufficient overlapping of the facets, experience dictates nt least six or seven rows of facets across tlie lap. This will permit one-third o r longer, straight, diametrical strokes without zona1 difficulties. F o r shorter strokes, the necesstiry blending of the facet action may be obtained by mixing in side, circular and elliptical strokes. I n the matter of facet tliickness, 3//1,;" is n good stcirting point, trimming the channels as necessnry until tlie pitch has settled t o A t this point the sinking speed will be only one-half wh:it it was a t ttie start, hut the diminishing deptli of the clinnncls will mtike it incre>isingly diffictult t o squeeze
out the surplus roupe mixture a f t e r each npplication, and get the mirror in proper contact with the lap. Tlie edge facets ülso iieed consideration. With the regular method of channeling, these a r e al1 undersizecl, nnd siiice sinking speed is a function of facet dinmeter, these margin;il facets will llave less resistance t o pressure than the complete facets farther in, resulting in tiirned-up edge. Trimrning the lap o r rounding the edges of tlie marginal facets will only make matters worse arid tliese dodges should riever be used in the preliminüry polishing, wlien tlie aim should be in the other direction. A soft metal s t r a p or plaster of paris d a m around the edge of the l a p \vil1 limit the flow, 6 u t these are hard t o keep in acljustment just below the leve1 of tlie pitch a s i t sinks. Another clodge is to d r y u p the l a p and paint airplane dope around the edges of the marginal facets, allowing it t o set hard before using the lap. Perliaps tlie simplest is t o fill in the channels between tlie marginal facets with pitch, since this will reduce their sinking speed by limiting the flow to t w o directions, and also help retain the rouge mixture. Poliahizy: Fine optical practice tlrmands slow intermittent work, with temperature ancl liumidity under strict control, using 50 liours or more to poiisii a 10" piirror, and an equal length of tiirie to figure. But who has the patience, or tlie necessary control of temperature and humidity t o reap the benefits of such slom work? F o r the amateur's purpose it is just as well t o polish a s quickly as possible by any method that will preserve a figure of revolution, givirig no serious attention t o the figure until the polisliing is
SO
MIRROR MAKIXG
completed. The mirror will, of course, emerFe from this stage looking undar test like almost anpthing but an optical surface. Rut with a little EXperience in zonal correction this can be rapidly changed to FL splierical snrface with practicnlly no eviderice of zonal hang-overs, and tliese disappear in tlie final figuring. This preliminary correcting not only adds t o tlie fun, but it tunes u p inind and rri~iscle so that in the last touching iip of the paraboloid, the worker, nnd not tlie mirror, is the boss of the situation. The main thing t o watch for is astigmatism, testing for this a t frequent intervals early in tlie polishing. If signs of this are found, work without pressiire; if not, give 'er the works. The reasons for the liard lap have been given, and the strokes should be short enough t o keep the marginal zone polishing somewhere nearly as fast as the center. The HCF lap, described ir1 "A.'I'.M.," provides almost a fool-proof method of bringiiig the mirror throiigli this stage with a brilliant, scratchless and sleek-free r~isual polish. Rut, since the pitch l a p will be needed for the final work, mariy will prefer t o go it on pitch frorn the beginning. And here one must he ever on the :ilert t o prevent scratches, taking a lesson from the busy spectacle maker who works with grit al1 over the place but seldorri scratclies a lens. H e is jiist ha1)itually prit coiiscious and keeps out of it. So rol1 u p tlie sleeves, scrub u p everything that is t o be touched, includirig the testing equipment and under the fingernails, and never touch anythinp elsr. C;irho perms a r e dead ones and won't hop u p on the la11 of their own accord. \Vlieti picking u p the rouge jar, bring i t around the lap, not over it. Etc. Frequent exchange of newspapers on the hench is good insurance, plticing anything t o be handled on clean slieets of white paper, Keep an eye on the visitors. These a r e always leaning on first one thing and then another, and just can't be made t o unclerstand. Most scratclies ocrlir imrnediately after placing the mirror on the lap. So be careful in applying rouge. Stir thorouglily each time it is used, wait about five seconds and then draw from tlie top with a large medicine dropper. Run a narrow line of rouge along the center of each row of facets, and set the mirror down carefully t o spread it out. Use ten seconds' tapered pressure, make a couple of small circular strokes t o distribute the rouge better, and then press ten seconds again before starting t o polish. Not only will tliis push any coarse grains down lrvel witli tlie rest, but al1 rouge granules will have a chance of getting a toe-hold in the pitch rather than being pushed off into the channels. F o r uniform action, the direction of the stroke must be changed often. This can easily be seeti the first time a pitch tool is used, before the surface gets too discolored. Apply thin rouge so that the fhcets can be plainly seen, and keep the strokes in one clirection. The facets will take the roupe charge in streaks ir1 tlie same direction as the strokes. These streaks will throw minute thermal b i i m p ~on the mirror, resulting in a "lcmon perl" surface. Change the direction of the strolíes 90° anil the firqt streaks will gradually be replacecl by others in the new direction. Now go into the clock stroke and tlie facets will soon take o11 an even hue al1 over. Lemon peel is too
irregular pieces shoiild be kept floatinp in a pan of soapy water, ready f o r use. The so;cp will riiake the rouge stick. F o r the roupli work the rouge may be niixecl as tlii<.k a s lwssible yet still permit the points of tlie HCF to be seen tliroupli tlie rnirror. But, for liglit toucliiiig 111)~ ltiter ori, tlie mixture sliould be tliinned down and the pressure relieved t o produce a smootlier action. For srriall pitcli polisliers, tlie glass feet used iinder furiiiture legs make excellent tools, giviiig a good grip for the fingers. They should be ground t o approxininte ciirrature apaiiist the rnirror wliile it is still ir1 tlie rougli grinding stage, and of course, no further grinding is necessary. Tliese polisliers riiiist be used with the mirror face up, witli a fine grade of rouge to preverit sleeks, :incl tliey require frequent renewal of tlie rouge rriixture. Deforrriing tlie lap to concentrate its action in certain zories, or remove its action in others, is standard practice u ~ i t hmany amateurs. This includes pressing d o ~ r ntlic niarginai, facets with tlie mirror, and pressing or raising facets fartlier in. Only a sliglit amount of pressing is required-just enough t o cause the facets t o take on a sliglitly eloody appearance from tlie greater thickness of ruuge niixtiire between tliem and tlie mirror, and t o eliminate their action for perhaps fire minutes while the rest of the facets are sinking to the same level. I n pressing tlie marginal facets, plenty of pressure should be used wliile tlie iriirr«r is slowly pushed around tlie rnargin of tlie lap, the idea being t o acc»mplish the pressirig witliout niuch polisliing. F o r pressing down facets farther in, lny on squares of p:ir;iffined paper and press with the mirror. S o raise them up, lay on sqiitircns of H C F and presr with the mirror; this time, the pitch, seelring the easiest nieans of escape, will flow u p into the H C F depressions. Go easy with tliis one. Whenever edge corrcction is necessary, it is aclvisable t o d o this first, so t h a t tlie slight irregularities left by the local work here will be removed by later work on the full sized lap. The H C F qetliocl described in "A.T.M." is our choice for this, levcling out as close t o the edge as possible, and then removing tlie last quarter-inch raised zone with the finger tips. To do this, place the mirror face up, with the handle down in a milk bottle, p;iint rouge around tlie marginal zone, and make about 1" strokes parallel with tlie edge of tlie mirror. Use tlie tips of the first three fingers Jiist incide of, and extending t o tlie edge: usiiig the thurnb as a guide against tlie side of the mirror. Use plenty of pressure and revolve tlie niirror alowly by grasping tlie flange of the handle witli tlie other harid, so t h a t each stroke adrances about oiie-quarter irich past the previoos one. Tliree revolutions of the mirror is enough of this witliout testing t o be sure the action is ~ v h e r eit is wanted and not producing a ditch. I n wiping u p the inirror use two pieces of cheesecloth lcrpt hanging, when not ir1 use, on clean hooks overhead. Use one to 6011 u p tlie surplus moisture, fan dry, arid wipe liglitly witli tlie other to clean off the drieci rouge. Wlien rernoving a central ~irotuberance, tlie first considrration is t o protect tlie edge. Cntil the bump is polished down to the proper level, t h e edge will quickly turri if allowed to d r a g over tlie lap. Irregular sliaped
44
M I R R O R RlAKING
pieces of HCF of such a size t h a t the stroke will just bring them t o the boundary of the burrip will quiclcly take the preliniiriary r«ugli cut and, of course, cannot possibly harm tlie edge. To make the mirror properly balance, threc small pieces of c l ~ a ~FICF z msy be placed arouncl tlie margin of tlie tool, with so:ipy water applied t o mtike tlie mirror slide eahily over them. I f the first attempt starts a hole in the middle of tlie bump, leaving a crater, never mind. Go aliead until the Iiole appeiirs to be clown ne:rrly leve1 with the marginal zone and then rernove the crater with an HCF ring, still using the balancers. In al1 this work the strokes should be extremely short. When the leveling off has proceetled t o tlie point of sliglit zona1 hangovers in the form of raised rings, these should be located with the measuring stick, and the stick used t o loc:ite the strips on the tool. A t tliis point severa1 zones may be worked on a t the same time hy placing strips a s indicated f o r each, giving a larger area of support for the mirror ancl softening down the action. I n using the blending overhang stroke, t o rcmove a central bump, the marginal f:icets should be well pressed down, using an overliang well out t o the edge of the lüp. As soon a s this is done the overliang should be pulled in a bit t o prevent forming a hole. If a hole shoulcl start, remove the crater around i t at once with a ~ p i n n i n g overhang, rotating the mirror rapidly with the palrns of the two Iiands against the side of tlie handle flange, keeping tlie crest of the crater just inside the rim of the l a p and gradually w o r k i n ~the mirror t o new positions t o equalize ttie facet action. What happens Iiere is easily visualized. The action tapers off to zero a t t h e center of the mirror; in spite of tlie fact t h a t the center is in complete contact. I n ;ill overhang polishing, üfter the mirror has been brought spherical, press often. About half a minute polishing, and 15 seconds tapered pressing with the mirror centralized, is a good rule t o follow liere. If the l a p is allowed t o bccome of shorter radius of curvature than the mi,-ror, it will produce a Iiole in the center of tlie mirror, regardless of the stroke used. Keep tlie edge of the lap hitting, a n d learn just what happens with the various strokeo under this condition. I n bringing t o spherical chape by tlie overhang method oii the fui1 sized lap, zontil liangorers will generally be broad ones blending wcll into each other, which may he rapidly reduced by pressing iri a few f:icets in come zones, ancl raising tliose in others, as the case requires. After a few optical surfaces have been made, the amateur learns frofn past experience how t o appiy the necessary preventire measures t o bring the mirror througli spherical and to elin-inate most of the correction mentioned above. But i t does no harm t o get ihto al1 this mess a t least once, so that tlie trirks will be learncd ancl l~el
46
MIRILOR MAKING
if too f a r out use thosc slio\vn in Figure 30, riplit. T r y t o deteririine the pro1)er strokes early in tlie fipuring and liolcl to tliem. Slie distributiori of iiititeriiil tu ht. remoreti can be seen by lnying a straiglitetlge arross tlie tal) of tlie I:ist curvc in "'l'lic. I)oiipliiiut F;riiiily." I t is also import:cnt t o prestarve tlie fl:itness of tlie central :irea mhen the knife-eclge is :it its ci.iiter of currature, :inri not develop t i hole. 'rlie first curve iii the family sliows tlir p r o l ~ c r cross-sectioii. 11s tlic differeiice between iriside antl outhicle raclii of curvature oppro:t<-lies +/R, work should be more and more leisiirely, witli plirity of tiiiie oii tlie testing stand for the mirror t o coriie to ecluilibrium. F o r tlic final test, tlic rriirror sliould be left several Iiours; fur Pyrex, une hour rvill do. For
Fine prin(1 hy tlic rcrrrsnl methníl (oiir (1ingh;it slio~vn in Figure 34) bringinp tliroiipli stroiiply overcorr
strolies just erioiigli t « 4iow :r fnirit liyperholie figure in tlie spit test. Tliis will he very ne:irly oiie-li;ilf strokes. Tlir Iirroeiic \vil1 I)r of no ac1vnnt;ige frorn t i tlicrinal starirlpoint wlirn Pyrex is iisc(1. but it will do arvtiy witli tliosr central air biihbles wliich tire bump proclucers. Frorn riow on it is clear sailiny. Don't botlier t o bring spherical hut aim for tlita ~,;ir;itioloitl frorn tlie heginnirig of poliihing. Get on a 40-second Iap and, as soon ;IS it is possible t o test, locxte tlie crest ~vitlitlie kiiife-edge in the half-u-ay positioii. S t a r t witli a strolíe wliieli \vil1 hriiig tlie edee of tlie lap not cliiite t « tliis crest :inil gire 'er n spell. On wiping up, the marginal xoiie \vil1 he foiiii(l to lie polisliiiig feist, witli tlie centcr scarcely touclied. Fine. Vnclrr trqt, tlie difl'ractioii edge !vil1 h;ive already put in its appcaraiice and will be :I giiide frorn now on. ;ipl)ro:iclies a paraboloid, the point will be found As t h r Iiy~)<~rl)i~liiicl where tlie I r f t diffra<stion rdge hegins t o lose its hrilliance, witli a softeiiing of tlie illumination jiist insicle-~vr.;rrning that turiied edge is approacliing. Tliis is tlie sigrial to Iciigtlien tlir s t r o l i ~ sjust ~noiiglito hring the diffraction line 1):ick ag;iiri. Tlie cause of cdge turriing Iierr is obvious. Witli sliort strokcs, tlie eilge of tlie I«p tiirrir iip, :ind as tlie mirror approaclies a sphere its edge ~villplow into tliis Iiigli pitrlr. Tliis lcrigtlieiiing of tlie qtrolie \vil1 qlom down tlie speed witli which the correctioii re(1iices. Rut remcriit)rr tli:it, witli tlie hard lup, tlir strokes must be niiicli longrr to procliice ;i spliere, aiicl to liuld a p;iraholoid tliey must be lengtliencd t o :rboiit tliree (luartcrs tlie diamctcr of tlie mirror. As a result, the correctioii will líc.(>prcdii<,irig rvith one-1i:ilf or eveii five-eiglitlis strokes,
whntever is necessary to liold ttie diffrnction line at the eclge or to bring u p tlie center polish. Well, tlikit's al1 tliere is l o tlie writer's metliod of rritikirip a iriirror. As soon as the figure reduces to tlie arabo bolo id, the stroke is lengtliened in order t o liold it there until the polisliing is completed. Wc are so familiar with the rnethod tliat we once got a little cocky and matle a xvsger tliat \ve could produce a inirror by "feel" alone during tlie grincling, ancl ";ippearanceV of tlie polish as it carne up; gettirig a correction witliin 25 percerit orer or under ~vithouttesting a t all. After tlie job \vas done wr piillicl iii our liorris nnd bouglit the cigars witliout argiirnrnt, ns the niirror was only lialf corrected. But, ariyliow, it took only ten miiiiites to finish.
Ancl now, as we sit back in relaxation after tlie arcluous tnsk of writing al1 we know about niirrors, :incl perhaps a little hit more, wr must pay tribute t o the nurnerous aniateur rnirror makers whose correspondence has been a coristaiit source of education, and wliose ideas \ve li:i\.e f r ~ r l yslviped. And if nsked to esplain the cause of :tn incurable case of rnirroritis, we \liould blame it about 50-50 upon the continua1 ltishing of r n c l e Epliram's wliip and the inspiration of early contacts with R.W.P.-15 Allengate Acenue, April 1, 1936.
SMALL TOOLS
Sub-dianteter Tools
A Co~rlposite C l ~ n p t e rof Experiences Prof. G . li'. Ritche?y. in ilstrophysical Journnl, Apr. 1909: Of much practical importirnce in its be:iririg upon tlie malcing of very large optical surfaces is the fnct that, in tlie case of tlie 60" glass, griiidirig :irid ~>olisliingtools of only about one-foiirth of the area of the glass were used witli <.iitirc siiccess in excavating tlie large conctive and in fine grinding :incl polishing; a fullsize, flat grindirig tool was used only in the prelirninary work of securing a perfect surface of rerolution. A circular grinding tool of cast iron 31%" (80 crn) iii (li:inieter, ras use<] in al1 of the firic grindiiip of tlie large concave surf;ice. Iii polisliing tliis coricavc, and in bringinp it t o an optically perfect spherical surface preparatory to parabolizing, a 90' sector-shapecl polishing tool of exactly cine-fourth the area of the large glass was used with the best results. I n parabolizing, a circultir polishirig tool 20" (50.8 cm) in diameter was exclusively used in securirig the necessary cliange of curvature from ceiiter t o edge of the glass; in addition t o t l i i ~the 90° sector tool, used with long diametrical and chordal strokcs, Tras fourid to be of great value in smoothirig out the pnrnboloid:il surf:ar;iboloid, onc modificntion only \vas fuund desirable in the polishing macliine described in my Smithsoninn pnper. The two crtinks wliicli give the motion t o the polishing tools were rerriade in such a way t h a t their throlv or stroke can now be altered a t will wliile the machine is running. The optician is thus enahled t o change tlie position.and stroke of the tool witli a perfectly smootli progression \\,hile parabolizing; these changes a r e actually niade a t tlie end of each revolution of tlie glass, ahd a very grent improvement in the smoothness of curvature of the paraboloid is a t once apparent. IInro7tE A. Loze'el; S a n Diego: Ellison mentions t h a t it is easy t o grind and polish tritli small tools, but does not say how to do it. A 12" Pyrex was rough ground face down for 9 hours over a 9" tool. A t the end of t h a t time the c u r r c liad reached full deptli a t the center, as determined by measuring the sagitta, but lacked about aii inch and a half of renchirig tlie edge of the disl;. (Tliis first grinding fiice down leaves the edge of tlie niirror untouched-not eren scr:~tclied.) TVlien the ciirre had reachecl full deptli iii the center, tlie mirror \ras turned face u p aiid the same tool used oii top. One simply makes 1:irge epicycles al1 aroiind tlic mirror, worltiiip mtiinly on the edpe of tlie Iiollom, uritil the curre rc:iches the edge, a t whicli time the curve sliould have becorrie splierical. Tliis grinding with tlie mirror f t ~ c eu p also required 9 liours, but (lid not deepen the center the sliglitest bit, so i t is important t o &o to full depth in the first grinding while tlie mirror is face down.
Tlie fiiie grinding is nll doiic. witli tlic rnirror facc iip. Tlie stroltes iisrtl are 1;lrge epicycl's nroiirid tlic iiiirror, :ilterii:ite- liiis t o cx;>eriiiiciit ;riiil Ieit i1t'tt.n tu si.? tlit. rc.>iilti. L \ ~ i yiiii\t:iI
.
SMALL TOOLS
51
with mirrors of short foca1 length. One word of warning: The mirror, when face up, is much more likely t o be scratched. U. E . I17arnsr, C'hicclgo, Zllinois: There is nothing particularly new in the use of the sniall tool iii rvorking optical surfaces, nor is the method of working a mirror "fnce up" a novel one. In fact, practically ti11 of the larger rnirrors are mnde in this manner. Nearly al1 rnachine grinding and polisliirig is done in tliis way. I n a o r k i n g mirrors by tliis metliod it is the mirror hlank, nnd not the tool, that is fastened t o the pedestal. S h e manner of strolcing is inucli tlie saine as in tlie conv~ntioiialmethod of hand working, but a certain precaution must be observed if dire liappeniiigs are not t o result. I t is iinperative that the workrr's wtilking around the pedestal or barre1 be very regular. If it is not, ahtig~liatismm;iy be groiind in, and i t may or may not be ground out in tlie su1,srquerit workiiig. One naturally woiiders, in first contemplating this process, why the mirror will becomc coiicave, wlieri with a11 of our prcvious experiences i t was tlie upper member tli:rt becaine concave, while tlie lower one hrcame convex. Let us supposr that in oiir grindirig we use a straiglit, center-<)ver-center strolce. is, when we are ready to start a Let us commence rvith U 4" stroke-that forward stroke the rlearer edge of the tool will be over the ncarer edge of the mirror. Tlie mirror, being 10" in diarneter and the tool G", a 4" stroke will bring tlie fartlier edges of tool anci mirror topetlier. In ninking tliis stroke we cut a swath 6" wide across the mirror, but leave the 2" margins on either side of the mirror untouched. Also, the swath we have cut is decper at the center. Now let us take another cut across the center of the mirror, a t riglit angles t o the first. Again we see the center of the mirror get the full abrasion, u~hilethe margins a r e untouclied. With er7ery cliange of direction of our stroke tlic sairie is repcated, and it becomes easy to see why t h r mirror will Iiollow rapidly a t the center. I n fact, the grinding is so rapid a t the center that, except in the earlicst stages of roughing out, the straiglit center-over-center stroke should not be used, a s it tends t o griiid an irregular shape, usunlly one witli rnucli sliorter radius a t the center. In prtictice the stroke used for al1 "excnvating" may be a 4", straight stroke in which the ceriter of the tool piisses over a point about 1" to the side of the center of the mirror. Shis leaves a margin of 1" of the mirror wliich receives very little a o r k . If we should happen to overshoot the desired depth we can flatten the curve by stroking the mirror with the c e n t e ~ of the tool, passing over a point ahout ll/z" or 2" inside of its edge. When employing tliis method of work, simply inverting tool and m i r r ~ r will not cause tlie curve t o reverse, and hecause we a r e able t o control ou:. curvature so nicely rve may rough our curve out t o its full depth. In fine grinding, if we bavc roughed t o the full deptli, we shall have t o choose a stroke t h a t mil1 not tend rither t o deepen or flatten our curve. A stroke in wliich tlie center of the tool travrrses a poirit aboiit 25G" froin the center of tlie mirror n7ai foiiiid t o obtain this condition. As tlie fine grindirig proceeds it becoines increasingly important that our
SMALL TOOLS movement about the mirror, and our stroking, become a s regular a s possible, nitliout cmploying mechtinical artifices. In worlí of tiiis kind the abrasive niixture will not have much tendency t o run off the erlge of tlie inirror, bec;iiise tlie l t ~ t t c ris conc;ive iip~v;ird :rnd liquids tend t o flow t o tlie centcr, lience it is possible t o mork in a much more cleanly miiriner thaii by the conventional metliod. Tlie greater cleanliness in working leads t o a greater freedom from serious scratches. Great ciire niust be taken iii the fine grinding operations to see that al1 previniis grnde pits are removed a t the margins of the mirror. The surface of the tool must never be used as a eriterion for judging the completeness of any stage of grinding. Many hours of fruitless polishing can be saved a t the expense of a bit of patience and thoroughness in fine grinding. One of tlie first things tliat 1 a m aslred, when discussing tlie use of the small polisher is, "How on earth can you avoid a turned edge?" Let us look into the probable cause of turned edge in the conventional working of a mirror. Suppose our mirror t o be a t tlie end of its stroke. The pressure on the handle of the mirror in a horizontal direction tends t o press the leading edge into the lap, becausc of the frictional resistance to the rnotion. Tliis results in increased polisliing a t the very edge, and oiir notorious turn down results. This condition is augmented by poor contact between riiirror aiid Iap. 1,et us invert our full-sized mirror and tool and note the result of our reverstil of stroke. If tliere is any tendency t o "toe in," the tool rnerely tends t o put the work on tlie tnirror's face a t a point f a r from the edge where, under ordinary conditions, it can do no harm. The kind of turned erlge we wish to avoid a t al1 cost, because of the virtual impossibility of elirnin~tingi t once it is present, is that nhich is very narrow, yet so severe t h a t it can be seen by casual inspection without applying any means of testing. The strvkes used in polishing are the same as those used cluring tbe fine grinding stages. A straight, elliptical, or zig-zag stroke of about 4" length, with a center about 2%" frorn the center of our 10" mirror, may be used, and will result in an even polishing action and a regular figure. The tcndency of the beginner is t o t r y to trvciid tlie edge entirely, in his efforts t o avoid turning it. I t is evidrnt, liowever, that our tool must pass over the edge if tlie edge is t o be polished. Tliere is pr:ictically no danger of a bad turned edge if the tool is in good contact with the mirror, even thoiigh the tool may extend orer the mirror's edgc by neiirly 3". A gradual turned edge of about 1" in extent will naturally result from the polishing operation. I t is possible to efimiiiate this by figuring. I n bringinp the figure to spherc frorn a more or less hyperboloidal curve, it u7as discovered that, hy placing the edge of the tool over the crest of the curve and then applying considerable pressure with tlie fingers over that edge of the tool, tbe effect of a very sm;ill polisher \vas obtainecl. However, because the ~vholetool was still in contart with the niirror, the use of the tool in this way did not produce zones, as miglit be expected. The broad turned edge previously mentioned, was treated in much the
SMALL TOOLS
53
carne way. The TDE was about 1" in extent. The tool was used so that its edge was about '/i" from the eUge of the mirror, with the pressure applied t o tlie edge of the tool nearest the mirror's edge. Tlie stroke was ;lbout 2" long. In using the tool in this way it is rotated in tlie hands-Just as in any other polishjng operation. The pressure does not, however, move with the tool, but is rnaintained over the same zone of tlie mirror. The local corrections were applied until, when splierical, the diffraction line could be seen al1 tlie way around the mirror while under Foucault test, even n h e n the knife-edge hacl completely darkened the face of the mirror. The parabolizinp was done by means of the same localized pressure on the polislier. In this case the tool was placed on the mirror so that the edge t o whicli tlie pressure was applied overlapped the center of the mirror by about 2". The stroke used was about 4" in length and zip-zapged back and forth across the mirror's face. U'henever i t was noticed t h a t any w n e waS not conformirip to the rest o < the curve as it developed, it was quickly whipped into line by proper application of local pressure to tlie edge of the tool. This manner of using the tool is not greatly different in effect from the use of honeycouib strips, except t h a t i t does not leave the sharp margins characteristic of the latter. The use of this rhethod of parabolizing permitted deepening the center of tlie mirror without disturbing the perfection of the edge. The speed of grinding and polishing with a small tool should not be much different from that of full tool operation. While the area of the tool is less, the pressure which can be effectively applied is iniich greater. If the practical limit of size of a mirror which i t is practicable to produce by hand work with the full tool is 15" o r 18", i t should he possihle, by means of the small tool method, similarly t o work a 30" mirror. F o r those who are afflicted with "dropsy," this rnethod should have its attraction, f o r the valuable member-the mirror-is securely fastened down and the liazard of fatal termination due t o gravitational attractinn is mitigated. All in all, 1 would suggest that telescope makers a d d this mode of operation t o their repertoiie. I f it does not replace the "biblical" manner of operation, it certainly should prove a most valuable adjunct. Hornce H. S e l b y , Cnlifornia: Although sub-diameter tools have been used for the piist felv years by this scribe, in the construction of a triplet refractor objective, a paraboloid, two Hindle spheres, 20 flats and two photographic anastigmatc, he will not atternpt t o write on the use or manipdation of such items. One Ti; will deepen a surface with a stroke which, in another's liaiids, will make a similar surface less deep. Of course, if aii the many varitibles of any one polishing or grinding operation could be rigidly controllrd, e r n l u ~ t e dand understood, this operation could be performed and repeated "ad nauseam" and the end reiults would always be the same. Then a r t and craftsmanship would change to science, and results could be attained in a straightforward, mathematical and very satisfying msnner.
Since the usr of small tools \vil1 not he discus~ed,tlie orily tliiiig remaining as an excuse for these coinnierits is the subject of construction. (;lass tools tire iiiore 1)ol)ul:ir witli ti~iiateurs ttitin are tools of :iny other rnttteritrl. Profrssiontils, lio\vrver, u\e tools of wood, artificial rcsins, cast iron, sheet stcel plus glass, hrtiss, leticl and hoilcr pltite. Of tliese last, wood is ctieapest :incl rnost easily formed; so consideration of i t is most hcartily advocated. Of tlie pliysietil properties of u~ood,the rnost important, from tlie standpoint of tlie TK, is ~)robnblytlie elasticity modiiliis, xvhich is a measure of the rigitlity. Tlie tipprosimnte rnodiili for tlie iiiust suitable wootls are: Yello~v hirch (Ilpt~rl
METAL L A P S
Concnzw Tools: The making of small cast iron tools Iins presented many dificiiltiei t o tlie :iver:ige ;irri:itriir. Tt is esprci:~llj' hard to pet ;L prrf(.<.tly spherical siirf;ice wticn usiiip tlie mdinary right angle cross-feed as found on an engine liitlie aiid, uriless one lias iiriliriiited patience ;tiid skill, tlie use of hiintl tools on rrict:ll si~rftice?is alriiost out of tlic. cliictioii. The following mctliocl mil1 piie consistently goocl results, and nrhile perhaps not iiew, is probahly iinl
Al1 d r a ~ v i n g sby the nuthor F I O ~ R1E
I'lan o!
f i ~ t . l i l )f o r
r o n r f l l . ~to018,
up if desired) and a %" holr i i clrilled '4" (lrep in the ground rnd. Place this center iii tlie tail stocli of tlir I.itlie (Fipurc. 1 ) . Place one eiiil of tlie r
56
METAL LAPS
With everj-thing set, strirt u p the lathe :iiicl, using tlie cross-feetl screw, feed the lattie lap across the tool toward the center. On tlic cornpletior) of this first cut, more tlie latlie tool point back toward tlie edge u f tlir Iap S" fartlier than the s t a r t of the first cut. Continue successire cuts iintil the edge of the lap is reached. Tlie final cut sliould be very light, made with a round-nosed tool nnd fairly high speed. Good finish is essential. Conca;i: L n p : A flatplate A, Figure 2, is clnmped :icross tlie lathe bed a s near the headstock as possible. A post R sticks u p from this, on tlie center line of the bcd, so that its t o p is sliglitly abore the cross-slide. A hole C is drilled and tapped in tlie cross-slide, in sucli a position tliat, when the lathe tool is a t the center of tlic lap, tlie Iiole will t ~ eon tlie rcnter line of thc latlie bcd. A piece of flat iron is drilled with two holcs-one t o fit over tlie post B
FIGUBE3 Plon of set-up for short rndilas tnols.
and the other over a stud screwed into hole C. the center distance of these holes beirig the required radius for tlie tool being made. A mandrel is madc, with i1 taper on either end and having suc!i length that, when one end is inserted in the lathe spindle taper and tlie lap blarik plticed on tlie t a ~ ~ eonr the other end, the back center may be run into a center hole on the face of tlie lap. I n using this rig the cut is started a n inch, more or less, inside the peripliery of the tool, and earh succeeding cut is started slightly nearer the center than the preceding cut-al1 cuts, of course, heing made from the center outwnrd. The compound screw is used for feeding the lathe tool iiito the work. So much for short radius tools. On longer ones 1 proceed as foliowcl A simple calculation i n ~ o l v i n g our old fridnd tlie sagitta formula r3/2R ("A.T.RI.," page 312), in which r is the radius of the lap and It its radius of currature, gires us the deptli of our cut. For cx;imple, required the depth of cut a t center on a tool 5" in diameter ancl having ;L radiiis of curvature of 165" ( a radius of 150" t o 200" is often foiind on thc fourth surfsce of un ordinary achromatic). Siibstituting in tlie formula, we get .019". For practical purposes .02" will give as good results. The tool is set up on a mandrel in the latlie spindle and a cut is taken
METAL LAPS
57
over the face. Run the slide rest back and, with a scale and pencil, divide off the face into 10 or 20 equal spacei (Figure 3 ) . S t a r t a t the center and end at the edge of tlie tool. Shus, 20 spaces each %" = 2%", tlie length of the r a d i ~of~ this particular tool. R u n u p the slide r e \ t and, with a scratch awl o r pencil, make a series of c o n c e n t r i ~circles o w r your markings. Your compound slide is then set parallel t o the lathe bed, the lathe tool placed a t the edge of the tool and the cross-slide clamped. Most compound slide scretvs hnve 10 tlireads per inch, with a micrometer head divided into 100 divisions. Therefore each rlivision is equal t o 0.001". Our total depth is .020", therefore if we advance our lathe tool in 10 or 20 (depending on the number of concentric circles we have rnarked off) uniform steps of ,002" or .001", we should arrive a t a stepped 5urface approaching a curve. Very little hnnd work with a wide-faced hand tool will smooth
--
.o=-
FIGURE3
Cuttin!~Iong r n d i ~ r stools.
u p the surface, and by the time you have run your glass through the 80 and 220 stages the surface shoiild be almost exactly riglit. I n making u p these long-radius tools, 1 usually make them u p in pairs, using exactly the method as outlined above for the convex tools, except tliat the cut starts a t the centcr and finishes a t the edge. A few minutes' grinding with 220 will put them in perfect contact ( t r s t with pencil marks). I t is absolutely paramount t o work witli exactitiide when doing optical work. The average amateur has little conception of just how exact lens surfaces must be for good results. ' f i e final figure of long-radius fourth surfaces should always be tested both for foca1 length and figure. A slight deviation from the exact prescription will spell the difference between a good achromatic and an exceedingly poor one. Moral-Take time and have patience. While i t has been the custoin to make small len<es by mean? of readp formed metal tools, their use for working lenses and mirrors of longer focus has not ( a t least among amateurs) been so general. Prior t o the invention of silvering on glass, by Liebieg, al1 mirrors had
58
METAL LAPS
of necessity t o be m ~ d eof materi:il wliich in itself mas cnpable of tnking a high polish. The softer met:ils (.;pr<:iiliim met:il, etc.) were practically the only materials urliicli woiil(1 fill : ~ l l tlie retliiireriients. Tliese tiietnllic inirrors were usunlly worlccd on metal tools wliicli Ii:id hecn tiirnrd in a lnthe and smootlied hy griiiding on n mating surface, the curve being gaged t o a spherical terriplnte. Tliis mas tlic gciiernlly accepted method of mnking a speculum prior to the rriiddle of tlie 19tli Crntury. The invention of tlic Foucault test greatly simplified tlie meclinnics of ~riirror ;irid Irris m:ilíiiig. T r i thtit tlie skillei: fitting of tlie l a p surfiice to its nintinp shell did not have t o be nenrly so accurately done, tlie fniilts of tlie semi-polislied siirface could be seen ancl corrcctecl as tlie work propresied; prior t o tliis trqt notliing much could Ije done toward correctiori until the speculum was nctii:illy tried on the he:rvrn.;. One outstanding rekison for tlie use of glass for tools is its clienpness. Any old piece of glkiss ~vliicli li;~sthe ncce.;s:iry tliickiiehs and clinrrieter c;iii lie and is so usccl. Most aiiiateiirs ni:ileriplicr~il speed should be cut do\vii in proportion. She important thing is t o keep the Carbo on tlie tool-not oii tlie sidt. of tlic splasli pan. Alalíe u p a ruriiier (brass or c:ist iron) 3" in tli:imrter zinc1 thicli. \jTarrn your glass Li1:ink (Pyres, lireferrcd) :in
víG"
METAL LAPS
59
of the glass on a n old tool of about the riglit curve, using No. 60 or 80 Garbo, or else, after 1 Iiave turned u p tlie convex tool, and before it is ground true on its riiate, 1 use it a s a roughing tool. A lot of rctruing of laps will be savccl by this proccdiirc. Wtish "11 everything very carefully. The pin bar and fingernails are botli favorite places for Carbo t o roost-so watcfi tliem. Change over t o 220, running your curve about 12" longer than rcquired (test with :S light). Get a good surface, but do not xvorry if your pencil contact hetrveeri gl:iss :ind tool is not 100 percent. q r a s h u p again. There is no good retison, when using a mechanical spindle, for using six or ser7en grades of Carbo, as in hand-work, since even tlie finer grades cut very fast and 220 pits will disappear in a few mornents with 3F or even 400 Carbo. The ordinary wet lasts from 30 to 60 seconds. One precaution, however, must be observed in changing your grades: between each grade run your concave tool for a t least two 6r three good wets on the t o p of the convex. In other words, alternate your grinding on tlie convex between the concave tool and tlie glass. Only in this way have 1 succeeded in maintaining the curve of my convex and also good contact between i t and the glass. 1 invariably finish urith 6F or 906, mixing with either 10 or 15 percent of ordinary talcum. A good, safe stiint, and a saver of scratches with this fine grade, is as follows: Apply with the finger a good dab of dampened compound t o the center of the rotating tool and spread it as evenly as possible. Tlien, starting a t the center, hold a piece of glass in the fingers and work the compound evenly outward towarrl tlie edge. Csing a "bruiser" in this manner will eliminate any chance of a particle of Carbo scratching your mirror. Stop the spindle and put tlie mirror on the tool, s t a r t up, and spin out the wet. Do not t r y t o put the glass on the tool when it is revolvirig -sure disaster will follow. Always give a t least 10 or 12 (20 is better) wets of this last grade, thus insuring f-eedom from pits. Run as d r y as you can-your earlier grades may be wet, but in order t o get a really íine surface this finest grade should be run as dry a s possible, short of sticking. Wash up. Polishing: Preliminary polishing should be done on HCF. D r y your tool and apply witli an old knife blade a very small quantity of "stickum" (heat some pitch and add turpentine until the cooled mixturc will just stay solid). S t a r t your spindle and, with your knife blade, apply a piece of stickum the size of a pea to its center. Bcar down hard and spread the dope evenlj- and thinly al1 over the tool surface. Do not use too much stickum, a s a tliick layer acts as a lubricaiit and your HCF will slide around under tlie heat generated in polishing. Cut a circle of EICF S'/'" O.D., warm slightly and press directly on the doped convex. Llse your palms and press hard. S e x t , latlier your Iiand with ordinary soap urid water and go over the HCF surface (incidently, the lathering inay help to get some of the stickum off your fingers). I n polishing, 1 would advise a s higli a speed a s possible. Personally 1
60
METAI, L A P S
use from 1500 t o 1800 r.p.m. Yse vcry tliliitc rorige and on no accoiint nllom the I I C F to get dry. After fivr riiinictrs' 1)olishing rrniove tlir d:ip and gltiss, ;ind con1 tlioroiiglily iiii(1cr tlie f;iu<.ct. 'I'liree or four 5-riiiiiiite 1)nlisliing spells (xvitli coolirig hetw(.c.ii) slioiil(1 ~iolisliyoiir gltiss cle;ir to tlie siniply spoils the lnp aiiil [loes eclge. Do not :ipply too miicli pres\urc-it not seerri t o spcccl iip tlic opcrntioii. Final polisliiiig :irid figiiring niiist he clone on n. pitch lap, by Iinnd. 1 llave trircl to figiire on tlie revolvinp s~iiiicllebiit Iiave never yct been ;ihle t o e\cnpc rvry serioiis zoiiinp. It is prok);il~le tlint yoiir firqt fr\\r iitt<'inl)ts will rehiilt iii 1i:tifly zoiieil surf:ices, ariil oiily hy repetitr(1 tritils \vil1 yoii arrive ni n. conihiii ition of stroke and prr.ssiirr wliirli \vill reiiilt ir1 ;i goo(1 sphrriciil surfacc. Filial figriring, as notecl :iliore, must be done «n ~iitclitirid by Iiand. It sometimes 1i;ippens t h a t tlir outer 5/2" of the glass will refuse t o polisli out oii tlie HFc I:ip. Tliis f:iiilt <-tinusiinlly I)c trticrd to iri\iifficit.iit fiiii::;; hy eniery and not, as thoupht, to the sni:ill clinmeter of the HC,F siirf:ice. If tlie I-ICF is m:ide larper tliaii the 4'/," diometer, tlie hiiphetir of tiirneíl edge mil1 surely (levelop. Also, if tlie glnss is fitteti t o riin oii tlie spindle nnd the 4%" polisher run ori top, tiirnrd edge will result. Siii:ilI polisliers are htird t o control, if allowed t o spin freely on top of tlie glass-the cuttiiig is very erratic, taking place sornetimes on the inner edge nnd sometimrs oii tlie edge nearer t o tlie oiitside of tlie spinning gl:iss. Rose laps are also very uncertain in their :ictiori when allowecl to spin freely. Making a pitch lap by the "dunkiiig method" (described under fl:it laps, in the :irticle on smnll lenses) is very easy, and the final polishing :incl figuring by ordinary 1i:ind methods is not ton arduous an undertaking for erren tlie poor, jaded mirror m:iker who liad hoped t o esctipc a little 1i:ird manual labor hy tiirning t o metal tools and a mechanical spindle. [EDITOR'SNOTE: 111 addition t o the pr:icticíil (lata. given by BTr. Clnrk in his ch:ipter, some pertinent points \r7ere contained in his private letter of transmitt:~l-so miicli t o the point did tliey seem, ir1 ftict, thnt permission t o add therri \$,as :isked. Witli tliat perrnission $fr. Clark gnve the w;irning thnt he does not pose as an expr.rt, and added that, by definition, an "expert" rvas any one more tlian 20 miles from Iiorne. H e had heen asked three questions aiid these, with tlieir answers, a r e arranged as follows: Q: "Just why is i t that people wnnt t o use metal tools?" A : "It appenrs on tlie surface t o be easier th:in usirig glass for a tool. As a matter of fact i t is much harder, tincl 1 cnnnot say t h a t it saves very much time. I t is, lionever, less fatipuing, and tliere is a certain fnscination in doing a thirig mrchanically in p1:ic.e of by hand." Q: "Can riietal tools be used in hand mork, lilce glass tools?" A : "They can, but there is no real tidvantapr; in fact, tliere a r e severa1 disadvantages, chief of which is the inahility to maintain good contact, due primarily, 1 suppose, t o the unequal h:irdness of t h r two surfaces." Q: "It is often stated t h a t a 1e:id tool gives a fiiier finish than a glass tool. 1s this the case and. if so, can you say wliy?"
METAL LAPS
61
A : "If one will piit n lead finislied surfacc ancl a glass finished surface together uiicfer a rriicrosro1ir, get tlie light riglit, :irid piit on 7.55 or 1005, one wil? firid no difl'ercric-r bctween tlirrri-thougli tlie Irbid mil1 more quickly ~ i v etlie sarrie (1t.grc.i. of finisli. R u t tlie ljits on the lead-finisliec! surface, srerri to Ii;ive tlieir sides covered witli a film of Icad, which 1 think gives the satiny appearance when the surface is looked itt without magnific;~tion. TIie same tliing is true of a surfnce finislied on brass-tlie extra fineriess is more apparent tlian real." Considering tlie discouragernent just quoted, why shoulcl the cliapter then have been inclii(1ed in tlie book a t all? One reasori mas tliat tlie discouragement is not cornpletc or categorical, and the other ha5 to do with human nature; it w\.;is hl:trk Twain wlio snid, "There is a preat (leal of human nature in man." M:iny wisli t o t r y a thing, just t o know about it, ;ind even if they suspect in advance that tliey will not like it very well. F o r tlie rest, see the final parngr:ipli on pnge 6 5 , "A.T.M." L r a d tools in;iy perliaps be mtide by casting. R. L. Beardsley of Los Angeles tells Iiow he :ittempted this by making a plaster of paris cast of his mirror, tincl then a positive cnst of tliat, and poured the molten lead on tliis. "But it boiled and biil>l~led,"he says, a n d lie :idds, "it is difficult to riinke a goo(1 letld lap that.way." Anotlier wiiy that has oftrn been uied is to hold a disk of lend in tlie li;in
& l e t a l & l i r r o r s anrl F l a t s - a
Coniposite Chapter
[ E ~ I T o R ' sNOTE:As giass has a better working disposition than metal, only relatively few nm:iteiirs liave occasion t o rri:lke optic:~lsiirf;ices on rnrtals. That minority, when dcfinite d a t a is w:inted, fiiid i t difficult t o sccure. Metal mirrors went largely oiit of style when Liebig found a way to silver glass. But a number have bven q a d e in riiore recent ye:irs-so~iietimes for n special purpose, sometimes for tlie fun of trying sometliing different, perhaps in some instantes "just hecause." Tlie worker is throwri back a long way, on the writings of tlie old-timers, such as Newton (in tlie Philosophicnl l'rnnsnc. tions, Nos. 80, 81, 82, 83, 88, 96, 97, antl in his "Opticks"), Cmith (in his "O~>ticks," XTol. 11, pagrs 301-312), and the younger Herschel, Sir Jolin (in "The Telescope," p;iges 126-178). h'oiie of these is modern. 'I'wo mo
METAL MIRRORS AND FLATS
63
di5culty is encountcred in procliicing a speculuni metal casting having a cast surfacr satisfactory for polisliirig anrl free cnougli from excessive interritll stresses so tliat the castings mil1 not crack wliile coolirig in tlie mold or nliile being polishetl. Developriient of the proper foundry technic Iias required considerable expcrimentatiun in o r d r r t o overcome these difficulties. A procedurc giving satisfactory results consists in melting tlie virgin copper in t i gas-fired crucible furnace under a cover of cliarcoal, and adding the tin when tlie copper is inolten. As a result of a considerable amount of experirnenting it was decided t h a t one half of one percent of zinc shoiild be adcled to tlie molten mettil as a deoxidizer before rernoving the crucible from the furnace. Tlie metal is cast at a temperature of approxim:itely 95OoC, the exact temperature deprnding upon the size of the casting. Green santl molds iiiade froni a g r d e No. 00 Albany molding sana are used, tlie surfaces of wliich are coated witli a mixture of rubber ceinent and Ceylon graphite, as tlie ordinary m ~ l d ~ f a c i nmaterials g have not proved sntisfactory in producing sinooth surfaces on the cornpleted casting. Tlie metal is allowed t o cool in the sand mold sufficiently for solidification, aiid then it is removed and placed within a hot furnace in which the metal has been melted. Tlie castings are'allowed t o remain in the furnace until the castings and the furnace liave cooled t o roorn temperature. 'I'his slow cooling insures a minimum iimount of interna1 straiii which under ordinarp treatnient causes the cold brittle casting t o break. Prof. Arthur Howe Carpentrr, La Grcrngr, Illinois: I n the ordinary sense of the word "alloy," speculum metal is not an alloy. I t is aii interinetallic compounri, CuaSn anti :i niixture or solutiori of eitlier more tin or more copper tlian jiist this composition which corresponds t o about 38.5 percent of tin. Aletallogrephers are c;illini these mixturcs "secondary solicl solutions." They do not liave real "metallicity" and are very hard and brittle. Tlie esseritial poirit is t h a t cvery grain or crystal of tliein is like every other graiii or crystal, and there are no parts of them harder or softer or different from any other part. "In the searcli for alloys 1 tliink there is a hint in this fact, and that we should look for alloys of this kind. Naturally, tlie alloys tliat are not brittle a r e more attractive, but tliey have intrinsic properties t h a t make it impossible t o work them successfully t o a firie surface. The grains are iiot alike, hut differ from gr;iin t o grain, even in the niost thoroughly annealed 'solid solutioris' wliich is tlie type of Allegheny Metal. Tliese plastic metal.; will "work-harden" in the case of polishing and aoultl give a great deal of trouble, as they nould not liarden uniformly and graininess ( a lemon peel effect) would develop. A mass rnade u p only of "intermetallic" crystals wtniltl not do tliis. Tliese crystals would be just about as hard as they coultl be already and would be non-plastic like diarnonds, although not so hard. hlost pure metals are plastic, and so are the kinds of alloys known as "solid solutions," but t r u e chemical compounds, like ordinary salt, are hard, brittle and unyielding, Le., are non-plastic.
64
RIRTAL M I R R O R S A N D F L A T S
Copper ancl zinc form :L sirnilar cornpoiind containing ahout 60 prrcent brittle zinc of aboiit tlie formril:i C U ~ Z I Iwith ~ , eitlier more roplier nr mofe zinc tli;in Just tliis coriipositiori. I t is tis brittle as gl:iss :iiiil very white. I t takes a higli polish. 1 do riot know :il)oiit copper :ind :iliiminuiii interinet;tllic corriliounds, but it is possible th:it some of tlierri niiglit prove hetter than rri;iny otliers. 1 am hure tlint a researcli irito tliis field riiiglit clrvelop or open u p corii~~oiinds that miglit be a rctil ndvtincement. Several have been proposed :iloiig this he.-811 Drll d z s e n r ~ e h'rpel.ienrr of L. G. B o ~ t w i r k ,NCW I'ork: The metal reflector that 1 llave is ni:icle of "hlleglieny .\letal." Tliis niateri:il is a clirorne-steel and is very tougli. After trying mtiriy inetliods of r«iigliing it out, iriclu
at the pdgc 1)rfore hrc*:il L " , before iirie griiiding. Four Iiours of finc grindirig witli No. GOO resiiltrd in t l riirr;iture of 70". A t tliis poiiit 1 triccl ~)cilisliirip.1)iit tlie siirface w;is I~;~clly scr;rtclird. Tt i> necessnry to ~vtrhli tlic. No. :M) :irid No. 600 C;lrl)o. l%«tli sizes cont;liii tr few 1:irgc grniris, ~vliicliis tlie eaiiie o f tlie scratclics. \\'lit.ii priiiding gltiis these 1:irgc.r grtiiiis tire broli'ii d o ~ r i iiic:ir tlie rtlgc :iritl tlirrt,by c;iii\c no harrn, hiit ~vitliiiirtzil tlie gr:~insbur) tlirrriselves iii tlic ioft tool (c;ist iroii) ancl ~ r o , j e c tIiigli rrioiipli :ii)orr tlie siirf;ic.e to ciit a. proa\-r in tlie dislc. 'llicy start as scr:itclics ancl rrid with abrupt Iioles. 'I'lie expI:in;ition is obvioiis: the shiiviiip of steel huiltls u]) ir1 size aliecici of tlie gr:tiri. At tliis st:ige 1 encounterect many tritils :ind fnilures. First, 1 triecl H C F witli No. 600 Car1)o. 'l'liis producecl a Iiiiriipy surf:ice. 1 nest riiatle a hard pitcli liip nnd, iiftrr Coiir Iioiirs of grin
66
M E T A L MIRRORS A N D FLATS
lioll
METAI, JIIRKORS A N D FLATS
67
5. Mirror finislied corrcctly to :ipproxi~nntely95 of r2/R. 6. Po5sihle error L/, rnillio~ithof ;m incli. -8054 South l i o n o r e S t r e e t . E r p r r i e n c e of J . D. Bonrdsley, TVnshington, D. C.: While employecl a t the Naval Researcli I,aboratory, 1 was absigried tlie task of rn:~kirig ari 11'' astronomical mirror of stainless steel, for a naval expedition t o Fairbanks, Alaskii. Many st:iinless steels such as 18 cliromium, 8 nickel are described a s <'austenitic." This nietlns that they are non-mtipnetic and that tlie iron is not in the ferritic condition. When such steels are turned or ahraded the surface becoiiies martensitic, ciiusing a very rriarked iiicrease in liardness, thus covering the face with a film having different pliysical characteristics. Steels containiiig nickel Iiave, in addition, a yellowisli tint. F o r these t w o reasons nickel steels, or any austenitic steel, were ruled out from the beginning. Consuttation with Dr. R. H. ~ a n f i e l d chief , metallurgist for the laboratory, guided t o the selection of Carpenter's No. A, containing approximately chromium 13 percent, carbon 0.1 percent, and zirconiurn sulfide 0.25 percent, with the remainder iron. The addition of the zirconium sulfide makes the material comparativev free-machinirig. A square blank was purchased, 12" by 1%" thick. T o s t a r t witli a flat piece of material, and "hog" out the curve with Carborundum or emery would be almost impossible, even with a machinc, a s this metal abrades perhaps 100 times more slowly than glass. It was necessary t o cut both the blank aiid ttie l a p t o ;ipproximately the correct curve. This w:is done by 1:iying the curves out on pieces of flat sheet steel 3/4" thick, which were used t o guide the transverse feed on a lathe, in conjunction with a roller and weiplit. This was done after tlie blank had been c u t circular a n d the back had been trued. The l a p was placed face u p on the grinding machine, the mirror face down. A wooden handle was cemented to its back with medium DeKhotinsky cement. This handle was provided with a hole t o accommodate the machine stroke bar pin. Rougliing was begun with No. 60 Carborundum, using a long stroke and 40 pounds' weiglit. After tlie blank a n d lap stiowed uniform ahrasion al1 over, except for the outer l/lH''of the mirror, No. 90 Carborundum R a s substituted a n d the stroke was reduced t o about 7". After al1 pita from No. 60, which were quite deep, were ground out and the edge liad disappeared, the abrasive was changed to No. 220 and the stroke shortened t o i/3 of the diameter of the mirror. Tlie grinding with this grade was continued until mirror a n d tool fitted quite perfectly. The machine and tlie room were then carefully washed, and al1 Carborundum was removed from tlie immediate vicinity. Grinding was then continued with American Optical Company's emery 51302, iising a 1/3 diameter stroke and no weiglit. A t this time, scratches began t o appear despite precautions, so i~ lap niade of tin and lead, backed by a 1" brass plate, was turned and fitted t o the mirror by means of prussian blue and hand
scraping. Ry usinp care with this fitting it was possible to continue tlie grinding witlioiit going back, tlioupli sever:il Iioiirs were coiisumed ir1 bringing tlie Iap to a perfect fit iisiiig, :
METAL MIRRORS AND FLATS
69
material ~vorkedslowly but scratched very slightly, due to the fact that it was not carefiilly wt~slied. After the spots wcre neurly gone, Iliggins' India Inli was used as the polisliiiig medium. Thc fine carbon p a r t i c l c seemed t o have siificient Iiardncss to cut very slowly, and tliey left the surfacc as smooth as water aiid as bright as a ncw silver coin. During thc extensive polisliing thc figure was occasionally obscrved. Dile to careful grindirig i t was nearly spliericnl a t first, hut became deeply hyperbolic later. Tliis was corrected by inverting tlie mirror und lap, after removing the haridle. By using t h r full size tool with a i/3 diametricnl strolie the mirror a a s brouglit back to a spliere. This figure correction was niade while still using rouge, as tlie otlier things tried cut too slowly. Al1 polishing witli zinc oxide and india ink was done with the mirror face up. This is advantageous for two reasons-one t h a t the polishing material does not run off, so the rouge breaks down thoroughly, the other that orit: gets some idea of contact by observing the depth of color of the polishing mixture as the lap mores back and forth. -3Z3 S St. N . E . Date
Stroke
6-21-'32
1p2"
Tool Full
-
Time Appearance Remarks 10 hrs Oblate spheroid with one high zone 6-22-'32 1%'' Full 5 " Oblate spheroid high rim a n d center 6-23-'32 2" Full 5 '' Oblate spheroid high rim a n d q c center 7- 2-'32 2" Full 5 " Regular oblate spheroid-turned edge 7- 5-'32 2" Full 3 " 1 -f Sphere with 1 turned edge 7- 5-'32 4" Full 3 " Sphere with central hill a n d turned edge 7- 6-32 3" Full 3 " Sphere with %" turned edge 7- 7-'32 1?4" 8" 3 " Turned edge narrower, b u t new hill 7- 8-'32 2'' 8" 3 " Hyperbola, 1" over-correction 7- 8-'32 152" 8" ring 3 " Hyperbola, over-correction At this stage t h e mirror was turned face apward. 7-12-'32 1 Full 3 hrs 7 1 Parabola, b u t n o t sufficiently polished 7-12-'32 1 2 '' Did i t with honeycornb Full 7-13-'32 1 Full 5 " ZnO a n d india ink,OK. parabola (pitch) with proper correction
m
r-,
x"
m
m
x"
T o t a l 53 hours FIGCRE
1
M r Beardsley's lag of t h e 12" metal mirroí job. Notzng the long, tedio@ S P e t k which makr u]> t l i ~r p c o r d , one zr remznded o f a nlow m o t i c n pictur8 -a feature uf metal fobs.
Astignia f ism By Q. E. TVSRNER Chieago, Illiiiois
The term astipmatism is applied to :in opticnl fíiult whicli c:iiises imnges of points not tu be points. Tlie word "point" is iised in the sense that a dot is a point-not refrrring to an arrow shape. Astigmt~tisrii is found normally inliererit in mony types of opticnl equipment. RIost commonly it is prescnt iii the of-axis imüges of telescope 011jectives, e s p e c i a l l ~ reflectors. This chopter. however, deals not with tlir normal astigmtitism, hiit ~ i t l tIi:lt i clitss ~vliicl~ is d ~ i eto abnormalities of tlie instrument t~rouglit about by faulty conditions of rn:~líing. To begin with, tlie astigniatisrn of a sprculurn is usually siich tliat tlie radius of curvature as measured across various cliameters is riot the same f o r all. I t is very mucli as if we took n perfectly figured mirror and bent i t slightly across one diameter. I n tlie illustr:itioti, Figure 1, tlie sctile is, of course, miich exaggerated. The rnirror is suppohcd to be deformed so that across the diameter A C its
Drawirigs b y R. W. Porter, after the nuthor FIUURE1
radius ic: a t Fa, while across BD i t is a t F1. With a mirror of this shape i t is impossible to get a true point iinage of a point source. Suppose we examine the shapes of the imnges wliich we would see if we used an eyepiece while the mirror was set u p A-la-Foucault. If we a r e sufficiently f a r outside of the plane through F2, our first view of the out-of-focus disk will show i t to be quite circular in shape. As we move oiir ocular toward Fa, however, tlie disk will become very elliptical as i t contracts. When the plane of F2 is reached the image will be a line of the width of the pinhole of our source, but considerably elongated. The reason for this appearance is evident from tlie illustration. A t F2 we a r e in focus for the diameter A C , but \$e are out of focus for the diameter BD. AS we progress from this point, moving our eyepiece toward the mirror,
we shall see the image become quite circul;ir, hut increasing in its diameter from the minimiim previoiisly obierved. \%'heii the imnge is most nearly circular, a t a poirit about lialf wtiy between F1 aiid F2, it is still f a r from perfect. I t is many times the size of a t r u e anastigmatic iinage. Because of this it can easily be seen how verp ruinous astigrnatism can be t o telescopic definition. When the ocular is moved toward the mirror, the image again assumes an elliptical form. narrowing in one dimension wliile it lengtheris in the otliei. This elongation is a t 90" from t h a t first seen. The ratio of the length t o the breadth of tlie iniage again reaches its greatest value when the eyepiece is focuseci on tbe plCiiie of F,. Wlieri the eycpiece is piislied \ti11 f ~ i r t h e rtoward the mirror, tlie image is
again seen t o exparid, first being very elliptical and gradoally losing its eccentricity a5 it grows. We can analyze how a n astigmatic spherical mirror would look under Foucault test by referring again to the illustration. Suppose we intersect the light coming from the mirror with a vertical knife-edge. If we insert it from thc left a t F1 we can see that it is thc light coming from ~2 tbat will first be cut off, hence that part of tlie mirror will be the first seen t o darken. As the knife-edge adrances into the cones it will, when i t reaches the center of tlie bcani, cut off the rays frorri R and D. The ray from C will still be iincut. UTe see, then, that the sliadow will first appear a t -4 and will have its edge parallel t o BD, as a t A , Figure 2. As we cut in, it will advance diagonally across the mirror's face, following the direction of A(' of Figure 1 . The blade is of course vertical, but the shadow appears like the one in Figure 2 a t B. Choosing tlie point midway between F1 and F 2 in which t o insert the knife-edge, \re can see tliat it will be the rays from A and B t h a t a r e cut, and how iml>ortnrit it is to proxide rvery kinri of assurance that no trace of it
is discoverable in a mirror wliile tliosr froni ( ' aricl 1 ) ;lre uiisc;itlirti. The a]>l>varaiice then will be like Figiirc 2 tit ('. When inserted in tlie p1:iric of F 2 the knife-etlge will first encouiiter the ray from B, and then, wlien tlie ceriter is reached, it mil1 cut tliow from A and C, giving us :in appenrarice like that of Figure 2 at D. I f the knife-eclpe cuts tlie corie of liglit rniich iiiside of F1 or outside F 2 the sliadow's eclge u'ill be more nearly vertictil, as in Figure 3 :rt E. The sequence of shadow sh:il>es th;it we moiild see, if oiir knife-edge was rnoiirited on an accurate carrizrpe, alinecl with tlie mirror's axis and cut into the cone just htilf w ~ i y ,~vouldhe like those in Figure 2. Tliis, of eoursc, ctlii cover oiily the case of a mirror that is spliericnl cxcept f o r tlie :istigriiatism. Other shapes of surfiices gire other appear:irices. The most conimon of tliese is that exhibited hy an astigmatic paraboloicl. hyperbol«id or ellipsoid-the iiioiittd. Agnin referring t o Figure 1, if we should orient either the mirror or the kiiife-edpe so that, when the latter is cut into the cone a t F1 it \voulcl be parallel to the foca1 line a t that positiori, it ~vouldtheii cut al1 rays roming from the mirror simultaneously and the mirror would be seen to darken evenly al1 over. With the knife-edge still parallel t o F1 let us ciit into the plarie of F2. Tlie ray from B is the first c u t ; then, a s the center is reachrd, the rays from A and C a r e intercepted anrl finally tlie D ray is stopped. The shadow seen is one whose edpe is parallel to A C and progressing from R t o D, opposite in direction to the cutting of the knife-edge. This is a normal indication, in a perfectly spherical mirror, that the knife-edge is cutting the cone outside the O cif C. Thiis, if we shnuld happen to set iip rvrn n severly astigmatic mirror and accidentally have either axis of tlie astigmatisrn parallel t o the knife blade, we would get no indication of this clefect froiii the shndow test. The infctllible test f o r the presence or absence of astigmatism is one performed with the mirror set u p in a perfectly collimated telescope. The stars' images procluced by it a r e examined n i t h as high-powered an ocular as is available. If astigmatism is present, racking the eyepiece slightly in and out of focus will show the tell-tale elongations. I n the shop a tiny pinhole as a source, not too brightly illuminated, and a short-focused eyepiece for examining the image, will suffice t o detect most ordinary cases of astigmatism. The ocular must be corrcctly alined with the mirror, othermise a confusing effect is sometimes seen. The astigmatic elongation of tlie sliglitly out-of-fociis indication as seen in this test-the image-must follow a rotation of the mirrof, otherwise it is a spurious effect due t o the test set-iip. The matter of determining the axes of the astigmatism is quite import a n t to tk worker of speciila, inasmuch as any corrective measures t o he applied will have t o be carefully directecl so that tlie figure be correctecl and not further distorted. Also, tlie discrepancy betu~eenthe F1 and F 2 points is of practica1 importante. There a r e several possible methods for gaining the desired information.
ASTIGMATISM
75
First, the eyepiec? metliod-notinp the two foca1 points F i aricl F2 :ind obserring tlie directiori of e1oiip:ition of tlie irn6ipe :it eitlier fociis. Iteferring to Figure 1 :ig;iiii, Tre c:in see tli:it if we :rre iri focus witli tiie siiorter curr:rture, as a t F,, tlie eloi1g:itiori of tlie im:rge will be iri line ~ r i t l itlie lonp Curvnturr iixi,. If tlir septir;rtiori betweeri F1 ;iiid F2 is not vt.ry g r i a t ("nder it i"Iifiicii1t to deterrnirie tlie ex;ict lociiti»ri of tliese p»irit\ ;ind the me:isurrrnelit is hiibject t o 1:trpe errors. Mirrors 1i:irinp severti1 zones, or in whicli tlie p;~r;ibolic corrections are preseiit, otier :iiiotlier difficulty, in that the ini:ige sern in tlie eyepiece is subject to aberration. The seroiid rnetliocl, a iriotlificttLiori of tlie first, is one ir1 \vliicli :L ni:isk is pli~cedover tlie ftice of tlie mirror wliile it is uncler test. Tliis rn:r?ik l i i i ~ two equal :ipertiires, c1i:rmetric;rlly opposite each otlier, orer tlie m:irgiri:il zoiie of tlie rnirror. With tlie mask in place the eyepiece can be very accur:itely re-focused because, wlien out of focus, the image will iippe:ir doiihlt~, like Figure 2, lower left. Also, if our pinliole is sufficiently small arid orir eyepiece liigli enough in power, interference fringes will be seen when the focus is reircliecl. Tlie fociis of our starting position of tlie m:islí can he taken :ts zero and then, r»t:itiiip tlie mask about tlie niirror's center, tlie foca1 lengtli clieclced at each of severi~lorieiittitions and coriipiirr(1 m-itli that of tlie oripiiial position. We mtiy tcibiilate our resultinp fipiires or ni:ike a graph to represent them. Tlie gr:iph of ;L simple flexured niirror rvill he siriusoi
74
ASSIGMATISM
grinding is done while the mirror is flvxed in one direction. While being polished, the mirror is frequently removed from its support for tlie purpose of testing and, as a result, its position on tlie polishing pedestal or macliine is periodically chnnpcd, so tlint the etiects of the various flexures a r e practically sure t o average themselvcs out. on t o p - t h e r e is less likeliWorking in the coiiventioniil m:inncr-mirror liood of encountering severe cases, but they can ;ind do stiow u p occasionally. Their principal causes are iiiiproper motion duriiig tlie grinding or polisliirig stages, usunlly failure t o rotate the mirror in tlie hands, cind tlie use of too large a Iiandle. A wooclen Iiandle will usually w a r p because of tlie liquids involved in tlie operations. Thc pitcli f;istcnirig \vil1 yield, but not fast
i'kp
author.
enough. If worlc ii done wliile the warping is in progress sufficient stress will be transmitted to the mirror t o cause trouble. Note hy John 11. IIindlp, Il'ittnn, Hlnckburn, Lancs., Englnnd: Astigmntism is such a n insidious thing t h a t 1 don't believe one amateur in a hundrecl knows how t o recognize it. Only the greatest care can keep it out. If the mirror is face u p during grinding or poliihing an improper support will undoubtedly cause astigmatism. 1 do not bar the use of small polisher.;, ;ilong with t h a t of a full-size, or a nearly full-size polisher t o maintain n surfaci of revolution, and 1 use small polishers on my dril1 press polisher for faulty zones, b u t afterwards use the large poli5her t o finish with. IvIuch depends upon the definition of a "small" polisher. 1 should say, one less than half the diameter. But t o entirely produce a mirror face t o the accur:icy iiecessary, and efitirely free from astigrnatism, by promiscuous hnnd poli,liiiig witli small polishers, does not seem t o me t o have anp probability about it.
Prisms, Flats, 1l1irror.s The Frrsori 0pric;il Coiiipaiiy, Ailosi, 1 I i s s i s s i ~ 1 ~ 1 i
[EDITOR'S NOTI:: In 1!):35,~rliriitlie :lutlior of thc rli;il)ter ahicli follo~vs;,con. tributed to this 1)ook tlie c1i;iptcr oii "Molding :ind Casting Springfirld Mouiiting Parts," he h;id rii;isequently, in early 1941 whrn wcir w:is iiiirninent, Iie quit Iiis rrgi~ltirvoc:ition ancl tiirneiiririg rriontlis of niost intcnsire drive to lezirn to rrizikr these most difficult prisms ( f a r :iiid aw:iy more precise tlian ordinary ripht angle prisnis) he acquired aii enriched fund of precision opticnl experirnce. Scientific Arriericari's Amateur Ruof Prism Prograrii of 1941-1943 was described in t h a t magazine, May 19.1.3. About 100 advanced amateurs, scattered across the nation, wcre organized jnto "The Roof Prism Gang." F o r tliis movement Porter provicled the inspirzition and invtiluable Iielp. Ferson, mainly by himself, liad ;ilriady ferreted out tlie working tcchnics, wliich did not tlien exist in published form. A t th:it tirne, early iii tlie war, tlie nation's nerd for tlieie prisms, whicli were biiffliiig tlie professional shops, was (lesperate. Ferson, from patriotic motive's, transmitted t o the others in tlie Gang al1 he had learned. I t proved that in this most difficult work some of the amateurs, because of pride, interest, and previous study of optics, could equnl or excel most professional producers, tlieir proportion of prisms acccptcd by Government and industry approximatirig 99 percent. Of the 28,:?60 roof p r i s ~ n sinadr and supplied t o the war effort by the amateurs, approximately equalling 3l/1 months' production of tlie largest professional producer, Ferson, with Paul Linde of Crossrille, Tennessee, contributed more thnn 11,000. Better than 99 percent of these proved t o be of acceptable st:tnd;ird. Concurrently, while working day arid night on his owri production, Frrson continued to lead the others in technic, selflessly arisuvring hundreds of inquiries about details of the work. blost of the chapter which follows is based on his wartirne prisrn manufacturiiig exprrience. H e has been requested to write in the first person -the natural "1" of conversation.]
Frorn a standpoint of cost, niaking :L single prism, or several of them, inVolves an outla. beyoncl tlie rtiliie of tlie prisrns. Required tools of special kinds, and materials, not ordinarily used in miiking mirrors comprise the sum. We will deal principally with right angle prisms for use in telescopes ancl binocuiars and f o r various laboratory purposes. Included, howerer, will be data on 90" and 600 standard prisrns ancl soriie notes on otlier forms.- The gerieral principies of manufacture here outlined are suitable for the construction 0f any form, ]>rori
t o se<. ~-1i:iterrors ;¡re t o he ;iv~iitlt.cli i i iii;ikiiig it, ~\.li;ittolcr;iii<~cs:ir(%:illo\\,e
Figure 1, cviitrr, il1iistr:ite.; l>yr:irnitlal error. 'I'liis t.rror (1rvi:itt~itlie liplit siilewisc- t ~ :ii trite p1:iiit' of reflectioii, ;iriro
PRISMS
77
light to be scattered in various clirt.ctioiis, and proclucrs :i markrdly il: effect. This is obvioiisly a srcoiicl critical coii-strtiirird it is (lifficult to bring the glasi of a prism t o a precise point and Iiare it stay there. \Vitli preserit-day niiiiealing methods tliis is not oftcn t o be encoiinterrd. Striae rnay caiise :iii exp:iiitled or fuezy ini:rge. Riihhlcs, stones, antl pressing clefects scattrr liglit 1)ectruse of strain patterns alwut tlirm, : ~ n ddiffr:ictiori. Seeds (small hiibbles) are not so objectionahle if riot 1)reserit iri nunihers. For some of tliese retisons the use of plate glass f o r prisms is out of ttie question. Tlie ream in niost rolled glass is not sidewise ?o the liglit patti, except in one direction in ttic riglit angle prism, and so it is difficult to judge jiist wliat will be tlie effect .on clefinition. Tlie color of plate glass is objectional)le, riot only estlietically hut for ;ictiial perforrn;rrice of the prisiii. In ex;tiiiiriing rnany sairiplcs of lirisnis niaclr froni plate glass of tlie ordiri;iry type 1 liave yet t o find one \vliicli g a r e good drfiiiition evtsn iri ctises wliere tlie evidentes of fine w~rkrnansliipwere conclusive. Separation of light into its colors is not usnally noticeable in tlie 90" prisrri, except tliose Iiaving :trigle errors niiich wider tlitin are contemplated in tlie prisms under rlisciissioii. Otlier prisrris, sucli for exnm11lc as tlie Amici roof prism, cause greater color effects I)rc:iiise of :idditiori:il reflections a t diffcrent angles. Tlie glass cornrnorily used toclay for prisins is horosilicate crowri gltiss having an indrx Nd 1.5170 V 61.4; or, as it is now written, 5170/614. We need llave no concern witli the indrx iii iiitiking ti 90" prisni, for it does iiot enter tlic pirtiire. That is, the refraction cif liglit is virtually elirninatetl hy the precision of tlie arigles. Borosilicate crown glass mny be obtained in slab or pressed or molded forms. F o r 1:iboratory use tlie pressed or molded forms are preferable because of tlie nced of slittirig tlie slab forms t o rough size, whicti requires a diamond sal\-, -,:iCarbo saw, or liettvy labor witli an iron band and Carbo grains. These niolded foriiis sometiriies hitve pressiiig defects, caused h y folcling iri some of the po\vder tlitit liries tlie mold. These defects are not usuallp deeply embeddecl, and will largely disappear during grinaing. S o make certairi tliat they hare bcen ground away the frosted surfaces of :he blank rnay be wet witli water and examined in a stroiig light. Relntively small defects will he evident on careful exarnination. Molded prism blanks may as this is written be obtained from tlie Hayward Optical Glnss Company, Rlaywood, California, the Bausch and Lomb Optictil Company, Rochester, N. Y., tlie Corning Glass \+'orks, Corning, N. Y., or from other sources. Commercinl Production Proccd~lre: Before suggesting waps to forrii tlir blank in the srntill sliop, I will run briefly thrcuph the procedure follolved iii commercial plarits, also give a runniiig accourit of tlie tools iised.
78
PRISMS
'I'lie first s t e p is t o grind one of tlir side f;ic(.s of t i riumber of h1:inks witli eoarse grit on a large fl:it Iiorizontally rotating iron platr, so tlitit tlir 1)l:inks rnay later be seated on tr flat iroii bloclriiig plate for the purpose o f prinrliiig the second side plane and partillel t o tlie first side. Tlie riietliotl of sciitinp is to warm the pl:ite arid the glass uiitil ~>aríifiiie or Cereiene will rrielt, setit tlir glass against tlie pltlte, allowiiia four bl:inlcs t o exterid beyoiid tlie e d ~ ea t four diametrical points for the purpose of miking tlie tliickness duririg tlie grinding, and then allow the whole t o cool. Tlie blockirig plate with its :ittaclie
plaster mntrix to liolcl the prisrri fticcs or lens ftices in a flat or sphrrictil plaiic. Any such ;issenibly is teriued t i "l>lock." The b1:inks p r e p ; ~ r e das jiist descril>ed tire se;rtc(l oii n fleit iron I)lockiiig @ate in ;I geoiiietrict~l patterri with ~iielted~>;ir;ittiiieor liglit oil. 'Tlie oil rnetliod difTers froin tlie par;ifiiie iii tliat no 1ie;iting is necesstiry, the oil giving enougli c«lirsion t o prrinit ti pltister block t o l)t. forriiccl \rritliout shiftirig the blanks frorii tlieir positions. Obviously, the 1)locking plate sliould be optically flat, notwitlistancliiig the fact that the seatecl surf:rces are finally grotind in block form I~efoi-e hring polislied. A f t r r seatirig iintl cooling (if tlie wnx is usecl) a metal band is securecl about the pliite to rrt;iiri plastcr. The l);ind slioiilcl he wicle enough t o cleor the liigliest bltinlí diriirnsioii. P1:ister is niixvd tincl poiired, and a fltrt iron btccking plate is keyed rritli plaster t o the k)locl<1)y nieaiis of filling lioles provis for Smrrll-scnl~ Pro(1uction: The list of principal tools and materials requirrcl for liand production of prisiiis is 21s follorrs:
Standard ti:rrclened steel square Accurate 450 tool 3 Pyrex diiks grouncl 1il:inr Bloclc of steel, toric surface Glass ring Micrometer, 0" t o 2" Small optical fltit Piece of flat boiler p1:ite
Carbo Nos. 120, 280, 400, 600 Eniery Nos. 950 and 1600, E. and L. or equi\ alent Gas plate for heating Plnster, U. S. Gypsum Co., Hydrocal A-11 Shelltic Pnraffine Lipht sourcr, monochromatic, diffused
The hardened steel square should have a berelrd hlarle t o facilitate vrry close reading of angles. T h e s ~tools tire made and sold by such makers as Brown and Sharpe Mfg. Co., Proridence, R . I., or L. S. Starrett Co., htliol, Mass. They are usu:illy accurnte. The smaller sizes a r e more easily handled than hearier large ones. Making correctioiis by use of the sqiitire and tlie SS0 tool is a hand operation requiring the use of a steel block with a toric surface (Figure 2, left)
80
I'1i 1 S J I S
ancl fine grit. Re:idiiigs witli tliest. tools iriiist 1)e rritide on clenn surfaces if there is to be assuriiricc tlitit tliry will 11e correct. 'Tliis is done apnirist :i diffuse liglit source, sucli tis fluort*scerit or frostecl bulbs, tlie light reflected from a white wall o r tranh~riitt~cl through paper. 'rhe liglit frorii tlie t ~ u l bsliould not sliine directly iiito tlie vies. r l camel's Iiair briisli is escellerit for miping ;lway fine pzrrticles of cliist and grit wliicli \vould tlirow tlie reticling out of line. Tlie eye slioiil
Witli ;L true sqitnrr, :r corrt.ct liglit soiirce, aritl a good eye, errors le\s tlian :N sccorids of a r c niay bc uiscernctl, even on prisni siirf:ices quite as n;irrow as Y?". Tlie 4.5" tool is not, as tliis ir written, commerci:~llymnnufacturetl hy nny~ to innke your own tool. JIaone knolvn to rnc. I t probably \vil1 I I nece.;sary cliiriist's blades provided witli 55' ancl 90" betuns tire sold, but tlie bl:~tlcs are not usiially beve!ed. Tliey a r e tlivrefure suitahle only fur approsirri:~tion. Figure 2, right, iiliistriites a form ~vliiclirnny t)e rnacle without excessire work. To set tliis tool witliout a st:iiiclnrd 41,' tinplc for coriiparison, a strntngrni may tle resortccl to xi~liicli,if c:irrie(i oiit to tlie lirnit, will gire required acciir;tcy. Correct one of tlie prism blanlis nroiind the ciitl faces witli tlic 00" toul-al1 ;inglei, sidewise ancl to eacli otlier. ?y severa1 rrncliiips tlint the ;ingles a r e riplit. Place tlie be:irri of t h r 4:j0toul ;ig;iirist oiie of tlie end faces, hring tlie blade t o a liglit-tiplit fit agairist tlie 1iyl)otrnuse f:ice, nnd clamp i t with the scrcw. Then r i r r r i e t o tlie other encl f:tce and note the :~ngleerror. Griiid tlic blenk by hancl, with prrssure on tlie cncl nredinp it, aiid repent the clirck. Continue until tlie fit is liglit-tiglit a t hoth enels, wlien the 4.5" anglcs must be correct, and tlie tool m:iy he set correctly ~vitliiria lirnit of error of aplxoxiriiately 30 secoriils of nrc. Tliis will tlirn be siifficieritly ncciirnte for its purpose. The steel block xritli the toric ciirre slioirld lie niade from a block of coldrolled keystock, or sorne sucli metal, about 2".x 6'' x 1" o r y,". Often this material can be foiind :is sliort ends in a mncliinr sliop. By dint of careful dr;tw filing this tool can be givrri a sliglit corivexity ori tlie short dirnc.nsiori, and one with a lonper raciiils nf curvature ori tlie lona dimension, as sliowri. By grasping one end of tlie file in eitlirr Ii;in
eral fringeh. Tliis tool rnaj- d i o hc groiirid witli ;il)lirol'riiitc riiotiori ;igaiiist ;L rotating le. A prisrii siirf;icc proiin
ovrr some of the sizes usunlly applied in a successivc series for mirrors and flats is not only possible l>iit prefcrtible. Tlie pit (lepth left by eacli size-for exarnple No. 120-is easily removrd by No. 280. No. 600 C:irh» is usrfiil a.; the final sise before a series of emeries. TIie eiiiery sizes are iised only üfter blocking tlie prism in plaster, about mhich more inform;ition \vil1 be giren in tlie 1)aragralilis on that subject nnd in tlie sections on fltits and mirrors. Tlie handiest stroke for correcting anples on the toric tool is clirectly back and forth, with the b1:ink grcisped firnily i ~ the i fingers of eacli 1i;~ndhiit witli such pressure exerted with tlie riglit or left hand as is necess:iry to relieve the angle error. The bltiiik is piven n few strokes, cleaned well tind rrieasiiretl with the angle tool. Tliese operntions a r e repeated until al1 anales a r e liglittight under the blades of tlie respective tools. Tlir Ring ,Ilrtho«l for Sin,qici I ' n i f j : If only one prism is t o be made, thc gl;iss ring shown in Figiire 3 is a vrry useful tool for the purpose. I t gives sufficient aren for truing u p tlie fringe systern witliout bothering about what m;iy 11;11)1wn to tlie edgc. of tlie ririg. I t c;in also be used iii m;rking master 900 antl 600 anples witliin a specific;ition of two seconds of a r c allowable error. Tliis tool is made by cuttinp a disk from the center of a larger disk of or 3iJf plate gltiss with a biscuit cutter, a mctliod known surgically t i q trepanning. Tlie sharp edges inside and outside the annular ring are beveled. Slots should be ground on the interior sides so tliat plaster will not slip upward under tlie pressure of polishing. Also, chtinnels should be ground into the face of tlie ring so t h a t air may llave free access t o tlie center for drying u p the emery wets, as will be expltiined in the section on flats. To make the block, brush some light oil on one of the flat Pyrex disks, seat tlie prism blank firmly in tlie center, and press the ring into position arouncl tlie blank. Mix Hydrocal A-11 plaster, 4 p a r t s of water t o 7 parts of plaster, by weiglit, and set i t aside for a wliile before pouring. Stir i t every five minutes until tlie plaster somewhat thickeris and then pour it around tlie blank. Tliis mixture will set in about 25 minutes froiri the time when i t is mixed. The 4:7 rntio of water and plaster giren is approximately the one used in many commercial shops. Mineral salts in the water sometimes delay the hardening and also soften the plaster. I t is a good idea t o use rainwater or distilled water. If the misture is made witli greater proportion of plaster t o water i t sets almost stone liard and causes recessing operations t o be difficult, also making difficulties in digging the prism out of tlie plaster. At the 4:7 ratio i t sets firmly enough t o Iiold the assembly correctly. Hydrocal A-11 plaster has some ;idvantages over other forms for this purpose and is commonly used in commercial mz?nufncture of optical elements, also in other industries wliich require e plcister with a very low setting expansion. I t s setting esptinsion is listed a s 0.06 percent and tliere is no contraction a f t e r setting. I t prrmits immediate grinding and polisliing of :t block as soon as the setting heat is relieved, compared with mixtures of plaster and Portland cement sometimes iised, whicli must set overnight or longer. Wlien the plaster has set, slide the t~ssemblyoff tlie Pyrex disk, recess the '/,tl
plaster nw.i) froiii tlic glass fncec, aitli n kriife-1)l:itlr to n dcptli of ii1)oiit %2rp (Fipiirr : j ) :iritl gire it txvo coats of orarigc slir.lli~e for w;iterl)roofirig.
Fine grinding of tlie I)lock riiay be eomrnencc~~l :IS soon ;ts tlie shell:ic is dry, and is c:rrrie(l oiit iii tlie rnaiiiier (lescrihed in tlie sectiori on flats, tliroiigli one intermediate and oiie fiiie griicle of eriiery. If a groiil) of prisriis tire I~eirig niade tlie hlockirip procedure niay I)e changed. Tlie bl:tiiks tLre seatecl on tlie Pyrex dislc iri a geometric:tl pattern with rnelted pnr~iffineor liglit vil. A p:~pertape of suficient width is attached around the eclpe t o Iiolcl tlie plaster, wliich is then poured. The block is rccessed and shcllucked üs alreiicty described. Wliether yoii use "siirroiincl~'or not is a rnatter of choice. Surrounds are pieces of glii5s of al)l~r«xiini~trly the sarrie 1i;iriliieis as tlie prisni blanks, such as plate glass, wliich are sc:itrd nt the edge of tlie block. If tliere is :L turned edge it then will he fourid oti this gl:iss instend of on the prisrns. Wide differences in hardness of gl:tss will iiot he siitisfactory l>ecause of rliffererit polishing speeds. If a prisrn block is to t ~ eattaclircl t o a riiachinr for polishing, tlie 1):ickiiig plate prrviously (lescribrd will be iiecess;iry. Fine grinding of the ring ;isserribly retliiires tli~it tlie pressure used be fairly equ:il on al1 sides, so t h a t the angle of the prism face will not be changed. Poli.shing: Believing that procedures in macliine polisliing may be of use to those wlio have riot become ncquaiiited with tliern, 1 will set them forth and, following them, gire sorne supgestioiis for their eriiployirient ir1 liarid polishirip. The systern commonly used in romriiercial sliops is what is knorrn as tlie "sniall polisher systern." The lap is smaller in diameter than the surface to be polislied. The surface is polished face up. Figure 4 is an illustration «f the arrangement, thoupli in commercial use the machines a r e not so sil dified. However, the simple arrangement will enahle you to do good wor
Polishino mnchine n t ii,ork o n hiock of ~ j r i i r ~ d m i c i s . P i n on b i f r ~ r c n f e d dricin,q nrrri I w h ~ c h nlnl, 1 1 ~lijtprl like n 1ti11ye) punhes lo??. Cross.nrrn rults betwepn sectorx ( s e ? spction d r . u u > i n y ) nt eitlivr v n d . Holes <11«1,gcross-,ir>n ndjust for stroke position, ndjuetnhle-throw crank nt o t h ~ r?nd o f conncr,ting rod f o r stroke tcngtli. Crrink ¡,Y worrn d r i r e n . I I ~ n r n t htahle, ~ ~ L I I P ou n wlorm year is belted l o n jackshaft, this t o s p i n d l e , w h i c h runs nt speeds other thnn lhnt o f opur s h ( i f t . Belt < l r i i e U ~ C L C ~ ~(1e11r P S iiuriri~licit!/. .Lt the l v f t : La),?j
the hlock will h:irr si~ffici<.nt jiolireacl \wII :ipart. l ' r ~ s s u r c o11 tlie fltit is iinriecesi;iry iirid ;irt \vil1 he criislie(1. '1'11~. two siirftices rriiist 11e recleaiied iiritil tlie friiiges spretrtl oiit froiii tlie xveiglit of tlie fl:it ;ilorie. Prcfcrtrl~lytlic l;il> ni:iteri;iI slioiild h;ive no tendency toward c:ise-liartiening etliii tlir scction on flats 1i:ive ~ ) r o v e dsntisf:ictory. If diirinp ~)olisliiiigtlie rouge is in esccss of rirctls nnd is iillowecl t o dry it will rol1 tiritl pi\.e ;i liglit, iriclescent frostiiig t o tlie siirface. Tliis is soriiet i m e tern1t.d "roiipe st:iin." Tt is very tliin niicl ni:iy he relievrd h y wntrririg the roupts arid l>olisliirip for ;L few niiniites. Tre;itrricrit of laps for irnlirorrrrirrit of siirftiers \vliicli are fourid to be resistive to efforts t o 'e:iuse tliciri t o ~o ul>liill or do~vriliillgcner:illy recliiirr-.; no m;i.ior ltip miitiliition. Tlie Inp mny I)e scrtitcli(~t1;iroiind tlie eclge for greatrr nctiori iii retlucing convesity, or scratcliecl in tlie crriter to briiig tlic hlñck iil)\c-;ird tow;ird fltitiiess. F o r Ii:in(l ~)olisliiriga dumniy polislier iri:iing its back with a niallct. It is nell t o do this brenking u p over a piece of old carprt so tlint if tlie ~ > r i s m scoriie loose suddenly tliej- \vil1 not hit ü Iiarcl ob,jert. There is no ctiiise t» worry orer tlie rough treatrnent. The plaster breaks readily ancl the gltiss is loosened enougli to come away from the broken pirces. 'úaturnlly, only enough force is put into tlie niallet strokes t o break tlie liltister ratlier thari pulverize it.
T ~ s t i n g : Since the nnnulnr plaw ring ~ircvioiisly descrihccl is very useful in niziking standard (iO0 :in
Figiire ti slio~vstlie o1itic;il trtiiii uf tlie aiitocol1im:itor. 1,ight from the slit is rrflcctcd by 21 srn;ill prism t o tlie olijective ancl is collimated-~);ir;illel liglit froin ;L point source-by it. Tlie slit dist;ince is a t the irifinity focus of the o\),jective, xhich mgy be measurerl by tlie sensibly p:~r:tllel light of tlie sun. 'i'lie srnall prisrn is otiset just sliglitly froin center, so that tlie image returning through tlie objrctive will cl<.;ir i t eind enter the eyepiece. A f t e r the light is collirntited hy tlie objectire it enters normal to tlie hypotcriuse f;ice of the 90° prisni being tested, is then reflected frorn either eiicl fiice t o the opposite one, thence is returned t o the objective by wliich it is tlien hrouglit t o focus and the image is examined by the oculitr. I n some cases w reticule is provided for rneiisurement of side angle deviation but it is not necessary for a standard pricm. The slit should, Iiowever, be in a position per~>endicul;ir t o the prisni as it lies iii the position of testing o11 its side. I f now the angle of tlie priim is not 90" within two seconcls of arc, tlie irnage of tlie slit will be dorihled; that is, it will return as two irringes. R:ick tlie e!-epiece iriwartl and iiote ~vlietlirr the images sprt.;i
PRISMS
87
nification is iisually siifficirnt, thougli a t times this maj- be iricreaaed if it is desired t o detrrniine wlietlirr tliere is (loiihliiig wlieri tlic, tloithlirig is of tlie small order of :i stcoii(1 or so of itrc. Fortiiii:ttely for tlir prihiii iri;iker sliop conditioris tire r:itlier riiore iroxirii:itelyíi ])(.rcent is rrt~iriieclover a patli sirrii1;lr to tlie oiic. of eiitriince, but is rtiried by tlie error of arigle. I n ftict, li;iving once view<.d tlie t~riioiirit of returried liglit, orie \vil1 iiot wonrler loiiger t1i:it tlie liglit loss frorri back reflection (witliout Iow-rcflcctzince coatings) in an instrument having ;I nurriber of siirfaccs is :L corisiderable pnrt of the light rntrring tlie instriirnent. Ainici roof prisrris also mny be checlced for tlieir roof ;ingles iri the miinner descri1)ecl. 'l'lie liglit 1):itIi tin(l.position of tliis prisrri a r e slioan in Fipiire 7, center. Iii coiiirrirrcial rii:inuf;icturr tliis method i\ less often al)plied tliari t t r i other nictliod ~vliichwill be c1escril)ed Inter. Tlie :iriniilzir ring systerri for riiztlcing a rery close corrrctiori o f an zirigl<. is employecl :is follo~rs.. After two faces of the prism-thc 1iyl)oteniiie ancl onr ciid fnce of a. 90° prisin, for ex;irnple-have been polished, the tliird side is blocked in tlie ring and the plnster is cleared away frr~iritlir hpl)oteniise fece suíiiciently so tliat the light may enter it and be reflected from 1)otli eiid faces (Figure 3 ) . The liglit, as lizis breri stated, eriters normal to tlie Iiypoteiiuse fiice, lience it will be necesstiry t o make a wooden fixture t o hold the ring aníl prism in tliat position in front of the autocollimator. Grind the third face of the prism in the ring witli fine emeries and gire it a hasty polish-say five niinutes. The image will be clull but still strong enough to determine the aiigle. After this riieasurement grind again with pressure on the side neecling it t o correct the angle and give another quick polish. Re. peat until the prism shows no doubling. A considerable number of seconds 1 ,, arc could actually be polished away but it is well t o have the angle nearly correct before beginning the major polishing. As the polishing proceeds, check the angle froni time t o time and make any necessary correction by greatrr pressure on the side indicated as needing it. The width of the ring not only prohibits introduction of preüt errors of angle during polishing but also slows u p the correction-which is just as well. At the end of the taslc no doublinp should be evident with 2 0 rnagnifica~ tion. This then mil1 be an angle haring two seconds of arc or less error from the ideal 90°, or 60". In terms of inches it will onlp be a few rnillionths out of truth. A 60' pri\m is corrected in tlie same manner. Likewise accurate 30°, 60" and 90° nngles rriny hc lia(1 in a single piece of gl;tss by griiicling arid polihhing it in tlie form :liou,n in Figure 7, riglit. By cliecking anrl correcting hoth 60' and 90" nnglrs it follolv5 froni gcurnetry tliat the 30° ancle iiiiist be correct.
Somctimes in tlir coiirse of lahorittory \i-ork tlie iise of opticnlly contnrted surfiices rnay he ciillecl for. I n contitctirip, t\ro ~)olisliedsitrfiiccs a r e prr\sctl into nlinost inoleciiliir contiirt. Surf:iccs i o (~orit;~c.tetl \vill Iioltl icciirely iri lilnce, l~rovicledtliz edpes a r e secileci ap;~iri,t ~iioistiirc\i.itli siiiiit~sucli sriil iis slielliic o r liicqiier.
m e r e a r r two secrets of o~iticitlronti~etiiig. (1) T h r \nrfiicrs t o I)c cont:tctr11 riiiist he ricwrly flat-siiy !jo fringe-a~id it is bettcr if tlicy iire »f 01)p d t e sigli of dcviiitioii. Ilomt.vrr, iiiiy siirface tliat is fl:it t o ?/itl f r i i i ~ eis sufficient. ( 9 ) The siirfaces niiist he vcry cleari. .i dust-free rouiii i u prefcr&le when rniicli of tliis worlí is t o be (lorie. Tlic cle;i~iiiiprriiiy I>e tlone ~ v i t h alcoliol arid ncrtoiie, o i l)y liri~tiiiptlie plnss in hot hor;is ioliitioii. Wlieri dried the siirfi~cesn r r I)riislirriisIi,iiricl ~)l;icedtop t h e r aiid pressecl by li;~iiiccs eiich :it 15> t o it, o r a t 90° t o eacli other.
Figure 8 ~ 1 1 0 solnc ~ 5 of tlic :ingles :ind tiie pthiicr:ii form. I t is n r r r u oltl i r i veiition hy tlir 1t;ili:iri Aiiiici (liHíi-1864) hiit coiiinioiily I)c:iri; tlrc ii:iiiit. of roof pri\iii I)cc:~ii%~, :is witl! otlivr tyl)es of roof 11ri\in, lliv ;irisinply, after a little pr:ictice an aiiplr error of n niiniitr of Circ may be t;ilíe~iaway in just a rniriute or so of tirrie. On the otlicr liarid, everytliirig Iiinges oii tlie ability t o produce a fl:tt surf -that is, truly fl;it ivitli no tiirricd rclpe or astigmatisni; and in turn, eT thinp deyiericis o11 beinp ahle t o m;ike a la11 so flnt that i t will terid to p r l , uce the flat pri<m in spite of other clifficulties. The 1;ip is poiired in the usual nianner but it must be r e r y hard. For an initial atternpt g r t Wm. Dison and Co.'s (Seivark, N. J.) d r y Rurpundy pitcli and harden thrre pnrts of this pitch witli o r i ~o € rosin. A l a p of 6" diiiirietrr, 3/isV thick, iq satisfnctory. S h e dummy polisher sliould h a r e the saine di:iiiieter and must be ground nearly plane-one fringe convex. After the pitch has been poured a n d cooled it is given a preliminary smootliing by warming tlie diimmy and lap and working the l a p with the dumniy until it has a smooth, glass-like appearance. Tlie 1;ip is then given small rliannels about ?&" apnrt scratcherl in with a sliarply pointed knife-blade. I n aclditiori, a hole of about n/lGft cliameter is p r o ~ i d e da t the center by heating a dril1 ;iiid with it working out tlie pitch. Again the clumrriy is warmed aiid tlie siirfnce of the lap is worked with it f o r some miniites with short strokes until the dummy has cooled and the lap is as smooth :is a piece of satin.
90
PRISMS
'I'lie rougc and water solution shoiild he rclatively tliick but thinly npplied. Wlirii iii correct coridition for polisliiiig it ~ i l give l sliglit iiiiises siic4i tis "a tiiiy COIV lifting its foot out of iniicl," :is niy friend D:ivicl Rr«:itlhea
d m i c i t y p e o f ronf nrigle p r i s ~ > i . A , r n r ~ l n pn t~ stiirt. IIC', rnuf pllgr. D , E , ruof frices. T s ? ~ ~ i ie l b u w t r l < ~ s c o l i e so11 n?rli-uircrnft g i & n director.^ anrl n t l ~ e r u r t i l l e r y r u r ~ g efinderu, t o ervct a n d rr?,vrt i ~ i i ' e r t e t l ,p e r v e r t r d image from obiective.
The speecl factor of tlic stroke will Iiave two dirrctioii5 of rii;iiiifrst:itiori. A light, rapid stroke generally procluces a coiic:ire siirf:icr (griiritiiig tlittt tlic lap is fl;rt). h firrri, slow stroke aids iii l~rotlriciriga cori\rcx siirf;ice. A f t c r ;L minutc or so the rouge will d r y atid rriiist be renewecl ;iii(1 ~vorkvd again mitli tlie dummy. By t e s t i i i ~tlie surfzice of tlie lirisrn by rneaiis of interfereiice fringc, \ve have a cluc t o tiie contoiir of tlie 1;ip. If tiie ~jrisrnsurf;\ce is coiivex tiicrp is a possihility tliat tlie 1;ip is concave, aiid vice-rers-tliough tliis ;ipplics oiily within lirnits, (Iiie to tlie iriirnner of stroking rapidly or slowly, ii1re;itly (lescribed. Tlie duiiirriy slioiild be testecl frequently by irieiiiis of iriterferriice fringes witli :ir1 o1)tical f1:ii. If tlie diimmy is still one fringe coiirex and the l a p exliibits :i tcrideiicy t o produce ;L more conrcx surface oii the prism, tlie lengtli of strokc-s of tlic dummy usccl on thc Iap ni:iy be extended iii order t o flntten the lap. 'I'liis \vill, howerer, gradu;illy recluce tlie Gumrny siirface to concavity and it tlieri mil1 he necessary to regrincl it. Heat effects niust also be taken into nccount, for tlie baclíing of tlie lnp nnd the contour of tlie dummj- \vil1 be subject t o tlieiri, except per1i:illi ~rlieribotli backing :rnd dumrny are of fused quartz. I n order t o know'wlint is I~vingdone i t is necessnry to hare n telcscope of ahout 20X rii;ipnificntioii ;lnd a stancl in front c i f it on xvliicli tlie prisrii is p1;iced for trsting. A target, consistiiig of crossed lines (Figure 9 ) aiitl ~ r e l l illuminated, is placed soirie (listarice a\v;\y-s:;y 20 feet-aiid a t riglit sriplei to the telescope. Tlie irriage of tliis target is transmitted by tlie roof prism to the telescope and is exomined with its nid. The tnrget is mnde either hy drawiiip hl;ick lines on wliite liaper or h y cutting crossc(1 lirirs on n rniiror ~vitlia razor I)l;ide and illuriiinütirig it fro~rrtlie back. 1 p r e f r r tlie lntter since, by its use, sliglit errors of siirface flntness tire exaggerated in tlie diffr:iction lines. Tlie riiles for deterrriiniiip tlie angle error a r e tlie snme as in the use of tlie autocollinintor. The rertic:il liiies of tlie target 15-ill not double unless zistipmatism is prcsrnt on tlie surfaces of the prism or unless striae is prescnt in the pI:iss. Tlie 1iorizont:il liries double rriore or less according t o the error. \VIieii tlie roof aiigle 1i;is beeri corrected tlie !iorizoiital lines \vil1 tlieri be superiiiil>osed, arid tlierefore only one line ni11 appear. T1i:it is, tlie two iiiiages, one froiri eacli roof ftrce, will coiiicicle. Also if the surfaces are flat al1 lines will be cqually slinrp, botli vertienlly nnd horizontally. Ari error of trvo seconcls of a r e will sliow just a sliglit swelliiig of tlie liorizontal line-prorirled t h r target is not riiore tliari 20 fcet distaiit a n d tlie aperture of tlie ljrism not under 0.75". There is anotlier may of knowing the excellence of tlie correctioii. Racli the eyepiece inward. l'lic crosscd liiies \vil1 s p r i a d sliglitly npnrt heforc poirig complctely out of fociis. If tlie nngle is excellent the spread lines \vil1 forrn n square; but if tliey forrii ;i rcctarigle verticnlly, tlie error is still plus; if Iiorizontaliy it is still minirs. Tlie liiies wiii sii
are not rvitliin tne ortlcr of two or tliree rniniitcs of nrc of tlie itlcal. Sonir aiigle errorh ~)rodiicervors? eticcts tli;iii otlirrs. 'I'liis ir1 iio \vny refrrs to tli(. roof aiigles hiit ti) sidr ; i i i t l axiiil ;ingle t tlicrcz will prok);il)ly 1)r a. teiictiiig to gras1-i tlie prisiii too rigidly iiiitl to intil;c liiir(1er ~vorlcof it t1i;iii i \ iiec.i.\s;iry. Go a t tlie worlc c:tlirily, witli relaxed rniisc1c.s. Frccliieritly test tlic siirf;icr being correctrd rvith a11 ol~ticaiflat. If it is heing roclícd siec:iiise of tlie excc~ssiveii;irtlii<.ss of tlit: lap-tliey seldoiri come frorn tliat sotirce. Of cbo:irse, if :L 1:lrgr grairi of C;irI)o grit is drol)l)ed on tlie mork :r clcep scratcli will be likely to rriiilt. In tinie the slicillow clianiiels of tlie lap rvill fill in ziricl rniist be renervecl. If tliey ,jiist :ibout fill in a t1:iy's morlc, the lap Iins about tlie correct 1i:irdncss. It rvill be fouricl more dificult t o avoid turned eclge if the l a p is too Iinrd. Tlie pitcli recipe prer~iouslymentioncd sliould be nhoiit riglit. JIany fornis of ctiritoiir \r-ill k)e encountrrrd in m;ilcing tlie corrrction. Thrse mil1 largcsly dis;ippe:ir w7ith pr:ictice-1)rovitled you lieep tlie 1;ili ,just as flat as it is liuiri;~iilypoisihle t o inake it. If tlie 1:ip stancls a felv niiniitrs rvitliout attention it will be noted tit «rice when reworking it with tlie durnmy tli:it is lias a rougliness. This roughness will tiirri tlic edges and must be rvorkerl out witli the durnmy. Witli corrrct angle tools, any form of prism, simple or coiriplictited, niny he made in tlie liome sliop or Iaboratory by h a n d - e v e n thougli such tliings 11s espensire V-bloclís a r e not av;iilable. Rrieflg sumniing u p the iiiformation alreacly given as t o ~ ~ r e c i s i o nseveral , points are empliasized. First, estnblisli a base from rvliich al1 otlier ;iiisles t;il<e tlieir relation; as, for exnmple, tlie choseri siclc referencc face of the 90- lirisiii. Second, make fully certain tliat al1 anples shorv n liplit-tiplit r ~ a d i n giinder ir standtircl tool for eacli angle. Third, he certiiiri a t al1 times of cleanliiiess, so tliat nngles ground t o precisioii may he carried with nearly tlie stirne precisiori througli hlocking and polishing oprratioris. Fourth, he satisfircl orily wrlieri tlie object meets the precisiori ~vliichYOU specify for it. Wright, Afanufacture of Opticnl Cl'2na.u and of Optical Systamn (Orclnance Department Document 2037) Gardner, Elenzentnry Optiea nnd A p p l i ~ n t i o n n to Fire Cortfrol I n s t r u m r n f s (Ordnance Departrneiit Docunient 1065) A D ~ s c r i p t i o nof the JIcintcfrcct?cre uf Optical ? ! ] o m ~ n t for s Fire Control 171s t r u m ~ n t s (Ordnnnce Docuinent !
Jacobs, Ftcndn11ientrt1.sof Opt icrrl En r/in( r ring southall, -Ilirrora, Prisnra, L(nsps Bell, T ~ i 'Pr l ~ . \ c o l ~ r Strong, P r o c r d u r ~ sin E.i))c.ri»~r~iit«l Physics Hardy :iiici Pcrriri, I'rincipi(,,s 01 Optica Twyrii:in, I'rism ctrid Lrria ,Mfthiny. DévB, Op ticcll I170rhshop l'ririciplr.
Accant on Grinding: Tlie principal fetitiires t o 1)r offrre(1 iii tliis sr.ctioii are ( 1 ) a iiiucli lietirier eriil>li~isistlian Iicts beeii ciistoiii;iry 011 riietliotlh of grinding for both flats cind rnirrors, and ( 2 ) tlie provision of riiore precise l;il) surfaces for polisliirig flats. To rnclny csl>erieiiced workers tlie metliods t o be described will not he new. They are offered 1)ecaiise a reltttirely less precise surfztce niay be chaiiged to ;L higlilp precise one by errililoyirig sriiall dettiils of 1)roceclure ~vliicli,tliough their exact mnnner of action is ofteii ol~scure,(lo arrive tit tlie desired effect. As a n ex:~rnl>le,we mny take tlie mc~tterof turned edge. Thc late Rev. Mr. Ellison stated in ATA1 tliat a man who can malce a ~ i i i r r o rtrue t o tlie very edge is an artist born, not niacle. Conr;idy, in hic tretitise oii de\ipn, stated that an objective sliould be fiyiired ovrr-corrrcted iii order t o escape uridrrcorrection caiised by ~)r;ictic;ildifficulties in avoicling tiiriied eclge i r i sliol>prartice. Tlie iiiferrrice in rnost sucli cases is that tiirned eclge is al~viiysa. resiilt of faults in polisliinp, iiot of gririlisli equ;illy wcll; tliat is, thnt grincling i\ a r«iigIi task of no prt.cisiori-:r sort of sour pickle hefore the main coiirses of tlie feast. 1 Iitlve not fouricl tlicit i t could he disrriissed as sucli. Tlirre are riile.; of grinding procedure wliicli must he followed. Their disobeclierice will leticl to unnecessary ancl unwnrr:~ntrdillr, ~rliichmust he relieved, if tliry a r e t o he reliered a t nll, t>y 1:il)orioiis poliiliirig. The mirror or fl:rt maker wlio finds after severa1 liours o f ~>olisliing th:it liis surfnce has deel) pits, aii irregular contoiir, :rricl a b:iclly turricd edge sliould know ~ r l i a tl a n s 1i;ive bern clisoheyed to briiip tibout siicli t~ coiiditioii; tliat is, nhether tlie f:iults arose from the griiidinp or tlic liolisliiiip o1)er;itioiis or hotli. Grinding EL surface iinl)ro1)erly will create ill conclitions. Tlierefore, it seeriis obvious that serious polisliing of nny optical surface sliould never hegin until it is true in contour and lias as slitillow pit deptlis as is pos.;ible. 1 will discuss, first, the riiakiiig of fltits, trnd givc ti11 accouiit of grindirig effects encountered in early efforts in tlie innnufticture of .rv;ir optics of a precise kind. Princip;illy, these wcre ~)risrriseriil)ed
u~liiclia r e beirip prouii
as a tool. The block does not Iiave a solid arca biit is hroken iip into nreiis whose dimrnsioris nre tliosc of tlie prisin faces. Ilereoftrr ~ r h e n e r e rthe terrn "broken" is used tlie rncaniiig mil1 apply t o any such non-solid surfnce. I t would ;ipply, for cxtiml~lc,to a clianneled tool of solicl gltiss. Whcri tliese griiiclirig rnetliods, successful o11 brokeri surfaces sucli as blocks of prisriis, were itpplied t o flats nnd rnirrors, troubles carne ir1 tryiiig to secure the sarrie iiiiiform grinding action as before. Tlie solid surf;ices, because tliey kept air from tlie grit, now proliibited drying the wets in tlie sariie rntiririer. The grit, ~ r l i e ni t finnlly dried t o paste forin, would not sprend ercnly over the t a o surfaccs but ~voiildgtither towhrd the center, learing nn anniilar ring near tlie etlge oii ~vliiclino grit \vas risible. I n adclition, tlie edge pickcd ul; coarser grit thnn thnt ~rliiclihad been broken down by grincling ir1 tlic criitr;il portions. As a re\ult tlie first test, after fire minutes of polisliing, p;ive <'vidence of turried edge arid greater pit depth in that zone. Various nttempts were mtide with botli flzits and-mirrors to apply the methods descrihed-that is, 50:50 tale and emery and drying u p the wets-but now it seerned strtinge that in the same hands the action was no longer as desired, in spite of the i t is true, tliese \rere broken fact tli:it Iiundreds of hlocks of prisrns-though surfaces-liad been successfully ground. Ohriously the basfc difference was, in the one case n broken surface, in tlic other tlie absence of it. Tlierefore, t o siinulate tlie broken surfnce of tlie prisiii block tlie surfnce of tlie glnss tool used witli flat or inirror w;rs deliberatcly broken; t h a t is, i t was charineled in a criss-cross patterri rnucli like tlitit of ;i pitcli lap (Figure 9, first circle). This prored satisfactory. Troiihle ~v;rsno longer eiicouriterecl in grintling on rriirrors or flats a true spliere witli no tirrn. By provi
t deptli ~iossihlr,hrenlcprinclinp action it pives. S o obtnin tlic s l i a l l o ~ ~ e spit irig dorvn of eveii the finest prit size used is ;i necrssity. Some coiniiicrcinl slio1)s do not em1)loy tlic firicst prit sizes tliat are innnuf;tctiirele, 1)ecausr scr;itchcs :>re ofteri directly ;~ttrihiit;il)le t o tlirni. ,Iiist wliy tliey scratcli is not obrioiis to riie, tiltlioiigli tlie s<.ratclies are evitliiit iri 1ir:~ctice. P e r h a l i s a rnorc. c:ireful gr:iding of grit \voiilrocedures of grinding, for that of a method of making fl:its whicli employs them, the isolated worker shoiild he cautionerl apainst heliering tliat, witli Pyrex, one liour with eath grade of Carho, followcd by emery, is siifficient. Pyrex is considerably hardrr than plate glass, which is a form of crown glass. I t resists ahrasion to a greater extent. Instead of being givcn a time for grinding each grade the norker is urged t o exaniirie tlie surface witli a magnifier anii ;L strong semi-converping light such as inny be liad a t re:i\on;ible cost in a penliplit \vith condensinp bulh. Pits deeper tlian those from tlie pracle heing erriployed will then he rriaile readily visihle by deeprr sli;iclows \vliich form in tliern. Fiirther, scratches will be visible in spite of the sc:itteririp of light from tlie neiglil)oring ground surface. If such an examinatioii sliows no in:ijor defects of tlirse kinds, it is time
to proree"l to tlie next gradc. TVlien this mcthocl Iias 1)er.ri follo!vetl it will h r fourid tliiit tlie tirrie for eiicli gr:iroti;il~ly douhle th;it "sually g i w n for 1il;ite gl:ihs. I%iit~vlititdoes it iri:ittrr? .ifter :ill, oiir piirpose is ti) procluce :L re;illy fiiic ol1tic:il siirfticc, riot t o cave a felv rniniites of grin(liiig to wtistc i i i otlicr lcss siitisfyiiig 1)iirsuits. No. (iOO Cttrbo is iiot i i suit;ihle finisliirig ot)r;isive. A fincr grnde, So. 1000, is aviiil~rble froni tlie C;irl~oriinclun~ Corii1)tiriy :riid is riiore iic.;irly siiital)lc.. However, tiie gr:i(ies of csriiery iitimed, or tlirir eqiiivaierit frorri otiirr riiariuftrcturers, lian
F I G L I ~9L For :t retisonable ad(1ition:il cliarge tlie Corninp Glnss m'orlis supplies (lisks groiirid roiiplily 11lnne aiici witli sidcs groiiri(1. 'l'lirse e1iiniri:ite iiiost of the roupli grinding for flnts. Tlie rough sidcs ntforcl more w f e t y in 1i;tnclling thari the slick, slil>pery sicles of a rriolcl-finishecl disk. Tlie cli~iiineletltool is iritrocliiced in tlie cl;issic sequerice of 1 on 2, 2 ori 1, 2 on 3, 3 oii 2, :iiid so oii, so that al1 four (lisks (or tliree, if so elected) will be pround :il>l~roxiinatelyfl:it. Tlie fining is carriecl tlirough a t least two wets of tlie finest gr;i(le. SIien tlie chnnrieled tool will come t o its greatest uscthnt of grincling each flnt ir1 t u r n tigainst it in order t o employ the grinding methods described, agninst :L brolcen siirfiice. Since it \vil1 b e ashiiriird tliat no master flat is arailnble-this beinp more often tlie cose t1i;in not-tlie lack c:in be offset witliout :iiiy grent mariipulation, and the contour of eticli surf:ice.
From now on the surface contour of the channeletl tool mil1 he known, as wcll as tliat of the flats wliicli a r e to be ground ag;iinst for final prc-l~)lisliiiig coritour; tlrid since tliese conditioris riow are knowri, \ve now have to that extent iriaster flats. ( A mastcr fl~rt,I)y tlie w;iy, is orily a "rnaster" to tlie exteiit of the ~necisiongiven it by tlie mtiker. The terrn can be arrihiguous.) I f tlie cliaiint.led, or l~roken,tool is convex another corivex disk nitry he pround against it to clear u p the two surfilces witliin one fringe of (1evi:ition. I t is good t o gire anotlier five miriutes of polisliing afterward, in order to rnake sure what has been done. In turn, e:ich clisk is brought within a friiigc of deviation froni fl:itnrss by grinding with tool on top or bottom as tlie contours dicttite. Finally, al1 surftices will exliibit tlie fringe reading desired. Pronouiiceolisliing. Obviously, tlie rear surfaces of tlie fltlts nred iiot be so plarie as the fronts. Neither do tliey neecl he as \ve11 polished. 'CTnlessthey are to be used as ref l e c t o r ~al1 surfacrs need only a fine visual polisli. I t is, however, very little rnore work t o 1i:lve tlie h a c l ~ sof tlic flats riearly or quite a s flirt as the business sides. PoTibhing: I n order to liold and iniprore tlie flatness whicli has tlius f a r been attained, stratageins must be used which will provide as nearly perfect 1:ip surfaces as possihle. The general rulcs of stroking were given in the section on prisms. Tem1)er;iture effects other than tliose froni tlie heat of polisliing must be avoidecl. Ver? inferior roiiges will scratcli, but tlie rouges available from such concerns as Raiiscli and Lonib Optical Co., Rocliester, N. Y., Americari Optical Company, Worcester, Mass., James II. Rliocles Company, Cliicago, Ill., and no doubt otliers, have been of good quality. The disk with circular facets nliich will be usecl to bring about a precise Itip surface will a t the stime tinie is, will act as a "bruiser." 12 hard la11 will not break do\vri tlie rouge-tliat t u r n the eclges of tlie fliits hut instead will work against tliat condition. So the lap should he well on the h a r d sicle: The fear of scratches with a hard lap is so nearly groundless, except witli carelessness, as to be of no concern. If the lap is hard enough t o allow only a slipht indentation with the tliunibnail n i t h moderate pressure, or if it ni11 allow small facets, made by pressing the face of it througli an onion sack, to flow in undrr work iii iibout two hours, it is ahout right. A rigid backbig, such as a glass tool or iin irori clisk, sliould be l?rovided. After pouring the Iap on the fl:it backing witli thr paper tape around it,
channeling may h r tlorie ioiiirxv1i;it as showri i i i Fipiire 9, second slietcli. Es))<.attention to dccc~iiteriripis iiiiriecrssary. 'Tlie la11 is then givrii ti ~)relirninary degree of flatiiess 1)y w;irrriiiig tlie face arid prrssing it ori oiie of tlir fltits. Aftcrward, onion sttclc wCll soalted witli w;iter is spre:id o\.cr tlic fl:it tiii(1 tlir 1ap face lientcirid Teiitli Street, Brooklyii, S. Y., is favored. I t is sold in tn.o grades, herd ;tiid soft. The hard 11i:iy be tcrnperecl witli tlie soft t o fit tlie w r k i n g teniperature. For my o ~ v npitch 1 uie rosiri tenipered with pine tar, b u t xio beesw;is, no oils, ancl no volatile substaiices sucli a s turpentine. Folloxvirig tlic preptlrzitioris described above, tlie side of the tool liüving the circul:ir facets is hrought into use. Such a tool is known to tlie optical trade as a "dummy" poliaher.. Having a plane surface, attained during grinding, it is uied to rub away the tiny protuberances and inequa!ities on tlie Inp left by cold-prrssing. Anpoiie who 1i;is corrected roof angle prisms on a srnall lap is fa~niliarwitli the fact tlint coltl-1)rt.ssing still 1e;ives on tlie lap a degree of rouglinrss. Tliis can be felt in a decided nitiiinrr by rul~birigtlie lal) witli n diirririiy. Tlie sarne residual roughness may also be rut)l)e«li>li. If tlie pclisliing is to he cloiie by htriid both clummy ancl flat slioiilcl be secured t o the bencli ~vitlibossrs, so tliat inversion will be sirii1)le witli eithrr one.
as drscril>colli ct.riter ancl cclgr, tind tlie rriirror tlirreforc liolislies evriily. 'iliis pvri~iitst i sIwrtt>r I)olisliirig tirric, sirice i t is tlicri iiot iiecrssziry to ovcrpolisli tlie <.<.riter.ii orcler to retlricr pits ttt tlie edge. Polisliirig fnce upwartl, tlien, lins a
ROh'CEII, Q U A N T I T A T I V E
A
Quantitatioe
Optical T e s t f o r Telescope Mirrors
*
Several methods Iiave hern pro11osecl ;inri used in t h r testing of opticai surfares. Aniong thcsr the Foucaiilt kiiife-edge test is the most popultir ;ic it is visu;il :ind rrquires orily simple :ipptir;itus. S h e Hartnian test, being photographic, is used tvherc n final tinolysis of the performance of tin optical instrumrnt is dcsired. About 1923, Vasco Iionchi proposed a method of testing, which has the ;ippear:irice of an intrrferencr rnetliocl hut involves only simple a p p ~ r a t u s . ~ J . A. L\nderson ancl R. W. Porter Ii;ive foiind the Ronchi test to be fiilly as sensitive :is tlie Fouciiult test tincl, under favorable conditions, capable of of :t wave-length in tlie wave surfacc learshowinp an error as sm:ill tis ing the principal plane of the instriimcnt.? Ho~vever,thc Ronchi test is only qiialittitire as it does not indic:ite tlie nmoiint of aberr:ition present. Wkiilr considrring thc throry o f tlie Roriclii test. nnd wislring that it were al50 qu;intitative, tlie writer (liscoverecl a simple schemc usiiig this principie witli the ;~dditionof a very sirriple tiuxilitiry apparatus, wliich resulted in a quantitativc test. The feature, makinp tlie trst qiiantitativc, consists in superimposing two fine pariillel lirir images, which serve as gages, on tlie lens or riiirror under test. The Ronchi grating is rediiced t o a single wire alinrd witli tlie gage lines and tlie optical slit. By movinp the wire ;~xially its shadow image is symmetrically expanded until it crosscs tlie fixed gage images a t tlie zonal radii under test, the displacement necessary heing a measure of the aber. ration existirig between these zonal radii. The exact method of forming the line images on the mirror is not important so long as it does iiot introduce errors larger tlian those of measurement. The method that first occurred t o the writer wns t o stretch piano wires immediately in front of t h spcculum ~ tind view them by the diffraction around their edges or illuminate them by a light of contrasting color from one side. I n the case of testing mirrors where the back (not tbe optical surf:ice) of the mirror is polished and reasonably plane, a cardboard screen, placed against tlie back of the mirror, having the gage slits and markings indicating the zona1 radii cut in it and illuminated from behind, would be very simple and perhaps could not be surpassed. The method t o be described produces virtual gage line images against the speculum by the use of a small glass diagonal and has the adrantage, thírt i t is niore generally applicable especially where tlie lens or mirror may be mounted in an inaccessible place. The distortion produced by the use of a small parallel glass diagonal in
* Reprinted by permission, from t h e Journnl of the Optical S o c i e t y of Ameri,ca, Sept. 1 9 3 4 t Membcr Terhnieal Stnff, Uell Telrphono Laboretories. Inc. Vasco Ronchi, La Proni d c i s i s t e m i o t t i e a , Bologna, 1 9 2 5 Anderson nnd P o r t e r , d s t r o p h y s . J. 7 0 , 1 7 5 ( 1 9 2 9 )
1
2
R O N C H I , (~LTAS'l'I'l'A'l'IVE
105
having the cone of rays frorri tlir speciilurri l ~ i s stlirougli it is proh;ihly smnll, since the diagonal need be notliiiig larger tlitiri ;i riiicroscope slide cover glass and c;iii he plocecl vcry close t o the eye. I t roay ercri be placed beliind the test wire riglit riext to tlie eye.
Tlie set-up of appar;itii\ i \ sliown iu tlie sl
speculum A (under test) ancl returri to focus a t G, the position of the eye for the test. Immediately in front of G is plitcrd a. terisioned wire C , arranged syrrimetrically in the returning cone irnd pnrallel with the optical slit. (The writer has used n wire about 0.006" in diameter.) An unsilvered diagonal D reflects the image of two pnrallel gage slits F, allowing them t o be viewed a t G, :rnd appear syrrirrietrically superimposed on tlie speculum A along with the shadow irriage of tlie test wire. The scale E is used in measur-
106
RONCHI, QUANTITATIVE
ing the displacement of the wire í' along tlie :ixis o f tlie rcturning cone. The procedure consistq of nd.ju5ting the gage slits iintil thcy appenr :is sep;tratecl about '/1 or 11, tlie dinnicter of the speriiliirn and tlicn leaving tliern fixed. Tlie test wire is tlien .itlju\ted along tlie axiq until its shadow image appears t o jiist touch tlie RCLF?imt~gesas in rc of Figure 2. The reading on tlie qcale E , F i ~ i i r e1, i q thrri notrd. TIie wire i \ tigairi m o ~ e d,ilong the axis until it5 shndow irndge iiitersect5 tlie gnge d i t im'ige slrnrnetrically a t zone r2 as in 1) of Figure 2. l'he reading on tlie sctile R i\ zigain iioted. 'rhe difference between tlie two scale readings measures directly tlie iiberration
existing between zone r, cind r-. Likewi\e, the remainder of the mirror outside zone rl may be tested with tlie gnge slits fixed. Should it be desired t o test quantitatively inside zone r l , the gage slits should be moved closer together and the above procedure repeated.
Figure 3, a, shows a horizontal plan view (not the conventional vertical section through an optical system) of the test when adjustment is made for zone r l as in i-r of Figure 2 and shows only the rays proceeding from zone rl t o focus. Similarly, ó of Figure 3 shows tlie plan view of the adjiistmerit for zorie r-. I n n of Figiire 3, y1 is the distance that the test wire C of Figure 1 is situated in front of focus t o appear t o just touch the gage slit images. The distance tliat the wire C, Figure 1, is situated in front of focus for zone r 2 is designated by yl, tlie shadow iniage of the test wire C appearing, in this
RONCHI, QUANTITATIVE
107
case, a s in h of Figure 2. A?/ is tlie (listance test wire C is moved to effect these two contlitions. Since in a and b of Figure 3, angles a l and a2 are equal (witliin lirnits affecting this test), it follows frorn ~iibst~intially similar triangles t1i:ct y 1 = y 2 and A y measures directly the aberration existing between these two respective zonal radii. I n the case of testing a spherical rnirror a t its center of curvnture, A y is equal t o t w o times the difference in radius of ciirvntiire of tlie zoneq providing tlie optical slit rernains fixed. Before disciissing the appearance of soIne common forrns of tiberration in this test, it might be well t o state, that the shadow image is not quite as
a
b
-!FTT
c-irgrrlnrrno es
-
Ll
*'
--
-
FICTT'RF 3 Horizonñzl plan vi~ws-looking down on test from above.
shown in the sketches. With a wide optical slit, the shadow image of the test wire is not sliarp on tlie edges, while a narrow slit causes secondary diffraction effects to appear. The fine ilit ad,justrnent seems preferable, since it gires tlie sharper shadow irnage t o the test a i r e . Too fine a test wire (0.001" tlinrneter) does not apparently improve the sensitivity of the test, since tlien the wire Iias t o be broiight very close t o fociis t o expand its shadow appreciably, again making i t di5cult to preserve a sharp shadow irnage. I-Iowever, in spite of the above, the writer has been able t o duplicate measurements a t least as accurately a s with the Foucault test. The test is much faster than the Foucault test when the latter is used with zonal stops and a t the same time the qualitative feature of the Ronchi test is always observable.
I n c-d, e-f, g-h and i-j of Figure 2 are shown some common forms of aberration as tliey appear in this test. Aberration of the opposite sign t o a-b of Figure 2 is sliown in c-d, the forrner being the case of outer zones too long in focus, ancl the latter, outer zones too short. The appearance of a raised zone is shown in e-f of Figure 2, and g-h shows a depressed zone at the same place on the speculum. Turned edge, one of the worst enemies in the figuring of optical surfaces, is easily detected and can be accurately analyzed by tliis test. I n al1 other tests the wire 6, Figure 1, has been kept just inside of focus but in the case of turned edge the sketches Figure 2 i-j show the appearance of placing the wire just outside the focus as this gives more prorninence to the effect. In quantitatively testing parabolic
mirrors of sliort f«c;rl rntio :it thr. tiveragi ceiiter of curvnture, the Foucault sli;idows become very derp. riecessit:~tiiip tlie iise of a large niirnt~rr of zona1 stops. Tlie present test would seerii riiore suitüble in 311~11cases sirice the use of stops is eliinin;ited aiid pliotoiiictry is unnrcpsiary. [EDITOR'S?;o.ri:: 11lan 1t. Iíirli1i:~rri of 'I'acorii;~, \i'iisliingtori, 1%-anlilin R. Wriglit of Berkeley, California, Loreii 1,. Sliuriiaker of Düytoii, Oliio, and possibly ottiers, were working o11 tlie stirne problrm-makirig tlie Ronclii test quantitatively-at nbout thc sarne generirl time as Mr. Kiiig, ziiitl eilcli dcveloped bis own metliod. l l r . Wriglit's was piiblislieIr. Kirliliaiii's !vas i~ffrrcd tlie Scientifir* . / I I L O ~ ~ C ~; >~Ln dwtis ;icc,epted, l)iit piil)lic.;itiori \\-as drl;ij-ed tlirouph the prrseiit writer's
HARTMANN TEST
The standard observatory method of grading the performance of large mirrors and objectives is the Hartmnnn test. I n general procedure and simplicity, the Hartmann ami Foucault tests bear a close resernblance. Both seek t o find t o what extent tlie liglit of a s t a r can be brought t o a point; t o do this, botli locatc tlie poirits of interscction of varioiis pairs of liglit beairis coniing froiii definite poirits on tlie surface of tlie rnirror. I t should be emphasize
L o f t : Plnte made photogrnphicnll?/ from 24" mirror. C e n t ~ r : Plate f o r 61" mirror--extra.foeirl position: pnttrrn comj~reesed tou'ard center. R i g h t : Plate f o r GI" m i r r o r , iriside of f o r , ~ s : j ~ a t t r r n c a p n n d ~ d . I n raeh case, note t h e u.rtrn tiole a t tlin t o p ; thi.5 is cfrt in tlir screen wtiich is plncpd ugainst t h e nairror, t o i d r f ~ t i f yt h e zero ~ i o s i t i o n on fhe p h o l o g ~ a j ~ h i cplate. E'or a fairly large mirror the holev are ?nade aliout X'' or so i n diameter.
laborious than the Foucault, it js frankly less adapted t o the needs of the amateur. Nevertheless, a s a slightly different approach t o the central problem of mirror making, it is of more tlian general interest. Let us consider first the simplest case, namely, the test of a parabolic mirror under actual working conditions, the light source being a s t a r on the optical axis of the telescope. With a perfect mirror (and perfect "seeing") the light from al1 pürts of the rnirror comes to one focus, the individual rays al1 intersecting a t one point on the axis. Now supposc that we cover the mirror with an opaque screen in which a series of holes is punclied along various diameters of the mirror. Tlie holes will be in pairs, so that each pair is accurately centered with respect t o the mirror. If we place a photographic plate considerably inside the focus, upon exposure t o the s t a r we s1i:ilI ohtain a pattern similar t o the array of holes iii the screen, since tlie individual bundles will have not come t o the intersection. Similarly, we sliall get another pattern with the plate placed out beyond
110
HARTMANK TEST
the focus. Figure 1, a t left, shows the p:ctterns obtained witli tlic H a r v a r d 24" reflector under this kind of experirnerit. W e now confine our atterition t o tlie light bunclles from :L sirigle pair of holes on one dinmeter, say tlie Iioles for :I r:idius of 12", wlicre al and a?, Figure 2, are the septirntion of the irnages on the two pliites, as rne:isured with a comparator (microscope rnicrometer) and til+d2 is tlie separation of the emulsion in the two positions of tlie plate. dl is thus tlie focus of the two areas of thc mirror witli wliicli we have been coricerried, referred t o the inner position of tlie sensitized surfacc of the plate. W c next compute the
SINCE WE HAVE SIMILAR TRIANGLES,
2,- , a2 d2
-=-al a l t a 2 dit d 2
a, (di +d2) al +a2
position of focus for al1 other pairs of apertures along the ,ame diameter, so that we may find the mean (or average) focus. But since the area and hence the effectivcness, of each zone is proportional t o its radius, we "weight" tlir mean 1 accordingly. Thus if tliere are n zones the "weiplited metin" focus
I f there are imperfections in the mirror, it will be impossible t o obtain a point image in any position of the plate. The optimum position will be a t the mean focus derired above. By similar triangles, the radius of the 1 I n taking a represcntatire average, it is always necessnry to give e m p h ~ i st a various elements in accordance with their cffrct on the result. T h e simple average focus of al1 zones o£ a mirror is f o u n d by adding t h e individual foci a n d dividing by t h e number o£ zones. B u t tlie inner zuues a r e o£ relativelc little iinportance. Hence. in finding a significant value o£ the average forus, wr "wright" t h e value of the individual zones, i n this case by rnultiplying each hy the radius of the zone. 2 The symbol S (Sigma) i? tlie short notation for "sum of." There is nothing higlibrow about it, a n d its meaning is readily inierred from the first equation in which it occurs. Likewise,
IIAlt'rMhN':
TEST
111
R(f
- Po) = -
image disk :it any focus is rd
1'" R being the rncliiis of tlie mirror zone in question. Tlie weightcd mran of the radius of tlicw sctitter tlisks is iiiean
As seen froiii tlic pele of tlie mirror this average disk ratlius iu1)tend.. :tn
of a r e (tlie factor 206.265 is tlie nuriiber of seconds of are in one r:i
L
Actual k c d s f o r rays frym zone of radius R
*<--Best position for mirror as a whole
evaluate it i i i tcriiis of the scale of tlir plate. ( B y sctile of tlie plate is meant, for extiinplr, tliat 1 nirn on tlie film eqiials 1 ininutr of arc iri tlie sky.) It is generally coiisiclcred that, for a good niirror, Ilartinariii's criterion must hr sometliirig less than 0.5. By comp:iring tlie mean foei along various diameters of tlie mirror tlie astipni:itism is determined. The Hartmann test may also be made a t the center of curvature with an artificial star, just as the Foucault test. I n tliis case, the patterns on the plate are not exactly similar to the array of holes in tlie screen, being compressed toward tlie center in the extra-foca1 position, and vice versa (Figure 1, middle and right, respectively). This is due t o the distributiori of foci along tlie axis, as giveii by thtt
W F, f
R2 qT -A
+
R4 x3 A
,-
equation. Comparison is made of the observed and theoretical distributions, care being takrii to make tlie fit ot a weighted mran position. Deviations in this case are four times as great as tliose made a t the primary focus with parallel light, ~vhichmust be taken into account in cornputing the Hartmann criterion.
-
W o r conseniencr i n matliemnticiil treatmeiit, it is freqiiently better to measure a n d e s in r a d i a n s r a t h e r than i n degrees. A r a d i a n i s tlie aiiale subtended by a n n r i r
The 1I;irtmann t r \ t is ti~iplird to ol).ic.ct gltisscs, hiit color filtcrh riiiist be uscd, siiice cliromtrtic aberretioii woiiltl rcntler tlir ininprs toii diffiisr for rrir:isiirerneiit. 'I'lir prrforriitiiice of tlie 1c~iis i i i vnriniis \liectr:il rt'gioiis is effectively stii(licd in tliis mtiiinrr. To suniwtctrizr: In trsting ;i mirror by tlie IInrtriinn iriethod, ;t zonc pl:ite (mask) witli rac1i;illy S)-~iiirit~trical 1111lesis pltrceil (1vt.r it. A pliotogr;ipli is taken insicle a n d outside of fociis, witli carcfolly measiirecl sep:irtitioii o f the two positions of tlir film. By inc;isiircmciit of tlie irntiprs oii tlrc platr, t h r intersections of the various p:iirs of rtiys a r e found by simple geometry. Tlie nngultir size (in sc*c:oiicls of are) of tlie b<-.;t possible imnge is dorivrtl, :ind tliis is ctillrd tlie "1I:irtiri:inn critcrion." That tliis is not ~i.5coiiil~lictitccltis miplit srerii a i l l bc. sliowii by :ir1 esariiplc wliere orily tliree p:iirs of r:iys along orie (li:~rtictrr:irc. corisiclerrd. \Ve will suppose tli;lwceinent to within .01" (incli), w1icre:rs tlie exact disttince from tlie filrri t o mirror ncrcl not he known better tli:in to .1". .\leasurenieiit of irriage on tlie clrvelopr
Plate oiitsi
Sepanitioii of imagc.s of !iolrs oii 7" rticliiis 3" X .00 .15.jG
{!):!-'l
.
di in (1, Fig. 11
=
=
067s X 1.00 -
'-
-
,, i;i,,
,1120 .o510 x 1.00 = .(;18/, <13 =
I
~
-
.Cif;c;g
"
j Fig.
1
.U234
>
/
'
!
l'hcse nrc tlir actu;il intrrsections of tlie rnys frorn tlie 7", 5.. nnd 3?? aones refcrrecl to tlie position o f tlie emiilsion inside fociis
FLATS
Flats I t Iias hren said tliat a truc plnric "is tlie riiost clifficult of al1 surfaccs to rn;il<e." 1 'ilrhetlier or not tliis is trur, it is rnost cert;iiiily U f;ict tli;it :i large fl;ct wliicli is xvitliin 0.1 friiige of plaiie, iriclu(1ing tlie edgr. ;ind wliich is corripletely free frorn pits, sleeks ;irir1 scratclies, is a truly difficult object t o coiistriict. Iri comp;rrisori, a high-quality paraboloid of equal size of aperture ratio (i or 8 is easily mtide. I n tlir folluwiiip ptiragrnphs only those methods and materials will he disciissed w7Iiich liare Iit.eri usecl by the writer and nhicli llave proved satisfactory. I t must be empliasized that, in other hands, other procedures llave yielded eqilal or superior results and tliat no one can have a rnonopoly in the matter of tecliriic.
Polishcd plate: Tliis is the usii;il material employed by amateurs. F o r most applications i t i s entirely suitable. In tliickriess greater tlinn liarmful strairis may be encountered. I t is ratlier soft (4.5-5.6 hIohs) and scratclies easily. The high linear expansion coeficient (8.8-9.2 x 10-6 per "C.) makes testing time-consuniiiig and tempcrature effects in use serious. P y r e r : ? F o r applications in wliich liglit does iiot trarerse the flat this material is superior t o polished plate. Scratches are less easily formed, due to greater h a ~ d n e s s(6.2 Molis). Disks of al1 sizes are uniformly free from large strains in the type designated a s "Telescope Blanks." Sight glasses and slieet Pyrex a r e not so satisfactory in tliis respect. Tlie low expansion coefficient (3.2 x 1 0 - 9 helps to mnke testing ancl use easier and more reliable than with plate. Bubbles, s t r i e and stones must be expected. Fused quartz:VTliis rather expensive medium is excellent for the construction of 10" and smaller test pl;ines and standard flats. I t is hard (7.0 hlolis) arid changes but little with rarying temperature. (Exp. 0.54 x
x",
10-6).
"Rlack" glass:4 Many types of opaque glasses a r e sold for building decoration, counter tops, etc. They resemble plate in hardnesi: and in expansion but some are not annealed and a r e useless for optical work. As test planes on whicli t o examine other flats, for moon diagonals, polarizing mirrors and Colzi sun oculars, the deep color forrns a background against which fringes appear witli great brilliance and which reflects only a small amount of the incident light.
-
R. \V. Porter, "A.T.31.," page 16. '1 Corniiig Cilass Works. Corning, N. Y. General Electric Cu. Echeneetady, N. Y.
T h e r ~ n a lSyiidicate, f.td., Brooklyn, N. Y.
4 Wells Glass C o . Kokoiiio Ind.
Pittshurgh Plat;
Glass
c;.,
Pittsburgh, Pa.
FLATS
114
Filler gla.~srx: These are colored gl:isses whicli trnnsmit restricted portions of tlie spectrum. They vary ~re:itly in working (lu:ilities. Siicli glasscs can be obtained from Corning (;las.; Works, Cliance Bros., aiicl Scliott & Ccnossen. They a r e obtainable both "r;lw" and polislied. Tlie polislietl grade usually has a surftice figure similar t o plate. Sperinl ? ~ l n t e r i n l s : l'liere sire rri:iny optical and otlier instriiments ~vliich utilize flat surfaces oii inirrors, Icnscs, prisrns and grntiiigs of otlier mnterials, sucli tic (Iozens of types of optical glass, various rnettils and such rninerals as fluorite, sylritr, rocksalt, calcitc, crysttil quartz, etc. These materi:ils rccluire such speciol metliocis of working that tliey cannot be considercd here. Grincling nbrnsizt~s: F o r surfacing, edging and perforating flats, Cnrboruiirlurri gr:iiris aiid powclers are quite suitable. She writer uses Nos. 70, 150, 280, ,100 :ind 600. Altlioiigh more rnpid and liarcler ahrasires, crushed steel niid carbicle.; of tuiipstcri and t)oron,j are :ir:iil;ihle, tliey need not be coiisidere
F Eilner (
FLATS
116
If precision of a high ordcr anci peririnrience of figiire are t o he attained, the material of -,vliicli a flat is constructed rniist he free froin large straiiis. I t is ~vell t o exarriine tlie strein figure of the rnaterial imrrie(1i:ttely iipon receipt, bcfore pcrforrniiig niiicli work so t h a t tlie pieces, if a t fault, can be rejectecl, reaiine:ilcd or disc¿irded. The testing is easily done by tlie metliod outliriecl in "A.T.M."V W i t h Pyrex and fused quartz, tlir f:ices sliould first be grouncl approsimotcly p1;inc and pnrtially ~~olishccl.Altlioiigli tliis consuriiw tinic, it is tlie writir's opinion that it is nell wortli wliile. Crifor-
L e f t : E d g i n g , toith tu'" Polishpd edges. E'lats of 4" e d g r polish. T h e first, third' srriallest are extra-dense jlint,
d i s k s of
'4"
plntr pitched
t o t h ~giass.
Right:
6" 8" a n d 1 2 " d i a m ~ t e r ,photogrnphed to show n n d fifth fiats f r o m the Ieft are P y r e x , the three
the others plate.
tunately, the truly opaque glasses cannot be tested in this wap. The visually opaque ultra-violet and infra-red filter glasses can be examined pliutographically by setting the analyser as for visual work, placing the specimen and substituting a camera, focussed for infinity, f o r tlie eye. Of course, an emulsion sensitive t o the transmitted band must be used and tlie lcns must be shiclded from extraneous, unfiltered light. I n general, photograpliic lenses transmit sufficient radiation for the purpose, even when testing tlie densest ultra-violet combinntions. Exposures are long in some cases, runninp as high as six hours for a Corning infra-red filter, 4 mm. ttiick, iising Eastman type 1-M plates, liypersensitized, and tungsten illumination. As an rxcelleiit subutitute f o r the Sicol prisrri used for strairi-testing, tlie srriall (40 rnili.)
I'olaroi(1 1" c;iri be usecl, ns can tlie rriore costly I%erriot;tr o f %<,isi. Tliey a r e cheapcr nrid o f e r tlie advantttpe of large ;iperturc. 'Llic ricxt ateps t o br corisi
irifra-red
1 6 8 Daitrrioiith t o warelengths
St.. Boston. JIasi. It m u s t be rcriit~mbc~ed that over 7000 A.C. and cannut be uhed, tlierefore, for
FLATS
117
criticized tcclinique, but tlie improh,ihilit> of nttaining true precision 1)) tliis mettiod lins heen amply indic,~ted to tlie writer hy Iiis past experi~nents, in wliich edge crrors of large rriagiiitude Iiave becn observed.
This simple operation is fully treated elsewhere.'l Important points are: Tlie usc of tlircc disks, even if biit one flat is desircd, is strongly recorrimerided. IVirrtl glass, woocl to whicli facets of ?i" ¡)late are pitclied or flat vitrified building tile can he used for the additional disks. All surface bleniislies sliould be reriioved coriipletely with each abrasive-a iiiatter riiuch more difficult than is usually tliought. The classic sequence sliould be rigidly maintaincd, as follows: 1 on 2, 2 on 1, 1 on 3, 3 on 1, 2 on 3, 3 on 2, 1 on 3, 3 on 1, 1 on 2, 2 on 1, 3 on 2 and 2 on 3. Evenly distributed pressure and smootli, quarter-diameter t o thfrd-diameter strokes appear t o yield the most satisfnctory results. Orford's method of miping the outer five percentl? of each dislc free from nl~rnsivetmo to six times diiring each wet is not essential but it is a practice wliich m:ikes for good eclgri if cmployt-(1 with No. 280 and al1 finer abrasives. Tlie "pencil" test is not recomniended due to tlie danger of scratcli forination.
As with grinding, polishing can follow the established technic familiar to tlie telescope maker, with A fcw changes. Rec:iuse no tools remain from grinding in niost instances, due t o the fnct that tlie disks a r e groiind upoii each otlier, additional tools will be needed. Tliey rnay be of glass, hardwood, metal or tile. If of wood, the tools sliould be used on top to prevent warping. For machine polishing tlie wood anrl metal tools are superior in that they can be drilled t o receive the stud which moves them. Effort can thus be applied quite close t o surface of the disk. Al1 things considered, polishing probably is best done with iron or with iron-weightid wooden tools, using extremely hard pitch, HCF or cloth. Laps of .95 diameter are t o he preferred, on top, run nt a speed of 100 to 150'' per minute with a .3 diameter stroke nnd loaded to 0.5 to 1.0 lb. per sq. in. I t is wcll t o polisli al1 disks long enough t o enat>le testing to be done, after which the best disk is used for cold pressing oiily wliile the other surfaces a r e being rompletely polished. When two disks are polislietl, the better is used for pressing diiring tlie time the last flat is beinp ~vorked. I n this u7ayi extreme errors of any surface a r e avoided. I t is pcrhaps good practice t o limit polishing periods t o one hour, after wliich the disk is cooled one hour while the l a p used is pressed on another disk. The third disk can be worked in the interim with a freshly pressed lap. Olazchrook-"Dictionary
o€ dpplied Physics," Vol. I V , pp. 336-339.
p p 76-81, '2
" I ~ r n sWork f o r Amateiirs", 1 9 3 2 , 1). 1 6 4 .
"A, T. M,,''
118
FLATS
This t e d i o u ~operation is experlite
FLATS
119
work t o rrplace a distant 200-watt hulb. The lona infrn-red radiiition from tlie Itimp had hfen absorhed by the water on tlie cdge of tlie disk (water is opnqiie to tlie f a r iiifra-red), Iie¿ctiiig tlie edge, wliicli robe iii expaiidinp and \va, polislird n\v;iy. Reriiovz~l of the ltirnp ctiuse
a Inp, or t o press it below the menn siirfacc nncl proveed as iisual. rZ 12" flat witli a 3" hole was refigured in this rntinner. X 4" area «f t i largi lap was depressed with w weighted (lisk. The lap wtis tlien nlterniitely pressed on a finished plane and u~orkedon the perforated disk, using 3'/*" strokes. Irregular errors of & 0.2 wavelength were elirninated in fit+e ten-rriinute period5. Wlien large laps a r e used, the piece being worked rnust be iiniformly supported, especially if thin. Probably the cheapest niaterial which is satisfactory is tlie resilient carpet backing, sold by home-furnishing establishm e n t ~ . I t is obtainable in several thicknesses of wliicli tlie thinnest is best for small, and tlie thickest for large flats. The barrel-head or the machine turn table should he free from general c ~ r v a t u r e . A t times it is aclvaritageous t o warm and soften laps. Glass-harked laps can be dipped in hot water, a s is often done in spite o€ the fact that the glass warpc while cooling, but wood-backed laps should be kept dry. I t is convenient t o employ a common electric radiant heater for this purpose and to heat from above, holding the reflector in one Iiand and turning the inverted l a p with the other. For long periods of cold pressing, the Lowers' method of using ten percent glycerin solntion in water to carry rouge is excellent. Sufficient glycerin remains after the water has evaporated t o insure freedom from sticking. Suitable guards should be placed t o prevent the upper piece from sliding on 13
Corning Glass X'orks.
FLATS
120
tlic lo\rer. The glycerin slioulcl 1)e removecl by wiping ~vitli clotli I~efore fipnririg is resurnerl. For sliort pc.rici
dkl THlN
-- IRON BAND
m o ~ e m e n t sof thc center of tlie Inp for nny stroke. These pntterns can be rery useful giiides wlien rrclucing zones. IVheii using heavily-loaclecl tools wliich Eire run near the peripliery of tlie ~ v o r k ,a jerliy riiovernent is inip:irted to tlie turntnble on wliich tlie work revolvcs. Witli even a well-conhtructe
2 nnd 4 t o the level of 5 . A iiewly-presscd. 12"'lzip, fiilly loa
strolíei for tlie iisiial tcm-miriute periods between cooling intervals of one liour or riicire e;icli. 'I'lir 1arge.tools were each faceted in a different ~nanrier, in order t o avoid tlie introduetioii of zones, thus:
A 2'' facets hetweeri %" c1i:innels
The toolq wrre usr
The worker i i apain referred t o "A.S.31." for the general methodi of testinp plane surfnces.14 Only hints ancl elaborations will be offered here. The Rap-leigh water test is thoroughly practica1 if a few precautions are observed. Although glziis lose5 relative density when irnmersed iii m,iter, tlie glass and container rriuit be a d e q ~ ~ ~ t supported. ely Vibration rnake5 testing impossible; so the observation is best conducted after midnight. The liquid surface must be free from dust, etc., for 5uch particles deforrn tlie iurfnce locally. h tliin coat of glycerin applied t o the under surface of tlie coxer glass prevent5 fogging and the addition of one percent gurn arabic to tlif l* Pages 52-56.
FLATS
122
water increases riscosity without caiising a troiihlesome rise in rrfr;ictire index, althougli the Tync1:ill effect does lower fringe contrast hliglitly. 'l'lit. container used should be 2" greater in diameter thttn tlie flnt, t o :iroicl ctil,iliary edge rffects. As the w:itc3r nrid glass surfnces approncli pnr;illelisrii, tlie fringes sel>arate rapidly. Tlie tliiniier tlie water filiii ziliove tlie flat, the brighter the fringe systern will be. L-nless the glnss surftice anrl tlie water surfxce tire cliemic:illy cle:iii, it is uiiwihe to llave a water filiii less t1i;in ;ipproxim;itely .03" in cleptli. I t niuht l)e remembered tliat tlic curvzitiire «f tlie plnnet in:il<es tiir w:iter surf:ice convtZx ti) tlie rxtent of .OJ ~v:ivelerigtli per foot. I t is barely possible tliat precise expcrirnents witli Izirpe fl:its coiild demonstr~rtedirectly the effects of lunar aiid solar tidal pul1 oii tlie surf;icr, but sucli :r ftictor iiced cause no ;iltirrn. Wlien testiiig flt~tsiii contact by interference,lj a liorizontal position is l ~ x l ~ l i i i i n t i u rofi f r i i i g ~fiiriiiatioii: PiO niiil P.0 n i ~ esiirfsci,i: p i ~ r ~ ~ e t i d i ~ ~t oi i ltlie ar plan,. o£ t h e ~i:ilirr, hr11ai.ateil by tiie sninll aiigii1;ir ~li.taiice 4. E'roiii enrli of tlir innriy poiiits iii tiie liylit siliirri, S, two \vavi. tr:iiii< \vil1 rr:i<,li tlie e y e hy rrtiirtiiiii friiiii P i O 2 n d P20. I t is obvioiis tlii~t. f o r fiiiite r:~liies of 6,tlie 11ntlis S1.E aiirl SLE \i-i11 l>e uiicqiial iiiiii tlint f o r rtxrtniii distnnccs SS, t h r ~);itlidiffrrei1i:ci \viII Lr xA 1,hA. l.iiil<~rencli bucli sitiiatii>~i.< l i ~ s t r i i < ~ t iiiti,rference ive will nrciir niid tlie 1)ltiiie I',,O ~ v i l l;il~lieard;it.k. I I a l f \r.ny tivtneeii r;ic,li 11air ~ i fd a r k slJaces. iii:ixiniiirii illiiiiiiiiati~iiiwill oiciii. fiir tlit, ti\,] Ti-ave tr:iiiis frriiii tliis ri.gion will be iii riliare ( p a t h differeiica XX + A) aiid iiiiitiiiil rriiif~irceiiieiit will result.
+
NX
C'ondriisc~i1friiioe r i [ ~ i a t i í i i i i . 7-L =
---
( I f S is a \vliole iiiiiiii,rr, tlie poitit
2 cos 8
rielved ~ r i l i1ir diirk. fui. \i.n\.c trniii- rliiiiigr 111izise. o n redectioii.) dencc,
CL
NA =
--
2
re-radiiii o i <,iirvntiire o£ f r i n g r of tlie n"' orrlpv rn+s-~xciiii. c i E <,iiri.iitiire o£ f1.int.e o£ tlie n"l S"' oriler R - ( i i f f r i ~ ~ i i i ~ ii,i i rziilii of rurviitiire o£ siirf:icri: t i i t r i i 0-niigle o€ iiiciririi~~r~ d-rn 8 - rn- i ~ e t ~ v e r iringes n con+idt,red li-tii of c u i - ~ ; ~ t i i rr e I J -di;iiiictt~r n f ilislr t c ~ t i , ~ l , tlic.~,,f r t i i ~ itlie i u ~ i d a r n e i i t ~ eiiu;itii,ii, il
If
+
+
F o r iiiiriiinl irlri-
FLATS
123
satisfactory for well-supportecl flnts of pre:it relative thicknesq, but perfect s u l ~ p o r tis difficiilt :irid sorrie pieces iriay he quite tlrin. Such disks are best tested verticiilly iri a rack nliicli supports the two a t two points about SO0 ;tpnrt. Tlit. rack c;iri be nracle of woocl aritl so coiistructed that it can be filled while liorizontsl aiid 1:iter rtiised to the verticzil for vi.;u;il or pliotopraphic testirig. 'I'liis riietliod is cspecially recoriimende
) , =
(r?n
+
s
- 7%) e08
F)
SR the folloming equntions can Iic (li,rired:
R
d cos O (rn
4- a
+
rn)
h = R f
=
-4 2
s),
The r a d i u s of c u r r n t u r e of a n y g i r e n friiigc i3 g i r e n by,
+-8h
0 2
r
=
fh
From tlie above e<junti«ns, it is a p p a r e n t that the nngle nt which fringes a r e o h s e r ~ c d ( 0 ) is inipi,it;irit, txveii for f ; r t s ~ i f sni;ill tliickne5s. l t is therefore important t h n t straiglit friiigcs i.al,c<,ially l ~ e r \ v ~ , e it il i i ~ , k iliitx. he ~~xtiriiiiiedonly \.ertically, L e . , fruin the eeiitrnl iiorr;inl to ttic surfaces, üiid froiii ;a great dibtnllc~.
FLATS
121
temperature a t a rate greater than 0 . 2 O F. per hour. The eye or the camera lens must be on the normal t o the center of the disks, as must tlie light source. Two arrangements which fulfill this last condition a r e sketched in Figure 5. Because of possible errors introduced by the inhomogeneity of the nearer disk, the poor figure of the diagonal plate, the errors of the outer surface of the nearer disk, the obliquity of extra-axial pencils and the distortion aberration of the camera lens, a control on tliese factors is needed. By accurately ruling a card with paralle1 lines and placing it between the flats be-
-------------------TRACING f CLOTH
BLACK PAlNT
EYE
1-1 BLACK BACKGROUND
@
\
BLACK BACKGROUND
M
fore testing, sucli a control is ohtained for al1 variables save pencil obliquity. I f no lines appear or photograpli otlier than straight a t any point with nny dislc, the arrangement can be assumed to be free from error. Tlie orientation of the nearer disk must be tlie same with and without the card and the fringes must occupy tlie same position as (lid the ruling. I f distortion is noted, it u~illhe necessary t o determine direction ancl magnitude for each disk and to apply the proper c«rrection. Corrections are difficult t o apply visually, but photograpliic application is easily mnde. I t is sufficient t o make a n exposure of the carcl in position and to compare the print with one from a n exposure of tlie fringes. This procedure is repeated for each disk of the series. Tlie exposures necessary must be found by experiment. F o r illumination, the writer uses a home-made gas tube lamp of grid form, one meter square, filled with argon and rnercury v:ipor and operating a t 10,000 volts and 1.1 ma. per meter of tube. Tl'ith Eastman process plates, the light 6' and tlie lens 3' from the fringes, exposiires average 40 seconds a t f/1.8. When testing disks of the same diameter which a r e mutually centered, a turned cdge is invisible unless i t is gross and wide. I n orcier t o examine critically the edge of a disk, i t must be on the bottom and the upper disk rnust be offset until the edpe of the lo~l-erdisk is clearly risible. See Figure 6. To the above precautions, the follouring must be added, for no oblique
FLATS
125
incidente correction Iias heen considered and it is obvious that n fringe cannot be photoprnphecl frorn the nornitil t o more tlian one point a t once: 1. Tlie lens sliould he a t least ten disk dia~netersfrom the fringes. 2. Wlien first placed togetlier, the disks sliould be firmly pressed a t the center of tlie top merriber.
The larger ~ i l a a o is frue from edge d@,íect, ns close inspf,<'tion of the true edge (tire circle of n ~ i n i m u m radius) will show. Beyonrl the edge, Iioweaer, reflection nrtifncts givp a d e r i ~ s of ~pu).iou.v fringca lchich the photographic emulsion rccords. I h e y are ~'iau«lly quite iiicon~picuoiis.
3. The flats should press horizontally for several Iiours before photographs are made. 4. Only diametral fringes should be used for tests.le
When testing a flat with a spherical mirror, the greatest accuracy can be attained only if the sphere is of moder'ate aperture ratio. That of f/8 is aatisfactory and f/10 is better. Due t o the fact tliat the writer dislikeb this 10 When ohserring a diametrnl fringe hetween true planes from the central normal, the e r i o r introduced by the obliquity of periphrral pencils is
v' d?+12 E = 1 (---- 1) d
wherr, d=lens t o fringe distance r = r a d i n s of disk t=thickness oí a i r film F o r 12%'' flats riewed from 1 0 , t h e error equals 0.0015t. Since t is a function of the a r d e r oí the fringe observed. which cannot be determined easily by t h e amateur, it is necessary to rrly upon approxiiiiate values. The writer h a s nieasured t in many inhtiinces with a crude spectroscope a n d h a s found valuas ranginp froin 10 to 40 wavelengths for small flats quite loosely fitted, to 0.8 t o 5 w a r e s for large disks after ten hours o€ pressing. Assurning that t = 10 W.L. I a n d tliat t h e four above conditions apply, the oblique error should riot exceed ;ipproximately 0.02 w a r e .
FLATS
127
Ellipticai diagonalc: can be cut h y pitching to thc circular hlank two coverplasses, cttstirig tlie corrihin:iti»n tit 45" iri a plastrr inold nnd drilling tlie entire cast witli :I hr;tss tulle of suit;il)lr diarrirter. (Sre Figure 7; to tlir right is sliowri a flat ciit in tliis iiitiniier. 'u'ote turned edge.) . 'rliis crin he done a f t e r fipiiring without grently deforming tlie rdge, if strain-free glass is used. Witli otlier gl:isses, tlie clrilliiig is hect done heforc polishing. Tlie drilled disk can tlien be afixcd to a cast-iron fliit and the work completed a f t e r filliiig tlie moat witli 1)eehwnx. Plane-)>crrccllels: IJnclrr this head may be listed, in approximate arder of precision required, Iiemacytometer corer glasses, light filters for photograpliy, sextant mirrors, echelon grating planes and interferometer plates. The necessary siirface accur;icy varies from 1 wave-length for the first, t o f.O5 for the last. Since these objects are relatively small and tliin, they a r e worked wliile cemeiited t o accurately plane iron disks. When one surface is finished, this surf;ice is placed in optical contact with the iron, the edges a r e sealed with wax and the exposed surface is ground and polished, clase attention being paid t o the total thickness of the block, which must be constnnt for al1 diameters, -1.01 mm. The ahove method is too inaccurate t o serve for testirig parallelism of grating ancl interferometer parts and optiral rnrthocls are used whicli a l ~ p l iHaidinger's fringes IQr simple reflection.22
+
1 9 Tlie iiiterfrrciice plirnomeiion t» which I-Inidinger's fringes o\\-e their rxistriice ocrurs betwren tlir wenk retiected va\.^ t~.aiiis ( I I ' C ' ) and the rxtreinely f r ~ l , l ~trrldy, reflected trains ( B P ' C ' ) . Therriore, wheii the patiis diffpr hy r A + A aiid mnsiniiini bright-
ness occurs, the illumination ndded hy tlie second trnin is very slight. for the low contrast o£ the riiig *ystcziii.
This accounts
If the testing arrangerneiit of Figiire 5, a t left, i 4 used and tlie plane-parallel uiider test occupies the position of tlie two R;its in tlie figure, a faint ring system can be observed by accoinmudnting the eye for infinity or by using a small telescope, preriously focussed for distant objects. If, wheri tlie flat
These a n d other similar groups of', two nearby are fringe photographs of jlats mude by the uuthor who w r i t ~ s l'lie n ~ a t e sof each p a l r are o j iden.rical figure, huviny b ~ e nworí(ed on the Lame lap for t h ~same periods during a minimuna of 50 hours ~ a c h . Each forms the s~cmefringe pnttern, a s does i t s mate w h r n in. contact u'ith a third pIane. The obliquity error in. no case exceeds .o07 toare. Illicmination was by the following spactral lines of the a r c : mercury 4 0 4 6 n.rc.; nrgon, 4 0 1 3 4 0 7 2 und 4104 n . u . F e i g h t e d m,ean Wavelength 4060 u.u." The onc? s h o d n a t the left, is a 1 2 ' / 2 " . Pringe separation', o n negntiae, 13.7 mm. l í a % . devintion, 0 . 1 4 6 fringe or 0.073 waz.6-each disk 0 . 0 3 7 wnvo. The one at right: Sep. 6.0. E r r o r . 0 . 1 3 fringe, 0.06 wave o r 0 . 0 3 wave for eneh pat. The d a r k lines weve inked on the photographs by'the author.
is moved in a horizontal plane, the ring system neither contracts nor expaiids (tlie central ring only shoiild he observed), it is a n indication that t h r s u r f a c ~ sa r e parallel. If the plane-parallel under test does not have parallel faces, the magnitude of the error can be deterrniiied by moving the plate a known distarice and counting the number of rings which form or vanish at the center of the system. The rings contract as the plate is moved towards the thinner section. Obviously, the plate should be moved along many diameters and that onc chosen for test which causes the greatest number of rings t o vanish. If 20 fringes were lost in 10 cm. of travel, the higher
-
In the figure. a r a p'.S from e r e r y point i n t h e illuminant, being parallel to a r a y from each other point, i s ' r e f r a c t e d by L to C, the asial focal pqint. Other rays, howe\.er, not striking the plane-parallel normally proceed f r o m S t~ A , n h e n c e a small fractinn returns t o B', is largely earried t o C', leaving a fraction to be r e f l e c t ~ da t B' a n d A", which also renchcs C'. T h c sume process oecurs around point A foiming a cone, the wave trains o£ the coiiipoiie~~ts of which rnutually i t i t ~ r f e r ea t t h e ci'rcle C'iC'?, which h a s a diameter D . D correspondu to t h e circle A'i.4'2, thc diamrtcr of irhich controls the phnse relntionaliip uf the B' and B" ravs. For every poirit S, a similar behavior occurs and, because t h e determinina f a c t o k a r e only the radii AA'z f o r any one example, the rings f r o m identical radii froni various points coincide, a n d a concentric system is forrned on O.
FLATS
129
point would be 10 wavelenpths aoove the luwer, relative t o the opposite face, and the plnte would be out of parallelism by one wavelength per cm.,
L e f t . Diarn. 22%". Fringe separation, 4.9 m m . M n z . d ~ v i a t i o n , 0.8 m m . o r 0.082 u s a v e , or each d i s k , 0.04 w a r e R i g h t , Diam. 12". S e p . 4 3. E r i o r 1 . 0 , ur .23 f n n g e , . l 3 wuve, or .O7 per s u r f a c e .
for thickness equals the central ring,
-?d-
ZLL cos 8
?L.
and this becomes, Spr vertical incidence and
Prismatic error then equals f / 2 waves, where
Bu
f = number of fringes disappearing, or change in n.
The fringes lack con-
L r j t A n 8" ? 1?/4" plane o n an. unfinished 8" 2: '/aw disk w h i c h 13 1.6 waae conver Frtnges correctly photographed X i g h t Tlie sume 8" dzsks improperly photoqraphed to show inltuence c j angle o f incldrnce-al1 fringe p h o t o g ~ a p h s t a i r n al n n a ~ i g l rshould be zzpwed w i t h suspiciun
trast and a r e difficult t o see, but the phenomenon can be interisified by very liglitly silvering both faces.20 20
Wood-"Physical
Optics," 3rd Ed., p. 209.
L e j t : 12;í". Se)~nue per sirrfate. li'iglit: G ? y " . .S*)>. 3 . 4 ntlli. JIax error, 0.5 ~rlm., , 1 4 7 fringe, .O73 u s a v e , or etrch tlisk, .0:16 {cave.
T h e Author B y pipcing t o g c t h ~ rsomr frnqmentn n l r ~ n d i j Pnovrn ahotit h i m , u ~ i f ha f e w facts ohtainrd b y fhird dpgrnp n;utlio i Amnteurdom" i t ~ m h a s b e ~ nconstructed: .llr. Srlbij is chief chrmirit f o r n, Cnlifornia foud yroducta ylant. D E h a ' al80 been n t r u c k driver, a ~ i d a d i s h u ' a s l r ~ rin n lumber c'amp. H i s avocation is r n n t h ~ m a t i c n lopties and he statrs that he dislikes t h e u'ork o j lnaking ol~tiral syslems, nrirl t h a t tlte only pleastcrcs n r ? to br f o u n d i n conlputation aiid use. He h n s c ~ » ~ p i ~and t ~ (conutricctecl l for his o w n ?tsp n n npochro, matic triplet tulrscope o l > j ~ ~ ' t i v rn, nlrmber o f astronomical oeulnrs, t w o anastigmatic photogrnphic objectives n?id sucli viirroacope yarts u s o B ~ r t r a n d l e n n . a wido npertclre achromntic condpnsvr and (1 1 2 ?nm. achromatic obiuctive. H P hns mnde a big paraboloid, t w o f / l ~ p h r r e snnd aboztt 50 pats. H e dislikes to w r i t e Z e t t ~ r s . - E d .
FEATS
131
Acccaaci For mnny npplicntions, t h r "quartrr-wave" lirnit of accuracy is sufficient. This applies to pliotograpliic filters, diagontils, prism faces and the plane surfaces of objcctivrs. For interferometer p1;ine.s 2 . 0 5 wave is none too flat21 and surf;iccs slioiild be p;ir:illel 2 . 1 mnve per incli. For coelostiit mirrors and for tlie outhide reflecting planes of telescopcs, huch as tlic Gcrrish, tlie acceptccl lirnit of error is e.1 w;ive. Freedoni from zori;il and periodic errors is assiimed. Pitine mirrors used iri the trsting of parnboloitls antl of completed telesco~~es a t tiirir foci must I>e of liigli quality a s regírrtls srnootliiiess o f figure (c0.1 w;ire rn;~rimurn),biit iiriiform sphericity of the order of c 1 to 10 waves can be tolerated, del~enclirigupoii the applicirtion. The supgestions offered in the abore short article a r e admittedly sketcliy and perhaps incornplete ancl the methods offered will be considered incorrect by some. T1iei;e criticisms are t o be expected, for the subject of flats can be thorouglilp treated only in a large volume writtrn by a triie master of the art, and tlie writer could by no means arrogate t o himself this title. 21 IIiclielson-"Studies i n Optica," 1927. 22 >I~liiistroiii, K1.i.. 81.i.I ~ i a t s . , \-. 7 . So. 5 ( 1 9 3 6 ) , PP. 216-7. Describes ver9 einctlg tlie riietkiod of sCpnratiun of exteriially aiid internally reflected images.
siic.
132
ASPHERIC SURFACES
N o t e s on the Optical T e s t i n g of Aspheric Surfaces The amateur telescope maker has at his command methods of testing spheres, paraboloids, hyperboloids, ellipsoids :~nd planes which are amply precise and thoroughly satisfactory. Many sucli metliods, however, depend on visual acuity, ocular contrast sensibility and personal judgment of geometric forms. These apparently new test methods a r e different, in t h a t they give results in terms of measurement and are, therefore, in some cases preferable to Hb
other methods. No crying need for these methods exists-they a r e not necessary f o r most work. Tliey are published here as possible aids t o the advanced amateur in solving specialized problems, and as "different" methods by which otlier methods iriny be cliecl<ed by the hobbyist wliose eartlily joys a r e rnathematics and optical esperimeiitation. The ellipsoid: The ellipsoid is, by dcfinition, the conic of revolution which will bring al1 rays cmanating from :I point to a focus a t aiiotlier point. The secondary mirror of a Gregori:in sliould h a r e an ellipsoidal figure. The common methods of trstirig ellipsoidal surfaces (Kirkham's, Hindle's and Foucault's) yield results of higli precision and are satisfactory. The criterion of perfection is the degree t o wliicli the surface approaches apparent flatness under the knife-edge, or the degree to whicli the bands approach straightness and parallelism if the tests of Jentscli or Ronchi are used.
133
ASPHERIC SURFACES
I t seems, however, that mnny experimenters find the judgment of flatness and straightness difficult and prefer a method of measurement. Also, instnnces may he found in which a definite amourit of under- or over-correction is desired. Such a metliod is outlined below, with the usual matliernatical developmerit. The only variables considered a r e tlie easily-measured distances, P, P', rll and D, tlie distance of the source. I n Figure 1, HI>SoH'I>is a n ellipse symmetrically described about o, the interiection of the x asis with tlie !/ axis. and I.', are the foci. V1lTltis the tnngent a t 11%. H I L S , bis the rn
a
=
OSo b
x2
y2 + b, = 1
=
OHb
In terms of P, P' and x, a 2 =
(P'
+ P ) d P I P - r2
=
y
=
z = OS.
bda2 - x2 a
a d b 2 - y2
5 =
b
xb dy = clx aJa2 .\/m
y = HnSn
P '+P b -
=
2
z2
dy - 2 P P J K r 2 --
+
2~P'P dz r(P1 Pl In t h e figure, H n C n is L V n T n . ' . L C n H n FZ = / C n H n F i Also/ S n H n C n = LH n V n ~n .'. / S n H n F'n = 2 H n V n S n S n Hn F', 2 tan H n V n S n - tan S n H n F', tan2 H n V n S n then tan S n H n F'n = 1 - tan2 H n V n S n + 2 tan H n V n S n tan S n tan S n H n Ff2 Hn Ff,
+
but tan H n V n S n = dy - = 2dP'
D - So S n
dx
, or
dP' - rZ and tan Sn Hn F12 r(P' P)
+
=
ASPHERIC SURFACES
134
Z D- ~ (P' tan Sn Hn F'% = ----and, since tan Sn Hn F'n
=
+P P ) (qPrF- dm) 2r d-p'P
Sn F'n
---,
+
+
r 2 ( ~ ' p ) [ 8 ( 4 P > ) ~ d P ' P - P-D~P P)+ ( 2 ;~'=p. (P' P)%[r2 - 2 ~FP~\/PIP-T 4 m ( P t - P ) 2 - d P ' P - r2(P' P)21 l+(dP'P ) 2 ( , / P 1 P - r2)2
Sn F'n =
+
+
+
+
~ ( 4 ~ ~ 7 - P 4)4 ?P]P .\/PTP-rr2 [D(P'
SoS n
=
+ P ) - y P'P~P'P?] (P' + P ) ]
}
+ P) + drPP' + P (P' + P ) d OSO - OSn = - dPCP(P' --
[ZD~P'
P~
P T P 3 a4pfP
-
2
Then A F' (from center to edge) = P - Sn F'n - So S n and A F' (fromzone A to zone B) = SBF'u So SB - SA FIA - SOSA where A is the inner, and B the outer zone.
+
Although the formulae a r e Iengtliy and appear to be complex, application requires nothiiig rnore than arithnietic tind the average example can be applied in an hour or two, once tlie distantes P, P', r and U are known. The ellipsoid can be tested a t "center of curvature," also, in which case, the lamp and knife-edge will more together from C n toward S o t o Co through the distance AC, which equals O('o - OCn.
T e s t i n g the paraboloid o n n e a r objerts: A t tinies it may he desirable t o test a telescope mirror or a complete telescope on a liglit source not situate at eitlier center of curxature or a t infinity. The forniulae developed below make such testirig simple. I n Figure 2, V n T n is t a ~ i g e n tt o the curve at Hn. H n C n is normal t o the tangent. c a I I n F is the normal rny path. F2HnF1n is the new ray path. Let S n H n = rn, the nienn radiui of zone 11, = y. So F = P, the equivnlent facial length. Hn C n = Rn, tlie radius of curvature of zorie n. S o P2 = D, tlie axial distanre of the soiirce froiri tlie mirror. the coordiriates of tlir pciiiit I I n . Xj Y
Equation of curve:
y2 =
4 Px
dy dZ
=
d P / x - = tan Hn V n Sn
=
V n Sn
then tan H n C n S n but x
=
r2
4P
Al\«, hiiicr
=
dx/P
S n Cn
SO S n
=
=
2 and Sn Cn
=
2 P and So Co
r2 Co C n 4 P'
x = --
=
Sn Cn =
2P
Ac
=
=
r4 F
-= v'x
r -,which 4P
is the usual
forrniil;~pii ing tlie nio~ernentof the kiiife-edge nncl wiirce together. Here it is interesting to note thtit tlie niirror depth is equal to the knife-edge travel.
FIGURE 2 Parn boloid.
If the soiirce is nt infinitg, tlie triie parziholoid will appear to be flat and evenlg illiimiri;itrd if ohservecl frorn F. When the sourcc is moved toward the rriirror, tlie apparent figure clianges and the blade must be moved t o a new position f o r e a d i zone. The difference of pobition for two zones is denoted SF a n d can be determined by use of the formula derived below:
tan F H n F'n
=
r
.'. tan S n H n F'n S n F'n -= r
=
4 Pr 4DP-r2
t a n ' ( ~H nnF -
= =
+ F H n F'n)
+ 3 Pr2) +r4 16 P2 r ( D P) 4 P(4 DP2 - DrZ + 3 Pr2) 4- r4 16P2(D P) 16 DP3 + 8 P2 r2+ r4
4 P(4 DP2 - Dr2
then S n F'n and So FIn
-
D-SoSn
--
-
16 P2 ( D
-
P)
=
ASPHERIC S17HFACES
136
when r = o, So F'n
:.
=
So F'o
DP D-P
= --
A F' (between center and edge) 4- r2)
= So
F'n - S o F'o =
~'(8
76-p (DL-p)
Unleis special equipment iq used, hoxc~ever, the center is not available, being blocked by a prism or by a diagonal. I t then hecomes necessary t o determine tlie foca1 differencc of tu70 extra-axial zones. M'liere A is tlie outer, and B, the inner zone, tlie equation becomes:
A F'
(between zones A a n d B)
=
r2.4(8P2
--
+
@A)
- r*1i(8P2
+ 1%)
16 P2(D - P )
Quantitntive t e s t of hyperl>oloirl«.l ~ n i r r o r a : Several experirnenters have recomrnended testing hyperboloids from the b-ck, among them, Ellison and the 1,owers. Tlie test has been but a visutil exarnination for i~iiootliiiriso f figure, liowe\c.r, ?iiitl rrieasureriierit of zoiial foci lias riot beeri attriopted.
I n 193.5, Robert Russell, in unpublished work, attempted to make such testing practical. I t is to Russell that the writer is indebted for the idea of developing a quantitative test. Such an idea had never occurred t o him before he was allowed to criticize Russeli's work'. I n Figure 3, VnV'n is the tangent to the hyperbola SoHnA a t Iín. HnXn is the normal. S o l o is the axial thickness of the denser medium. H n S n is the perpendicular to the axis from Hn. As is usual nitti Cassegrain telescopes, F3So = P' and S o F l = P. L e t Hn S n = rn, t h e radius of zone n, = y So l o = T, t h e thickness, axially of glass (or of glass a n d liquid. e s in t h e King Test.)
x, y
=
Equation of curve:
the coordinates of Hn x2 y2
~ - F = I
dy-
y=
b d x 2 - a2 a
x
P'P O Sn =---(P' - P ) d2 dP' P
=
. . tan H n X n Sn Since O Sn
=
P'
-
0 So
xb - a2
dx -
+ r2
dy = tan H n Vn S n
dx
r(P' - P ) 2 .\/P-FdP1 P
= --
(P' - P ) d P ' P
.2
4
m
+ r2 --
+ r2
'
,
P
+
P rz (P' - P )
-- and Sn X n = 2 x / = 4 P 1
=
2
. So S n
=
+ r2
(P' - P)(,/Pf P 2
So X n = So S n - Sn X n
-
,/m
y'P')
=
(P' - P ) ~ ( ~ P ' - F ~ --T TdPTP) + 4 P' P d P ' P 2 dP7P(P' -P ) 2 P' P When r = O, So X n = So Xo = , P - P .'. A R
=
(for zero thickness)
=
So X n
- So Xo
+ rz
=
(P' + P ) Z d( m r i - ,EP) 2 d P ' P (P' - P ) LTsirip the above as a basis, I R cna be cnlculnted for hyperboloida of I;n«wn tliickness and refractive index (n.,) as follows:
+
(SOX n - T)t / r 2 Sn xn2- nz2 7% n2 S n X n So Xo - T and IOX'o = ---n2
10X'n
=
ASPHEItIC SURFACES
138
Then A R
=
l o X'n - l o X'o
$(SOX n - T)drL+
=
snXn" n2 Sn
,,
nJ7rr] - Sn X n (So Xo - T ) Xn
SiiI)stitutirig iind rearranging,
=
[(P' + P ) ~ , / P ~ + --T (P' ~ - P ) ,/P('2T
.-
+
n?(P1 - P)?]
+
4r'[(P1 P)2 4 pqpz 4n2P' P (P' - P ) dP'pP+7 -4 p f Pd\/P' P
+ r2 ( 2 P'
P - TP'
+ T P)
+ P'
- P)]
Hou' to & l a l i ~Rouge US IIOL
There are but three iron oxides wliich iriterest us-ferrous oxide, F e o , wliich is an intermediate oxidizing in air to ferric oxide, Fe203, wllich is red rouge. F e z 0 3 can be changed to ferrous ferrite, FeOFe203, which is black "rouge." S e x t , conimon rouge and liow it is macle: a. Ferrous sulfate, copperas, FeS04, can be ignited in air to form ferric oxide. Product batl. Retlction: 4FeS0, O2 -+ 2Fe203 4 S 0 3 b. Ferrous liy
+
+
+
+
+
+
+ +
+
+
+
+
+
+ +
+
[E~IToR's NOTE: AS the attentive reader will have noted, tliere are several points in the note on the precedinp page :rt wliich additional instructions niiglit Iiave been inserted. For exaniplr, ,just how t o "igtiite out of contact with air," also how to handle tlie low an(1 Iiigh ignition temper;rtures mentioned. Accordingly, it n a s suppested t o tlie author, wlio is a chernist, that Iie expand somewliat oii these points. His reply was tliat most of "tliose who do not find it possible to rnakr rouge from the d a t a given would only bungle the job if told how to do it. Probribly," Iie continued, "a certain background of laboratory experienre is needed, so why iiot liead the story 'For those chem. hounds alone wlio want t o experiment with rouge making, we give is cheaper t o buy this dope. For otliers, if it isn't clear, better not try-it rouge, anyway.' " No duubt this is trire, but it still is not entirely in accordance with the nature of Iiunian niitiire. Past editorial esperience with the huinan race in general indicates that many will not take such a no for answer, especially where tlie situation cont:iiiis something of a challenpe. Hence tlie likrlihood was foreseen that, down throuph future years, many inquiries would be addressed to author and publislier, each asking for "full details" on rouge rnnking laboratory teclinic, and so the rnatter was referrecl to Dr. S. H . Sheib of Richmond, anotlier chemist-telescope maker, for opinion. I l e replied, "1 think Selby is exactly right. Give thern warning that rouge makinp is not as easy as it looks and tliat, unless tliey have kiad a year of lab. work, preferably two, tliey had better not tackle it. If then tliey insist on doing it, let them prepare for i t by studying in the Lib. This sort of work must be done in a properly equipped laboratory. Take, for example, igniting ~ u of t contact witli air. That means heating in a metal bomb with a tightly fitting screw top; or else, if every trace of air rnust he removed, some sort of refractory container provided with air inlet and outlet tube by means of which the air may be swept out by passing some inert gas through tlie container. I t is not a job for a beginner. This thing isn't like silvering, for which one requires only a pan and a couple of tumblers. Here yoti nerd pretty complete and expensive equipment-gas gerierators, combustion furnace, etc., and it fundamental working knowledge of chemistry." Doubtless by this time some are sure they want t o t r y t o make rouge. Hence, if you are one of these, good luck, and may no hard-hearted cynic label your product road ballust.]
SMALL L E N S U'RINKLES
Small Lens
Wrinkles
Judging from the letters 1 receire from me11 w11o hare made their mirrors, and are now contem~ilatingor actually miiking tlieir eyepieces, it would seem that ari increased interest has s p r u ~ i gu p among arnateurs wlio desire t o complete their entire teleícol>e~witli tlieir own Iionds. 1 llave for years urged mirror ~ n ~ k e tros t r y their hand a t small lens making, telling thein that the difficulties a r e no greater, and t h a t the fun is just a s great. 1 have picked
u p a few more ideas on the subject since y r i t i n g the cliapter on eyepieces (page 66, "Amateur Telescope Making,") and am here offering them t o the "fraternity," along with a description of the spindle 1 have been using here a t Pasadena the past few years. Figure 1 shows the general set-up, the spindle and motor bolted t o a cast iron slab. The motor is 1 h.p. (1726 r.p.m.) giving arnple power for the larger work running iip to 21,"" dismeter. TIie spindle is 6" long, X6'' in diametei and runs in baii bearings. The dish ,4 is removable, and a horizontal stud at R allows turning the spindle easily into a horizontal position f o r centering work. The di\h can be claniped, C, in any azimuth so as t o bring the lerer a r m D t o the most comfortable pnsition. The lerer a r m is provided with a universal joint E, and the rod itself can be slid endwise and rocked, so as t o bring the pin P, carrying the lens, t o just the right place over the lap. Two pulleys on tlie motor and two on the spindle, of 5/aW, l", ll/L>",and 2" diameter, allow a v i d e range of speeds for tlie different sized lenses.
1 experience
of a liirge macliiiie sliop. Tlie patterns were al1 expensively cored, the castiiips nlu~ninum. Rut thc rssenti;il features .;lioiild be retained-nnmely, a smootli ri~nningspinclle (plwiil bearinps will do, 11ut rriust be kept earefully oiled and protected frorii g r i t ) , a smooth ronning brlt, ;i detaclinble dish, and provisiion for bringirig the spin
SMALL LENS IVRIYKLES
143
with a surface that comes to a polisli in a few moments. Scrutchrs iisually show u p with 600 Carbo. A fruitful cause is letting the lap 1)ecome too dry. ~t doesn't take long for tlie rapidly rotating tool :iiid s11iiiiiiiig leris to rnove the lubricant ;rw;iy from their central areas. Should tlie worst 11;il)pe.. the lens will seize to tlie pitch, tlie pin on tlie lever arin will jurnp out of its pivot, and tlie lens 11i;ry fly off into tlie disli ancl vcry likely suffer ;r chipped edge. Perliaps a hardwood disli, or a dish of sorne material that will cushion such a blo\v, \voulcl be adrisnble. 1 find it pays tu (lo sorrie tliorougli house cleniiirip wlieri clikiriging from one p a d e to one finer, also that it I>aus t o put down fresli riewspapers, t o
scrub the liands well witli a scrubbing brush and clean the finger nails. Y y four grades of abra5ives are kept in four glass cups-caster cups-(at tlie five-and-ten, a t a nickel each). I ground their edges on a sheet of window glass, then cut u p the window glass into cover plates for them. I n polishing I cover tlie tool, or lap, with only about Iji<;" of rather hard pitch and, wliile still warm and rotating on tlie spindle, smooth it u p t o shape with it5 mate (wetted). The prepared fine-ground lens wfil do about as well. The rouge polishes faster if the pitch is rechanneled often. I t only takes a moment with the blade of a pen knife, and Figure 3 shons the way 1 do it. The pitch a t the center of the tool cdn well be removed, for it permits tlie pitcli under pressure to flow toward the center as well as tlie edge. The tyro must n o i k out his own salvation until Iie kriowc jiist liow far t o let his spinning lens move away from the center of tlie rapidly revolving tool, in order t o have tlie polish conie u p evenly on tlie glass. H e will notice that, witli the center of the lens directly over the center of the tool, tliey
a r e hoth going a t the snme r.1j.m.-thry are trs one-and no action is taking place. Theoretically, itnd assuining perfect contact and also assuming that the tool retains its shnpe (wliich it nvver does), ;L position for the lens center from the tool center will he found wheri tlie lens censes t o spin and cornes t o rest, and beyond that critica1 poini it will s t a r t spinning in tlie other direction. But pitch, :is rnirror makers know to their sorrow, is queer stuff, and possessed of seven devils, and oiie must find for himself about Iiow f a r the lens should pass across the tool. What is :ictii;illy tnking pl:ice between the glass and pitch surfaces is rather complicated. In Figure 6, b, witli the tool rot:rtinp anti-clockwise as shown, tlie areirs on the ton1 tit :f t ~ n d(' \vil1 tend to gire the lens tlie same rotation as the tool. But around B the tendency of ihe tool is t o t u r n the
lens in the opposite manner, namrly, cloclí~vi~e. Rloreorer, heat is heing generated, the pitch is floning, and the slope of tlie surfaces is continually changing with the stroke. In general it can be said tliat enlarging the central cavity in the tool will bring more of the polishing action to the outer parts of the lens, and trimming down the size of the tool to less tliari that of the lens will have the opposite effect. The length of stroke i.;, of course, important. As with niirrors, it is de
SMALL LENS WHINK1,ES
145
doublet-are viewed untler monochromatic light. The interference rings a r e not evenly spaced, there are too niany of them, and they depart from circles a s the lenses are rnoved eccentric t o eacli otlier. Centering comes next. When the lenses are polished, the dish is removed, the clamping nut H (Figure 4 ) unscrewed and the spindle brought horizontal. F o r centeririg 1 use an attachment (Figure S) that slips over the seat formerly occupied by the dish. This gadget comprises the rod I í carrying the edging plate L and a screw df acting against an arrn of K, and the guard N. The right adapter ( A , in c, Figure 6 ) is pressed on the tapered spindle end anti a little liot pitch dauhed on the flange a t B. With the flame of a bunseii burner (Figure 6)-nn alcohol lamp will do as well-the adapter and spindle end a r e given a warming and tlie lens cemented against the flange B (Figure
6, e ) . 2 y giving the qpindle a fetv turns and loolring a t {he lens, the reflections froni the lens (of different parts in the room, lights, and so on) will he seen to uuhble. The lens is then moved a triAe on its aeat and tlie spiiidle again given a turn. If qou llave reduced the wobble-if the reflections show less moremrnt-you nioved the lens in tlie riglit direction. If not, and i t has increased, you ha\re made a b a d matter worse. A few tries and the secret is out and you know which may t o move the lens t o reduce the wobhle and finally t o wipe it out altoprther. UThat you see in the lens a5 it rotates rernainq fixed. The axes of tlie spindle and the lens coincide. Probably the pitch has cooled off before the joh is done, but a few pnsses of the flame allow the adjustment to be cnrried on indefinitely. W e a r e now ready t o edge tlie lens. On goes the edging plate L (Figure S), and the screw ,lI is advanced until the edging plate just touches the lens. The disli is placed as shown, witli some 1 F Carbo and water in it, and a
146
SMALI, L E N S \VRTNKI,ES
spoon. The motor is started, the giiard N droliped nn(1 tlie C n r l ~ ospooned on t o the edging plate. As thc pltite is hrouglit t o hear on tlie leiis under tlie action of screw Jl, and th? Cart)o is dri~pgerl under tlic lens edge, the e a r detects a vibration of tlie plate ciur t o tlie poiintlirig c;iiii tictioii of the lens. I n a short tinie, as tlie gl:iss lrenrs clown, tliis poiin(ling (lihappenrc and one has only to ~ i ~ t cwitli h an outsicle calipers (O, Figure 5 ) for tlie
Iens to come do\vri to thc required diameter. The lens is removed undcr a little hent, placed in kerosene (or gasolene) orer niplit, wlieri it c:rn he wtished clenn with soap and water. UThat 1 Iiare here described (as well ÍIS in Chnpter 91, page 66, "A.'T.>I.") tire tlie \vriiikles and metliods worked out by niyself witliout beiiig prt.jiidice(l by a knowledge of professional practice. Undoubtedly sorne of tliern will appetrr crucle and amiising to the professional. For exnmple, it rii:iy he tliat a better way of making t~ lens run t r u e o11 a spindle is t o use a fork ( ( 1 , Figure 6 ) and, as explained on ptiges 69-70, "A.T.M.," 1 llave usecl therri hotli, but 1 rernemher a h:i(l scratch that developed when 1 used the forlc. Tliere m:iy be other simplrr tina more ortliodox ways, hut it's heen lots of fun ~vorkingout one's own technic. To me a lens is a \von
An Introduction to Small Lenses By R . E , C ' I . . ~ I Z I <
The practica1 instructions on small lens making piven in the popular books on telescope making do not go into enougli clctail to ennhle a beginner to make a really sotisfactory lens. Nrarly al1 amateur? retluire minutely detniled instructions to start with, hut with practice tliey become more expert, and find their own w:ty around the pitfnlls which are sure to develop. The makinp of optical goods is one of the most highly specialized crafts there is, tind yet your ordirittry amateur usually expects t o go ahead and do first-clttss work, practic:~lly without instructions. The following notes and sketches a r e the result of several years of practical lens making experierice tind, what is more important, contain the answers to nunihrrless questions put t o me by otlier amateurs. 1 woul
148
SMALL L E N S E S
Chasrr's cemrnt, optician's tools, etc.: Wm. Dixon Pz Sons, 34 Kinney St., Newark, New Jersey. Surfacing machine: Shuron Optical Co., Geneva, New York.
It is the usual procedure in starting an article of this nature to give a list of tools and materials. The following list takes care of the absolute necessities, and your ingenuity will probably suggest a nurnber of variatiuris, any or al1 of which may or may not be in order. Try them, anyway; i t may add a small measure of zest t o your other tribulations. First and foremost is a small engine lathe, which should be capable of handling work 8" in diameter. Length of bed is of little consequence, as
FIGLRE 1 Lpft . Grinding stand. Right
:
Vertical spindlr.
most of your work is under 18" long. I t should be equipped with a four-jaw independent chuck, be capable of cutting u p t o 40 threads per inch, and be adjustable for turning a t v e r . Several such lathe.; are on the niarket, costing a t present (193.5), complete with motor, ahoiit $100.00. Get as good a machine as you can possibly afford. Practically al1 the operations of lens making can be done on a lathe, but i t is not wise or advisable t o use such a machirie for glass workirig, as a good engine lathe is easily ruined by Carborundum and water and, conversely, a gnod len5 will be iitterly riiined i f it is dropped on the iron bed of the lathe. A lathe is, however, an absolute necessity for turning and truing laps and gages, and in making moiintings for your finished lenses. Acces~ories for the lathe should include a cut-off toul, a niedium knurl, and a Jacobs or other first-class chuck capable of taking a 1/2" drill. Purchase a small double-ended prinding stand (mail order house-Montgomery W a r d & Co., Sears Roebuck & Co., etc., see Figure 1, left), equip on one side with a 1" face, 80 grit, Grade G5, 6" diameter Carborundum wheel, and arrange a splash pan and guard for wet griiicling. Tlie other end of
SMALL L E N S E S
149
the spindle should have a vitrifird bond Carbnrundum wheel-about 60 grit, i/," face. This last is used for tool sharperiing and niiscellaneous grinding; i t is used without water. When buying your stand, purchase a wheel dresser -true wlirels are essential. Tliis point cannot be emphasized too strongly, as a wobhly wheel is an abornin:ition, and will simply result in broken glass and sore fingers. Do not over-speed your wheels, also keep your head to one side while grinding, since serious injury can result if a whccl breaks. The tliird essentid tool is a vertical spindle (Figure 1, riglit), arranged. to run a t four speeds: 100, 300, 500 and 700 r.p.m., and havirig a t its upper end a taper and ün internal, female thread, into or over which your various laps will fit. If you live near a larger city, arrange to vi& a manufacturing optical shop o r a spectacle grinder's. Ask t o see a "surfacing machine." Ten
Glose-up of spirdle shown i n Pigurs 1 . Some of tho small work to be described luter in t h e chapter shows below i t .
rninutes' close observation will give you more dope than a whole chapter of instructions. Notice particularly the arrangement for stopping and starting, by means of a knee or foot switch ( 1 iise an auto dimmer switch which, although built f o r 6 volts, has lasted three years with 110 volts). Also notice the means by which tlie pin bar is swivelled, also the adjustment of the pin on the bar. A few judicious questioiis will elicit a world of information. l f you are one of tliose fortunate people who have lots of money, by al1 means buy a factory-made surfacing machine. However, we shall. take it for granted t h a t you will make your own spindle. The photograplis and drawings should make clear the general arrangement.
150
SMALL LENSES
To m;tke orie, procure ttn olcl Ford gerierator, Model A-1929, arid strip al1 the coils from thc case, nlso rt-moke everytliing froiii thr sli:~ft except ilie hetiring concs. I3e ccireful not to bend tlie sliaft. Ssve al1 the screws and mil1 be used in reasseml~ling. Clean thoroughly and reassemble. holts-they Both ends of these shafts have a taper. Buy a die-cast, 6" diameter, "V"
S ~ E P/0/6 EI 17ia24
A11 drawings by tlie author
Sh/crsh -
Fao
- /e-6
Cob,á.
FIGURE 3 Details of t h e ~ r r t i e n ls p i n d l e .
helt wheel (mail order house-nbout 75$) and taper the bore accurately to fit the end of the shaft which projects from tlie open end of the generator case. Fasten with the original cap screw and washer. Also dril1 and t a p the hub of the wheel for a %" set screw, making a good tight job. Place betwcen the centers in your Iathe and t r u e iip tlie groove and rim of the wheel with the axis of the shaft hearings. Tlie other end of the shaft will carry your laps and should be equipped with a tapered nosepiece and splash guard (Figures 2, 3, 4). Ttiis splasli guard acts as a deflector and keeps grit and dirt away from tlie spindle bearings. It is made slightly larger in diameter than the central hole in your grinding pan. Procure three pieces of 2" x 2" x '/a" angle irqn 1" long and fasten thcm
SMALL LENSES
FIGURE4 Details of t h e veittcal spindle.
152
SMALL LENSES
form feet (with the coi1 screws) t o tlie outside of tlie generator case-tliese (Figure 4), wliich in turn will be bolted t o blocks mounted on your work bench. A piece of %" boiler plate 8" wide and 17" long is next fitted on the iipper side of the generator case anrl firmly bolted t o it. This plate forms the table for your splash pan, and also has screwed into i t the pin bar shaft. The assembly and details of these pieces is sliown in Figures 3, 4, 5 ar.d photo of the author's spindle (Figure 2 ) which shows the splash pan in position. The foregoing three machines-lathe, grinding stand and vertical spindlea r e iriclisperisable. A small drill press will prove very useful, but is not absolutely necessnry. If, a s 1 imagine, you are already a hobbyist, you doubtless have sorne of the following hand tools and materials: 2" micrometer witli ari adapter Lo lake from O" t o 1". A 6" steel scale or combination square with scale and centering head. (Fig. 21380, Wm. D. & Co.-42.40). One double-ended brass calipers for gaging lenses. (Fig. 21315 Wm. D. & Co.-25 cents *). One each, iriside and outside, 4" screw-adjusting calipers. (Fig. 21558-9, Wm. D. & Co.-$1.10 ea.). One small center drill. One thrend gage. Some 6" and 8" srnooth files, also severa1 old files 6" t o 10" long (to make into scrapers and hand tools). 1 lb. pine or coa1 t a r pitch. y' Ih. Chaser's cement-black. (Fig. 20387-2-354, Wrn. D. & Co.). 1 jeweller's loupe, I1/?" focus ( a good magnifying glass will serve). (Wm. D. & Co., Fig. 21512 No. 8-75 cents). 1 alcohol l a r ~ i por bunsen burner. 1 lb. each, No. 80-220-F-600 Carborundum grains (buy original packages) (Carhorundurn Company, ~ i a g a r aFalls, N. Y.-50 cents lb.). 1 lb. No. 6 F ernery (Hamilton Emery Co., 30 Church St., New York). 1 lb. rouge, M309 (American Optical Co., Southbridge, Mass.). Severa1 pieces thin brass sheet, 16 or 18 gage (scraps 3" wide or over are large enough) (Williams & Co., Pittsburgli, Pa.). Brass tubing-al1 &'' wall, in 12" lengths and the following diameters:
%", 3/sV, %", %". Brass tubing (for eyepiece mouuts), 1/16'' wall, l1L" 0.D.-24" lerigtlis. Brass tubing for adapter tubes, +$-" wall 1%" 1.D.--12" lengths. This last item should telescope easily over the 11/4" eyepiece tubing. Al1 of the
* The anthor states prices as o£ 1935, but many of the'se will vary from time to time. Therefore prospective purchasers perhaps had best obtain current prices before remitting. The arnounts statrd above will nevertheless, serve to gire a general idea of eost6.-Ed.
.~!pu.s
iu?)$.Lan ay? / o El?v?gQ g
wnory
:~hovc.sizes of tiihing may he prcicurecl frorn Desley & Company, 118 N. Clinton St., Chicago, Illinois. 6" each rolled brass b a r 1%", 1Yz" and 2" diameter. Come odd pieces of cold rolled steel from 1" t o 2" in diameter.
1 will endeavor t o explain hriefly the re1at:onship t h a t exists hetween the curve of n lens ;~ri
f
f
FIGVRE 6
L p f t : Plono.concex l e n ~( f = Z l ¿ ) . R i g l ~ t : Plano-concnva lens f f = Z R ) .
not only unnecessary here, hiit will prore bewildering and can serve no useful purpose. I f , howevcr, you are o f 21 mathematical t u r n of mind, see the articles in the latest "Encyclopedia Britannica" under ("Lenses," 13th ecl., 6 pp., and under "Microscope," 13th ed., 10 pp.) or in Conrady's Works, etc.
The focus of a lens is that point t o which the lens will converge parallel rags of liglit. Figure 6, at left, is a sketch of a plano-convex lens. 11s F
FIGTRE7 L p f t : B i - c o n ~ e xlrn? ( f = R ) .
Righ t : Bi-concaue lens ( f = R )
(or foca1 length) is for al1 practica1 purposes equal t o the diameter of the sphere or circle of which its curved surface forms a part. Thus, in the
SMALL L E N S E S
155
illustration, if the circle is of 1" radius, thc F of the plano-convex lens would be 2". I n otlier words, F = 21t. Exactly tli<. sarrir rrlatiorisliip rxists in tlie l~l;~~ici-coiic;ive lens illustrated in Figure 6, right, except that this has only U virtual (imaginary) focus and
Left : Crossed conz'ex lens ( f = 1 . 3 3 " ) .
Right
.
C r o s s ~ d concavr lrns.
cannot by itself cause tlie convergente of rnys t o a point; it actunlly causes a divergeiice. A bi-convex lens, Figiire 7, left, liaving both curvei of the same radius, tias a fociis equal t o tliat radiiis ( F = R ) . A bi-coiivex lens wliich has the same rndius of curv:iture 21s a plano-convex has, therefore, only of one half its f»c:il length. This also hold? t r u e in the case of :L bi-concave or doublecoiir:tve lens (Figure 7, right). l'he refractive index of tlie glass used has not beeri considered in the ahove figures. Tlie result, hou,ever, is very nearly exactly as stated, with ordinary crown or plate gluss.
Left: Positivr m ~ n i s e u sZrns. Right
Plano-coni.cr a n d plnnu.concare.
To avoid the confiiqion whicli exists in mnny text5 on optics, t h r following convention has heen aclopted tlirougliout these notes: Al1 convex surfaces are plu5 :ind al1 concare surfaces a r e minus-this, regnrdless of the direction 6, impinging light rays. The focus of eitlier u crossed convex or concave lens (Figure 8, left, anS Figure 8, riglit) having curres of different radii, Inay be simply calculated as follow5:
SMALL L E N S E S
156
Ri equals thc radius of one curve and H2 equals the radius of the second curvc:
A s an example, the first radius, R1, is 2", the second radius, R2, is 1"'. Tlien :
'
= +$ or 1.333Ip, the foca1 length of the wliole lens. 2+1 1,erisrs may h a v ~one convex side and one concave side. If the convexity predoniinates, so tliat an imtige of a light is formed, then the lens is called a positive riieriiscus (Figure 9, a t left). I f tlie concavity predominates, it is called a negative meniscus. Thc above formula. is used t o calculate these ineiiiscus leiises, except that a plus sign sliould precede a conrcx radius and a mirius sign the concave radius. F o r those who a r e rusty in their mathemntics, remcmber that, when multiplyirig or dividing quniitities witli like signs, the product is plus. If the signs preceding the quantities differ, then tlie product will be minus. Wlien adding unlike signs, subtract onr from the otlier and affix the sign of the greater t o the answer. If both have lilce signs, tlie answer will have tliat sign. I n subtraction, change the sign of the qucintity subtracted, and add the quantities together. As an exaiii1ile, a meniscus lens has a plus (convexj radius of 2", a n d n minus (concave) radius of 3". Then:
It is ofteii necessary t o duplict~tea brolcen lens. This msy be m a n a g d in the fnllowing way: The tliickriess of the cunvex lens, or the depth of the concave lens, may be measured witli a micromcter or double calipers. Figure 9, right, represents in full line a plano-convex lens, while a plano-concnve leris is sliown in dotted line. D is the diameter, and T the thiclcness. The rrtdius of the curve will be-one fourth?the square of the diameter added t o the square of the thickness or drpth, and this sum divided by twice the thiclrness:
of
As an example: A plano-convex lens has a diameter of 1" and a thickness a t tlie center.
S''
1s i t is a plano-convex lens, the focus is twice the radius, or 1.25".
SMALL LENSES
157
Opticians iisr a splierorneter, :t smnll instriiment with three fixed legs and one movable graduated leg, for fincling tlie curve of lensrs. It is possible t o contiiiue givirig formulae and definitions but, a s mentioned
above, thcse are not necessary t o the bepiiiiier arid only serve cither t o bewilder him thorouphly or else discourage him completely.
W e will start with a definite purpohe in view-and will take as our exI t will have a focal length when ample a plano-convex l e n s of 1" radiii,. finished of 2" and it will be very useful as a mngnifirr in your other work. A thickness in the center of $VE1' will give a diameter of approximately 1%".
FIGURE11 Lpft Rras8 hnn(lle D .1/32" less thnn I D . of t u b i n g Cpnter blank m o u n t v d r e a d y for grtndzng. X t g h t Mountrd b l a n k .
Rough~d
Procure a piece of "Crystallex" plate glass (The Pittsburgh Piate Glass Company) several inrhes square a n d y'" thick. If this glass is not available, use ordinary windshield glass. Cut out, with a glass cutter, four pieces, each 1%" square. Break off the corners of these sqiiares with your pliers, so t h a t your blanks a r e roughly circular. Lightly grind one polished side of each on your wet Carborundum wheel (Figure 10).
Cut four pieces of y+" 1)r:lss tubing 2" long. Do this in your lathe, so that the ends will be syuare and siiiooth. Turn u p ;i small brass liandle with a shank 3/s" long and 2?4521' in diameter (Figure 11, left and center). 'I'his will give a n easy fit inside of %" tubing. A rttdius of ahout 1" will fit your palm, and will prevent blisters. Place your blariks over your burner, interposing a i/16"sheet of asbestos between them and the direct flame. Allow them to heat u p until, un toucliing a piece of Chaser's cement to tlie upper slightly ground surface, i t will melt and form un even coat al1 over. Remove from the heat and place on your work bench. A word here regarding your bench surface: Keep it clean, and covered paper which has a shiny finish is prefera t al1 times with paper-magazirie able t o newspaper. Take onc of your brass tubes and heat it. Apply Chaser's cement to one end, rotate in the flame and get a liberal quantity t o stick, place dircctly ori your still warm blank, center as closely a s you can, and allow to cool somewhat. With the mounted Iens in one Iiand, apply by rnelting ;trid dropping, come more Chaser's cement t o the hack of your blank. Carefully pass it through the naked flame and, with the moistened fingers, form :r neat smooth surfaced joint, Figure 11, right. Make sure of a good job, a s nothing is more annoying than t o have a lens fly from its holder. Set u p al1 four of your blanks. On your wet Carborundum stone grind each of your blanks as nearly circular as you can. Also shape the surface t o your trmplate as closely as possible. Allow perhaps ?/í6'' over your finished diameter for finishing. When roughing out your curve, it is well t o leave a spot of polish X6''or SO in diameter in the center of the blank. This will enable you t o keep yoiir roiigh curve fairly central.
3"x3", the other Cut two squares of 16- or 18-gage sheet hrass-one 2%" x25/4". Clean both witli eiriery paper. On one side of each, scratcli diagonal lines and lightly prickpunch the center. Next dril1 two I/g" lioles. Thrse holes a r e for stringing j o u r gages together-otherwise they will surely get lost. I f you have a sm:ill set of figure punches, mark the radiiis on each piece plainly. D o not wait until your gage is complete before punching your ~iiarks-to do so will inevitably lead tu distortion of your curves, which must be avoided a t al1 costs. C o n u ~ x ( M a l a ) Gages: I n the center of one side of your 2%" square, securely sweat a short piece of %" round hrass rnd (any small scrap that you can hold in your lathe chuck will do) and chuck it in your lathe, true u p by the corners and t u r n to exactly 2" diameter (use your mike). Bevel hoth sides of the edge %", leaviiig the edge wide. D o not attempt t o finish either the bevels or the edge with emery paper-use a sharp tool and get as true a circlc as possible. Concave (Femalo) Gages: Next, chuck your 3" square. Use just ennugh pressure t o hold the piece firmly. Center by your prick punch mark. Dril1
v,c
SMALL LENSES
159
and bore n 2" hole, hevel tlie sides %" back, leaving the rdge 7,4;4'' wide. A t the risk of being tiresonle 1 repeat: Do not use eniery paper on the edge of a sharp tool. Use your convex gage t o get a n accurate fit. the gage-use
A good push fit i s what you a t e ofter. Tnkc plenty of time ancl work accurately-l/looo" is too much between gages of this sizr. h'ext, use a hack saw (do not use shenrs or lirrrnmer and chisel) and cut in two on the line AB, Figiirc 12. This will give you two conrave gages. Bevel each corner %'' with a file. Check both gages against your convex
FIGURE1 3 Convex template, 16-gage.
gage, I f your work has heen accurate you should not be able t o see light between your güges when they arc held between the eye and a strong light. Figure 13 shours your finished gages. Small gagcs may also be bored and turned from solid bar stock.
160
SMAI,L LENSES
L n p M n n d r r l . Refore making a lap, i t will he well to make u p a fixture or jig. This will insure true rurining laps aiid i\ also a great time saver. Procure a piece of cold rolled steel 6" long ancl 1y8" in diameter. On one erid t u r n a standard taper t o fit your lathe spindle. Place the tapered en¿!
in your lathe spindle, face and turn the projecting end t o a taper of 1%" per foot (0.1854" p r r inch) for a distance of 1y2"; the end diameter heing ?/S" (0.875") and the larger diameter 1.078" (0.875 0.203). Between the two tapers t u r n t o 0.938". Bore and thread for a %" standard 11 thread t o a deptli of 1%". It is well t o mark your lathe compound rest with the exact
+
R I G ~ R E15
L e f t . Conves lap.
Right
Conenve l a p .
degrec of your 1y8"per foot taper. Your larger laps will be fitted over this taper, and marking your slide rest now will sare lots of time and troublc later. Figure 14 shows this taper mandrel. Laps: Chuck a piece of 1Y2" diameter brass or fine grained soft cast iron bar, uiing your tail stock center to steady the work. Turn t o 6/R" diameter fo- a distance of 5/8" (Figure 15). Relieve t o 7/i6" diameter and thread the y*'' portion. Make an easy running thread. I t is well t o get a standard 5/," bolt and n u t and t o use these as standards for al1 of your threads. Turn
down tlie next %" to 1" diameter, being siire that yoiir 1" cliametrr face is true. Dril1 or bore a 3/8" hole 3/4" vr 7/X" deep. Finiih tlie bottom of the iiole coniral. Cut off t o 1%" long over all. Make several of these lap blanks. Convrx L n p Place your t;iper iiiaiidrel (Figure 14) in your spindle and t a p it Iiome with a picre of wood. Screw a l a p blanlc into the projecting end. Tlie reason for square faces on your jig and Iaps is now apparent-if
FIGURE16 Hund tools.
they were not square, your l a p would wobble. Tiirn u p your curve as nearly as possible and finish with a hand tonl. Figure 1.5, a t left, shows a completed cvnvcx l a p and the same figure, a t right, shows a concave. üood hancl tools for finishing laps can be made from old flat files. Crind smooth on al1 four sides for about 2", ruund the end, a s shown in Figure 16, giving the end a r a k r of aboiit loo. IIeat red hot aiirl plunge in either water or kerosene oil. The tool sliown a t the left is for concave laps and the one a t the right for convex.
Left:
FIGVRF:17 Convex l a p . K i g k t :
Cnncare lnp.
Run your latlie fact when uqing these tools, and take extremely light scrapes. With a little practice a pair of laps can be accurately cuts-almost fitted to their templates and t o each other in a very sbort time. A smnll spot ?/16'' t o 1/8'' in diameter and perhaps ?(;4" deep shuuld be taken out of the center of al1 your laps. Very little prinding is done on this p a r t of the lap. This slight depression should be kept open a t al1 times. It serves as a reservoir arid aids in giping a better distribution of Carbo a n d emery. The foregoing instructioiis a r e fur rnaking a lap which screws into your
162
SMALL 1,ENSES
spindle. Tn making very sm;ill laps it is of advantnge to he ahlc t o use 7/8" or 1" rourid brass stock, thus making quite a s;ivinp in material and time over the gcricrally uscd female taper lap, tlie shank of wliicli has iii al1 cases to be itt least 1%" in diarneter. F o r laps 1%" or larger in outside diameter, tlie taper method of driving is f a r preferable. Procure a piece of 1%'' or 1%" ruund brass or cast iron stock, cbucl< and center c:irefully, turn t o IY!" diameter for a clistance of l", bore t o the s:rme depth, and very carefully t;ipcr tliis hore Iy8" per foot (see Figure 17, lower part of either dr:iwing). A small conical liole dcep slioulci be turned in tlie center of the bottom of the bore (this will enablc you t o spin one liip on another when grinding curres together). The diameter of your bore should be such t h a t there will be a space of '/'" t o 3/l(T between t!ie top of your inandrel nnd tlie hottoni of the bore wlirn tlie former is t:ipped into place. Dinieiisions of this t:iper bure are given in the snme drawings. Cut off yoiir hlank t o the desired length and finish the convex o r concave surface with the l a p mounted on your mandrel (Figure 14). It will probably save some little time, however, if you put the final finish on your laps by grinding them topether. Great care, however, should be exercised in doing this, as it is very ensy to get away from your template curve. After hand turning the laps as closely t o the templatc as you a r e able, screw the conrex lap in your spindle, moisten with water, and apply a little rnoist 220 Carhoriinduin. Place the convex l a p on top, adjust your pin bar horizontal, ancl your pin square t o the curve of the convex lap. Iiisert tlie pin in the 3/s" conicill-bottomed hole in the back of the conrave l a p and, with a back and forth movemeiit, allow the concnve l a p t o spin freely. TJse your lowest speed. After balf n minute stop your mnchine and wash u p the convex lap. Match it t o your template. Experience will teach you how long your laps sliould be run together. Should your concnve lap become too deep in the center, screw i t into tlie spindle and allow the convex to spin on top, or with the convex l a p in the spindle, and the concave helcl ;ilriiost, but not quite, central over it. Run together for a short time, wheh the edpes of the concave will become slightly flattened and so brouglit back to t h r template curve. Variations of position of tlie laps with regard to ench other, will be found t o have very different griiiding actions aiid, as ir1 mirror making, length of stroke, etc., will have very definite uses in altering yonr curve. It will be found in general, that in the earlier stages of grinding, a true l a p cannot be made t o generate a t r u e curve ori the glass. This may sound paradoxical, but it is nerertheless a fact. In making a con\.ex leris (either mounted on a hand holder o r by the spinning method) the glilss tends t o be toa high in the center. In other words, your curvc bccomcs of ;i snialler radius than its template. Iii ordcr t o offset this tendency, 1 alw;iys fit my concave laps so that they touch the teiriplate in the center anrl 1i;ir.e a few thousandths of an incli clearance a t the periphery. With a coiicavr lens tlie opposite tendency will be noted (that is, the lrns curve tends t o deepen too
murli in tlie csnter) :ind ttir template, therefore, should be inade t o fit tlie edpeh of tlie la11 arid be slightly ciear toward t h r center. Howevrr, if you are ;I begiriiier, it is advisable to get your laps ;is close to your trmplates and to each otlier as you possihly can. lioughing Out.' Screw y«iir concave l a p in tlie spindle, and a t 100 t o 200 r.p.m. proveed witli No. 80 Carborrin(l11m t o roiiglriiig your bl;ciiks t o ciirve. Keep moving your blank across the Inp in arcs, ílt the same time alluwing it t o rot:ite evcry once in a wliilc. un tlie br:iss handle, whicli shoiild he held in thc p:dm of your liarid. A little dextirity is reqiiirecl t o do this properly. From tinie t o time apply L: little Carborundum and water tu the plass. Keep it in firm contact :tnd examine frequently with your lens. Stop when no more marks of your preliniinary grinding on the C:rrborundum stone can be secn. Do not pay too rniich attention t o the curve a t this stape. Rouph out al1 four hlanks. Wash u p everytliing a n d place cleati papers on your bencli. A \vord here about your Carborundum. F o r each grade that you have, including eiiirry, procure a glass caster c u p about 2Y2" or 3" in diameter (5 :ind 10 ccnt store). Cut squares of window or plate glass '12"larger than the 0 . D . of the cups, and srnooth u p the edges of these pieces on your wet Carborundum stone. With a little 220 Car1)orundum and water, grind the edpes of each cup on onc of the sqiiarrs of glnss. \?'tisli u p thoroughly and keep each square gl:iss cover on its own individual Carborunduin cup a t al1 times. 1 have used these caster cups for several yeítrs, and after trying tin boxes, salt sliakers, sprinkler bottles, etc., 1 fully agree with hlr. Porter t h a t they are by f a r tlie best schenie so f a r devised tu keep your Carborundum uncontaminated. Mix a little water with each grade and use your fingers or a match stem t o apply the Carborundum t o the glass when grinding. A few drops of alcohol in the finely ground grades makes them easier to wet down, and 5 or 10 .percent of fine talcum in your 6F emery may save scratches. Be careful not t o get a roarser grade into the finer grade. Wash your h:irids frequently, keep your finger nails clean. Use plenty of changcs o f p:iper on your bench and bear in mind that, "cleanliness is away ahead of godliness" as a prevetitive of scratches. Your blanks a r e probably quite a bit off curve, especially the last one run. Take it, No. 4, and grind for 30 seconds -4th 220 Carborundum. Wasli, and t r y it with your template-if it i s nearer t o the curve than it was before this treatment, give i t a second short shot and repeat until no more improvement in the curve is apparent. Next, t:ike No. 3, No. 2, and No. 1, in that order. If, howrver, No. 4 does iiut begin t o come t o curve with 220, it is because your 80 grinrling wore something froin the surface of your lap, in which case your l a p will have t o be trued u p t o your template. Wash u p your Iap nnd place it in your lathe, usirig your taper mandrel. With a piece of emery paper polish the concave, a n d witli your hand tool proceed t o tiirn or scrape out t11:it portion of the lap mhich is too high. Go lightly, as probably one or tu70 thousandths of nn incli are al1 tliat it is necessary t o remove. If the polishing witli emrry cloth is omittcd, you will be unable t o make a hand tool cut tlie l a p ; a little fine Carborundum and
164
SMALL LENSES
glass has become irnbedded in the pores of the metal Iap from grinding, and uriless reinoved with emery paper, will spoil the edges of your tools in a fraction of a second. Wlicn you think that you a r e trued u p sufficiently, t r y a short wet with 220 on your No. 4 blank. If you llave gone too ftir in truing u p your lap your glass will be very likely t o become too shi~llow,wlicrr hefore it was ton deep, or vice versa. However, if fairly close, carry on and grind al1 four hlanks. Examine each one carefully with your magnifying glass for pits which are deeper tlian the general surface. The center usually takes care of itself and it is the edges which need watching closely. Wlicn no more deep pits can be seen, wash up, change papers, and s t a r t on your next graclc ( F ) . Tliis time, however, s t a r t gour series with No. 1 and work through to No. 4. Go through exactly the same procedure a s outlined above, truing u p your l a p if nerded. Watch carefully for large pits and srratches. Tlie 1;itter usually mean t h a t you have not been careful in cleaning up. Do not let your laps run dry, and do not use too much pressure-scratches will surely resiilt. Run your spindle on slow speed and true, easily polisiied surfaces sliould result. W h e i ~you feel satisfied that your F surfaces are as good as possible, wash u p carefully, spread clean papers and change t o 600 Carborundum. The curves on your lens must be truly spherical and must be an exact fit with your templates. If they are not i t will be a n impossibility t o make them take a good polish later on. True u p your laps, b y turning, as was done with the coarser grades, by grinding together under power or by grinding together by hand. This last metliod is not a s fast a s machine grinding but will, with patience, assure you of a good fit. Take the laps one in each hand and, mitli a little F Carborundum and water, rotate one on the other, first one hand tlieri tlie other. I t is slow and hard on the fingers. If you ~:ill take time t o make u p a couple of thimbles t o fit your lap threads, i t will be much easier on your fingers. Procure a couple of 5/h" standard nuts and turn the outside t o the shape shown in Figure 18. Starting with No. ,i'blnnk, proceed with No. 600 Cnrborundum until no pits whatever show on your qurfaces. Do not over-grind with 600, as i t is easy lo get away from your curve. Take short wets and be very sure t o keep things wet. Wash u p thoroughly, change papers, and gage carefiilly. ,Make a thick slurry of GF emery and water, about lialf as fluid as cream, dab a little on your l a p and some on the g1:iss blank, a n d run until alrnost dry. D o not pre's hard or scratclies will result. Do tliis witli fresli portions of eriiery tlirre or four times. Wasli and exainine closely. Tlie surface should be almost sntiny and if you uscd brass for your laps it will sliow a blackish sheen in the center. Glass, fine ground on cast iron laps, wi!l not have this semi-polished appearance but under the microscope i t shows just as fine a grain as a surface whicli has been finished on biass. Polisliing: Clean and wash u p your grinding stand, bench, hands, laps, and c\.crylhing e l c e iliat rniglit llave a speck of Carborundum on it.
Procure a smnll wicle-moiithcd jar-one with a good wide base so that it will not be casily upset-clean it very Clioroughly ;rnd mix iii it two or three teaspoonful\ of rouge n i t h w;iter. Your niixtiire slioiilcl be rathcr thicker than crezim-ici f:rct, it sboiild be of such consistency tlirrt a drop will riin with difficulty on a vertical glass plate. Procure a piece of sheet rubber (S" red sheet packing) 1" lürger than the mouth of the jar, pusli the halidle of
%" round camel's hair brush through t h r c e n t ~ rof the piece of rubber and you have as clean ;ind convenient n cover nnd daiiber as you can get. Meltdo not boil-rt small piece ( 1 oz.) of your pitch, strain throiigh two thicknesses of cheesecloth into a clean can. Continue heating until a cooled drop can scarcely be dented witli your finger nail. Get your pitch f a r h:rrder than you would use for mirror poiishing. Your pressures ancl friction are f a r greater in lens making, and 11:ird pitch is a necessity. Warm your lap just enough t o dispel the small droplets of moisture which sliow on its cool surface when held in an open flamr, wipe d r y and pour four or fivc drops of hot, liquid pitch into the center of tlie concnve. Paint one of your Ane-ground blanks with a little of your rouge mixture and a t once press i t directly on the warm pitch. Work the glass around so that the resultont pitch liip is perhaps ?&'' thick. Thiclc laps (I/g1' or SO) get out of shape very easily. If your pitch hardrns before you can prcss i t out properly, hold the l a p over tne open flame for a few seconds. P u t more rouge on your glass and press until your pit<:h coat is eveiily spread over the concave of your lap. Tliis operation can also be performed with the l a p running in your spindle. Cool the l a p off thoroughly under tlie t a p aiid screw into your spindle. Speed u p your machine t o 400 or 500 r.p.m. and with the sharp point of your pocket knife trim down the pitch Iap t o aboiit %'' in diameter. Use plenty of water while doing this. Also cut out a small circle from the center of the lap, %" t o 3/36'' in diarneter. Cut clear through the pitch, down to the metal of the lap. Also cut two or three circular grooves between this center hole and the edge. . Wash u p thorouglily. Paint your fine-ground blnnk with a good coat of rouge and, with your spindle running a t 400 or 500 r.p.m., prcss the glass firmly o11 the lap. Probably it will squeal and chatter for a few seconds. Press down fairly hard. Your lap will warm u p a
166
SMALL LENSES
some and, in so doing, the pitch will flow t o the exaet curve of the glnss. The wliole thing-lap and glass-must, Iiowever, he kept wet. On no account allow it t o d r y off. I3y the end of this first short run your glass should show a very distinct semi-polish, more noticeable in the center tlian on tlie edge. If your polish does not s t a r t in the center, something is very serioiisly wrong with your curve and you might as well go hack to 600 or cven t o F Carborundum and correct your curve. A lens which polishes evenly from the center (1 do o t the ceriler of the not mean a small, sharply defined, locally pulislied s ~ ~ in leris hut a n evenly graduated polish starting in the ccnter) will polish out quickly and give you a good lens. A lcns which polishes a t the edge first is absolutely hopeless; in fact it is next t o iml~ossiblet o finish polishing such a surface. 1 have worked for a n hour trying every expedient 1 could think of to get such a lens t o finish out, wliile the same lens, had i t started to polish properly from thc center, would have finislied u p in less than five minutes. Sincc rxpcrience is a great teacher, t r y such a surface yourself and you will, 1 think, be firmly convinced. W e hope, however, th;it you will not run into tliis siiag, a n d tliat your lens is coming along in good shape. Keep ttie central Iiole open a t al1 times, a n d renew the circular cliaiinels as they become closed up. Five miniites will easily bring your lens t o a complete polish if everything is going right. Examine the dried and cleaned lens closely with your magnifier. .Small pits a r e extremely hard t o see-in fact i t often happens that, a f t e r you llave finished your second surface and are able t o see through your glass, a multiplicity of fine pits can be seen on one surface or the other. Re thorough, giving the lens just a little more polish after you figure that i t is al1 finished. B y this 1 do not mean to overpolish-which, b y the way, is even more fatal t o performance than leaving a few pits. Over-polishing will distort your curve and so spoil your image. It is possible and permissible t o alter your lap, either making it larger or smaller, by opening the renter hole or by cutting zones in your pitch, to contrive so that your polish will come u p evcnly. However, siich doctoring of laps should be left unt.il you Iiave acquired a little more experience. If you run into trouble in polishing, 90 percent of the time your Ane grinding arid curve were a t fault. The following quotation frorn "Orford," one of the leading English opticians, explains the importante of polishing from the center out: "It has been sren t h a t 1 always make thc polisliers t o take in the center, and a t first thought i t seems that 1 am intentionally polishing the lcns away from the curve; but if we look further into the subject, we shall see t h a t t o get a fine surface, we must proceed as stated. In a series of experiments 1 cnrried out some years ago, 1 tried al1 kinds of polishers and methods of polishing, carefiilly noting every effect the different methods had on a test image. 1 found that, whcre a surface hnd been polished seemingly level, i t turned out very badly under test, and a surface polished from the edge was useless for showing a perfect image, while al1 lenses polished froin tlie center invariably gave good results; so t o the workmen i t is always their aim t o s t a r t polishing
SMALL LENSES
167
from the center ar. levelly as they can. . . . So it is seen that the edges of the polisher when in full work, must cut nearly twice as fast as the center, and if we had started polishing levelly, i t stands t« reason that the curve when hright woiild have heen totally different from whnt was intended." Your Iap should easily l a ~ long t enough t o polish al1 four of your blanks. I f it does not, rnake u p n fresli one a n d go ahe;~
F ~ O L ' R E 19
Flnt Znp, cast iron.
Detnil ahown at nrroui is ( h e same as i n Figure 17.
properly done the glnss will come away rleaii from the tubing. Place in turpentine, t o soak off any cement adhering t o the glass. Flat Laps: Procure a piece of cast iron about 8" in -diameter and l/z" t o 3/4" thiek, chuck in the lathe, drill a hule 3/8" deep in thc center and ciit a 5/sM standard thread, so tight that :i %" s t u d will be tight when only three or four full threads are engaged. Take a light facing c u t over the face of the cast iron, so t h a t this side (the back) will run t r u e with the nxis of the stud. Relieve the threads on the stucl close t o the plate, cut the stud off to %" long, remove from thc chuck and screw into your taper mandrel. Face u p as accurately a s possible and t r u e the edge. Figure 19 shows the details of this lap. Thc ahove directions are given for those who do not wish t o go t o the expense or trouhle of liaviiig a proper flat lap casting made, or wliu happen t o have :t flat piece of cast iron on hand. I t is f a r better t o finisli the back of these larger laps with a standard taper sncket. However, it entails making a pattern from which t o havc your casting made. In malring a pattern, allow about 5/s" per foot for shrinkage (for a finished diameter of 8", allow about 8%'' t o for shrink and finish, and have the boss made 1%'' in diameter, so tliat you will have plenty t o rlean u p on. Make a fillet around this boss of ample dimensions, say 3/s" or even %'' radius). Ask your foundryman t o pour this casting with the face down--
1G8
SMALI. LENSES
this will hclp to eliminate sand nnd hlow lioles in the face. These, when using the lap in fine grinding, serve to hold grit and perliaps c a w e scratches. A wvrd here will not be arniss regarding tlie gracle of iroii used in your laps. A fine, even-grained, soft iron that is free frorn hard aiid soft \pots is of prime importante-notliing is more exasperating than to have a lap pr;ictically finished, and then ruri into a sand hole or U hard spot. Srleral years ago, in the practici of my profession, 1 had occasion to do considerable work with casi irons, and carne across a specially lieat treated i r m called "Meehanite." This iron is ahsolutely frce from hard or soft
F I G X R E 20 3 % " mn.ner, brasa o r cast iron.
as possible"; and it is wiqe to give the founder a line on the sperific use t o which the material is to be put. The U. S. agents are J. S. Morrison & Co., Oliver Building, Pittsburgh, Pa., who will put you in touch with the nearest fouridry a h o have the local agenry in yoiir vicinity. Meebanite costs 15 cents to 20 cents per pound in small lots, as against G cents to 8 cents for common cast iron, but is well worth the extra few pennies. [Prices as of 1935.-Ed.] Next, make a flat runner. Face and edge a piece of cast iron to 3%'' diameter. With a sharp-pointed tool t u r n a small conical hole in the center t o a depth of ?/í6''. Cut off so t h a t your piece is i/4" thick. Make three o r four of these runners. Figure 20. Screw your flat lap in your spindle, run i t a t 100 r.p.m., place a little 220 Carborundum and water on i t and, taking your first blank between your finger and thumb, proceed to grind the flat side. With your double-ended brass calipers gage the center frequeiitly until the thickness i\ within 0.05" of your finished dimension (in this case ,1875"). The amount to leave varies with the size of lens and with your dexterity of manipulation. Kerp a n accurate record of the thicknesses of your blanks a t this stage and after they are polished. I n this way only can you judge how much to leave for grinding and polishing. A very handy gage for measuring can be made as follows: Cut a strip of brass or steel exactly 5" long and '/," wide a t one end, and taper i t t o
SMALL LENSES
169
a peint a t the other. File the edges smooth, and straighten as strnight as possihle (Figure 21). Mark off distinctly each quarter inch, making the half inch marks twice as long as tlie quarters. The gagc rnarks will have a value of 0.025", and lcsser measurements can be made by placing the calipers between marks. Be careful t o wash your blank each time the calipers are applied. Don't press tliem hard over tlie curved surface. Make al1 four blanks tu tlic same thickness. Tliis detail is iniportant. Carefully wash u p tlie lens and place i t flat side down on your asbestos pad. W a r m so that yoiir cement will flow quickly and easily over the polished surface. Do not get any on the fiat surface-if you do, clcan it
FIGURE 21 Brass gage, 5 " a! 5", 16-gag?. off. Next, warm u p your Hy2" runner and apply a liberal coat of crinent to the plain side. Remove while still hot t o a level place on yolir hrnch, and a t once place your hot blanks-polished, convex side down-on the liquid cement. Arrange them symmrtrically around the center. Allow them t o cool, so that thc runner can be inverted without the blaiiks dropliiiig off. Place the whole thing, blanks down, on a piece of d r y plate glass. Next take your bunseri, which should be connected with flexible tubinp, and play the open flanie direttly o11 top of the runner. The cernent will soften u p and tlie glass blanks will level themaelves on the p1:iLe glass. Do not get things so hot t h a t tlie cement will run al1 over everything-just hot enough so that the blariks can adjust tliemselres in the same plane. Allow t o cool. Cut or break n numbcr of fragments of the same kind of glnss as you used for tlie blanlcs and place them over your burner-get them good and hot. By this time your riiiiner should be set. Take the hot pieces of glass and drop them, flat side down, in the spaces betweeri and around your blanks. Press liglitly on each one, so t h a t their under surfaces will be iri coiitact with the runner and their uppcr surfaces fairly level, although quite a bit higher than the flat surfaces of your blanks. Before 1 s t a r t to set a runner, as outlined above, 1 usually place my blanks a n d pieces in a syrnmetrical arrangement on an empty runner. In this way 1 can get a hetter idea of the sliape of tlie pieces needed. Figure 22 shows a mounted runncr-the main idea is t o get the built-up surface as nearly continuous as possible, having a t the same time come glass outside the outer edges of the blanks. If this precaution is not taken, the finished flat surfaces will show a decided turn-down in those portions which were adjacent t o the periphery of tlie runner.
170
SMALI,
LENSES
With the flat l a p on the spindle running a t 100 r.p.rn., take the runner and carefully grind dowti tlie surface of the small filler pieces t o the same level a s your blttnks. Use your calipirs on the pieces arourid the edge, getting tlie same me:rsurements from their surface t o the back of tlie runner. No. 220 Carborundurn will cut fast, ttike care So that you dcn't overdo things. When al1 seerns level, wasii u¡> tiie ruiirler, place a drop of oil in tlie hole in the back and, with tlie pin bar horizontal and the pin vertical, üllow the runner t o spiri for a few secoiids on the lap. Do not allow it t o p m s over
3 % " mountrd r u n n r r .
the center or edge of the lap. This spinning witli 220 is not essential-it is sirnply done to insure a leve1 sdrface t o s t a r t with. Wash u p thoroughly, place clean papers, and give a short wet with F Carborundum. Thirty to sixty seconds stiould serve to take out your 220 pits. Examine the edges-ttie center will take care of itself. When no more pits can be seen, wash u p carefully, charige papers on your beiich, aiid proceed with 600. Do not spin longer than necessary, a s your l a p is getting out of truth a11 the time and thc less grinding you do on it the better. UTatch the edge of your runner for pits-when al1 a r e gane, wash u p again, place fresh papers on the bench, and cliange over t o GF emery. Run three or four wets of this, nllou,ing tiie lap t o become fairly dry between each wet, in this way tlie individual particlis of emery a r e broken down tlioroughly and a better surface will result thnn if the emery is kept too wet. I t is interesting to gnge your runner betwcen each grade of abrasive aiid see exactly how much is taken off by each.
Y a k i n g the Flnt l'itch L n p : Wash u p your cast iron lap and warm it thoroughly. Melt and strain about one half of your remaining pitch and pour i t into a clean tin piin large enough in diameter t o take your lap. H e a t u p your pitch thoroughly a n d a t once d i p tlie hot lap, flat side down, into the pitch. Do tliis several times, endeavoring t o g r t a thin, bubble-free coating on the face. Hemove from the pan and, holding it vertical and rotatirig it slowly, play the open flame of the bunsen on the pitch surface. Most of Llie pitcli will run off, and al1 the bubble Iioles should clase. The ideal lap is perhaps i/iU" tliick. Placc your Iap on the beiich t o cool, making sure that i t is level. If the surface has waves, pass your flaine over it a few times and tliey will soon
FIGCRE 21 8" d i a m e t ~ rpat pitch lop sume detall as In Ebgure 1 7 .
T h e part i n d ~ e a t e d b y bottont arrow calls for t h e
leve1 out. Allow it t o cool slightly and, while waiting, clean u p a piece of plate glass (old windshield) about a foot square and paint it over with rouge and water. Invert your l a p on this rouged surface, work it baclr and forth, iising plenty of elbow grease and lreeping the lap revolving. If your pitch is fairly warm, oiie such working should serve t o give you a good pitch surface. Small air bubbles l/s" or so in diameter a r e rather desirable than otherwise, provided their distribution is fairly even over the whole siirface. Figure 23. Cool your l a p thoroughly, place i t in your spindle and, with your pocket knife, cut out a '/2" hole in the center. Also cut channels, clear down t o the iron, about S" apart over the wholc surfacr. Wash in cold water, scrubbing the surface lightly to remove any particles of loose pitch. Rtglaee the l a p in your spindle, coat thoroughly with rouge, place your runner in position with the pin in the oiled Iiole aiid then s t a r t your motor. Probably your runner will chatter on the rough l a p for tlie first few revolutions, but
172
SMALL LENSES
Iiold it down firmly and it will soon quiet down. It is well t o have a cup of water handy to your rouge pot while poliqhir~g. Keep your Iap thoroughly wet with rouge and water. Use only iiioderate pressure. Dori't allow the runner t o get set ovrr tlie center of the lap-it mny stick if it does. Your polish should s t a r t in the center and work evenly t o the edge, exactly a s was the case on yoiir ronvex surfaces. Polish clear out t o the edge of the runner, wash u p and examine with your lens. Al1 pits, no matter how minute, should have disappeared. Remore the lenses from the runner, by heating until tlie cement i5 perfectly liquid. Pick them off-don't slide theiii to the edge, or scratclies may result. Do not atteinpt t o wipe or scr:ipe tlie cement off, but allow it t o cuol aiid place the lense5 in turpentine a ~ o u p l cof hours or, better, over night, t o soak. Thii will looíen al1 cement and grit. Wash witli warm water and soap, rinsc thoroughly, and wipe d r y with soft tissue paper.
Brass centering t u b e and centering fork.
C ~ n t e r i n y :When the mechanical and optical axes of a lens coincide with each othcr, the lens is said t o be centcred. If these axcs a r e not coincident the lens must be thicker a t one point of the edge than i t is a t another. I n other words your lens, taken as a whole, is prism-sh,cpecl-light rays will be resolved iiito a spectrum and very unpleasant effects will re5ult when any bright body is viewed through sucli a n uncentered lens. See Figure 57, a, page 69, "A.T.M." Chuck a 2" length of %" brass tubing in your lathe, center it a s accurately as possible and, with a pointed tool, chamfer the end both inside and out. The resultant edge should be quite tlii11 a n d niust run perfectly true. Figure 24, left. With an alcohol lamp heat the end of the tubing and apply a thin coat of cement t o the extreme edge. W a r m u p one of your blanks and apply cement to the convex side. Next, reheat the tubing and stick the cemented convex side as centrally as possible on t o it. Then, with the lathe running a t its slowest speed and with the alcohol lamp in one hancl, warm the tubing. A t the same time, and with a forked shaped piece of soft wood (Figure 24, right) in tlie other hand, gently move your blank on the tubing so that a reflection from its fiat facr will stay absolutely still. This job takes quite a bit of patience. Do not press so hard that you will stop the glass from revolving-to
SMALL LENSES
173
do this will invite a scured ring on the convex side. Take luts of time. When perfectly centered, allow t o cool. of grinding the edge of the lens conThe n i x t step iii ceiitering-that centric with the axes-rriny be performed by using yoiir tool holder and cross
Left: 10" z
4" r
FIGURE2 5 '/4" t r a y . R i g l i t : Gtrut f o r c e n t ~ r i n gd i n g b a t
feed saddle. However, it is rather messy, as Carborundum and water usually get over the lathe bed, etc. A better scheme is t o cut a piece of %" board 2" wider than tlie lathe bed and 12" or 15" long, and place this on tlie bed before you start centering your leiis, cover it with paper and, in this way, protect tl>e lathe. Also, shoirld your lens slip, it is not so likely t o get chipped.
FIGURE2 6 C e n t e r i n g gadget
Make u p a shallow tin dish 4" wide, 10" lorig, and 1/4" high. Figure 25, left. Take two pieces of wood 9" long, 1%'' wide and S/s" tliick, and hinge them together a t one end. Procure a strip of mild steel 1" wide and 7" long. Bend and dril1 it as shown in the same figure, a t right. A j/," bolt with 3" of thread and two ten-cent iron clamps complete the outfit. Set up as shown in Figure 26, using one clamp to hold the outfit securely
SMALL LENSES t o your lathe bcd. The otlier clariip Iiolds ti small strip of 16- or 18-gage sheet brass, in place on the upper member. Adjust so that the strip is just in contact with the edge of your Iens. Do not press hard. Apply 220 Carborundum (if your lens is away off center, use 80) and, revolving the lathe a t its Iiighest speed, proceed t o grind the edge of the lens t o your finished size. Stop grinding when the lens is about 0.01" larger than desired. Remove al1 of yoiir rigging exccpt the bottom '/," hoard, wash iip and finísh with a Carborundum slip. P u t a slight bevel on each sidc, wash again, wipe d r y and, with your alcohol lamp, warm the tubing. Remove the lens ancl cool. Place iii turpeiitine t o soak, wash iii würrri water and soap, d r y on soft tissue paper-and yoiir lrns is completed. Spinning: I n most writings on lens making, the spinning method is given preference over the handled method outlined above. It is by f a r the best method for lenses of longer radius (either convex or concave), but with are several inherent difficulties short radius convex lenses-1" or under-tliere which cannot be surmounted. Chief of these is your inability t o make a small radius convex lens travel away from the center of your lap-either the lens clings tightly o r else lets go suddenly and flies off its runner. Concave lenses, no matter how short the radius, can be spun successfully and, if properly managed, as Porter says, "will leave the l a p a s a perfect surface of revolution." T u r n u p two small runners 1" in diameter and l/s" thick and cement t o each of them a glass blank (same size a s before-1%" square). Grind these roughly on your w r t Carhorundum stone-one concave t o your convcx tcmplate and the other convex t o your concave template. Place your convex l a p in your spindle and, a t 300 t o 500 r.p.m., s t a r t and rough out your concare curve. I t will save the curve of your l a p if you make u p a special rough lap and use i t to take out the major portion of t h r plass. Go throiigh the same steps with your 1" radius concave lap, and 1 think you will demonstrate t o yourself how hard i t is t o make your convex blank beliave itself. Your concave blank will go along fine-watch the curve closely, it is very easy t o spin away from the template. Keep the pin pointing a t a slight angle t o the toward thc cclge of the lap deepens surface and keep it moving-spinning the center, while spinning with the glass nearer the center wears down its edges. Wheri workirig a double coiicave or a meniscus, make your runner t o fit the curve t o which i t has t o be cemented. P o r a conrex surface your ruiiiier sliould have a slightly deeper curve than the glass-this gives a iittle more cement in the center. F o r a concave surface make the runner curve slightly shallower. This puts a thicker cushion of cement in the center. In finishing a n achromatic pair whose second and third surfaces are of the same curve, i t is well t o cement the first surface (work i t first) t o a runner, the back of whicli has been finislied exactly tlie sanie as a lapconical hole and screw complete. You can tlien spin your third surface on top. Your curves, with proper manipulation, will then run together. Acliromatic combinations a r e given in the latter p a r t of these notes.
SMALL LENSES
175
Several Icnses of rather flat curvc may be run tngether as one uriit porter has explained and illustrated the making of these, in "A.T.M.," in a very lucid manner. 1 linve devised several jigs and fixtures for rnaking eyepiece mountings. The time spent o11 tliese will be repaid several tinies over if you contemplate making even one full set of eyepieces.
Take a piece of steel 4%" long and 1%" in diameter and turn u p a mandrel to fit yoiir latlie spindle (Figure 27). Make the threaded p a r t exactly 1.157" in diameter, and cut 40 threads per inch on it. This thread will fit the interna1 thread of your eyepiece tubing. The threads shown on
Stpel ring.
pieces in Figures 27, 28, 29, 30 will be standards for al1 your future mountings, so take pains with them. Turu u p a steel ring, as showii in Figure 28-making your finishing face cuts with the ring screwed on your mandrel, thus insuring these faces being absolutely square.
Next, rriak~ tlie piece sliown in Figure 29. The interna1 thread of this should accurately fit the m:indrel, Figure 27. I t will be best t o face u p this piece, bore and thread it, tind then finish the externa1 thread with the piece mounted on tbe Figure 27 mandrel. The externa1 thread is the same as
the outside threads on your eyepiece tube, and forms the gage to which to make the inside threads of your caps. I t s diarneter before threading should be 1.25". The mounting proper consists of four parts-the tubr, the two lens rings, and tlie eye cap. Al1 threads are 40 per inch. The tube is started as follows: Cut off 1%' of your 1%" O.D. brass tube. Center this piece accurately
FIGCRE30 Thread gage.
in your latlie chuck, and face one end square. Cut 1%" of thread inside, and 1/4" on the outside. Make sure that these threads are an easy fit with jigs 27 and 30 (Figure 31). To make your lens rings, chuck a piece of 1%" O.D. brass, several inches long, center dril1 the tail end, and run u p your tail stock. Turii tlie outside to 13;16" ( a s these rings will be standard aricl riiade to fit any ordinary lens, you may as well make up 10 or 12 of thern at one setting). With your cutoff tool, cut into the bar to a depth of 3/,", leaving %21' bctween cuts. (See Figure 32). This will leave your rings %2'' wide and eonnected together in the center by a b a r 1/2", more or less, in diameter. Next, turn off each ring t o
SMALL LENSES
177
1.157" for a distanre of '/x", leaving Vj2"t o the full diameter of 13/lfif'. P u t a f i n e knurl on this narrow flange and thread tbe 1.167" p a r t ( t o fit your gage No. 28). Figure 32 shows four of these rings. The 1.157" is arrived a t as follows: 1.12.5" is the internal diameter of your tube. 0.0'32474 is the double depth of a 40 thread. Therefore, 1.125 0.032474
+
FIGCRE31 E y e p i e c e tube.
= the bottom diameter of your internal thread. Leavc off the last three decirnals and your thread will run nicely. Eye-lans Caps: Chuck a piece of 11/'" round brass (Figure 33). If over 6" long, use a steady rest. Face off the end. Bore t o a depth of 1/4" and face the bottoni of the bore. Cut a 40 thread inside t o fit your standard on No. 29. Turn the outside tu lgG"for a length of ?/4", partly cut off t o a depth of 5/," a t 5/16'' from the face, put a fine knurl on the 4/1,3" wide face, a n d finish cutting off. Details are given in Figure 33.
FIGCRE32 Rrass lpns rings.
E'inishing and Fitting a Lens Ring t o a Lens. Place mandrel No. 27 in your lathe spindle, screw jig No. 28 o11 the end, and into jig No. 28 screw one of your roiighed brass rings. Your lens may be of any diameter u p t o about 1". Dril1 and bore your ring t o about .006" smaller than the O.D. of the lens (this gives a shoiilder .OO.?'' a11 arouricl for the lens t o rcst against). Counterbore to within ?&'' of the back of the riiig .002" larger than t h ~ 0.D. of t h e lens-.001" al1 around is about right. Next, with a sharp tool, t u r n out the face around tlie Sore ro a dapth a little lower ($&'') than the upper tace of the lens will be when resting against its should--, leaving a
wall as thin as you possihly can (.002" or less) st:~ndingu p :iroiind tli? hore. Use n magnifying glass for this operation, ;ind keep yoiir ton1 shn.rp. Finish u p with fine steel wool. Figure 34 sliows: a 1i:ilf-section iind side elevation of a finished ring a n d lens for ;i Ramsdeii ryepiecc. Reversirig tlie lens in its s e t t i ~ i gaiid bevelling tlie shoulder will rnzike tliis settiiig suit;rble for a Huygens field lens. Blackeii and polisli as detailed in :i later parzrgrapli.
16 FIGURE3 3
Brass eue c a p .
F a s t e n i n g the Len* in I t s R i n g . Procure a piece of S" round hrasi welding rod ahout 6" long, file u p the ends t o a blunt point of about 342'' radius. Smooth u p the ends very carefully. Run u p your steady rest and adjust i t so t h a t it is just helow tlie center of tlie leris ririg. Place the cleaned lens in its settinp anrl, holding it in place -71th tlie t i p of one finger of the left hand, qtart tlie I:rtlie. Run 4ow and, with t h point ~ nf the brass rod wliich is held in the right hand, resting on the ste:idy rest, very carefully b u r r over the thin wall of brass onto the lens. Do not press too hard. Take plenty of tirrie, and gradually work tlie brass into shnpe. T r y speeding u p a little-
F I G D I ~34 E Lens ring.
sometimes the brass will turn orer easier a t speed than when running slower. Do not omit the final stage in blackening your mount; that is, heating as hot ns pos5ible and coolinp under tlie tap. Rrass is somewhat annealed by this treatment, whereas steel would be hardened. The brass wall or collar itsclf should be of siich height that when burred over i t just covers the bevel of the lens. A very hard, smooth, steel point is recommended for this burring operation, also a tool with a small roller a t the rnd. 1 have tried both, but have found t h a t soft brats such as welding rods are made of, is less likely t o tear the delicate brass wall.
179
SMALL I.ENSES
Tlie wholc appearanm of a n otherwise perfect mount can be utterly spoilerl by a poor joh of burring, so take time and work carefiilly and slowly. Finisliing the l'ubr: First determine tlie separation requircd. This is given in tlie table (Figure 35, left) a s 0.77". Tlie field lens is 0.20" thick and the eye lens is 0.10" thick, or a total of 1.07" from plano- t u plano-surface of the two len\es. Both riiigs stiould be borecl and shoulrlered ho that the plano-surface of the lens will he 7/&" (0.03125") below thc outer flat surface of tlie ring. I n other words, the total separation will equal the distance required betweeii ririg flanges. Place mandrel No. 27 in your lathe and screw your lI/?"long threaded brass tube on i t ; bore out t o a diameter of lig;;," for a distance of 0.43". Tliis will leave exactly 1.07" of thread in the tube.
teft
F I C U R35 ~ R a m s d ~ n (Haotingn), e.f.1. 1.015". R i g h t .
Finished pye cap.
Make the inne; shoulder square, so that the ring of tlie field lens will fit properly. Remove from mandrel and screw in your rings and their lenses and look a t a diffused light. .If you can see any marks (dust, etc.) on thc field lens j'uur separation is too long, so replace the tuhe on tlie rnandrel and turn out a one or two tlireads. This allows the lenses t o close u p slightly-finally point will be found when dust on the field lens cannot he seen. This is the best practica1 separation, altliough not correct theoretically. Finishing the Eyepiece C a p ; Screw jig No. 29 on your mandrel, and a roughed cap on the jig. Face iip smooth. Dril1 a 3/16'' hole through the center. Chanifer the edges of this hole t o 2O0, clean u p the eye hole so that i t is cxactly round and srnooth, then t u r n a depression deep in the face, starting '/X" from t h r outer edge and t o within %6" of the rhamfer aruund the central hole. Finish al1 over with fine steel wool. Remove any slight burr on the inside edge of the eye hole, and your mount is complete. A finished eye cap is shown in Figure 35, right. Black oxidized finish is applied as follows: Tc~ke your smooth finished pieces (lens rings must of course be blackened prior t o the insertion of the lenses) one a t a time and dip them in a solution of 76 percent nitric acid and 25 percent water in whicli has heen dissolved (with heat) as mucli copper wire as tlie acid will take up. Cool aiid decant into a plass jar and cover. Keep a few pieces of copper wire in your solution al1 the time. Dip tlie piece
SMALL LENSES
180
in your solution, and then hold it in the hunsen flanie (turn on al1 the air, in order t o keep the flame oxidizing). The piece will dry up, turn green, and finally black. Immerse it a second tíme a t once, while still very hot, in your copper nitrate solution. Heat up again. Repeat a t least four tirries to get a good coat. After the last heating cool under tlie t a p and wipe dry. Procure sorne powdered graphite (soft pencil or an old soft carbon brush). Mix with a little machine oil and, with a rag, rub some of the mixture al1 over the piece-especially the threads. Screw on the proper jigs and, with the lathe running fast, polish lightly with a dry, soft rag. The eye caps are finished black al1 over; then, holding a picce of fine emery paper on a flat wood block against the face, polish a ring a t the outer edge 1/H" wide and another ?/i6''wide around the eye hole bevel. Only the outside of the tube is polished bright-al1 other parts should be thoroiighly blacked. Class: Finding suitable glass for siiiall eyepiece lenses has always been quite a bugaboo tu the amateur. Rollrd, annealcd plate glass, as made by modern metliods, is entircly suitable. I t s index is th:rt of ordinary crown. The Yittsburgh Plate Glass Company make a beautiful colorless glass which they have appropriately named "Crystallex." 1 have used it in making orer 75 Rarnsden and Huygen's eyepieces and have yet to find a flaw o r striae of ilie rninutest kind. Furthermore, the surface of this glass is so perfect that pieces 2" square will show practically perfect interference fringes when tested with a n optical flat. Not al1 of this glass, uf course, has such a perfect surface, but very little selectiori is iieeded t o find pieces entirely suitable for diagonals and otlier small work. EYEPIECESPECIFICATIOSS:The following prescriptions for eyepieces have been collected from a number of sources-Bell, Porter, Orford, Conrady, Hastings, etc. 1 have made al1 of them a t various times. Come perforrri rather better than others, but in general it may be said that for ordinary amateur use the Ramsden type is prcferable t o some of the more complicated ones. Hastings' solid oculars, especially his Type D ("A.T.M.," page 178, 3rd edition, 4th edition), give a small, clear field. However, they are very sensitive t o slight variatioris from the set formulae, and are especially hard to center properly. The stated radii and thicknesses read frorri the front of the field lens to the hack of thc ege lens in each case. The figures given are for an e.f.1. of l", and should be divided or multiplied in order t o increase or d e c r e a ~ e tlie foca1 length. ("A.T.M.," page 71, 3rd and 4th editions). The diameter is drpendent on the radius ünd the center thickness, and can be made anythiiig desired, as can your edge thickncss. The crown and flint glass used in these eyepieces should, unless specifically noted, have the following approximate constants.
Crown Flin;
V
D
63.6 3 6 .'7
1.5137 1.6164
C 1.5113 1.6120
F 1.5194 1.6288
The former can he procured u p to .G25" thick from the Pittsburgli Plate Glass Compaiiy, Pittsburgh, Pa., and the latter from Mr. L. D. Keller, 2344 N. 19th Strret, Philadelplii;~,P;t. However, as mentioned before, ordinary rolled, annealed pldte will prove very satisfactory for any of the
+,
Ramsden
1"
e.f.1.
Ri
Plano .20" +.66611 ,666" .666"
TI RI T2 R3
+
.lo"
T3
Plano No stops or diaphram required. R4
1.178" Plano
1.015" Plano .2"
.la"
+.Bol"
+.62511 .93811 +.625" .09" Plano
.77" f.727"
.lo"
Plano
Huygens
e. f.1.
0.941" +1.00" .20" Plano 1.10" +.401'
0.978" 2.58" +1.10" +2.001' .301' TI .19" Plano Plano Rz T2 1.20" 2.90" R3 .40r' +1.0Ou T3 .lot1 .09" .15" Plano Plano Ra Plano Make the diameter of the stop the same as the oiitqide diameter of the eye lens and adjust until the edges are sharp. The last example is from Conrady.
Ri
Kellner e.f.1.
+
0.75"
Eye lens .318
N/d
V
Bausch & Lomb No.
1.5744
57.7
200-3 Flint
j
.15-R2, a n d R3 cemented E y e lens -
.75
1.6041
37.8
110-1 Crown
Ra T4 Rs
+.70 1 .12 }Field lens - 1.517 Plano)
63
20-3-Crown
Hastings Three Lens Ocular. e.f.l. 1.00" Dense Barium Crown. Light Flint Ri t.735" Rz - 276" diameter Ti .06" Cemented R3 +.276" R4 +.279" Tz .196" Cemented R5 - .279" R6 +.745" T3 .056"
1
i 1
N/d 1.5725" 1.5795"
V
,448"
-Flint
Bausch & Lomb No. 56.8" 110-1 41.0" 190-3
.400"
-Crown
.448"
-Flint
H a s n small field and beautiful drfinition.
Steinheil Monocentric (original specification), 1.f.1. 25mm.
Ri Rz R3 R4
+19.78 I 7.98 f 7.98 +19.78
mm. mm. mm. mm.
Ti
T,
Steinheil Monocentric (later speiification), 1.f.1.
+::i:::}Flint
Rz T2 RJ
283f'i
Flint
diameter 0.4"
diameter 0.4"
The glass specified for both of the above is:
Crown Flint
N/d 1.51705 1.61358
diameter 11.00 mm. 22.12 1"
diameter 0.8" tapered t o 0.4''
k.282") .507")Crown *.226")
+:510u
22.12
Tz
N/h 1.52767 1.63207
Achromatic
Ri TI
Rz Separation
RJ
e.j.1. 1" -6.15" .035" Field lens-is a very thin meniscus. +1.25OU Crown glass. Diameter 0.5" 0.746 Plano
R4 diameter .3125" (eye lens)
R2 Rl Same glass as used for the above Steinheil monorcntric. The original source of this particular formula is unknown. 1 havc made a number for use with telescopic rifle sights and they work well.
Solid Ocular. Original made by Brrtshear and now is in possession of Mr. C. Goin, of Pittsburgh, Pa. .
e.j.1.
0.75"
Ri
0.5"
Rz
0.3" 1.28"
diameter at laríre - end 0.736" diameter a t small end 0.446"
Ti
This ocular has a diaphram groove (a-la-Coddington) cut into the glass. This has a diameter of 0.3" a t the bottorri of the groove, which is located 0.35" back of the front of the field lens face.
The following table gives the dimensions of Huygens and Ramsden eyepieces, for an e.f.1. or 1". The values given may be varied to suit particular conditions. Note the variations of Conrady's Huygenian as given above. In general tliey will be found very suitable to general needs.
Huygens e.f.1. Focus of field lens Radius of field lens Diameter of field lens Focus of eye lens Radius o£ eye lens Diameter of eye lens Separation of lenses Diameter of stop
1.00" 1.50" .75" 1.00" .75" .375" .375" 1.125& .375
Ramsden
1.00" 1.25" .625" .75" 1.25" ,625" .375" 332"
1 would strongly advise the beginner to r n ~ k e;L numher of simple lenses, hoth bi-convex and plano-convex, before tackling the Coddinpton (I-Iastings) t y p e 1 have a whole set of solid iincapped eyepieces of tliis lype, frurri 1" to I/i,," F. The last has a n R2 of 0.04" and a total Iengtli of 0.16". T r y one of these small lenses a s an exercise iri lens rnaking. If it turns out well, yo& sliould apply for full nienibership in tlie nearest Pollyanna Club-you surely deserve it. I f any amateur who reads this article has any criticism or question to ask, please do not hesitate tu do so-it has beeri written witli the sole thought of arousing interest in tliis particular brancli o f telescope inalcing. Prob:lbly
Plan a n d rlrz.stion of tlrv frrlthor. L r f t : TAis sholcs the hnndlr shotcn in Figure 1 1 . R i g h t : Looking f o r scratehes. [Yr.Clark i v C h i e f Bngineer of the i i r n e ~ i r a nZirlc and Chewiical C o . - E d . ]
come of yuu have evolved formulae for eyepieces, microscope ohjectives, o r other optical apparatus which you a r e not in a position t o develop yourselves or t o have developed hykprofesqional opticians. 1 should be only too glad t o lend what small ski11 1 have t o the furtherance of such developrnent, and t u add in some small measure t o the splendid work already accornplished by amateurs in the past. Letters may be sent t o the author a t Langeloth, Pennsylvania. 1 arn deeply grateful t o Messrs. Ingalls, Porter, Sheib, and Scanlon, f o r their interest and correction of the origiiidl rnanuscript.-Langeloth, Pa. (Box l l s ) , August 1, 2935. A Postscript o n O b j ~ c t i a e s : Those who wish t o make a finder objective will be sure of good results if the method of Donald Sliarp ("A.T.M.," 4th edition, page 311) is followed carefully. I n testing, the followirig aet-up is u\ed Make your lens and its mount, and set up half way between tlie knife-edge and the pinhole, whicli should be separated by foiir times the foca1 length of the lens. The shadows are interpreted as with a rriirror
Your final shadows should lonk exactly the same as tliose of a spherical mirror, for good results. Watch for a turned cdge-it will spoil your image. 1f you have a flat, follow Ellison's auto-collimation test. 1 have made a number of finder ob,jectives, from 8" to 20" F and from 11/2'' to 2Yz" diameter, by the above method, with good results. The correct centering of object glasscs over 2" in diarneter is quite a problem for the average amateur. If undertaken in the manner so Iticidly e q l a i n e d for small lenses by Porter ("A.T.M.," 4th ed., page 67), scrious troiibles are sure t o develop a t the outset. The chief difficulty encountered with Porter's method, wlien applied to larger lenses, is due primarily to their greater weight. While the pitch is
FIGURE36 Branh,eavls method.
still warm, there is a decided tendency for the ~ l a s sto slip from its correct pusition on the brass tubing. E x t r a pressiire has t o be used on the polished surface of tlie lens in order to overcome this, with the result that slicks and small scratches very ofteri result. The obvious remedy for this condition is to make the axis of the brass centeriiig tube vertical instead of horizontal. If, liowever, this is done, it is alrnost impossible to warm the tube without grave danger of crackitig the lens. 1 have employed the fullowing method. The accompanying illustration (Figure 36) will help t o make things clear. A vertical spindle A , which must run true, is required. The chuck B has four screws tapped into it 90" apart and a t a n angle of 30" from the horizontal. The top surface of B is finished with a shallow seat of about 3" radius. Piece D has a corresponding rounded surface of the sarne radius The upper surface of D should have a tapered hole to fit the tapered stiih
on tlie unclerside of lens holder 81. This lens holder slioiild have zin oiitside diameter ;tboiit 2" less thiin thc lcns wliicli is hring centered. Tlie iiiinular ring on its upper side sliould t)e finislied witli a roundecl section, so that line contact only, will be made between it and the lens. The following rrietliod of using tliis rig will be found convenient. Assemble the various pieces as sliourn in the sketch, wiicl hy me;ins o f tlir fniir screw5 bring the top riiig o E E as netirly triii ;LS possihle. The final truing is best accomplished by taking a fine cut, preferahly with a grindcr, on tlie aprx of tlie ring. Remove the leris holder arid m:irm it. l i u u a little pite11 around the top of tlie ring, place the alrearly marrned anrl turpentinecl lens on it, and press into firm contnct. Replace the Iens holder on the chuck and, by menns of a reflected liglit, center tlie lens as closely a s possible. If, a s usually happens, tlie pitcli Ii:lrdens before the job is perfect, it is a simple mutter t o warrri tlie niiderside of the lens holder, ancl contiiiue tlie adjustment until no further adjustment can be made. The actiial grinding of tlie edge of the lens is best accomplishetl by means of n soft iron disk, running a t fairly liigli speed and fed witli Garbo and tlie side of tlie disk, :irid not the edge being placed in cont:ict with the edge of the lens. The lens should be revolved a t sucli speed, that the Carbo will not be thrown off by the centrifugal action. F;iiling ;i grinding rig, a piece of brass or hoop iron, bent t o a partial circle, will niake a very satisfactory substitute. Ellison's metliod of 'Lmiking" the edge thickness leaves much to be [lesired. Both surfaces of tlie lens are curved, and great difficulty will be experienced in placing the tables of the micrometer a t exactly tlie same radial distance around the lens. Five ten tliousandtlis (0.0005") of nn incli difference in edge thickness is rather more than the difference between a first class lens and a mediocre one. Such an error can easily be rriade, especially by one wlio is none too well versed in tlie use of a "mike." That there a r e differcnces of opinion regarding this operxtion is' evinced by the "discussion" between Ellison and Fecker ("A.T.M.," 4th cd., pagc 459). F a r be i t from me even to question the accuracy of the former's methods; so, as aii alternativa 1 submit tlie foregoing scheme, wliich 1 feel sure will be found more nearly fool-proof in tlie hands of the average amateur.-R.E.C.
SIMPLE OCUI.ARS
Oculars at Small Cost By W. T. PATTERSON, R . O. Gurlph. Ontario, Canada
Having read in "A.T.M." several articles on oculars, and noting that the tools required included an expensive screw-cutting lathe, 1 decided, in the interest of soiiie amateurs (myself included) who are not fortunate enough to own sucli a rnachine, to seek some other way out of the difficulty. Figure 1 shows the details. Tlie main thing was to find a source of ready-made parts. Accordingly, 1 procredrd to shop ahout for suitnble materials which could be obtained a t BAKELlTE CAP-,
'BAKELITE c-
OR PRESDWOOD
LENS CELL
FIGURE 1 A simple e y e p i ~ c eand anotlrer tcith remoaable lens eells. siriall cost, and the following is a list and description of parts obtained. They served tlie purpose very well. (1) Bronae car bushings marlced "C. G. B." These have an outside diarneter of 1%", the standard size for abtronomical use. They were obtained at a garage for 8 cents apiece. Another and perhaps better substitute, sirice tried, may be obtained from any electrical and plumbing contractor, and consists of nickeled cuttiiigs from brass pipe. Four 2" lengths, 1%'' outside diameter, were obtained for the sum of 10 cents. (2) Sheet Bakclite, salvaged from a homemade radio of t h r old type, which can be obtained from most any "ham" or a t radio shops, which are glad to get rid of it. Masonite Presdwood may also be used, by giving it more solid body with a n overnight soaking in shellac, but 1 found Bakelite better, as it holds screws more firmly and makes a neater job. (3) Plano-convex leiises of sliort focal lengths, 1" or less, may be obtained from pocket magnifiers, etc. 'i'hose used in most of the oculars
188
SIMPLE OCULARS
descrihed here were obtaincd from íi cheap telescope and iiiicroscope of Japanese make, obtainable for about a dollar each in many optical stores tliroughoiit the country, or frorn the Orieiit Tmport Co.. Detroit, Mirli. The objective lenses of the microscope were usrd for onp ocular, and tlie erecting eyepiece of the telescope yielded four lenses for two others. These lenses are of good quality and are mounted in brass cells, which simplifies the work of assembling. Lenses can be obtained fruin view finders taken from old carneras, f i d d glasses etc., if one is fortunate enough t o obtain them. The alternative is t o grind and polish your own lenses. 1 have used blanks cut from flat spectacle lenses, the plane side of which is already finished and, being of good quality optical glass, these will produce good lenses. (4) A few dozen rimless spectacle screws and a t a p of the same size. These may be obtained froni ariy optician, and were found exceHent in asscmbling the parts. A No. 60 twist dril1 is the proper size for use with these screws. A few other tools are needed as well, which most mechanics have on hand. These consist of a few small drills, a sharp knife, and files. The total cost of materials used in four oculars is as follows: bushings $ .32 Aakelite .O0 1.00-double aplanat (2 lenses) pocket magnifier telescope 1.00-using eyepiece lenses alone microscope 1.00-using objectives lenses alone screws and t a p .50 Totalt83.82, or about 83 cents apiece for each ocular. The eyepiece of the rnicroscope can also be used t o make a negative (Huygens) ocular, but the quality of these was found t o be a little uncertain. However, it is good eiiough for experimenting and will give fairly good results. Now for the actual work. The bushings a r e rolled from sheet brass, consequently they have a seam down one side. This seam should be soldered, in order t o prevent expansiok. First, the searn is opened slightly with a knife blade. The bushing is then heated over a gas flame and soine solder is flowed into the opening. The tube is then held in t h e hand and filed down t o the exact size, using a broad, flat file and giving i t a circular motion as the tube is rotated. Any high spots can be removed and a perfectly round tube produced, with a little practice. Be sure not t o file off too much, but just sufficient t o bring the diameter back t o ls",SO that the ociilar tube will fit snugly into the adapter tube of the telescope. F o r truing u p the ends of the bushing a strip of straight cut paper is rolled around i t in such a way that one edge of the paper is straight in line with the underlying edges. The ends a r e then filed square, using the paper a s a guide. Repeat the process with the other end. 1 have since used seamless brass pipe, wbich has a better finish and
SIMPLE OCULARS
189
eliminates tlie necessity of sol
F field lens=11L2". Spacing =-
Equivalent focal length of combination
1l,$" 2 34''
2
---=
The centering of \rriall lenies is n simple matter, for any spherical lcns which is perfectly circular and of equal thickncss around the edge is bound to be exactly centereci; so al1 that is necessary is to check the edge, whereupon any slight variation will be noticed and remedied by grinding a little off the side wliich is thinnest. Care should be tciken to have the plane of each lens exactly parallel with that of the other, as a slight tipping will produce an uneven focus. Having completecl our calculationi, the disks a r e Llien fastened in the tube by mean\ of the spectacle screwi. Tliree or four equally spaced holcs are drilled around the circumference of tlie tube a t the location of the disks,
SIMPLE OCULAItS
190
and about 1/qn into the etlgcs of the disks themselves. Thc small t a p is then used and the screws turned iri. A worcl of caution reg:irding drilling and tapping Balcclite-do not force the drill, but proceed slowly anci rcniove :ind clean it after each few turns, as Bakelite clogs tlie groovcs. Rurining tlie drill into tr ctrke of soap will 1ubric:ite it and reduce friction. The lense.;, t~lrenclymounted in n brass ccill or w;isiier, are now fastei~ed to tlie Bakelite disks by me:ins of tliree or four equally spaced screws, care being taken to center thein exactly. A c;rp disk mtry tlien be cut frorn slieet br:iss or 13;lkelite sliglitly larger thtin tlie 1 tilbt. di;iiricter (l'i," is tiboiit riglit) :ind tlie ceiiter is cut out so
x"
LENS BElNG TESTED, USED AS EYEPIECE TO FDCUS CROSS LlNES
y,,,
,,,,,,,,
Lv'.. "NODAL
SCALE READING IN DlVlSlONS
,,,,,,
POINT. FOCAL LENGTH 15 MEASURED FROM THIS POlNT
.. .. -. ' . ,, ,
.
.-
g,, .
,
CLEAR CELLULOID OR GLASS TUBE
1/32
'-WHITE
r.
CELLULOID CAP WlTH CROSS LINES
.
..
.
.- -- .. . .
I t
WOODEN DOWEL SLIDING IN TUBE
that i t will fit down over the eye lens cell. The c a p disk is then fastened t o the eye lens disk with severa1 screws, and the ocular is completed. The first ocular 1 made turned out so successfully tliat 1 decided t o make a set, and 1 now have six. The Ramsden oculars prodqced are a s follows: (a) High power of '/," focal, leiiglli, using the objective lenses from the dollar microscope. ( b ) Mediiim higli power of 1/3" focal leiigtii, using the eye lenses from the dollar telescope. (c) Medium low pnwer of %" focal length, uiing the erecting lenses of the same telescope as in (b). ( d ) Low power of 7/8" focal length, using lenses froin a pocket magnifier. These oculars were first tried out on a standard French make of telescope, draw tube type, of 25X magnification, and gave excellent definition u p to the highest power. The oculars listed give magnifications as follows: 28X, 50X, 7.5x, and 100x.
They were later used with a 3" objective of 42" focal length, and gave u p t o 126X magnification with perfect definition, but slight achromatism with
STMPI,E O C U L A R S
191
liowever, this was due to the ohject glass heing corrected for lower powers. Testing Smnll Eyspiece Lenaes for Foca1 L e n g t h : Figure 2 shows :L simple instruriieiit for testing small eyepieces for focal leiigtli. Probably the easiest way t o measure lenses of long foca1 Iength is by focusing sunlight t o a point. With sliort focus lenses one will at once meet with difficulties, since accnrate measurement is then impossible. Accordingly, this simple instrument was designed, arid will give the focus of small lenses accurately to witliin 1/3?'. A small tube of Celluloid o r glass is used, bearing a small scale graduated a s shown, and a small round stick of wood is madc t o slide u p or down snugly in the tube. On the upper end of the stick a small, round cap of white Celluloid is cemented, bearing a number of fine cross liries scratctied on its surface and filled in with india ink. 'í'o measure a lens, simply place it on the iipper end of the tube, a s if it were an eyepiece, and slide the stick u p or down until a sharp focus of the cross-lines is obtained. The reading is made direct from the scale a t ttie poirit to which the sticl. has been moved. One half of the thickness of the lens is subtracted from this reading. I t is t r u e that this amoiint is not precise, since a simple lens has many focal lengths changing from zone t o zone and color to color. Also, the observer will not be able t o accornmodate for infinite distance wheri testing. However, i t is pointless t o seek a degree of accuracy which would be fictitious. The method is quick, tlie equipment is simple, and tlie resiilts a r e prohably as good as are needed for making Huygens and Ramsdcn eycpieces. B y means of this instrument a quantity of assorted lenses can be matched in a few minutes &d paired off for use iri eyepiece8.-108 1Vyndham Street. 168X
TIIE REFRACTOR
T h e Refractor-M~tnl Parts and Mounting
UThen tlie amateur looks through or into the telescope wliich liis rraftsmanship has created, and beholds the Moon, Saturii, Jupiter o r sciriie other nonder of tlie heavens, he experiences, in most cases, a justifiable sense of pride and sntisfaction. His investment in time, effort, and expense, becomes paltry, automatic;llly forgotten, and he will probahly confess that the work of coiistruclion has been of ahsorbing interest throughout. By sharing the pleasure and enjoyment which a telescope will give, he can leaven liis wliole neighborhood, including other friendly rontacts, with enthusiasm and interest in thc stars. A pood telescope is decidedly worth while. The airn of tliis cliapter is to aid tlie amateur with a description written in considerable detail, of the building of a refracting telescope similar t o the instrument illustrated in Figure 1. This will not include comment on, or directions for making a n eyepiece o r the highly important objective. Information on tliose subjects will be found elsewhere in this book. F o r the early history of tlie telescope, its development, and a comparison of the refractor and reflector, the reader is referred t o "The Telescope" by Aell. A hrief digression from our subject may, however, be permitted here, for the addition of the following running quotations, each of which carries its own punch of information: "The refractor is practically fool proof , "hecau~eof the great corivenience of its use and maintainance" . . . "little affected by changes in temperature. You can, by using a s t a r diagonal on a refractor, cover any part of the heavens, while comfortably seated. "Refractors are satisfactory for daytime use, because the eyepiece receives no light except t h a t w1iich coiries througli tlie leris." "The refrücto'r can be made a tliing of great beauty. Much, much more could be said in praise of the refractor, but our digression is limited. If the reader has a technic81, mechanical t u r n of mind, and is possessed of inventive and creative ability, he may choose, after reading this article, t o vary the design and procedure recommended. On the other hand, if he wishes to follow a definite programme, he will make no mistake in adopting the detailed directions found in this chapter. If these directions a r e accurately followed, the result should be a refractor (metal p a r t ) which is not alone precise and accurate in operation but good t o look a t , as well. S k e : Wlieii we come t o the consideration of size for a proposed refractor, one general rule or saying can be laid down: namely, performance is of greater importance than sizc; also thc wcll-known expression, "a good little one is much better than a poor big one." Fraunhofer, it is said, did most of his revolutionary work on the s t a r spectra with a 1" objective. Olcott says, "a three-inch refractor is ideal for tlie airiateur." Hale says, "a fourinch refractor is al1 that can be desired for looking a t the spectra of stars."
..
. ..
. . ."
...
-METAL
PARTS
Kirkham says, "If 1 had it al1 to uu over again, 1 would make a smaller refractor-four or foiir and a half inclies." The 60 mm. ( 2 % " ) refractor shown in Figure 1 is a highly satisfactory instrument with regard to size. The owner and builder of a 10" reflector, while observing with it remarked, "1 can see as much in this as in rny 10" reflector; my image is a tiny bit bigger, that is all." Refractors u p to 4"-possibly I a r g e r - c a n well be mounted on a tripod, if the latter has sufficient weiglit and solidity, and are easily portable. Ref r a c t o r ~of 5" aperture or more deserve, and should probably have, a permanent mouiitiiig of rock solidity, with a protective covering.
Phoiographs by the author
FLGCRE1
A 6 0 millimrter ( 2 % " ) refractor m a d e , e x r e p t i n g the e y e p i e c e , b y the author.
So, in choosing the size which you wish to build, remember it is not size that is most important, but the quality uf perfurrriaiice. T h t following paragraph, culled from correspondence after the above was written, is addcd here hecause the comment is so authoritative and valuable that the beginner should have the information before he unwittingly falls into uiaking decisions which he might later wish were different. This paragraph was written in a personal letter by a professional whose name is widely known and whose accomplishments in the field of telescope optics are much respected and admired-his name is withheld t o save him any possible embarrassment because of his frankness, privately expressed. "1 would like to point out one thing," he writes, "which beginners overlook. A really fine 4-, 5-, or 6" reflector will keep aii iritelligeiit persoii busy a full lifetime. 1t is much t o be regretted that the fad for large
194
T H E REFRACTOR
diameters has gone iis f a r a s it 1i:rs. Astrnriorriers and practiced observers will te11 you tliat a good 3" refractor will show you everytliing that an amateur will want t o see. 1 can vouch for thüt. and perhaps you will be surprised t o learn t h a t the only telescope 1 llave a t preserit is a 1',$" refractor." Some will possibly disagrcc with the above quotation and, if you dci, i t is your privilege, for in quoting it there is no thouglit of stepping on tlie toes of anyone, but only of giving the begiriner an autlioritative opinion on refractor sizes. Make your own decisions, and may success attend you. Material: Brass has been so generally iised for refriictors 1111 to, say, 5" that it is the undisputed standard. Wliile otlier materials have been used for tlie main tube, they will be found in general less desirable than brass. The amateur who makes his entire refractor of brass will riot be disappointed. Brass tubing in a wide variety of sizes and gages is obtainable from dealers in tiihing. Come sizes can be furnished in either yellow or red brass. Yellow brass for the entire job will be easy t o obtain. Small tubing, such a s telescoping draw tube 1?/," to 1%'' in diameter, in red brass, is not listed ir1 dealers' catalogs, therefore red brass should not be considered for the entire telescope. Yellow brass tubes with red brass trimmings make an impressive finished job, but if you adopt this combination be sure t o instruct your foundry correctly, when castings a r e ordered, i.e. red brass Por al1 trimmings. I f you patronize a foundry where virgin or new metals a r e used instead of scrap metal, you will get castings of better quality. It is well t o remember that plumbers carry in stock brass pipe in a variety of sizes, some of which is heavy-wall, and some thin. Uses for brass pipe will t u r n u p a s the work progrcsscs. Stuffing box rings, as dcscribed in the text, can be made from heavy-wall brass pipe, with little waste of time or material. .Some hardware stores carry brass rod in diarneters from, say 3/s" u p t o l", which is desirable stock from wliich to make small parts such as special screws and tliumbscrew heads. C o s t : The price of brass .tubes in lots of less than 20 pounds varies from 30 cents t o over 40 cents per pound (1935), according t o diameter and gage. Castings in brass are quoted a t similar prices, with the same spread. The following were the costs for tubing and castings for the 3Y2", 52%'' focus instrument shown in Figure 2. Tubing, $10 (main tube extra h e a v y - e x plained later in t e s t ) . Castings, about $6. T o p of tripod cast in german silver, very heavy in design, $4.50. Tripod legs with hrass spacers, holts, etc., say $3 t o $4. Castings for an alt-azimuth mounting, similar t o the mounting shown in Figure 1, will cost about $3. With clever planning a n d recourse to used material, which in many cases is just as good as Iiew, tlie above costs can be greatly reduced. So, with a gross expenditure of approximately $50 for materials, including glass for the objective, it is possible to create a refractor of high quality, equal t o an instrumcnt which in thc market would cost from, say, $350 up. After reading the foregoing, as a n introduction, the prospective builder
-METAL
PAHTS
195
may have formed a definite idea a < t o what Iie wants his refractor to be in size and material. The di*u\sion whicli follows presents practical directions for making a refractor-that ia, tlie ~rietal parts-of higli quality. Practical: Making working drawings is wisely the first practica1 move, followed by making or getting patterns for ca\tings anci ordering the main tuhe, and the telescoping tubing for tlie draw and focusing tube\. Here a r e two important points, vchicli should not he forgotten when you figure the main tube requirements. If a refractor is to be used successfully for ter-
FIGCRE2 4 3 % " refractor which w a s not c o m p l e t ~ du n t i l a j t e r the foregoing part of the chapter had been w r i t t e n . T h e photograph i s included j f r the puryose of og'ering s u g g e s t i o i ~ a i n design.. The rrfi-actor haa a 5 2 % foc
restrial observation, i t requires a prism erecting system. A suitable Porro prism, in its mounting, will take about 4" of the cone of light. In other words, t h e prism shortens the operating focus about 4". Therefore, 4" of tube shortening must be allowed for when the length of the main tube is planned. Tliat tliis poiiit Iriay be tliorouglily understood, let it be again stated from another slant. Avoid making the main tiibe toa long. When the focusing tube and draw tube a r e telescoped into the main tube t o the shortest adjustment, the length of the whole assembly, from the objective t o the eyepiece end of the draw tube, should be a t least 5" shorter tlian the foca1 lengtli of tlie objective-4'' which the prism system will absorb, and 1"
for operation and use of high power eyepicccs, thus malting up thc 5". A 6" allowance is not too much. The second poirit, iiidependent of tlie first or previous poirit, is: to the required length of any main tube, a t this stage, add 1%" to the length. Sbortly it will he explained how this extra length is to he cut off the inain tube in the form of two rings or bands of sample thread. Answers t o some questions which you may be silently asking may be contained iri tlie following data regarding tlie iiistruineiit shown in Figure 2. I t has a clear aperture of 3yz", with a foca1 length of 52%". The main tube dimensions are: Length 42", which includes K" of No. 28 thread on length was ordered. Outside diameter 33/4", with a wall each end-43'/," thickness of .128" (approximately %"). This wall thickness is extra heavy and will probably stampede some of you. However, let i t be said in defense of this heft of wall that the extra weight insures a very stablc or rigid
A close-up of the eye end of Figure 2 , sho,u>ingthe rnUirwineter focus control. The wide knurled band is the rotor, which i s 2" i n diameter. The two knurled rings to the left are atufing buz rings. The ample-sized rotor is easily ~ e i z e d with the bare or gloued fingern of either hand, from any position,, thus rnaking focusin.g both simple and convenient.
tube, one not easily damaged or thrown out of line by accidental kiiocks from different sources. An added cost of two or three dollars is little o r nothing on a fine instrument.' A heavy tube, when properly balanced, has a smooth and ponderous action, not easily affected by every little breeze that blows; also of notable importanee, a l/a" wall thickness permits reducing the diameter on each end of the tube sufficiently t o form a good shoulder and cut a No. 28 thread for the control end asserribly without weakeniiig the tube. This assembly will weigh 6 to 8 pounds and will continually take the brunt of manipulation when in service. Amateurs' telescopes are generallyyes, generally-built too light; seldom if ever too heavy. Machining the M a i n Tube: The plan of threading the main tube l/z" back, to a shoulder on each end, has been adopted as offering the surest means of gaining and maintaining a mechanical axis with a high degree of truth. This plan also offers ease of assembly and dis-assembly, clean sightly design eliminating small screws, and requires about the same time and skill to produce as other methods.
-METAL
PARTS
197
Without further discussion on this point l r t 11s get down t o husiness. Observe, pleasc, tlie secluence of preserit:ttioii, or what to do iiext, :ir; it is importtiiit Iiere and through the remaindcr of this chapter. If carefully followed you will he saved the emharrassment of doing your work over. I n a screw ciitting latlie, owned, borrowed, or rented, and of sufficient length to take the rriain tube between centers, chuck a billet of well seasoned hard wood (maple) about 12" to 14" in length, with sufficient stock to finish, when turnecl, to a diameter slightly larger than the inside dinmcter of tlie main tube. Support the loose end with the dead or tail center. With a wood turning gouge in the tool post of the lathe (do not t r y t o turn by hand), machine the billet of wood to a diameter, say, ?&''larger tlian the inside diameter of the main tube. L e t us cal1 this diameter "No. 1." Reduce this diameter 3 o r 4 thoiisandths of a n inch over most of the length, leaving 1" approximately of No. 1 diameter on each end. This reduced diameter is No. 2 diameter. Again reduce the diameter, as before, leavirig 1" of No. 2 diameter on each erid. Continue reducing the diameter, as above, uritil you are sure the diameter of the wood is smaller than the inside diameter of the tube. With a hand saw cut the wooden cylinder transversely into two equal lengths, which will give two tapered plugs. Do not remove the plug from the chuck, but move the tailstock back. Into one end of tlie main tube drop the loose plug. Over the plug in the chuck, assemble the otlier end of the main tube. Move u p the tail center t o its depression in the tail plug. I n the drive end half inch (chuck end) of the main tube, drill tlie brass and bore t h e wooden plug for a wood screw. Drive the screw, and with a hacksaw cut off the screw head close to the brass tube. The screw keeps the tube from turning on the plug. If tlie main tube is to be worked with a file and sandpaper (preferable for brass) t o a finishcd surface, this is the time t o do it. The tail end of the brass tube is now macliined forward 1" to a shoulder, reducing the diameter i/16" or more. The chuck end of the tube is riext machined hack 1y2", lncluding the screw head, to a shoulder, reducing the diameter to corresponcl with the reduccd diameter of the tail end. A standard, No. 28 thread is cut on the reduced diameter of each end. With a partirig tool set to leaie 1/1" of the thread from the shoulder, cut rings from each end of the tube. Be sure to do the tail end first. The chuck end ring will include the screw. These rings of sample or key thread should be promptly witness-marked with the end from which each camr. While i t is in the lathe, wrap the main tube smoothly witli one or two thicknesses of firm wrapping paper, sticking down the edge and leaving the thread and shoulder on each end exposed. This covering protects the tubc until the refractor is finishrd. Remove al1 from the lathe. Prickpunch t h t end of the scrrw and drill i t out to free the ring on the chuck end plug. Even if the main tube, when mounted in the lathe, stiould look and revolve a t the start like a plorified frankfurter-to exaggerate-it will make no difference. The machining and threading of each cnd, as described above,
x"
THE REPItliCTOR will make the two ends concentric and pnrallcl, witli a common mechanical axis. T'Re ('el¡: Tlir cell assernbly for aii «b,jective is import:rnt; it sliould be carefully rnade. There is u wide vziriety iii ccll design (See "A.T.M.," also Bell, "Tlie Telesco~>c"). Section:il drawiiigs and description of only two forms of cell will be included in tliis cliapter. The cell assembly is wiseiy rnade in two cections, one section being the
A n o t h e r close u p o f a v a r t o f W q u r ~2 , .vhouing tlte refractor mountin,q, al80 t h r short focus reflector. T h e azzmulli bearang zs a 6" tapered cone 2'h long. Coosunecks support 2%" diamrter h u b s wltteh are t h r brnrtngs in a l t ~ t u d e . T h e , ~h u b r nre tntegrai z~itli Irenry a i d ~p l n t e ~ Z L I ~ L (tn ' I I t u r n are f n v t ~ w d t o a h e a ~ ysupporttng alreve. Phe rnntn tubu slhdps through tkla clobe fitting Y L P P V P to tlie iequlred balance, and ~ , , h e l d from drtfttrty by rrwaria uf lryht preaaure f r o m t h r t=o t h u m b s e r r w s o n 1 curued, cork fueed, bravv ~ L Y ~ Y . T h e d e v ~ c ean the h u b o f the b e a n n g an altitude regulates a n znternul expanding brcike T h u mirror end of the reflector, with t h e mtrror holdlng a.s-sembly, acrews o n the ~nrrintube For a v i e w o f the ~ n s t d e sur , Figure 8 Tltr dicigonal suppolt zs integral wlth t h adnpter ~ tirbe, the whole a-vsembl~ng f r o m inside the m a t n tube into a chirck u'hirh hnlds tlt!.q n s u ~ m b l g firrrily 7 1 1 nrLli~rtirrent T ~ clanzpiny P rzng o f the chuck c a n be aeen l u s t beyond the face of the eyeptece T h e threeíled s h a f t ~ 1 2 t hthumbacreu headv on eac71 e n d , moues the u ~ h o l eeyepzece uxaembly, zncluding the dzagonai, longztzcdinall~i zn and out of focas Phe reflector m o u n t l n g has a semi unzvrrsal joint zn f r o n t , w i t h a push pul1 s y s t e n ~a t the mlrror e n 4 f o r adlzcsttng a n d lochinq Ijy looszng four t h u m b screws, t h e reflector w i t h complete m o u n t i n g can be t a h e n o f the refractor, and ay e a v i l ~ r ~ p l a c r d , wzthout Sisturbing a n y ad?uetments prevrouslv madr. Whzle thzs reflector vnay be u ~ e das a jinder, it uau not rnounted u n the refractor primartly for thnt purpnsr but maznly because the sante m o u n t i n g sprups both telescopes [ I t comes pretty close t o b e ~ n ga rtchest field telescope-aue chapter 0% thal aicb~ect-Ed ] Al1 brtght s u r f a c e s , w ~ t hthe exception o f the refractor mazn t u b e , are finished in baked.on l a c q u ~ r .
-METAL
PARTS
199
outer cell, whicli screlvs to tlie rntiin tiihc, tlie other section or inner cell, wliicti Iiolds the objective and screws iiito tlie outcr cell. See Figure 5 , Ieft and riglit. S h e t w o forms here presentecl are ;i departure from standard desigri. Tlie first form or design is adjustable and is m:rchined frorn one casting. Tliis requires making n pattcrn. TIic sicond form or design is not adjustable, and is made frorn lieary-\~allbrass tubing, tlius climinating the necessity of rnaking a patterii aiid :I c2istirig. Some professional makers prefer üdjustablc cells, ispecially for ob,jecti\res of 3" and uver. O t h i r
All d r a w t n g s b) the author
FIGCRIí
l r f l l i a n d rlrnwiny i v a n ndlttitcrbl~ oiitrr rpll, ~ 1 1 t h t h r ~pul1 ~ YC~PU~L'C l Z O T h a p a r t , t h u r qivirig [zmztud ndltirtrntnt hi, rolllng thp haines o f the cell o n t h e douhli enti rone. I n thz. rlvutgn thr < i o u i i artd prnt of thr nbjectiar ar? niounted darpct cn th? objrct rnd Iialf of t h r o r ~ t e r rrll T h t tnnrr crll ronstrurtznn siiorr~n at t h ~ i g h tzs also suttablu and drstrable t o tcse zn the othrr deazgn .VI/ addznq tliree purh s c i e w s t o t h p t h r ~ rpnll irreuvr t h r re11 1.071 be made atrnlght puslipull zn operatzon, thici niakzng t h e dotcble und con? u n necesvarv T h e doublv end corte c o n s t r u i l i o n , u~itli three piill scrptur, zn the bptter d ~ s i g n ,r h i r f l y beeauor, u z t h the doicblr r n d cone, thr loint z * rnade p r a c t t c a l l ~ ~dihst proof, thus cuttzng d o w n o n t h e nnzount of cleanzng neoessarv t u k e e p t h r objertzve zn good conditton Th6 ~ i g h hand t drawzng shou)s a n znnPr cell constructzon %n n n o n a d l u s t able outpr crll castzng. A n y combination of t h r t w o drawzngs rnay be made t o s u i t t h 119~7'7 ~ rrquirements I t tuill add tu thp appearance of the fin~shed job if the r i m of the protrcting enp zs hnurlud, also the odge o f t h e sleeve o f t h e znner cell a n d the o b ~ e c t end edge of the inner cell P
expert makers will tell you t h a t all work of centering-i.o., coordinating the optical axis of the objective with the mechanical axis of ttie tube-should he so perfectly done as t o make an adjustable cell unnecessary If cell adjustments a r e necessary when your refractor is completed, i t will be highljgratifqing if the cell is adjustable. The right hand stctional drawing shows how the cell is designed when an iiiner cell is t o be used; the other shows how the objective can be successfully mounted in the end half of thc adjustable nr outer cell, thereby
200
TIIE REFRACTOR
eliminating t h r making of aii irinrr crll. Wliile tliis latter plan shortt-ns tlie work, arid would prove satisfactory iri srrvice, i t lacks tlic coiiveiiirnceeasy aricl safe rerrioval of t h r objective for cleaning, etc.- protection, and coinpleteness of tlie first plan, whicli calls for an inner cell. IIere follow some prrictical details for making the complete adjustable cell assembly shown in botli drawings. For clarity, tlie teriiis outer arid inner cell will be used exclusively. The inner cell sliould be made first, in case the inner cell type, nt the right, is chosen. I n the lathe, chuck a piece of brass tubing of sufiicient diameter, wall thickness, and length. (Length includes desired lengtli of inner cell, length of threaded sleeve, backing harid, lcngth of tubing held in jaws of cliuck, plus, say, 3/4" for facing and four cut-offs). Use your owii design for the inner cell, o r follow the design shown. First, face the end of the tube. Increase tlie inside diameter of tlie tube t o the actual o r planned diameter of the objective (the objective may be made t o thc cell, or the reverse) to forrn one side of a collar or flange. This collar provides the front seüt for the objective. Cut a thread on the inside of this new diameter, for the sieeve. Reduce the outside diameter of the tubing, as indicated in the drawing, in order t o form the bkirt of the inner cell. Ciit the outside thread on the inner cell t o the seat previously machined; this thread, of course, screws into the outer cell. With a parting tool cut off the cell thus f a r constructed, according t o your requirements for length. Lay this cut off portion aside until the sleeve and backing band have been made from stock ivhich remains in tlie chuck. The sleeve sliould he made first. Reface the tubing a t the cut-off and knurl the edge of the end before reducing the diameter and threading. The machining of the band is obvious. The fit of the band in the cell should be the same a s for the objective, Le., so t h a t i t will just drop in without forcing-loose but not "sloppy." After removing tlie tubiiig from the chuck, chuck a piece of cast iron or brass. This is t o be mactiiiied and threaded as a mandrel on wl~ich the inner thread of the inner cell di11 screw. Screw the inner cell on the rnandrel a n d finish the front or objective end of the inner cell. The Outer C e l l : I t is assumed t h a t the casting for the outer cell is now on hand, having been made froni a pattern, a s shown in Figures 2, 5, 6 a t No. 1, and 8 a t No. 2. The one-piece casting for a two-piece outer cell is firmly chucked and the rough surfaces "hogged" t o approximate dimensions. Bore t o requirement the inside diameter of the casting and cut the thread for the outside thread of the inner cell. Next, increase the inside diameter on the outside end of the casting, forward a s required (see drawing) t o a seat, for the seat ori tlie outside diameter of the inner cell. This new inside diameter on tlie casting should be '/y'' larger than the largest outside diameter of tlie inner cell. The seat should be deep enough, or f a r enough from the end, t o permit the inner cell t o be buried and leave a t least y!" on the inside end of the casting, on which t o cut a thread for a protecting cap o r
-METAL
PARTS
201
cover. Machine the outside of the casting t o the required dimensions and firiish it. Drilling holes in the flangr nf the casting for the adjusting screws is wisely the next step. Do this drilling on the dril1 press, removing from the lathe the chuck holding the casting. On the finished front face of the flange prickpunch the lncation of the drilling centers for the acljusting screws. A t this point you can choose between the oiiter cell design shown in Figu r e 5, and a push-pul1 design. The push-pul1 will require 6 screws, lorated in pairs--one push, one pull-around the flange, 120" apart, and will not require the separating band with cone end bearings (Figure 5, a t left).
FIGURE6 T h e v n r i o u ~ patterna u s e d i n m a k i n g t h e r e f r a c t o r s h o w n i n Figure 1 . F r o m left to n g l r t . h o . 1 ad]ustable ceU. Thta p a t t e r n separates between the u p p e r a n d mtddle r m g for'moldtno. T h e cyllnder nboar tile t o p rtnn zs a core p r ~ n t Thc bottolh cylinder i s cnit solid, f u r holdlny an the lnthr chuck. Nos 2 a n d 3 are for the mountrng h a 4 in a m n < i d ] t ~ r t a b erll l ~ w i t h core prznt o n t o p and solid c y l ~ n d e ra t bottom, f o r holda~ry 2n thr chuclc N o 5 zs fov the control end asmemblg. T h e core should r u n throunh t h e c a s t m g . N o . 6 ts a dtxk f o r the protecting cap
If the adjustable cell design is adopted, only three pull screws need be used. They should be located 1200 apart on the face of the flange. No. 8 round-head brass screws are a good s i ~ eto use. Remember to witness-mark the flange of each half of the outer cell; also that the tapped holes for the push screws should go through the front half but not into the second half of the cell; that, after threading the holes for the pull screws in the casting, the latter is divided into two parts; and t h a t the pull holes with a thread, in the front half of the cell, should be enlarged in order t o allow the screw t o slip through the hole. Replace tlie chuck, with the casting, in the lathe. With a parting tool dividc the casting into two, parts, by cutting transversely through the flange from the circumference toward the center, leaving %" of flange thickness or leugth for each part. Face the half o€ the casting which reinains in the chuck, and bore and thread it t o take the thread on the No. 1 end of the
202
THE REFRACTOR
main tube, using the No. 1 ring cut from the No. 1 end of the main tube as a saniple or tritil threacl. Macliine tlie outsitle entl of inside di:irrieter with a 4.50 taper, as per Figure 5, at left. Cut off from stock in cliuck. From a suitable piece of stock put in the chuck, a mandrel is made, on which to screw the front end of tlie front half of the cell. After the front half of the cell is mounted on tlie ~riaridrel, face the flange aiicl cut tlie 45" taper for tlie double-end cone. Machining the short band or doiihle end cone with 45. taper on each end, from a piece of brass tubing, completes the niiter cell. Cell A s . ~ s m b l yiifade f r o m Henvy-wdl Tubing: The procedure in making a double cell (double: meaning outer and inner cell-altliough in this example the inner cell is not completely buried or encased in tlie outer cell) is practically the same as for the adjustable cell already described, except t h a t thrre are no patterns to make, no castings to get, no flanges to divide, no adjusting screws t o locate. After the inner cell is complete and cut loose from the tubing in the chuck, as described above, and the threaded sleeve and backing band or ring made, i t will become obvious that the tubing in the chuck is to be threaded t o take the inner cell. When this thread is complete, screw the inner cell into place and finish the field end, and machine the outside surface of both cells. A t the joint of the two cells i t will be desirable t o cut a shallow V, as a finishing touch, also t o indicate tlie line of separation. To cut tlie thread on the outer cell which screws on the main tube, the outer cell is mounted on the mandrel described under "adjustable cell." The objective, when not in use, should have some form of protective cap or cover. A brass disk with a knurled edge, whicli screws into tlie field end of the ccll, is most complete and impressive and therefore tlie most desirabre. To make this cap is not, in any sense a problem, except in securely holding the stock in the lathe for machining. Here is a wap to use the chuck fnr holding, which will probably prove successful if you do not attempt to take heavy cuts-in other words, if you will nurse the work along. Chuck a llh iron " pipe coupling, face the end and remove it from the chuck. Chuck a disk of brass of suitable size, either cast or Iieavy plate, face a n area of a size niore than equal t o the end of the pipe and remove i t from the lathe. Solder the faced end of the pipe to the machined surface of the disk, centering them as best you can. Return the iron coupling t o the chuck and machine a collar of suitable diameter on the brass disk. This collar should be not more thari 1/4" long, with a wall tliickness of I/s". 0 1 1 tlie outside of this collar cut a thread which will screw into the thread in the field end of the outer cell. Knurl the rim of thc brass disk. Machine the chuck side or face of the brass disk, leaving the knurled rim %" long or thick (however you view it) and cut the disk from the coupling. Support the disk in the chuck by expanding tlie jaws of the chuck agaiiist the inside wall u i tlie collar. Daub a little pitch paste (pitch cut in acetone) on the jaws of the chuck, in order to kecp thc disk from slipping. Face what becomes thr outside surface of the disk or cap, to a nice finish.
204
THE REFRACTOR
refractor. It may riot be an exiigperation to add t h a t the new design simplifies makirig a rack and pinion control, while offering a superior device. Let us s t a r t a practica1 consideration of tliis new control by giving each major p a r t a name, with n rough pictiire of how the parts assemble. See Figure 7. The shield is fastened to the main tube by means of four screws with nuts. The barrel extends throrigh a hole in the shield, and is fastened to the shíeld, preferably by "sweating." The sleeve which carries the Iialf-riioon-shaped piece which supports the rack, slides into the barrel, and is locked in place witli a set screw in the wall of the barrel. The cylinder carries the eccentric pinion shaft, piniori, and finger wheel, and slides into the sleeve, being lockecl in place with a set screw in the wall SlDE
INSIDE
'STUFFING BOX
FIG~RE
7
Detaib uf thr: focus control.
of the barrel. This screw passes through a n enlarged hole (for adjusting the sleeve with the rack) in the sleeve t o hite on the cylinder. A 2" length of rack is fastened t o the focusing tube (not the draw tube, which slides through the focusing tube) preferably with a neat job in "sweating." Brass rod, round stock of suitable diameter-1%'' or more-should be used from which to make the barrel, sleeve, cylinder, and finger wheel. Study the sectional drawing in Figure 7 until you have a clear mental picture of just what t o do, and how to proceed. Make additional drawings, with dimensions. First, machine the barrel. Bore and niachine the sleeve (note the flange on the sleeve, the rim of which should be knurled). Machine the outside
-METAL
PARTS
205
diameter of the sleeve from right tn left, up to tlie flange. F i t tlie sleeve to the barre1 by trying the harrcl on the sleeve. The cylinder is rnachined in tlie s:iirie rn:rnner as tlie sleeve, except for boring. The flange on the cylinder shoiild be the same size as the flange on the sleeve, and ttie rim sliould he knurled. F i t tlie cyliricler to tlie sleeve by tryiiig the sleeve nn tlie cylinder. Later, wlicn tlie chuck is free (nothing in i t ) , carefully chuck the cylinder and finisli wliat hecomcs its outside face or end. Drilling the eccentric Iiole ir1 tlie cylindcr is preferably done ir1 tlie lathe, by chucking tlie cylinder in the four-jaw independent chuck. Machine the finger wheel to any drsired design, and knurl the rim. T o locnte the rack on the tube for sweating, scratch a line on the tube, squaring i t witli the end of the tube (use a t r y square), or put the tubc in the lattie and scratch a line on i t with a pointed tool in the ton1 post, by sliding the eompound slide rest from right to left. Carefully clamp the section of rack to the tube a t this scratched line, and "sweat," Arst tiiining the surfaces. (Note: Supporting tubes or tubing in a lathe may be greatly sirnplified by using a revolving cone tail center. The cone should have the standard 60" taper, and be a t least 3" in diameter a t the base of the cone. This size gives a wide range in usefulness. Such a revolving tail center is a n important lathe accessory and should be made ball-bearing.) W e will again take u p the sleeve, in order to complete it. The sleeve carries a half-moon-shaped section of a brass disk (see Jl, Figure 7 ) on whieh the rack rides, made as fnllows. Machine a hrass disk to the outside diameter of the sleeve (slightly smaller), with ;L width or length equal t o the width of the rack, plus lh2". Machirie a sliould~ron the disk, letting the disk fit into the sleeve 1/32" (tlie two pieees will later be joined a t this shoulder by "sweatjng"). With a hacksaw cut the desired sectioh from the disk, finishing this cut on the section, in the lathe, by facing in a twojaw chuck. On this finished face, each side of center, (length) prickpunch for two 3/ltit' holes. Dril1 and t a p them. Turn two small corks (bottle stoppers) into cylinders whicli will screw into the X6'' holes. To cut the revolving cork use sandpaper. Fastcn a small cork bottle stopper t o a piece of j/," round brass rod, with hot pitch or seatling wax, and put the brass rod with the cork attached into the lathe chuck for turning down the cork. "Sweat" thc half-moon-shaped segment or section to the sleeve. Screw the cork cylinders into the holes and, with a razor blade, cut off the corks to within 1/S2" of the face of the segment, according to your requirernent-in other words, so that the rack will ride flat and square on the corks. The shield, when finished and mounted, should be about 2" square-curved, of course, to fit the main tube. Make it of annealed sheet brass 1/1,3'' thick, accurately formed to the main tube, o r froni a section of brass tube of suitable dimensions. This should be machined on the inside for fit with the main tube, and finished on the outside to harmonize with the remainder of the job. This latter riiethod is a definite procedure and takes, probably, no more time to make than bending sheet brass into a clase fitting shield, though
it iiisures it snperior r(-si~lt. Siip1)ort t l ~ ihIii(-l(l in tlit* t\vo-.j;t\v cliiick, in or(1t.r t o boi-c. tlie Iiolc fur ;i ~ u fitg mitli tlie btirrcl. Prick1)iiricli tlii four coriicrs of tlir sliielr;iss \crr-ws. (AI:ike your vv;il-lie:id scrcBwsl)y turiiiiig ;i fllit-lie:~
FIGURE 8 F T ~ l iIs f fI ~t o riglit: S u . 1 , i s ri 1tii1t-a~7jr~sl~r7~le rrll. Yo. Z is n puslz-gzcll r~11. S o . :: i s rr P o r r o /)tis?n box fi~lrt.rtirigx!í,ste>n, hor<siiiql. .Yo. 1 is t l r ~tr,i~rplfrte
~rscfliii
i ~ t n k i ~ i\-o. { ~ 3. S o . 5 is tlrr i ~ iI.'iyil?us 2 (!7111 4 . A-o. 6 is t h e
i.c,pr,<,tor8Ilo~cniri E'igttro
triirror enrl nssu~riblgof tlir rr~.flr,r~tor sliofcli adapter ttcbe a n d rliayo~irilsulillort of tlie
4.
m o r e tlie shielcl froni the main tube. Prickpunch around a line scr:itclied on tlie main tube, on tlie line, a little more than %" npart. TVitli aii '/S" drill, drill tlie piindi rnarks, t:rking o u t tlie circular piece. Finish tlic rougli iriirrgiiis of tlie liole witli a file. W i t h tlie e t screws in tlie hcirrel, fncing down, fit t h e barre1 into tlie holc of tlir shield a n d "swent" t h e joint in a bunsen flame. Small bits of solder should be located a t tlie joint vn tlie back of t h e shield. I f the outside surfacc o f tlie shield nnd b : ~ r r e la r e t o be I~rcquerecl, this should be done a s tlie next stcp, before the sliieltt-barre1 cornhiiiation is fastened t o tlie mnin tubc "for keeps." The pinion-a steel pinion is preferahle with a brnss rack-is swentcd t o tlie steel shaft. See Figiiri 7 a n d note t h e cone beuring of the finger wlieel
in thc cyliiitlcr, :ilso iiotr tlir cork \v;islier l,.íc;"tliick hrtwcen tlic 1iiiiiori itrrtl cpliiider. Wlit~ii;issc~nl)liiigtlir 1)iiiioii sliaft witli tlie piriioii, i i i tlie cyliridc~r, coiriprehs tlic c ~ i r kwiislier :i~;:iinsl tlie cylin
208
THE REFRACTOR
tiilic (Iiiil(1irig tlie dr:i\v tiilic) iiito tlic oli,jectivc ciid of tlic. 1)c:iriiig in tllc c:itiiig, iiiitl slitlc it tliroiigli. li'roiii ;I piec.(. of f d t !/1,;" or sliglitly pr<*;itrriii tliickiiess, iisiiig :i rezor l)la(lt, :ind str:iiglitedge, ciit :L stril) !.í,;" to %" wide, ticcorcling t o recluireiri(.nt, long enoiigli to wr:ip ;iroiiiiroiiplit irito proper :itl~iiistiiierit witli tlie rii<:lí hy turniiig tlie eyliritlc.r, ;ifter wliidi tlie cyliricler i\ lock(.d witli ¡t.; sct scre\i7. A siii~ill:inioi~~iLc~f noti-riiii~ling Iiil>rie:int c:iii he iisecl oii tlic rack ;ind piriion. 1I;ike srii;rll soft copl)er clisks on which tlie set screrrs can bite, tli~is :iroiclirig tlic scoring of the niccly iii;tcliine:ieed10" tip:irt tlirciugli tlie rn:iin tulie, "1) t o tlie field encl of tlie dr;iw tiihe, tliis will corripletely fiilfill tlie reqiiireiriciits. (Esposed siirfaces slioiild be fltit bl:ielieiied.) One wny to iri;ilíe :L siiccessfiil diapliragrn is t o espnnd ;L strip of l(i-ourice cop11cr or brass 1" wide, inside tlie main tulle, witli :L %" o v e r l : ~ ~ Scr:itcIi ~. tlir overl;ip, rt.iiio\-c :iii<1 sitlcler. Tliis btind is soldered inside tlie b:tricl, t o a fiat ~iiecc*of 16-ouricc ¿-opper or brnss in wliicli a suit:ikile sizcd Iiole has hren rri:icle. After tlic b:ind is soldered t o tlie flat piere, tlie siirl)liis of flat pit.ce ;iroiiricl tlie I);iri
in plan, siiit;ihlr fnr srri;ill rtxfr;ictors : ~ n dthe orclinary rrquirernents of the amateur. Ivlitkr working dr:iwirigs. 1Cliike woodrn p;rtt<.rris ('/," t o the foot oversize, to allow for coritritctioii arid finisli of riietal) for castirigs. (See Figure 6, Xos. 2 i~iid3 . ) Finisli tlie coiit:rct or frictiori hurfiices i r i tlie latlie. Finish tlie reriiaintlrr of tlic c:istings liy siirfi~ccgriririirig or witli ;I file. Miicliiiie the <:oiie stutl, piring it a 6" ti1pc.r. C'ut ti tlire;id o11 tlie sm;rll eiid f o r a i/," iiut. Cliuck (two jaw) the tripod Iialf of the riiouritirig, ancl bore antl
FTGIYRE 9 Detalla of ' a n alt-azimuth m o u n t i n g - t h ~
onp
s71ou-n in Figure l .
thread for the cone stud. After drilling, the two castings are awsembled with a %" brass bolt, with a spring Iock waslier undcr tlie nut. The secret of the srnooth holding friction in this joint lies in the cork washer between the surfaces. Use cork gctsket material, 1/1,3" or less thick. This may easily be found in hardware stores. To machine the cone stud, you have set tlie lathe rompound t o 6". DO not cliange tliis setting until a f t e r tlie t a p i r i d Iiole in the tripod head casting has been m;ichincd. Ohviously, this tapered hole is t o receive the tapered stud in order t o make a tapered hearing. After the hole is niachined for the stud, grind the stud into the hnle, in order t o get a velvet bearing, using optical emery and oil. In service the stud can be lubricated by rubbing i t lightly with yellow launclry sonp or with cup grease. The bnnds wliicli hold the main tuhe to the saddle casting should be made of annealcd brass thick. The width of the band should be equal to the diameter of tlie objective. To measure tlie required leiigtli, wrap a strip of firm paper over the main tube, creasing the paper with the thumb nail along the joint of tlie tube and casting. Ccratch flat brass stock from the paper measurement, and bend it in the vise. The use of bands for fasten-
210
SfIE R E F R A C T O R
ing the rnain tube to tlir snrlcllr i s siiperior to f;istcnirig tlie tiibc with s r r e a s t o tlir s:i,jr.<.tive. (Frictioi~clr~~eii(ls ir1 1:irgc rnezisiire o11 ~irtS\siircx, o : r e : ) SIiiis, 2',i" frirtioii f;iccs for ;r 2%" ol),jcctive, .$" frictioii f;icc.s for :L 4" oh,jc(.tivr (ori tlir l>iiis of f/l.'>,wliich :iiitoii~:iticiillypircs tubes of relntivr lengtli). A s;ido(l in the m:itter of :issiiiibly, thzri you should dcsigri yoar tripocl t o rneet tlirse requircrrierit.;, ;ilso t o mcet any indi\.idu;rl f;iniy in sli:ipe of Iegs. Iii :iiiy cnsr, b~iild for solidity. Dimensioiis zind otlier (1ct:iil of tlie tripocl sliiiivii ir1 Figiire 1, wliicli in serrice has proved Iiiglily sotisfactory, a r e : wciglit 26 lbs., over-:ill lengtlr 6'. Encli leg is made of tulo pieces «f oalc (white nsli is equ:tlly goocl) 6' Iong, ?$'' thick, 2%" \vide a t tlie top arid 11/," wide a t tlie hottorii, sl);tced or se1~;iratecl witli 1" sectioris of 1ir:ivy brass pipe, thrciugli wliirli p:iss ?/lG" hriiss bolts. The herid of the tripod is a c;istirig iii Gerriiiiri silver (brass is suittible a t two tliircls tlie cost) with wiiigs 1" in tliickness, located 120" np:rrt arouncl a 2'/2" cylindrical centcr portion. See Figure 9. This tliree-ivinged casting should be machined t o a singotli surfnce on top and hottom or two en&, a n d bured witli n tapereti tioie, flat surf$ices on the tliree wings. Surface grind t h r m if you hnve the equi]iinent, or use a filc. Tlie three wings and tlie tops of tlie lcgs, slioiild be (Irilled for 1/2" hrnss bolts. LTse Iieíivy liriiss washers on eitlier end of the bolt, with n sprinp lock iv:isher under tlie nut. Dril1 the legs for tlie leg bolts, ;it 4", 12", 32" ;ind 32" frorn tlie small enil of the legs. 'Po aaseriible, put tlie ?", brnss bolts into the 4" and 12" lioles, use washers, mnke III> tiglit. Spririg tlie leg linlres iip;irt, t o drop in tlie separnting pipe sectiori at tlie 32" Iiole, and do tlie sanie a t the 52" Iiole, leaving tlie top end t o nsserrible last. Thc foregoing detailecl description will be c:isily followed ancl understood by t h r rx1)eriencid craftsrnari. 'I'o tlie less experiencrd, or beginiier wlio has a facile grasp of thinpq micliniiicul, let it be said, i t is not nrcessary t h a t you shoulcl rnemorize the entire procedure in malcing a refractor, a s Iiere presented, or tliat you slioul
l)l;rr~is to follow tlie st.qiieiice of 1)rrcciitntioii frorii tlie st;irt, taking sliort scctioris to (ligest ;iiicI tlieii t o iiiake. Tliis srqueiice tliing is iiot a dee~>-d~c.d monster, biit a fricridly lielpcr; it has beeii "clicclíed :irid doublc cliecked" for your I~enefit. F o r tlie coii\.eriierice of tlie reüder wlio clrsires infoririation uri wherc t o purcliase in:~terials referred t o iii tliis cliapter, tlie followiiig firiiis witli
T h e author.
addresses a r e added. ZTndoubtedly other firnis rrnrlcr eqrially goocl sirricr t o the customer., This is desirable inforrriatioii ancl in no srii\e intendctl t o be a n aclvertisemeiit. For hrnss tubing (bullt.tiii lihting a i z e s ) : Patterson Brus., 27 Park Itow, New York, N. Y. For rack and piiiion parts (catalog): Doston Gear Worlis, Iric., Sortli Quincy, Mass.
Thr Rrfl-acting i ' ~ t ~ s c o l > ( * - l ' r i n c i p ¿ í , of s 1)rsign nnd C o n s f r n c t i o , ~ H ) J It I I \ \ i ~ \ h t > 3Ieriiber Tccliniral Staff, Erll l'eli~ptionc Laboratories Ini.
While it is true that ;i rrflectinp telescope can be rri:ide by the tyro-yes, even by the school boy, the productiori of a re;iPIy firic ~ n i r r o rfor it is a tahk t o t r y tlir abilities encl patience of ;t skillful, experiericed worker. Therr can he no deriyiiig that a great deal of pleasiire may he 1i;id frorn observing with ;L telescope whose perfection is f a r below th:it wliirli ir possit~le,anrl tliat the ultirnate dissatisfactiori with siich an instrurnent frequently le:ids t o another arid usually rnore successful attempt. Be al1 this as it m:iy, the production of a fine optical surface requires ;I greot deal of skill. This may he acquired during the first attempt, hut riiore frequently comes after severa1 disks of glass have slid back and fortli ncross 1;tps oii tlieir way t o more accurate figure. The writer lias been privilegrd t o see and comment on many letters from the veritahle ;~rralanchewhich, during rccent yenrs, has descended iip«n the slioiilders of A. G. Ingnlls. These letters iridicate that there are n large nuniber of riieii (and a few women too) wlio Ii;ive the mechanic:il ecjuipnieiit and tactile skill nrcessary for tlie production of an accurate optic;il surf:ice. The helief t h a t the refrzlcting teiescope commends itself t o amateur construction, and is more satisfzctory for the amxteur use than the reflector, furtliered the thought that an article covering this typc of tclescope in detail, and written for those ~vliose equipment consists of more than a barre1 of rocks, would be welcome. It is fnr from the writer's iiitention t o belittle any efforts, liowever meager, or t o deny that beautiful reflecting telescopes have heeri produced by those whose skill traiiscended the need for any tiut the sirriplest tools. However, the optical and mechnnic;tl parts for a good refractor cannot be made on the kitchen table with a cold cliisel and hammer, nnd a perusal of the photographs in "A.T.M." will indic:ite t h a t rnaiiy of the followers of this cliissic a r t did not make their instrunients with the above-mentioned tools. So, despite the satisfaction which may be obtained from crude telescopes made with a minimurn experiditure of money ancl ahsence of fool eqitipment, tlie results from a n iristrument involving long, careful work and a not too great stricture of tlie pursz will be pratifying. What follows lays no great claim t o originality. It sets down thc rcsults of the writer's experience and thnt of his more accomplished "brotlirrs in cornbat." The methods of griiidirig ancl polisliing glass t o he described are those of the profession:rl opticians of liiphest rank and, wliile tliese rnetho
iioped will I>e regtirdcl<.\ iiivolvrd iri tlie 11erform:iiice of :ir1 :ic~lirorii;itic object glass. UTliile :tpprosii~iate rrietliods of design irrr iihccl, r~.fcrriirrs tire zippended tlizit will pcrrnit tlie c~~itlriisittstt o wziricler off irito tlie fi<.lJectjvc.s of widc ;ingle, if Iiis coiir:ige Ie;id hirn this far. 'rlie typv of ob,jcctive describerl, Iii~v.~evcr,will Icavtx little t o be erly esc.<-iitccl;iri e r t urntio, re nnd che;ipness. Tlie perfect iirliroiriatisrri of tlie reflector is iipset by ordinary eyrpieces whrn iisetl mitli riiirrors of tlie usiitil f/8 r:itio. Huygcrii;~n eyepieces perfnrrn uns;itisfilctorily ;ts regzirds both s~)liericzilancl color nbcrr;itiori f o r rtitios rniicli l>clo\\l f/12. Tlie prrcisiori of figure iieccss:iry is very clifficiilt t o zittain, espcci:illy l)y tlie Foiic;iiilt test :it centcr of ciirv:itiire. The silvrr co:it rniist frecliieritly be rrnewed in rnost urb:iri localities and re-collimation of tlie iiihtriiiiierit after returning tlie rnirror t o its cell is a tirehoriie tiisk. \Vide :il)erture ot)jectivcs are very sensitire t o collixiiation ;irid tr'slight niis;ilinemr~ntis riiinoirs to the iinagr. Tlie oiitst:inriess;irid for celestizil pliotograpliy. For tlie latter piirpose ;in f/5 rnirror is a voluable tool, t ~ u to rnirror of siicli Itirge relative ~ i p e r t u r elies f:rr heyoiid tlie capabilities of t h r average ebeginner. The refractor suffers from three disac1vnnt;iges. Optical gl:iss siiitahle for a first clt~ssleris is espensire-tlirre to ten times the cost of Pyrex or Ternpas, deperiding on the di;irneter. Tlie telescope runs t o :iwkward lengths in the larger dizlriietrrs, since a foc:il rativ of 15 is emploj-ed for those o i r r 4" aperture, :tnd it will not be nearly as satisfactory for photograpliy, where liglit concentration and achromatism count most Iieavily. Refractors m:iy be designed for pliotogrtipliic use and corrected for the violet end of the spectriim. Properly designed as t o curvature, tliey ~vill rmbrace several square degrccs, with good definition t o tlir edge. The latter ~ierforrriance cannot he equalled everi hy the new Ritchey-Clireti~n curves and other optical tricks whicli have recently been developed for reflectors. I t is possiblr t o rriake a three-lens :ipochromat for photo-visual work in which the more actinic rays a t tlie violrt end of tlie spectriim come t o tlie same focus as tliosr in the visually brighter green-yellow portion. Sucli a combination permits obscrrntion and subsequcnt photogrtipliy a t tlie same focus. While tlie mechanical construction of a tliree-lrns ob,jective offcrs iio particular difficulties, the computation for such c i lens is involved. Special glasses wlinse ratio of dispersion t o refractire index lies off tlie I)e;iten patli are rrquired, and are very vxprnsive in ronseqiience. 'IPie clesign of such
:in ol),jertive, intt.rcstiiig :is it i k , lics li(.yoritl tlic scopc of tliis :~rticle, as a ilesigii 1)y t<.
wlierc *4 is tlie iliarrirtcr o f tlic- iil),jceti\-i.. ' ~ ~ I I I ;IS 4i/:" (1i:iiiieter telt~scope will jiist sc.p;ir:itc two sttirs wliosr srl>:lrtitioii oii tlie celt.sti:il splierc is ciie secoiitl of ;I rc. I t 1ii;i)' tic iiirritioiie(I ~):irciitlirtic.aIly tli;~t ; i i i iiri:igcs of a fiiiite otjjec.1 siil~trriclstlie s;iiiic ;ingle ; ~ tlic t fociis ;is tlie ol>.iect. I'or r~iiiii1)le,tlic. iiiooii subteiids aii :iiiglr of ii~)l)roxiriiotc~Ip 30'. l'lie size, tlierefi)rr, o f tlir irii;ige V)
W
r
tlORIZONTAL
Ctt
KJ -I-I-
-J
a ORH
Al1 drnwings a i i d yhotogrul>lih 11). tlie ;iutliol.
Fic;ri;i<
1
(;i-n)>/ii<.ilirfliod OJ d ~ t c r r > i i n i n ydialnrter.? of din),lrr,lp)i! s f o l i . jocll.silig fui>?, n n < í , h . ~ znf ~ j ~ r i ~ r n . I n t l i a /<(!,out( L ~ O I > P .tha 4 " I ~ I I P 1.1')1r?~rnt.sf h r o h j ~ ~ l i ~I I . I rI ~ ..id flrp i ~ t i n g u s i z ~ . n!, r>~cn.suririp n l o n g t h a hortznritnl n.ris l o f h r lot'ations of t h r i S n r i o ! i s i t c m s , r l i n n i c t r ~ . ~rin!j ~ hu s p l p ~ t p d tvkirIi i,,ill ) I ~ S Sn / / t l , ~light jrrirrr t h r o I > j ~ < . t i !i,hrlz r~ JO~LIR OIP I a ~) % object t k e S I Z C o f t l i ~rnoo~z. S P C tr.rt jor d e t ~ r r n i ~ i ~i r~r (i«yy ~dizr.
of the moon is determined hy tlie foca1 Iength of tlie telescope, and is independent of the ilinrrieter of the oI>jecti\e. The s i ~ eof tlie iiiiage is important in reflector.; wheri selectina a pri51n « f proper size, and in refractors when determiiiinp tlie bize of holeb in cliaplirapms arid eye tuhes. S o take a concrete example, consider a 4" telescope of 60" focal lenptli. The tanpent of 30 minutes is approximately .009, so that .O09 x 6 0 " ~ . 5 4 " , the diameter of the imape. If a ~ c a l clayout of the qyqtem be drawn, with the lens diameter and imape size full scale and tlie focal Iriipth 1/12 scalr, and lines a r e drawn connerting ttie extremilies of tlir lines representing the lens and iriiagr, as sliown i i i Figure 1, t h - riiinimiirn iliametrr of iliaphr,igms and
tiiI)~-\1ri:iy 1 ) ~grapliic;illy (1t.tcrtiiiiii~il. .\ir c~>-t~l)it~c(~ ttil~c,prihrii 11iagori;iI. ;ind ~li:il~lir;igni;ir<*iiitlic:itrtl oii tlic íigiir~.. Note tli:it tlie i i i i i i i i i i i i i i i iiiooii's ;irigiil;ir proximately tlie snme as tlie siiii's) is sc.lt5clr(l, \iiice :ortiori:iIt o its :ire:i, it f o l l o ~ \ ~t1i:it s lies tlir liplit g ~ i s 1 1115 4. LTrifort~iiiatrly,iiicre:ise iri crtiircs. Ilvll strilirs ;L li:t~)pyiiitsriiip u.\, :iftrr tliii.; dipressirig, t o wli:tt prttei\iori of surf:icc is rer~ cli~ired. I.ct lis, for tlie stikc of coiiip:irison (wliicli S l i : i k r s ~ ) e ; ~coiisir;i(-ti<.ally pcrfect (lttfiiiition -tliat is, any irnproverririit in tlie figure of the ol>,jective mliirli \vil1 rediice 1 ~ 1 t l dift'rrerice i to :r v:iliie I)elo\r tliis ;irrioiiiit will iiot iioticcobly irriprnre tlic irriapc.. As :i mzitter of f:ict. ;t ~i:ith clift'ereiice of twice tliis nnioiiiit rri;iy be toler:ite(l, ancl tlie deteri9r;itioii of irn:ige resulting I I I : ~be ~ anr~ulled hy rriinute re-fr~ciising. As tlie 1:itter coriclition recluires a siirface sufficiently (lifficult to produce, we will considcr this tlie allo\r.able tolerance aiid proceed froni this hypotliesis. For a reflectiiig siirfnce t o retiirn liglit rays :irriving pnrnllel l o tlie opticnl ;ixis t o a fucus, its sliíipe rniist be par;iholoiclnl. From tlie rnntliern;itical properties of tlie paraboloid it iiiay be discorered tii:it the cfmtcr of ciiroatiire of tlie srnall eeritr:il zone folls on tlic optie:rl :?xis a t a point iienrrr t o tlie curve tliriii tlie ceriter of ciirr:rtiire of Llie rdpt, zone. Tliis differerice in distance is defiiied witli suficirnt accuracy by tlic relation:
alicre
D is the separtition Iiet\rceii tlie points r tlie radiii5 of tlie cdge zone
I i tlie rorlius of curx ature
TIIE IZEFRACTOIZ
21'7
Foucault's ingenious rrietliod. J . H. King (aiicl indrperideiitly Kirkh;irri :incl Wriglit) lias niorlifie
where df=chnnpe in focus (:ixial distance) dp=difference in path Iengtli f=:cperture
A
figure of the telescope.
Xssuming tliat 1/2A=.00001", nnd n focal rntio of 8, we get, by substituting in tlie above forrnula: df =.OOOOln X 8 X 6%=.00B" npprox. Now, since the pinhole stands still, doubling tlie motion of the knife-edge (our old formula r ? / R ) , and since the transition frorn liglit oripiri:rting a t tlie ceriter of curvature t o light originating a t infinity halvei the aberration, we have an allowable error in reading the knife-edge of 4X.005", or .020", before exceeding our criterio11 of allowable error. It will be apparent t h a t this is not beyond the realm of possibility and it, in fact, explains why it has been possible f o r so many amateurs t o make mirrors tliat perform creditably. Tlie accuracy required is a function of the focal ratio, and a substitution in tlie formula for a n f/B niirrur will indicate that, for this focal ratio, the knifc-edge miiit be placed within a n error of less tlian .008" for good performance. Tliis is a rigid requirement and one that can be met by but few. If it be borne in mind that the error allowed in the above diqcussion must be lialvecl, in order t o obtain a practieally perfect rnirror, the difficulty of t r s t i ~ i g a t center of curvature is made clear. So difficult, indeed, is the
prnurlioseof corii~):irisori, corisitler tlie iiiteiisity of tliis crritr;il ;irr;t to be unity. 'Then tire followirig t:ihle list.; tlie teliitive illuiriin~itiori of Iliii spot for vnrious patli dift'ercnces: T o t a l path variation Percent of light in (in wave-lengths) central spot 0 . . . . . . . . . . . . . . . . . . . . . . . . . . 100
55 . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
80 1. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Thus, f o r a pnth difference of % X the liglit concentrated in this crntrnl spot 'ivill b r 95 prrcerit of that i r i tlie iniage forrriecl by ;I theoretic;illy perfect objective. M1itli %A only 20 percent of tlie liglit possible is sc:itteredwliich is not too 1):id. Xlicliclson's foriiiula for thc nllownble varintion from truth of a surface for ',&A p:itli difference follo~vs: =
---
-
X
cos r) where ~=vnriation of iiirf;ice i -;ingle of iiicideiice, =arigle of refr:ictiori or reflection Y F o r n reflectirig surf~ice,with eiitering light pnrallel and pnrnllel to the axis, tlie angle i is very srrinll ; ~ n dits cosine is, tliereforr, nearly iinity. For example, i = 2" for the edge ray froiii a 6", f / 8 mirror. Since tlie angles of inciderice anrl reflection are equül, r=i. Substituting thebe values in thc equation ure have: 4(cos i
- p
X (,A = - 1 for reflection) 8 This tells us tlint, in n reilectinp telesrope, for an edgr ray t o meet n r a y from tlie center so tlint their patli differcnce shall be %X, the surface may not dcp:itt froin rnatlierriatie:il triith by more tlian Y8X. For a refractirig surfncr our rxprecsion becomes: e
e-
X
4(p cos r - cos i)
-
4(p
x
X - -. - X 1 - 1) A(,A - 1 )
wliere: p is tlic iivcrtige r<.fr;~cti\ciiidt~xof tli? Ierii-s.iy Siibstitiitiiig tliis \;ilue, \ve grt
1.5.
A
= -
2
Thus it ay>pe:rrs tlitit tlie siirftlce of :I reflector mrist he figurcd t o an accurticy forir tiiiirs as g r v i ~ tiis i i iiii ;ciid the 10" refr;ictor a t tlie Fr:inklin Institiitr a t Pliiladrl~iliia. Tlie seeiiig \vas poor, whicli seriously handic:ipl>ecl tlie larger nperture but, crrii ;illowing for tliis, the perforrniince of the refractor sliowed a marked sup<.riority. Haviiig tliiis outliried xrhat is a t best tlie writrr's opinion of the desirability of rnaking a refrticting telescope, anrl sorne of tlie tlieoretirtil and prncticiil re;isoiii suppcrrting siicli contention, we will proceed tu tlie notice of the properties of nri achromatic Iens. If, by tliis tinie, tlie reader feels that he has hecome involved in a higlily mathernatical situt!tion for wliich he Iitis rieitlier the talent iior iiiclination, he may he reassured that, slioulíl he fail t o undcrstand a single word of what has preceded, or tlie optical discussion wliicli inimediately follows, he can still mnke an excellent refr:ictor by following the rtitlier simple instructions undcr the heading, "Miiking an Achromatic Ohject Glass." I n fact, the lenses of many of the world's greatesl refractors were mnde hy men wlio actually had no concc.rri with the niatliematics involrrd, biit wlio possrssed tlie necessary patience, and througli prtrctice ncquired the ski11 needed for generation of the most precise the perfection of this beautiful task-tlie surfiices possible-surftices t o mrtisure wliose defects, the liglit wave-a fifty thousandtli of :in incli-must needs be split in right liarts! The matlieni;rtir:il \vork iiecehsiry for tlie corriplete design of a sirnplr achromatic lens is far from simple. Optical computation is perliaps not so dificult as it is ciinit)ers«riie, hut this need not coricerii tlie timtrteur unlrss his interest lcads hini in t1i;it clirection. Grriit rriath~iiiaticians httre redu<.e(l the intric;icies t o such f«rrn tliat a good leris m:iy be cornputed hy a i i . orie who ciiri suhstitiite iiiirribers fr«rn :i ttiblP into a simple formula. So wlitrt imnie(1i:ltely follorvs may t ~ eigriored by thow rvlio, perliap5 witli sonir rrason, c:ire iiotliirig for tlie ~irincililes inrolrcd, hiit wlio
tlie a<,eomplishmrntortiori;il (lispersion bob 111) continii:illy iii tlie r r r i i i t ~ u l a rof optics, it iriay lie of intcrest to get R grasp of wli:it tlir terms iiican. The trxts tell lis tliat whrn &I ray of light passes froin :I riieciiiirn of one refractive index to onr of :inotlirr it s u f e r s reflection ancl refr;iction. Tliis sounds very complicated hut ir1 re:~lity is very sirriple. F o r exailiple: for-
getting the t r r m "refr:ictirc indrx" for the moment, let us suppose a r a g of light A B , iri air, strikes tlie surf;ice of a plate of plass ohliqurly. Referririg t o Figure '>, TI(' i.; lirrpeiidicular t o the surf:tce 1)I': ;intl is termed tlie normal. P a r t of the liylit is reflected :ilong Al,' i r i sucli manner tliat tlie angle 6 t h a t tlie reflected ray makes with the norriial is equal to aiigle n of tlie incideiit ray. P u t concisely, the law states tliiit whrn a r a y of light is reflected from n surface, ttie angles of i~iciingles a r e a s shown in the figure, tliat portion of tlie liglit wliich is not refiected will eiiter the glass arid, iii so doiiig, will suffer a bendirig. In this case passinp, as it does, from o rare to $1 dense medium, it will I>e berit toward the norninl. Tlie measure of beiiding is called refracti\e index and is the. ratio of the cines of angles
made with the normnl heforv :in
(111 :I riglit triangle t h r cine is tlie niimher ohtaiiied hy tlividinp tlie sirle opposite nn nngle by the 11~r)otlienuse. Tlius in :i tri;trigle linririg for its :iriplcs : < O o , 60", :ind 90" tbe sine of :proxiin:itr.ly. I>iri
is arhitr:*rily t:iken t o h a r r ;I rcf. iri(lcx of 1, so it follows tlint our glnss has :in inclex o f 1.5. 111 gen'eral, tlie deiisrr tlie gl:ihs tlir Iiiglier tlir refr:ictive index. 'I'he synibol @ (tlie Greek letter @, pronoiincecl "mcw") is used t o desigri:ite ttiis quzintity in tlie t:ibles which list tlie p r o ~ i r r t i r s of optic:tl glass, mliilr s«mc writrrs use 11, Iiencc botli will be iisrd iri this clinptcr. If tliis Irtter 1i:is :iritrtlier letter as :I suhscril)t to it, tliiis p,,, tlie subseript desigri:itcs tli~aspectral liiie f o r tvhicli tlie refr:ictive iritlex is giren. II ;;bure, tliereforc., woul
tiori;it~.ly. Sir 1s;i;ic Nc\vt~iii, i i i l i i > c.l;is\ic.;il <~x11<~riiric~iits :tlorig tliis line, tlrri,. tlie crroiicoiis ri~iirliisioii tli:it dislier~iori ;iiic~)pc. \Vi. ;irt. iiow ri.:i(ly for tlic c.oii+itlc~r;iiioiiof c.;irii ot' liglit i h ~);i.hc(l tliroiipli tlit. first 1)risiii i t \vil1 Ilc l~r06ciiiip into ü spectriim in wliicli tliv retl ( l t ) ;iri(l violet (V) r;ijs will I I ~ . x p a rüted a s sliown. If a seci~rid prisiii he irisertctl sIio\vii tlie violc~t riiy erit~riiigtliis prisni xrill be ret'rticted iriore tliaii tlie red aiid a t tlie 11oiiit A will riicet it. 'rliis is tlie ~>riiiciplrof tlic ac1iroiii:itic leiis. lieferririg to I'igiire 4rr, tlie doiihle cuiir-es Iciis by itself wuulcl sel~oratca. ray of wliite ligiit criteririg
FLlNT COLOR CORRECTION
it into n ipertriim, nncl tlie p i t h cif tlie red anrl riolet r:i!< \\.oiiltl be :is itiy tlie lines. If, nonr, a coric;rve lens be inserted in tlie lieiini, tliese retl tiiicl xiolet rays \vil1 be refriicted iri the ol>posite clirectioii Figiire 4i1, ;ind if tlir ciirr,itiire aiid optictil properties «f tlie seccind lens are of the corrert ni,igriitiicle tlir red and riolet rays will be brought to a corrimon focus ( F ) , Figure 4c. I t follo\vs frorn tlie above that the properties of two glasses siiitable for the forrriiitioii of an aclirouiatic ohjectire are, thnt the refractive indices shall be clifferent and tlie partial dispersions througliout tlie sprctrurn for oiie glass be ex;ictly proportional t o thuse uf the otlier. The refrsctive i~idices must differ since, were they the sarrie, one lens ~voiildexactly annul the effects of the otlier and no convergente of light t o a focus would result. Further, if the clispersions were exaetly proportional, al1 the colors ttiroiighout thc spectrurn would he brouplit t o the same focus and perfect achromatism would result. Lrnfortunately, no glasses are available which have tliis latter property, and tliose ~vhicli nl)pro:~cli i t a r e i e r y cxpensire and, because of other optical reasons, require rery steep curvatures t o make ari objectivr of the usu;il ratio of foca1 lengtli t o diameter. In the arerape co1nbin:ition with which we a r e concerned, partial achromatization is srcurcd hy brirlging tlie C and F lines of the sl)ectriirn t o a commoii focus. U'ith pood gl;iss, al1 thc colors between ttre red-orange and yellow-greeri will come very closely t o this. sarne fociis and combine t o
ni;llie xrliitc liglil. I>ii<. to tli(. flirit ((wric.:ivt1) Irns rrfr:ictirig 11i
violet is t r u e also for red, but tliis light is of siich low visibility as t o have practieally no effect oii the ini
I n this, Conrady diffcrs sbme\vlint, iising 5 instead nf 2.8. Tlir forrner seenis rzitlier larper th:iri neecl he. I n iiny c:isc nri ot)jcctive of a~iproxirn:~trly 5" diameter urould, by this formulzi, have an aperture ratio of 15. More exactly it would be 14, biit tlie lioiiit of tlie rn;itter is tliat objectires of smaller diaineter can be worked t u smaller foc:il rntios, while larger ones shoul? have rntios in cxcess of 15. Tliiis n. 3" objectire could be workrd to f / 8 and be expected t o have ;1 color correction equal to that of a 10" u7itli a focal ratio of f/28. It is tliis unfortunate situation that led t o Prof. Conracly's opinion tliat ver- I:irge refr:ictors :ire imliractic;il. Severtheless a n exarninntion of the photographs t;ikeii witli tlie r e r y large ref r a c t o r ~ a t Amrrican obscrratories would indicate, t o tlie laymnn a t least, that not much improvement could be desired. Having disposed of correction for color, we \vil1 consider tlie correction of spherical aberration. Consider a double conrex lens with two rnys of liglit iricident to one of its surfaces, zis shomn in Figure Bn. It wili be noticed that the ray passing through tlie lens near its eclge crosws tlie uptic tisis Al1 of tlie leris :it a point ne;ircr tlic leos tli:in the r:iy p;i\sing tlirr~uglitlie leris nearer the axis. Ariy coriverging Irns, witli sphrricnl siirfaces, ossible with a single lens. I t ~villprrhaps be apparent froni tlir riature of tlie figure that, if Llie froiit surface of the
lens he giren siich n sli;il)r as to iricrc;isr it, r;i(liiis of riirrntiire as the edgr is :il)l)roaclied, this defect coii!tl be riiiiiiriiizc
by a plano-conrcw flin: witli it< <*oiica\t25iirfacr fitting tlie ronrru of the crown. In tlie prodiiction of coiiiiiierei:il oh,jectives it is iiriport:int tlint the surfaces of :i11 leiiscs be sl,lierical, since iion-splieric:il siirf:~ces c:~nnot be producid airlornittic;illy t)y riiiicliiiie. W e :iiiií~teurs ciire iiotliiiig ;il)oiit tliis, because oiir finiil jol) will he to rcriiove sphericnl nherr;ition hy figiiririg, .iiisL as it is done iii rn;iking n irflcclor. UTe sliztll not, Iio\vt.rer, 1i:irc to giic.ss when orie sliatloxv is tlie siirrie as ziiiutlier. Iri oiir figiirinp, tlie Iiriifc-eilgc is placed a t focus :ine(-ii;iiiiiiilleir:illcl t o tlie asic will still l>t. broiiplit t o the proper focus. Since oiir fielcl of iiew need ernhr:ice but a few xninutes of nrc, this is not :L serious matter, hut n leris suffrring f r m i coiim niiist 1)e accur:itcly adjusted so thnt its optical tisis :intl that of the eye-piece coinciilc tic closelq- a s rniig be. If thia prcc:iutioii he iicglrcted z1 s t i ~ riniage like "a," Figure 10, "A.S.M.,"page 429, will result. Thus, if coiii;i he present in :in objective, great paiiis muht be taken in squaring on. ltealizing this, \ve still consider tlie ccmented ohjectire suit:ible for our task. As iioted elsewhere, a eemented objective raniiot, in general, be corrected for coina. IVliat little is present in oiir objective can he reduccci corripletely for Llie ttngular field required by cnreful adjustment (collirnation) of tlie optical parts. I n a refractor, once these adjustmcnts a r e attended to, no re-adjustment should ever be necessary. The various properties of glziss mentioned above, with additional necessary data, are listid in the manufacturers' tables. A n explanation of these tnbles follows Itrter. Homever, mvst optiral g1:iss mnkers select certain lirnited glasses t o recommend for our purpose and their srlection may be relied upon. Aside from the selection of glass f o r i t s refractive and dispersive powers, the quality of the gla\s itself is extremely important. G l a u which is suitablc for the exacting conditions imposed for telescopic usage m i ~ \ t be precision annealed, frce from large bubbles, of high transparency and free from s t r i z . Imperfect anuealing ic a x e r j serious defect and ha? two deleterious coiisequeiices: first, strained arcas in tlie glass, resulting from stresses due to unequal cuoling, hare a different refractive index than tlie glass surrounding these areas, :ind will thus t u r n light which passrs througli theui t o a focus different from that of the lens a s a whole. Such light, if it falls near
tlic riinin fociis, proiliires ;iii ovcr1:ippiiig bliir wliicli ~1rtrrior;rtesthe sliarpiiess o f tlitx iiiitige. Secondly, cooling strc3hsv>will relievc tlicrriselvrs as the leiis is grouiid ;irid eaiihe it to w a r p slightly, so tlicrt c i true hiirf;rcr o€ revolution cannot be obtained: which le:ids t o anotlier serious defcct-tistigrriatisrii. Glass may be bought in slabs and in some cases tliis is clicaper tlian huying especially selectrd dislcs. Tlie Ictbor of m:iking a square disk round is considerable, t~ritt o tlie hobbyist this woiild be a matter of little coricern. Slab glass, in gerieral, lacks tlie pcrfection necessary for ob,jectivcs Iarger than 2" or nt rriost 3". I t is pour prtictice t o econoriiize in thc purclicise ])rice of glass. S b e rliff'creiice in price betwcen first grticle glass. gii;ir;inteed liy a reput;ible maker, end second grade m;itrri;il, is not suffieient to cornpeiisate for tlie poasible failure of the finished objertive t o define. One exprrience with :L lens which, wlien finished, proves useful on terrestial objccts done, will convince the amateur of the t r u t h of this assertion. Soi~rcesof optic;il glass are limitrd. r2iiiong thrm are Rniisch arid I,onih, of Hochestc.r, N . 17.;the Fisli-Scliurrriiiri C'orp., 2:$0 E:ist 4.5 St., X e w York, U. S. ;igc.nt for Scliott (Geriiian) plass; Chcirice Brolliers, J.td., Srnctli\vick, 13iriningli:im, Enpland. Import prices, including duty paynhle a t loc:il post ofñre, approximate domestic prices. F o r slab glnss, L. D. Keller, 2314 North 19th St., Philadelphia, Pa. Disks are usu:illy supplied ground round (except for a frw polished fliit spots o11 the edpe, t o permit tlie makcr t o test the glnss) and rcasonahly flat and parallel on tlie surf:ices. The optical constants of tlie glass a r e noted on a slip of pttper supplied a i t h the glass and are usu:illy thc result of accurate determination. The rough diameter allow\ approximately 10 pcrcent for centering arid the rernoval of t u r n r d down edge. Some optical glcisses a r e more fr:igile tlran ordinnry c«riimerci;~l platc nnd extra precautions should hv obsrrred t o ;iroid cliippiiig or worse. Believing t h a t an example is now in order, there follows the computation of a 4" acliromat. The prescription is that it be made of a doiible-convex crown, followed b y a plano-concave flint. Since we have decided that the first lens is t o be rqui-conrex, fitting tlie curvature of the flint, we have no control over the fourth sirrface of the fliiit if the glasses are cliosen first. Thus the fourth surface will come wliat it will. If it departs from flatncss enougli t o be measured by medianical means we shall make its curve t o the figures. To return: the focus of our objective is t o be 15 times its aperture, or 15)<4=60". The glasses choscn are Schott's BK 7 and F2. Tlie properties of the glasses a r e as follows: Crown BK 7 nd=1.51G3 V,=GS.O Flint F2 nd=1.6200 Vd=36.3 We now determine tiie focus of the crown componeiit, using the formula. fc = F X (1) and for tlie flint, using the formula
V. - Vr Vc
whrrca: F=fociis cif o11,icrtive (iiasiiirie
f
=
166'2.0 64.0
=
25.969" crown focus
Sub\tituliiig iri ( 1 ) \re grt
Check by reciprocüls:
For the rndii of an equi-rorirex lens \ve iiare r = 2 f ( p - 1)
For tlie hnch surface of tlie flirit nliose frorit iurface has a radius of 2G.816" x e hnrc:
r
=
26.816 X 45.785 X -26.816 - 46.785 X
-62 .62
761.21 - 1.57
=
485" convex
Whrther tliis 1:ist r:idiiis i (soiic;ivt. or c~iiiivrs is
after trarersing ttie prism, the erncrging r:iy suffers a second refrnction upon leaving tlie gl:iss, in addition t o tlie hc.ncIirig it underweiit on entering. I n this second instante it is passing froni n dense t o a r;ire mediuin and is bent away frorri tlie riorrii:il ~ i n driieets ttie base linc a t D. If, liowever, the prism tiad the thiclcncss indicated 11y tlie (lasli lirie thc ray ~vouldiiot 1c:ive the glass before cutting tlie b:ise line and ~vould, tlierefore, follolv the path RCE. I t is appareiit froin tlie above, tli;it tlie heiiding effect of :L tliick prism is less than tli:it uf ;I tliiri oiie: Siiice :i portioii of a leris m:iy be considered u prisrii it folloivs tlitit the efFect of tliicknrss on a double convex Iens is t o make it weoker, ¡.e., of loiiger focus tlian computed with tlie thickness ignorecl. Tlie forniula for tlie focal lengtli of a double coiivex lens of thickness "t" follows:
Notc that tlie expres\i«ii
u
is siii~tractedfrom the quantity desig-
p'TiT2
ri;itinp tlie rrciproc:il of tlie focal lcnpth. Tf tlie reriprrical of n qunritity he [nade sm:rllcr, tlie quantity itzelf bccorries larger-thus the focal lerigtli of ¿i doiihle convex lens becomes loriger as it is inade thicker, assur~iingthat the curvaturei of burface reiiidin the same.
Niitr :ilso tli:it, slioitl
i((i
In tliis ense tlie eorrrrtioii is ntljective (as muuld an uricorrecte
1Cro~vii Flint
1.5153 l.íi214
60.0 36.1
Focus of com1)ination 90"
-
r1 = r2 = r3 = 36" r.i infinity (flat) Focus rrown Focuq flirit
:I.i"
(nrglectinp thickness)
58.9''
Since Ellison has inílulperl iri ~oirirs:ilil)r»\irri;rtions whieli are lepitiinnte for liis purpohe, \ve nill re-compiite tlie o t ~ ~ i e c t i \so e th:it rio questioii can
;iris<. i i i reg;irtl lo llie \ . : i I i i ( . i of t l i i siii:ill c]ii:iiititirs tXrit<~iiiig tliroii~li oiir al)lilic;itioii c i f Ilii tliieliiiihs f~i.iiiiil;~.
tllllh
= :36.95" E'or tlie fliric
r l , r2,
r4 = 195'" convex (;is inc1ic:itrd by tlie riegictire sipn). Shis is t o al1 interits flat anrl will be so eoiisidrrrd. TVc will riow : I S S U I I ~ C i~ thickne5s iif .;" f o r tlic c-rown leris and ser wliat liappeiis to its foius ~vlirri tliis tliickiicss is rorisiderrd. Our formula iigaiii:
Tlir exprru>io~iiri tlic brackrti is tlie reciprocal of the foca1 length a i origirially dctrrrninrd, so n r liaxe:
Tn otlicr \rorcls, tlir fociis o f tlict cronii 1i:i~I i ( ~ . i i iiicrc;iscd 1iy 0.1". \vliicli is olirioiisly :i ric.gligil)l(. c~ii;iiititgfor tlir \rorlí iii \rliicli \\,e ;irc crig;igcd. Tliiis 1~:llisciii's rccoirirricri
Ttie great mnkers, homerer, leavc thcir objectivcs orercorrrcte
F where
=
fl x f 2 fl +fz - d
F = focus of combination f l = foci~hof one lens fZ = focu5 of otlirr lens d =-
Let us ~ r o r ktlirougli an example, in arder t o demonstrate the cffcct on focus caused l)? sep:ir:cting tlie corii~iorierits. As\iirne a double-conrex lens liaving :r focus of S", <~oiiitiinedwitli :L double conc:irre leris of 1 0 " focus. Tlie fociis, F, is t o lie (leterriiiried whrn the lrnsrs nre iii contact. Here f --5 " and f 2 - 1 0 " . Substitutirig in thc aborc forrnula \ve get, (since
S o w suppoie tlic abore Irn4ei n e r e separ:ited hy 1".
\Ve then hare:
Thus tlie fociis of tlie coiiil~iiiiitioii Ii:is I)<.cri rr(liiccd Ili," ))y scl,:irntinp tlicin 1". 'I'liis is tlie e
+
v
= 1.5163 - 1 = 58.87, instead of the value 64 for C-F .O0877 .O0877 In ir similar rnariner tl\e T' for F 2 bccornei 33.6 inrtead o f 36.3, as tabulated. If \ve iiow run tlirougli tlie cornputatioii for an objectire o€ 10" focus, usi~igtheqe new kaliies, the eRrct of correcting for red will be rriade clear. First Irt us work the exaniple for achromatism for C and E', selectiiig as before, U K 7 and F2. =
-21
F o r our new values (aclirornatising D and F ) we get
Note tliat tlie cromn is 1.6 1)~-rcentnntl tlir flint 2.4 perrent strt~npert1i:rn was tlie case for :LII ol>jectire ilt~siprieeratiori. To [lo it acciir;rtely tlie refractive iriclicvs for 13 o f tlie gl;is\es slioiil(l be known. l'lic>c rriap I)e found by i i r i enipiric:il forinul;i crrtlitecl t o Vori Rolir, or brtter still, frorii tlie g1:iss ni;ciiuf:ictitrcr--or witli yoiir own sl~ectro~iieter.n'liirli rolors :irr selectrle over-vorrectiori. Lest tlie cnrrc: t>c riot cliiitc clcirr, rioti. tliiit tlic <listarice frorri tlic fovli\ of C t o (;' (in iinits oí' .O0001 of tlie foc;il leiigtli) is 1YO iinits for tlie Frauiiliofer ob,jectire, \\.hile it is but !)O uriits iii tlie Griibb (estiiritited hy cxtenlui. t.nd of tlir. \prctrurii focuses back of C fiirtlier for Fr:iunliofcr's ubjcctire tli:in for C;rul>l>'s. If a crriieritcd ob,jectire proves t o IIe 11:1<11y correctecl for color wlirn complt.ted, nothing rtmains but to clianxe tlic curriitiire of tlie b~iclisiirfiic.e. Ari oler-correction is nltered by ~ve:ikcriirig tlie flint leris. If tlic fourtli surf:ice he concave, nn iricre:ise in its r:i
(nd - l ) ~where ,
c
1 = -
1,
taking account of sign. Curres which r1 r2 nrc convex to incident light are considered plus and tliose which are concave,
J
minus.
The expression for tlir focii\ rlf i1nc lcns of nn :iclirom:rlic pair I>ecorues:
c = -1x f
(Vi -
V2)
6%
wliere bn = mediiim disl~ersioii Tlie following glasses a r c selrcted :iii(1 cin cxriinple wrorlírd tlirougli by the til~uvc f«rriiular. Crowri Iri = 60.8 6n1 = .O0848 nrl = 1.5155 Flint \', = 36.0 6n2 = ,01729 nd = 1.6229 Requirecl, then, ;tn riclirornutic ohjectivr h;iving o11 N" focus aiid using tlie above glashes.
1
1
S 1
(60.8 - 36.0) X .O0848
Crown:
C
= - X -
Flint:
C
=
1 -X (36.0 - 60.8) X .O1729 8
C
=
1 1 -r1 Tz
=
.5944
- 2915
Now Crown:
(21
where the subscripts designate the first, second, third and fourth surfaces. If it is chosen to rnake the crown equi-convcx, then r2 = - rl and we get by substitution:
a n d since C =
1 + -1 rl
.L=-=-.5944 r~
(by equation (2))
7'1
2972" radius
=
2
2
r, =
3.365" radius
a n d r2 =
- 3.365" radius
F o r cementing
rg
= rz
IJence, for the last radius, by substituting in (3)
1 P'rom which, since Ta
= -
2972, we get
Which iric.ari5 tli,~ttlie I;ist siirfacc is concave t o incident light (actually con\ ex). Now siiplw5c \re wizh to ch;iiige the ob,jective so tliat the last surftice sliall be :I plzine. r4 then is infiriite.
If a cemented objective is adhered t o - 3.431" aiid
r2 = r3 =
Since in our first example rl = 3.365", it will be noted that for a plane fourth 5urface rl has a slightly sliorter radius (more convrx) than before. Note also tlidt iii tlie abole metliod of desigri tlie refractive index for D does not appedr, hut tlitit only tlie dispersion from C tr> F ( n f - n c ) is used. Also tlie foca1 lerigth Eor tlie iiidiridual lensrí .ire not determinrd-ttioiigh they may be, if desirid. using the usual formulae. F o r tlie w k e of cornp:~risoii tlie saine exnmple appears below, worked by ;he conventioridl method.
Check by reciprocals. Arid, by tlie way, dori't neglect giving your figures a check. It i\ moch easier to cliange a few figiires th:in to regrind ;L finished
It.iis wlii<*li11;~scoirit. oiit witli tliv wrorip foc5iis I)r.<.:~usrof cSrroi.s iri :irithuictic. .8Ulji6 - .18145
,1250
:
-
E q i i i - c o ~ i v ~for s f = :<.2(iM r 2(p - l)f
= 2(.5155)3.26
-
R.:3611'
l'liis iliffcrs by .005" frurii tlie rrsiilt foiinil Iiy ('orir;i
A-c .O0287 356
<;ltiss
Pa
Rk 7 J? 2
1.5163 1.6'200
C-e
6 L.0
P;irti;tl 1)isprrsioris IPK 7 e- f f-g ,00367 .&55
.O0545
.O0906
.319
.531
F 2 .O0800 ,469
C
1.61504
.0080(i .Ol'i06
36.3
.004:39 545
1.51385
Jlrcliiim tlihp<.r\ion (('-F )
Vd
Rcfrc~etiveindices r3K 7 d 1.511333 .O0008 F2 1.62004 .O0012
.O0432
g-h
.58íi
.O0356 .4 L2
.O0995 .588
.OOH(ii> .505
g 1.52623 .O0018 1 .G4206 .O0013
Thr column labelled *tl is the refractive inclex for gloíving lieliurri gas (yellow) and not for D, the sodium line, as is the prnrtice with English manufacturers. is the so-called medium clispersion, The column labelerl "
A deep red H red C. orange U yellow
E green F blue G' violet H violet ( j u s t visible)
In Schott's t:it)lcxs smcill Ilorrian lrtters (1, e, g, a ~ i d11 ctre used. These denote otlier liries usctl bcc:iiise of tlie c.oiirriiit~tii~t~ o f otit;iiiiirig tlirsr col~r:.iil tlie 1:tt)or:itory witli ;irtifici:il sourcc.s of lipht in tlie spectroscolir. d is o11t:iiiirtl from gloaiiig I~cliiirii e, ~,ztriclli :trr respcrti\el' tlie greeii, hlue :mtl riolrt linrs of tlie iiierciirp are. 1 0 r e t u r r : th: coliiiiiii I:il)rllr
=
Vd
the value giren in tlie tahle. P:irti;il disperiioiic :trt. pivrn for various color bands; A t o C, C to e, etc. l'lic siiin »f ariy ci~iisvculire vzi1ue.r from these lirtinps will give the dispersiori tietweeii :iiiy linrs listed. l'hui, if the dispersion froni C to e he adtled to tliat from c t o F (.00.1.:39 +.00367), tlir result will be tlie dispersion frorri C to F (.OOHOíi). r llirsr disprrsiori figures are tlie differences between the refractire indices of tlie plns\ for tlie colors involved. Tlius, for BK 7 the refractive indices for g antl C are 1.52623 1.51885 by subtraction .012:3X the dispersion from g to C. Frorn the tahles the dispersions C-e, e-F, F-g a r e .O0439 .OC367 ,00432 by additioii ,01238 again giving us the value p-C. 'I'hus, from the partial dispersions, the refractire index for various colors may be deterrnirird. Unless advanccd mcthods of computing an objective are used, the amateur will have little use for the various refractive indcx values. The explanation has been included, however, for the sake of completeness. I t will be noted tliat below each dispersion figure another number appears. F o r exainplc, iirider tlic F-g dispersion for BK 7 tlie figure, 536 is noted and, similarly, for F 2, .583. Thesc figures denoting proportional dispersions a r e ubtained by the formula.
.
F - g
B-C
For BK '1 this becomes .O0432 --- =.53.58 which the table calls .536 .O0806
In tlie clesipn of ;in ;icliro~ii:itic ol),jt.ctivc, wlicn \v<* I,riiig t h r C ancl F lines l o thc. s;inic focus by rii:ikiiip tlic fo<.:il Ivngtli\ cif tlie coriil)oiicnt Icrises iiivirscly prol)ortiori:il to tlic "Y' fipiires for tlic pl;issrs i~ivolvecco111e irn1)ort:int. 111oiir little es;irrifilc ;il)ovc, tlir disl)txrsioii frorii 1' to g rii:iy l)r s:ti(l to Iic. 53.6 percent of t h a t from C tcr 1' for g1:iis I3K 7, I)iit for 1" 2 tlic corrt.sl)onding vnlue is 58.6 perccrit. l'h:it is, t h t prol>i)rtion:rl .iolet "outst;inding." S I i i effect is not serioiis in objectives of the sriiell di:ittieters with wliicli me :ire coiiccrrird, h u t it is Prof. Conr:idy's opiniori tli:it inttriy of tlie world's 1;irprr refr;ictors are of questionable value because of tliis unforturiatr state of aff:iirs. 111 large iiistruiiients the colors are spreticl :ixially to siicli ztn rxtent tliat ;it no place may i~ defiriite focris be seciired. So, if you wtint ii 21." telescope, it is siiggestecl tlitit you make n reflectrir or, what is probahly alrnost 21s easy, huy one. Before leaviiip tliis
-
--
ref. intl. for D = 1.51625 I n a similar manner the ref. iiitl. for C;' is ol~t~tiried by adding ref. ind. for g = 1.52623 .O0018
ref. ind. for G'= 1.526-&1 Xote hy editor: It l i n s hecii siip~estc~d tci y t l i u rt>arlt,r, it sliould be rnade
them t o represeiit in!or?natiun ~c'liic11 rriiyiit bu usuf1c4 t o
SIie writer ;tgrecs witli 1"llisoii tlittt ;ici<*csst o or posscs\ion of R lathe i l o l ~ ci 1 1 tic o ~ s l r ~ ~ t o i o In 1 1 1 1 t I I I I I ~ L ~ I I . Tlie ;iiii:iteiii. wlio Iiah iiot tliis f;icility 1 i ; i t l tii.st sti<'I; to r(.t)cctorri. A goo(1 optic;tl Ilat is tilso ii<.ccs\:iry. 'Sliis slioiil
S
I
Shis is equivalent to better than /zl fringc, which is not too difficult a task in diarneters under 6", especially if Pyrex or siniilar glass is utilized. Hegirding tlie m;tkirig of flats, mj- preferente is tlie three plate methodassurning tlint no flat for a standard of eviiiparison is arailable-rather than testing apainst a spherical riiirror. The latter method is useful in the production of tlie large flats used in tlie great ohserr¿itories, but is not accurate iri the liaricls of tlie amateur. By the former, fringes can be definitely seenttiey do not clepen
its low<.r siirf:~ce, hiit nc.c.tl iiot r~<~(.t.shiirily 11(. so 1 ) ~ ( % ~ : 1 r ei c\ l )collit~i:itc(l, , i.$'., iri:i(le p;ir:illt~I, thc Ieiih, :irid f : i l l \ f ) t ~ r ~ ~ ( ~ i ~ ~ lo11 i c iIlic ~ I : t ~r lv~osiirf:ic(~s beiiig tested. I i e t i i r i i i n ~ Iiy rcflcction froiii tlicse, tlie liglit again passes througli tlie lcns, throiigh tlie pl:itc, :lntl coiric.~to :I fociis. '1'11~eye pl;i<.r coiiiplctely irntl l)rilli;intly illiiniin:itctl witli t h r iriterference friiiges pl;iinly risil)lr. If thr colliin:itiiig lriih tie sni;iller tli:in tlie surf:tce\ to lie testrd tlir fl:ct in;iy I)e inored in :i dirc,ctioii par:tllel to the direction of the frinpes. A str;iigliteclge, long cnoiipli to spiin tlie
this position as the flats mor^-if tliey are fl:it. If this is unfortitnately not tlie c;tse tlie fringe urill Ie;ive t h r edpe, inc1ic:itirig n retiirri to the lap for fiirther correction. Iri pl;tcing t\vo flats topetlier, especi;illy ivlicii iising n rnlunhle standard, it is well to pl:ice three tliiri tin-foil sp;icerh t)ctxvern t h r siirf:icrs. l'his ni11 aroicl scriitclies ;itid prevent tlie surf:tces froiii rnolding Lo exch uther's curvature-;is tliey will if iii very elose contact-ttnd thus giring :I false pict u r e of their form. The in:lcciir;icy introcliicr(1 by vie~vingthe surfaces ohliquely may he understood from the fol1olving:reasoniiig: Aii en1;irged rielv of tivu surfiiers nearly iri coritact is sliown in Figure 8. llny 21 is reflected frorri tlie iipper surf:ice and r:ty H frorii tlie loii-er. If the dist:ince ('D pliis I ) E ib 11;ilf a wavelength, or odd iniiltililes tliixreof, gre:iter tlian F E . tlie liglit from B will arrive a t E 1.5 n;tvelength o u t o f 1)h:ise witli tlie liglit from -1, nnd win aniiul it. Shus, a t al1 places where the distnnces ( ' D E tire eqiial, there will be dttrkness :ind tlie dark stripe thiis foriiietl is callcd ;I fringe. Corisider now, a pnir of pl;ilrs, a4\umed to be :ibsoliitely flat, qlacr
Irig Iongrr thtin '10,~iiiike\:i rriore ;tcutr ;irigle witli tlie surf:~cc, and for tlie sarrie rc.iis!iii oiir pittli E (Figure 8 ) will be loiigcr aii(1 iiiterfererirc of liplit will tlirrrfore ;il)pe;tr :tt t i poiiit ncarer tlie cye nlirre, due tu the \reclgr rrl;itioii of the surfaces, the path is :rgain cclii:il to C I ) E . Tliiis tlie friiigc \vil1 ;ippe:ir to ciirre forward, :is slrown in Figure 9. If ;i collirri;iting leiis is iiecl, this conclitíon c:tiiriot rxict, since the light strikes iiiicl le;ives tlie siirf;tee ~ierpeii
precision not h i t t r r than % wavelength is required, the coriventional method of rnerely rirming the surfaccs in diffuse rnono<.hromatic light will suffice. The best light source is tlir grern line of tlie mercury are. Tlie Gerieral Electric Comp:iii- makrs a beirutiful rriercury arc lamp witli a screw base, intrncle
f:ices are not recliiireil oii filtrrs for tliis piirpose, so tli:it tlir clie:ipcr grncle rii:iy 1 1 ~ . iiscd. Sotiiiirii liplit, I~cirig ]c.si lioiriogc~ric~oii.; tli:iii tli:it frorii tlie merciir? iirc, (locs iiot givc :is sii;irp ;L friiipr, nor c;in iliterferencc 11r ohtaitietl wlieii tlir s ~ ~ r f i i v c:(re s iis witltly srl);ir:itetl ;is t11t.y 1ii:iy with the prtScn o f riicr(,iiry liglit. 'I'lit. hodiiirii sl~ectriirii (fl:rrri<.), Iio\r~erer,c«iisists of a pair of yellow 1irir.s very cbIose torrellirr, ;riid iiot riiiicli elsc. I t tlierefore rrquires iio filtcririg, :is is tlit. case witli the mcrcury are. Per1i:ips tlie
d s p h e r o m e t f r nmde with n diai gago (r~ri
bunsen ñame, burriirig through n ring of asbestos sonkecl in salt, is as good (1s xnytliing. It is the sirnplest n n d clieapcst. A spherometer is íilmost?-a necessity in this work, tlie simplest rariety of which may he constructed in accordaiice with the pliotopraph (Figure 10). For the beiiefit of those wlio may not he fzimilinr with this uscful tool it rnay be said tliat the ipherometcr does not rne:tsure rndii. Tlie points of its tliree legs rest on the sp1ieric:il siirfnce t o he nivasured, ancl tlie central poitit is moved until it ~ l s ocomes in contact with tlie surfacr. As iisii:illy niade, some sort of micronieter screw is iised for tliis purpose. Tlie rnanipulatioir of micrornetrr rnr;isuring scrFws, lioxvrrrr, is ;i th. F;ri«~r.irig, tlicri, tlint tlie tliree l e p :irc ori :I circlc of givcan r;i
Reference to Figurc 11 will miikc the rnzttcr clear. As will he noted, this is another forni of our olcl friencl ir1 iriirror iiiiiking:
Tlie ciifference i5 thnt the inclusiori of tl' in tlie niimer;itor is import:tnt iri tlie case of tlie deep ciirvrs involve
I n making such a spherometcr, it is important t h a t the three legs be located accurately on the circumference of the circle selectcd. When turning thp plate ( f o r lioldirig the legs) iii the lathe, a deep scratch m:iy be made with a V-pointed tool. 'I'he diameter of tliis may be accuralely measured and, before takinp the ~il,iteout of the litttie, the central hole for the didi spindle may be bored. I n locating tlie holes for the legs t h r scratcli will guide a center punch, so tliat rio diEculty should be eaperienced in precisely positioning tlie l e p . Precision of spacirig iiround tlie circurnference is not SO important but will, of course, be carefully attended t o by ü good workman. Siiice tlie sqliare of tlie raílius selected appears in tlie formula, ii coiivenient number for this quantity is 1.414", the squnre of wliicli is prnctically 2. The conipletion of tlie splierometer provides tlie first iiie for tlie optical flat, namely, settirig tlie dial t o zero (infinite r;icliiiq). P1:lce the splierometer on the flat and twist tlie frame wliicli carries the graduütioiis uritil zero coines
;tlsn iiritler thc poiiitcr. ,\ rii;cg~iiflrr is 1i;iritly i r i srttiiig tlir iiistriimrnt ir1 estiriiating fr:ictiori;il p r t s of ;i (livi\ioii \rlirii riit.:csiiriiig ;i riirv:rturr. h ' o t l i i ~ i ~is to l)r g:iiiiey t%tiiii;ttiiig rt.;itliiips clowr tli;iii .000'2", ;cs tlie ;iver:igr :icciir;icy of tlie gagt. itself ih riot riiiirli hetter tli;iii tliis.
'rlic oh,irctiic* trr;it(.s tlir forrii of : i r i rclui-roiivt3s ('roivii \\.llohi. st~ron(1s~irf:ice fits Hit\ COIICII\.<' fa('' of ;i plario-cunc*;ti-e flirit. C:tst irori I:ips ;)re used tliroiiplioiit, ;iiid it is for tliis rriisori tli;it iin «t),it'ctivc Iitiviiig tlie riiiiiirriiii~i riuiiil)er of riidii of curvature
has heen selrctecl. Becniise the seconcl and thirci surfnces are to hnre closrly (iiot niore than 10 fringes of sodiuiii light, or ~ í o , o o c i "the ) snme sagittnl (depth of arc) dinirnsiun, tliey will be cerrientrd. While it is iiot usu:~l t o cerrirnt objectires of more than 2',4" di:iiiieter, it is wliolly practietil to (lo so. Crmenting aniiuls tlie second and tliird surfaces. I t is a s if tlie objectire wcre a solid lens. the front portion of oiie refractive index and t h r back of another both u.elded into nn intcgriil pirce. Heflections from t w o surfaces (loss of almost 10 prrcent of incident light) are avoided and, more important still, light refected back and fortli betwern thesc surfaces will not be brought t o a focus a t the eyepiece t o fog the imape. Well-to work. The romputation of the radii of the lens surfaces may hc done in one step instead of two, a s per Ellison. h n example of a 4" achromatic is run through elscivliere, for the henefit of those aliose algebra may have rusted u p a bit. Time is saved in roupli nnd fine princlinp by the use of rnetal (iron) laps. Disks of cast iron may he purch:ised from dealers in iiiacliine tool suppliesfor exnmple, the Victor Machinery Exch:inpe, 251 Centrr Strcct, Ser., York City. They cost 7 or 8 crnts per pound (193.5), which mtikes them little more
e r p n s i v e tliari plass tools. l'lic rlihlí is chucked ir1 tlie lathr, sqiicrzing it no iiiure tli;iii iircrsstiry, :ind ilii reqiiiri:d rrrcliiis ti~rried oii its hurfare. Sincr tlie ~wocliictioii of :i sj)li~ric:ilsurf:ice iii tlie 1:itlie is :i
wliicli repeats itsclf ench tirne t h e cireurriference meaiires itself off on the Line. If, instead of a. point on t h r circiimference, a point Q on tlie radius ic selected and the circle rolled as before, a curve called tlie trochoid will be described. I t will he noted t h a t ttie radius of curvature of this curve a t its node is longer thnn that of the cpcloid a t tbe same position. I n fact, if tlie rndius bc sliortrned to zero, the mo%ing point then becoming the center of tlie circlr, it \vil1 descrihe n straight line (infinite radius) wlien the circle is rolled. Hnving thus outliiied the operating principle of tlie derice, a desigri of a practica1 ciirve cutting niechanism is in order. Referring t o Figure 13, a rack R and piriion P forrn respectively the straiglit line and generating circle. The pinion Iias its journal J inserted in and rigidly constrained by the bearing 13 mliich, in turn, is free t o slide ir1 the giiide C. A movwhle radial bar is attached t o the pinion, and so arrnnged t h a t the pin D may be placer1 at rarying distances from the centcr of the piiiion. Tbis pin en-
gttg<.
'
I:n(lircn drncrihrd b!, B = 3z O' ' S o t r thnt, whun R = h n l f O A thc 0.1 - 2 R ' de?lo»~i~lafor bucomrn zrro n n d tlir rnditls driicribpd is t h r n i n f i n i t ~ ( s t r a i g h t linei.
a triily 5pherical onr h> linling its r:idiiis gra
Tf :in i,l(vstrii t ~ ~ o l l i o sgriritlcr t is :ir:iil:iIilr~, :i fiii:il k i i i i iii:iy lic tnlirii t i f f tlir scirfii<.t. ot' tlit* l:ip. iiiiiig :a s l ~ l i r r i ( ~ i;il~r;isiv<, il wlir<.l Yi" t1i;iirirtir o r lesi. Tliis will gt.I riil of tlir l i t l l i Iiigli s11ot wliicli is ho ilifficiiit t o rciiiove froiii tlic. ic.iitc.r ~vitlii i i i ortliii:iry 1:itli~~ tool. ' l l i i ili~istioiiIi;is Irccii :rlicd \vlic.tlier c:ist ¡ron l:ips c:iiiiiot Iic iri:it riiotioii fro111 tlie ¿lr\.ice w:is iriil>r:ictic:ililr. l'iic. link:ige will he descrik)eil, iio~rev<.r,iri tlie Iiopc t1i;it i t in:iy sliggest :I siriipler inr.tlioil. Itefrrriiip t o tlit. figure, tlie poirits O ;iiiI.A., M.Sc., Thr Eresidriicy Onllegr, hIiirlrnh, Iiidia. ir esyrcially reconimendid, as it 1s felt that this iiicthod. transiiiitted iii tlie urcsrrit footiiotr (\\.hiel1 was addrd in final nroof hecausr iiot I>rerr al1 roiind its base. lloreover, if the splierr be riiade to rotate rouiid nn axi;. SPQ passing tlirougli tlir 11oiiit B. thc. base of ttie cyliiidrr ~vould,duriiig tlir rotiition, tr)ui.li the spherc nt evrry point orrr tlie (.:ilj A R D . So tliat if the rdge of tlie cyliiitler ver? a cutting orie. i t ~ i o i ~ lhe i l able to gencratr the sl~liericalsurface 4 HD. Fritiri tlie figure !ve tiavi. C B / X B = sin O. l f thc ase- intcr-cct oii tlir riglit o£ the plurie I l D , a corirrx siirfacc w i l l bt. gttiicrateii. "It is seeii that the iiirtliod o€ daveloyiiig sucli sui'fai.rs, rssentially requirei aiiy A
Sincr roiigli griiiclinp tlie It,iis is lilirly 111 iil~scttlir ciirvr ori tlii. 1:111. iinlrss cciiisitler:it>lr :ittciitioii is ~i;iidto tlie rri:itter, il is r:i\icr to roiiplr oiit tlie 1:ij). rougli grin(1 tlic leiis, ;iii(l I~ririgtlie l:ip h:~ck to :iccur:itc r:itliiis oii the Iaitlir for tlir fiiica griiidiiig o~ii~r:ttiiiiis.'I'liis h;is thc ndposr wr t:ike for examplr Ellison's "threerqut11-curves-:irid-a-fl;1t" cil),jicti\~e. A coric:ire aiid convex 1:ip of cc11i;il ;ind opposite r:iclii :irc ni:itle nii
-
- -.
-.
--
--
arraiigtxinciit \\.licre therr can he. t\vo ase., hoth in tlic sariie 1iorizoiit;il plarir.. tht. nngle brt\\-eeii tlit. I m n beiiin cnl>nble o£ \-ari;itioii orer tlir iiri.i,siai.y r;iiige. Tlic riiilliiig innihiiie \vith its fittirigs \vil1 prnvide al1 thcse rrquirriiients. The arbar can IJ? removed and t u tlio Iieadhtozk spindle c a n be :ittacli@d a cgliiidi~r,n i t l i i~ iiuriiher of cuttin; ~ioiiits
arrangeii
iin tlie rircnmferener o£ i t q circiilnr fare. Tiiis when it rotates \vil1 constitiitr Trie urf;i<,i. i h to I>r <-nt raii ),c. ;itt;ii.lietl t o tlie iiin<~li!rie's spiridlo aniny i t fiiinly iii ],i?'itioii. :iIl otlier adjuctiiieiits iircass;irj for tlie settiiip are enhily i>rovided11sthe i~iacliiirritsclf."
tlie euttiiis rneclianisrii.
T\ro h o l d ~ r sa r e nom to he madr, t o t:ikc tlic (liiks. Tlicse in;iy I)e Ii;ird woorl, w:ix-iinl>regri:itetl :ind I):irk<.cl witli :L m<.tnllic diik iri orclrr t o prereiit warpiiig, 11r inay he rii:rle to grind tlie leiis on top, whcther the surface is convix or conctivc, ljut it will be Iieccsstiry tn :ilterri;ite tlie lens nricl 1:ip on top, in ordrr tlicrt tlie r;~diiis of ciirvature of tlie 1:ip will be retiiined. Tlie leris is coarse prourid to tlie reclilire(1 radius ;irid not stolip~.d sliort of it, a s witli glass tools. A conv e n i ~ n tv:iy to :iccoiiiplisli this is t o t u r n tlie ~>olisliingrn:irhine spiri
Grincling mitlr tlic fiiier siz1.5 of C;irlio Ii:iiitc.s rriu<*liof Iii\ succrss in ;~roitlingtiirrictl-do~i'n edgr t o tlie iise of k(.r«seiit.. Aiiyotir wlio Ii;is l i a d th<. opportiiiiity t o esarriine orie of Iiis mirrors under test will, howcvrr, be conviriced tliat sucli perfectioii of surf;ice as he ohtains is dile not 21lonr to tliis item. I t m:iy h r wortli mentioning tliat the gr:iiri size of an :ihrasive is not the only criterion of perform:ince. A n abr;tsive witli srnall gr:iiti \izr mil1 pross:try:iftrr ~)olisliing. Three lioles, cqually sp~icrclon, hay, a 3'' circlr, tire clrillecl 1);irt w;iy into n metal ]>lote 3./8'' tliieli, ~11ic1are couiitrrstirilí iis if tlicy \vire to rrccive flat-
bei~(lscrc.\v\. Iiitir tlic coriiv:il iiii\li rcsts oii tliv toli siirf:iee of tlir Iriis, ;~lioiit?31,;" froiii tlrc t.tlgc, ;iiitl tlit. rt.:icliiig is iiot<.iritllr is riow liftecl. tlic Irris r o t : i t t ~ l t o :I iic.n- 1)ositiciii (lift o* frorii tlic I)iills, l o :iv~iid scr:itc~lie$) :iritl rc.tiirrit~li~~:itc~ rc;i(liiip oii :i poiiit ~)rrvioiislyiiie:i\iirrtl. Agrrciiieiit t o ti(.tter t1i:iii .00015" rii:iy 1 1 ~c.sl)c*et<~l. 'I'lic fiii;il c.lic~*kftrr ctlgr tliickric~ssslioul(l 11r rii:ile. Morc. tliiiii .oI)?'' is ver!- iiiitlrsiriil>le ;iiitl ti prr:it s;icrifive of di:iineter 1\-11ri1cbei~tcriiigfollo~vsf'rorxi :L 1;irgvr v:iri<~tioiiIliciii th;it. fI;iviiig Iiroiiglit tIi(, Iriiw\ t o ;i "l)~rli\li" witli 1,evig;itvcl hliirriiri:~, prt'1iiriiii:iry tc~sts;trc rio~vi i i ortic;il eeiitt.~:,, 11iit \vil1 I I ~ c.loe ciioiigli ;it tliis poiiit if c:ire li:ih I~ccncxercisccl iii Ii<.<.l~irig tlir ctlgr t l i i c k r r i ~iiiiifor~ii. ~ 'I'lit. iccoiitl iiiitl tliird surfi~e<'s of tlie leiis are. ;iiiiiiillcrl 11y iisiiip :I li
252
'I' H S(: It IC S+ It A C'
'r O 11
witli (leeper ciirves, esl)eci:illy witli gliiss tools, :iii;l Curnrcl (lowii cl/," . Siricr (liffic~iiltyiii gcttiiig c:irtiircs I I ~ I V C I)c*eii c o r r e ~ t r < I tlic , polisliilij: iind lignririg will non- be iii or(1t.r. Surf;ice 3 is I)roriglit t o ;i c~oriiplrtc polisli f;ice clomri. IIC'F ori soft pitcli is ~ i \ e ( lfor ;I 1:ip. Startirig o11 nriy glttss or iron tool, :t pite11 1;ip i\ iii;tdt~i i i tlic IISII:I~ rn:iniirr, exw1)t tliiit t l ~ rliitcli niay to ;tclr:iritiige be oii tlic. hoft sitlr :irid foririrtl wliilr Iiiit Iiy t l i ~siirf;ic~rto he polislird. A cir(.lc of I I r F is iiow 1;iid oii tlic still w\.iiriri 11itcli aiii(1 prrssed witli tlic gl;iss. Slrfore tlie pite11 li:irr.esw;ts t)y ri)e:ins of :r clieesecloth s~v:il>o11 :t hlii-k. Tliis riialíes ;in excelleiit lap :ind ;~roitlstlir clifirult prore\s of cli;rriiiilirig, ~ r i t l iits crt.r-lircserit possihilitp of cracking off pitcli iicciderit:illy, <~sl>t.ci;illy at tlir edpe. 1 , t i r t r r t l i e tliird surf;ice is I)roiiplit t o a polisliecl sphcre, a s trstecl by reflectioii by thq Rorichi grating. Sincr, iri n 5" ol)jectire, tlie tliirtl siirface rii:iy Ii:irr ;i rarlius :irouiid 10" (etluir;ilcrit of :in f / 4 niirror), it is irriporttrrit tli;it tlie slit aiid Iionclii grating be close topetlier and y J. H. Kirip,* (ir l>y tlie interfrrencc. frinpe rnetliod agniiist tlie tlrircl surf;ice. Tlie use o € lioldrr\ for the leiises will be appreciated Iong before the work Iias progressic1 tliis far. A littndle cemented t o tlie leiises lias tmo (lisaclrnntagrs-it miist be accurntely centerecl iiri(l inust be reinored e;tcli time t h r optician ~risliest o look tlirougli tlie Irns. SIie liolders, being lathe turned,
* Tliis test f o r canvis curfaros is perhnpc tlie ~rratestadmnre iii testing optlcal siirfaees since tlie auto-collitiiation nietliod fiiid. >\.hile soiiie additiurial nliyaratun 1s recluired. tlie tinie exgeridid iri grt.l~:irationis rlc
Rrf? pc~rfertlyc'oricentrir :iiitl m:iy 1)e rririorctl iriht;int:inroir~l~-.Tlic f strtiiri froiii ;L 1)itc.lietl-ori li:tn(llt. i5 likr\risv :iroitlitl. Piii:illy, \rliilc tliis statciiicrit iii:iy ;i
be near tlie focus. Whrn the pinliole imape slioms no flares, nncl tlie iliffraction ringh oiit of fociis (if ;irir) a r r concentric, es;imine tlie figure a i t l i tlie Ronrlii test iind kriife-edpe. The figuring of thc objcctive is completed h y workinp tlic. fourth sirrface. Centeriiip, if not alreody taken r a r e of, is riow in order. Tliis is extremely iniportiint, especially in ohjectives wliictr liave not beeii computed for the best condition as repirds elimiiintion of corna. Since corna cannot iii general be corrected for in an ob.jrctire having eqoal (and of coursc opposite) currcs f o r the second :ind tliircl siirf;ices, careful íittention slioulil be giren this rather fussy operation. Aii ex~il:iii:itiori uf jirst \vli:it happens in centerinp rnight not be aniiss, ;ind will he rriarle clear frorii an inspection of Figure 15. Centering c'onsists of so edpinp n lens tliat its geornetric axis contains tlir centirs of rurl-;iturr of hotli siirfaces. Figure 1.5 represents L: lcns witli grently exaggerated diffrrence of edpe thickness. If an
(',
t e i r f . Tt \vil1 tlirii 11c rlv:tr 1li;it :i crcsccrit sli:il)r(l piccc- of gl:i.;s \vil1 li;ivt~to be rt~iiiov~(l, iii orclvr tli;it ;iny 1)oiiit 011 t111, c(1gr of tlic Irtis s11;iIl l>(. ;it tlic. i;riiie distiiiic*(. froiii tlir iil)tic,:~lcciitt,r tis ;iiiotli(.r. L T i i l r s ~tliis coiil,crtii'\, :i ~)ri\rri:iticc.tiect \vlieri liplit ~ > " s wtliroiipli \ ¡l. 'ITlii\ ~viil tli\tiirl~tliv <.olor corr~.c.tioii:iriil, if I);i(l, \\.ill pi\< :iii ;istigiii;iti(. i i i i ; ~ ~ i : '1'lii. c*irc*iil;ir ciit ; ~ ttlit. riplit of the figrrrt., irrtlir;it<.s 1iy dots tlic ~ ~ ~ r r t i oo rf i pl:i~,i t o l ~ i . rviiiovitf, wliile tlie
!'IC:VI~~;
16
tirhr not ?,pf p i f r h e < i to 1111~rlisk. nnd sl101iyr'i.iib11~~1'p«il l:o/ f v o t i ~ t l r r tnil~slockc r , ~ i l r , r . ?'h@ r l l n ! gngr i.5 l i r / < l rir:nili*t tl,,, ! 1 . 1
f
1 I
1
h
.
S o t ~1,rrrsa
dasli linc5 iii tlie in:iin diiipraiii irierf»rnieci. I,enhes w\.liic~la r e left baclly oti in edge tliickiiehs iti grinding ~ v i l lbe Vcry rriateriíilly rcciiicetl ir1 l:iril<s:it 1i:irid. h anniilus reinoretl f r o ~ r itlie i d g e of n. 4" leris reduces its nrea h y nlrnost 10 percent-:i not iiicoiisie pc.rrnnnently ccmented with linrd C:inadn h:ilsarn, centerinp 1i;id k~t-sthe left i ~ n t i ltliis o1)er:ition is coriiplctc. If iio Ii:ir(l c3ernentirig o r r~iiieiitiiip\vitli liqiiid hali;im is prirposed, c:icli IPN>:will of riecessity be separatrly crnterc(l. Iri eitlier cverit tlie process is t h e sanie. Tlie lathe
(loes iiot 1ciicI itseif t o cciitcriii~. ; i \ too iiiiich ski11 is rrqiiiretl to 1n:iint:iin tlit. liitc-li :ct tlic. prol>rr t~~iiilic~r:itiirt~ ti) pcrriiit tlic. le115 to I)c sliiftr(l oii its sI>iricllc : i i i t I yet iiot 1t.t it slitl(x tlo~viirvlit.ri relr:iser tlic sl,iridl~.aiicl :i low ~ ) o \ v ~ tvl<.\c.ope r (2 t o (i 11111vcr)cqiiil'l~.tl witli ; I I I t.yi.pit.<.c. tvit11 (*rossliiiir.;, i., riioiiritcO0 F. or o , liy iitiiiirr~iiipit (iiot i i i coiit:cc.l witli 1)ottoiii of vcssrl) i i i colt. fouiitl tliut i t i ciiiirrietcr ~vlierictlge(1 is srri;iller tli:in tlie finislie(1 cro~vri. 'i'liis \vil1 iiecessit:ite ritlier re-idpiiig or 1i:iving two differeiit diaiiieters iiisicle tlie inoi~ntirigcell-wliicli is, of coursr, undesiriihle. Tlie crown slioiil(1 iio~vhe etlped ;ind slioiiltl be ciirried, :is precisely as may he, t o tlie s:irrie di:cineter :is tlic flirit. Tlie etlges o f botli lcrises sliouliridle rerolves a t n inoderate speecl -200 to .tOO r.p.rri. The cell is nolv iii orcler. Tliis is a lathe job ancl hncl best be made of alurniriiirri (witli X perrent r o p p r r ) castines. Tlie Iiorrie founclryman will fincl th:it j u ~ i l i autornohile crankc;ises are excellent material for tliis purpose. Wliere the lrns carinot witli safety hc left in the telescope, a sub-cell to facilitate rapid renioval of the objective is desirable. \
'l'hr ol),jectivr is pI:trril iii t l i ~ct~ll:ind t c \ t r d for nstigmntism nnd crnteririp-1)rrft-r:tlily i i i tlir telc.scop(h oir :\ sttir, biit :t ~iiiiliolr will tlo. A Itirpe ($',,;" (1i;iiiirtcr) ~ ) i i i l ~ oisl ~o~k ) ~ c r \ ~ c~r-itli ~ I :iii vyvpicct- by ; t ~ i t o - ~ ~ ~ i I l i i i i ; ~ t i o n ~ 1rril)rrfcc.t cciit<~riiipwill r(.\c;tI itsclf 1)y color i r i tlir folloir-iiip iii;ciiiier: :it focus, orir sicle of tlir 1)inliole will sliow :I rrtcrfi~gc.. ~ ~ r o p vpohitiori. r I f ceiitcriiig is siitihf;i<.tory, ;I rc.:il o r ;trtificinl stiir is ncxt in orcler. t o t r y tlie clrfiriiiig powcr tintl ;itl,jtist tiiiy srrittll astigiii:itisrn tliat iii:iy l)tx prcscrit. nlnkc it srntill rcfcreiicc. liiic witli :i cliiii:i rii;irkirip peiicil, ori tlir 1):ick siirfiice, before :iiserrihlirip tlie ol),jecti\.r oii tlir t c l r c o p r . A siri;ill i'liri~tiii;is tree b:ill, t i glol)iilr of iiirrciir- on tilack v e l v ~ t .o r :i hall hc:iriiig rriiiciitc~tl t o :i tlire:i(l is liiiiig iri tlir siin a t 20 focitl lengtlis (or iiiorr if corireiiirrit) ;i\rr:iy frorii tlic tclescol)c, so t h a t tlie sun's tiiiy irri;ige m;iy he ol)serv~(I. 1)iffriiction rinps iii ;ind out of focus rn;ly be olisrrred, likrwisr tliiit l)iigl)r:tr o f :iny optic:il siirf;i<-e. ;istigrriatisrn. If tlie I;itter i\ prrsetit (anil it iisii;illy r-vil1 he, in sirinii :iirioutit a t Irast) rotnte tlie crown leiis :i fcw tlrprees-10 o r i.í-;it n titrie iiritil tlie best position is foiincl. \Vien tliis is discovrrrts o f Can:tda halsnm dissolved in Xylol. I t sliould he tlie coiisistrricy of r e r y tliick molassrs a n d liglit yellom in color, :rlthoiigli if d a r k r r little liarrn will rrsult, since tlie film hctwren the leiisei !vil1 be r e r y tliiii. I f tlie soliitiori is riot viscoiis enoiipli, it shoiild he tliicl<ened b y ndding lurril) C:irietl:i b:ils:irn warined a n d disso11-erl in Sylol, wtirming tlie wliole niixture ir1 a w:itrr b a t h (150" F.) a n d stirriiig witli t i clean glnss rod. A cle:in clotli pncl ih prepare(1 ancl lnid on tlie table to receive t h r lenses ~vliicli,Iiaviiig first heen tlioroughly cle:iiiecl, a r e licated t o 150" F. iii ;i water hath. Nitric ~ c i do r tri-socliurn plios1)liate soliitioiis tire goo(l for cleiiriirig, and t h e job sliould be alrriost a s fiissily doiic as for silvering. Ilust is t o be scriipiiloiisl~ avoi
diist-tiplit glnss Iiooiil;ite tlic piirts. If tlic. I<.iiscs ;irc. Iiriite(1 wliile siipportetl iri :i clir~scclotlislirig, thcir r r rnov;il froiii tht. Iiot (150"-200") w a t t ~ rxvill I)r f;iciiit:itrti. '1'lii.y are ri.iiiorc, is 1:iid coric;irc sitle iip. 'I'lic sc.roiitl ;~iitltliircl siirf;icc..; hlioiil(l hia cnrc*fiilly ex:iinirietl frir ~ i o i l ) l i grra;ise . spots :irrcirtioii of liili~i;ils;irii is riow 1ioorc.d iii tlir cciiter of tlir flirit 1c.iis. T f tliis is c;trrfiilly ;iiitl 10 stores), siicli ti.; is iisccl to :ittacli as11 tr:cys t o ;iiito wirierIy(loric, tlir centrr of tlic. If~iis will rii;ike its first coiit;ict ;it tlir crriter of tlie pool of bt~ls:irii ;1ii<1rio 11iiI)l)les uill rr4ult. I . ; i r g ~1~ul)i)lr.:tire of no irnportanec, ;is tliesr mil1 rtipidly síliitLtli.e oiit, liiit s111:111 1)iilihlrs ( l o ~ ~out ~ c slo~vly:irid SIIOUI r e c i i i ~vitli g :i firrri pressiire. Exrc~*sh;ils:irii nill oozi oiit :iroiiricl tlie rdpe iri ;i sticky mes.;. 1.ift tlic crriieritril Iciist.~, wipc- r i f f tlie excrss b:ils:ini witli a r:ip c1;irriprneil (not w r t ) witli Sylol :ind p ~ i ttlit. ol).jective in its crll. Tliis \vil1 center tlic lerisc,. Now sill)l>ort tlie bnck of tlir flirit lrris (not tlir ccll) oii ;I soft p;1(1. P u t :i 1 ~ ovrr ~ 1tlie ibromn, ;iiiy thc xt-riplit ari(1, iintil tlie h;ils:rrii yields, tliey \vil1 be lield in tliis stressed coiiditiori. Slie siipremr test of :in oh,jcctive is its nbility t o rrsoli*e. Picli out n pnir of doulile st;irs frorn tlir t:iblei. ~rlinsesey>;ir:itioii is eqii:il to or hlightly preatcr t1i:iii the t1ieoretic:il resolring ~ i o \ r c rof yoiir ' s c o ~ ~ e .If you rtiii iiii(l lxiir 1i:iving :i~)~)roxirri;itely c~111:ili ~ i n g i ~ i t ~ i (;iiicI I e \vliicti ;!re from tliirci to fiftli in;ignitudr ir1 briplitriess, so rriucli tlie bettrr. T r y to sep;ir;ite tliein. I f you fiiil on several differerit ereiiiiigs, rlon't give u p in rlisgust. TIie seeirig
.
1i:is t o Ilc gontl iii orclrr t o givi' yoiir oh.it.c.tivi. ;I fnir ch;incc. \iirc, thr iii\triiiiit.iit i \ \vvII colliiii:~tctl, t i \ tlcsrri1)ril i i i "A.'1'.31." [;iiitl tlit. prczvrit vol1 - 1 . A roriirrioii iarror is t o Iii~vctlie ryvpit.cr i i ~ i sl)iir;ill?l to I)iit riot roiiicitlc.iit witli tlii. ol)tir:il ;ixis. ~ 1 : i k t;i~ ttxiiipor;iry rig, iii ort1t.r to t r y tliis oiit-tlioiigli witli líitl~<~-iii:itle c:istirigs ti11t1 se:iriiltls~ :ilriiiiiiiiiiii tiiliiiip, tliis coriditioii is iiiilil<ely t o occiir. l l o ~ v t ~ v e r;L , ver- qliglit tilt of tlie oli,ji.ctive will riiiii tldiiiitiori. 1V;itvli oiit-of-foi~ist1ifi'r:ictioii r i i i g ~:iri,l fiiss iiiitil tliey a r e coiici.iitric*. -4 ~vr-ortlo r tn-o ;~lioiit oliscrriiip. Sliiiri Iiigli I)oI\-r.rs. E x c t ~ ~ )for t tlie rrsoliitioii of clo\v tlo~il)lv.,t'yt'l)ii'c'c< of I i o r t c r foc:il lt.iigtli tli:iii :)&" mil1 liriiip I I 11" ~ fiirt1ic.r c1rt:iil hiit wili coiiLri!)iitv ; \ i i <~\:ipg<~r:ilir~ii of n-1i:itt.vt.r
pov7ers :il~ove 150
prisrii tli:igon;il. As iisiinlly rn:itle, tliis dt.rict. <.oiisists of ;L prihrn iriounted iii ; i liox witli two tiil)rs f;tstericliro;icliiiig tli;it cif tlic gl;iis o f tlie priirii, vcry ~ i e a r l ya11 liglit strikiiig tlic rii;igoii:il f;ic.(. \\.ill Lic. tr;iii~iiii~t<.as5 ori oiit tlirotipli tlie r i ~ i ~ l oliy . ;I ~iiitlicioiis \clrc*tiori of liqiiicls, tlie ;iirioirrit of liglit rrflc.cte
l-.l(; c-rti,. 1 S Tlir ci.11, rx), n ~ i d r o t n i ~ i i n g~ i n grlctnils o ? f h i , 4 ' 1 " r u f r « c t o r slcou,'n prrriuics figtivc. Jlndr, /,U ti,? n u t h r ~ rD i c t iiot ~~i~iilioii+~rl i i ~t h e te.rt.
in
fhr
on tlie cyeliirce ~x.ill t ~ rsiiiñrierit ti) pcrniit obserr:ition, even with tlie objectirc opcri to fiill ;iperturc. 'I'lie pre:itrst cautioii slioirl
I t will Iiave lieeri appnrrrit to :iny nrlw Iinrr iisr(1 Foiiraiilt's rnetliod that, unless tlie eye he plncrcl vt-ry rlosc to tlie lciiife-t.r;irs mliic*li gro~vsIarger ;is the distance froiii kiiife-eclyc. to t.ye iiicrc;ises, It.;iviiig oiilj' tlie ceiitr:rl portion of the objectire illiiriiiii;itcd. A sliglit l~iteral rlislil:iccrriciit of tlie eye is
suffirient to more tlie j>iiliil ~iarti,ill>oiit of tlir bearii of light, causing a dark crescent t o appear ori oiir side of tlie ohjectire. Both eflects increase in rnagriitiidt: as tlir foc:il rntio of tlie ob,jectire under test i\ dccreased. Witli ratios lecs than f / 6 , tlie cye inust be placed inconveniently close t o tlie knife-edge if thc peripheral zone is t o be seen illiiminated. Tf, however, a t r l e x o p e of from two t o four power, is s r t u p almost in contact wilh the knife-edge and focu5sed on the objective lens under test, arid if adjustments are made so that the disk of tlie objective is seen fully
1 ' l I E I< E P R A C T O R
26 l
i1luinin:itecl :ind in t h r rcnter of tlir fielcl, tlie cyc m:Ly he moved nbout with«u1 losiriy thc irriage. 'l'lic con\.criirrice of tliis ;irriiiigeni(.tit is iriucli greater tliiiii oiic woiily tlie opticiaii, if tlie sh:idows :%reto :tI>lie:ir its 1it' is ;icciistonie
Therr :ir? so m;iny .iv:iys of 1)iiildiiip ;i tcli.scopc siglit tlint to dr.;crihc nny siiipli w;iy is alriiost cvrttiiri to irivite lic;irty d i s ; i l > ~ i r ~ ~ifv ;iiot ~ l tlerihiori from \r;lrious sourcc3s. llo~vt.vrr, iii tlie follo\viiig :ic.coiiiit, TVE.<. sli:ill lietl
-
f
SEE TEXT
Raü paths throiruh o fi,)~ii.nlr i j l c
~ P / Y A ( ~ O P~ C
igl~t.
Optics and Optical Desipn" or Iíindrrd trentises. of wliicli tlie one mentioned ic rro tLouht t h r most esli:iustivt~. Figure 1 shoms tlie li:itli> of liglit r:iys eni:tn:iting frorii c i i i elrment iri t h i bull's-eye with the r i f e ksperlly ainied. Tlie rays are consi(1eri.d to he 1):trallel u11 to O , tlie oh,jective. They cariverge to ti fociis VI, after which tliey diverge, falling on Z nnd 1'- the erector lenses, mliicli cause tliem t o coriverpe ;ig:iixi t o a ncw focus nt F2. A t F1 tlie iiri;igc is iriverted, wliile a t F 2 it is ercet and is virwed tliroiipli ;I 1mv poxver eyepiece. Iii order t o Iiave the requisite eye distancr, tliis slioulriiii their seli;iratioii \vil1 re5ult in tliffererit m;igriificntiori. Tlie iise of this property in securing :id,justahle rii;!griificoti«n is rievertheless :it-
tenclrd witli consitlcrnhle clifliciilty, sirice tlic wliiile iirrit must move a s tlie s c ~ ~ ; i r : ~ t iis « i irtiri~*tlif tlie t<~lescopei i to rctii;iiii iri frice~is. l'lie cxit ~)iil)ililitiiiietcr is 1ierli:ips thc lwst l>l:tc<.to bcgin in firiding Ihe cliai~i(~ters of tlit. Icrises iirijertive, tl,, divi< t o 4 X , with exit pupils 'A to iricli di:irrieter, is suggestetl. For tiirget sliootirig, sintiller exit pupils may be i~riililoyc~tl, ~ . \ ~ < . r;is i \ i i i ; i 1 1 :ih ?/i,," ti> >/i2'', wliicli riiakes hiplier Iiowrrs obtuiriable. 'i'lic ;ipf);irc.nt fielcl of ric\br is ;tboiit ec1ii:il t o tlie stop di;irrieter S- seen
x-
:it tlir (.y(. tlistiiiict.. Tlie tlinriirter of tlie cycpic.cr .;lioulci he eqiial t o tlie stop (liarrietrr ~ i l u stlie exit pupil diameter. Tlie err.ctor lenses sliould be f:\/f, tirries tlir cxit 11iipil di:trnrter, :ifter ;illo\ring a rirn for rnoiiriting. J f tliey :are sep:ir:rted somcwhat, make them a trifle larger anrl put a stop of t1i:it c1i:iriietc.r I)ctwcxeri. ~ h e ' d i : i n i c t c r of tlie stop SI is riow f 2 / f 3 time8 tliat of S2. The objectire diaineter i\ giren by
The first part of the cxpressioii gires the "effective diameter" mentioned ahove, wliile tlie sc.cond p s r t is thnt wliich is ;iddcd for the disp1:icrnient of the cones of r:iys frorii ohjects :it tlic edge of the fieki, :is sliown in Figure 2. Tlie widtli of trny fieltl w, :it a dist:ince D ( i . c . , t o :i tnrget), is w= ( S 2 / F ) D , to a close approxirri:itiori. Ciirratiire of ficld dcpends directly on the focal powcrs of al1 the Ienses :tdded togetlier, hence very 5hort focus lerises are t o he rigorously aroided in any desipn. Figure 2 indic:ites Iiow the lensrs should be turnecl, and also sho~vsthe ~ x i t h sof liglit rays from an ob,ject a t thc edge of the field. Figure 3 gires the coristruction of e;~cli lvns. Tlie liatclied component represents ordinary Aint glnss of rcfrnctire iridex 1.615, antl dispersion 36.6. The conrex lenses may he rn:i(le frorri horosilicate crown pl:iss of refrnctive index 1.917 íind dispersion G4.5, or of b:irium crown harinp an index of refr:iction 1.976 and dispersion 57.3. TIie r:i
!vli;it kictter color corrcctioii, ;iii(l ;i coii\ie rriountetl witlioiit :riiy tvsth. 'I'li(. ol).i<.etivcb;(lid e;icIi coiiil)oiitsiit of tlie rrcctor ilioiiltl be tested, ~vitlic.rowiis faciiig tlir liplit, 11ytlie rri(.tliorl fii\.t'ii ir1 "A.'I'.Jl." iiciir tlie I~ottoiiiof 1);tge 1,11,. 'l'lrc* ciir\.iiig of tlic Itoii<.lii Ii;iri(ls, iii
tlie lenses shoiild I>r "tiiiriirriy-ceriirnted" mitli glycerinr, t o take the place of tlie balsarn wliich urill finnlly be used. Figuring done on ceiiiented surfzice.; is practically witlioiit rffect. 'I'ry tlie crown L~otliways (if i t is rqui-convex) aricl leave it t h i w:iy it will require the lcast figiiririg. U'lirn tlir rrrors ore al1 rerriored, aricl tlie Roriclii bnrids are practically str;iiglit, tlic lenses are rendy to be baibamed togethkr. Tlie b:ilsam sold by most opticians, for cementing microscope corer glasses t o slides, is satisfactory. Clean the lenses absolutely spotless, put a. drop of balsarii oii tlie flint, ;ind lowcr the crown squarely over it. Finally press tlierri togetlier, bcing careful not t o let tlierii s l i l ~:tround on one nnotlier, until al1 surplus balsarii is sqiieeeed o u t of the edges, wliicli inny be wipeci clean frequently witli a r:ig b n r r l y ni»istc.nr(t with xylol. 'I'lie leiises a r e tlicn 1):tked f o r tliree or four Iioiirs at ti trrri1irr;it~irejiist above \vli:it tlie liarid r;Lii hear. Little will be sairl about tlie mounting (Figure 4 ) , since it would he a most fiitilr t o ntteriipt tlie jol, witliout soirie I;iio~vleclpe :irid i.kill iii mechanics. Tlie mounting presrnts notliiiig urinsu:il in tlie may of latlie work, but the lenses sliould be r;~tlierfiririly iiioiiiited, witli quitc ;i wide rim for ~i seat, in order to witlist:incl t h i recoil. 'I'lir reticule is situated a t tlie focus «f tlie eyepiece, und shoiild he adju.table to and frorii it, for prrrallax. Focusing
m a y he nccornplislir il iiiiit, tlit' l i ~ t t e rhciiig tlie prt.r:~iliiig prnctire. Tlie relicule coiil;id. P r a r tic:~lly, it sc<*iiiit o rri:ili<. littlc or 110 (litiercricc, iiricl tlic Iiiiilder niiry siiit Iiis wliiriis. iil) t o Ii;ilf eginniiig, \vill rrcliiirr. :in iirirc;isoii:iIiI~ 1:irgc ol>jcctive. l'liis -
1
Forrr rifle---rr,li
r i t r ,vi!/lits i?!t
s!i i,fv
!,i
/,U
thp
rrfrtlirlr.
7/1i,ir
, ~ i o ! l l l f s - a l t r r r . / i r l ? ~ > l t . it n
fhf'
is n f n r inorc iniport:int coiisi(1cr:itioii tlian tlii. first. Since tlir second piirt of tlir forriiiila giren for tlir ob,jcctire (1i;rrneter :tckn-nrrl (:S iri Figure 2 ) frorn tlic s t o p :it E'2, '10 not succeecl in getting tlirougli tlie objc.ctire, tlir oirly etiert mil1 be a sliglit di~ninutionof t)rillinnce :it tlie edpe. Witli l:irgr exit p~ipils,one coiil
266
I1IFI.E SCOPES
Tields. Tt is often difficult for the Inyman t o renlize that thcse systcms are .;ilways desigiirtl t.itlier kiy wliirii, (ir t)y ;ir1 ortlcrvtl cffort :ilorrg (~x~)rririierltal lines, in or(1t.r t o obtnin d c i i r t ~ lericls, ari(1 tli:it tlierc: ;{re iio rri:~gic:tl formulas wliicli will ;iiiswrr tlir qiiestion, "Wli:it kiricl of sig1:t ters tiie prrscnt one wili he used ,chjefly 1iy re;idfsr!i wlio li:lve iiot Ii;riiilt~:ibly rcfr:ictors as well, ;iiicl otlivr optical
,,'/Id
$;
EDGE
FEATHER
EDGE
CROWN
CROWN
ND V
FLlNT
ND V DIAM.
r, r2 3
4.5101'
CROWN N, = 4.5{?"
= 60.4"
--
1.6f83' 36.6'
[5/8'CLEAR)
=
fi.6'
=
-4.6'
-
V FLlNT
7
--
64.5
FLINT
-
4.5104" V 60.4' ND ;4.6450' V 36.6'
ND =
-
No 4.6483' V 36.6' DIAM. 94; (I/;CLEAR) 1 r4 = +2' rs f0.66' r6 -1.2'
-
Drawing by J. F. Odenbarh, n f t r r tlie
niitlior
FIGTRI: 5
Scnlc rlrnz~~ingof n nliePijfc ri~7r niqht, icith sp~cifieations. Dntn 611 t h e nuflior. Tlir pve(-tur 1 1 1 0 1 . 1 ~ (I h o i ~ t 14 I~ir)1(11.t111a.r a < l j i ~ ~ f ~ ~3'11~ # n t .u?t~I(~r nliriul(i bu movnhlr., i n oriificntion.sohtniripil, ci,itli tliu ctiepieces i n ( l i < . ~ ~il i~ ~dtlie tnbln (lo?urr r i g h t ) are z5 nnd x33Lu, r e s l ~ r c t i c e l y . "
gadgctq. Riit how qlioulcl tlic riflrman, lacking tliis previous expericnce, proceed t o do the joh? If lie n7ere clcrcr he probably could go ripht :it it, after studying parts of the prrsent volume, or of this and "A.T.M." See, in the prcsrnt volurne, Porter, nlqo Clark, on srnnll lenses, :ind Haviland on tlic refrticting telescope; in "A.T.Af.," Porter on rnaking eyepieces and especially Ellison on the refractina telescope (the 1I:iviland chaptir in the present book covers the inme general ground as the Ellison chaptcr in "Amateur Telescope Making," but in a more advanced and probably for tliis purpose an unnecessarily refined manner iince t i terreitrial telewope doeq not ordiii,rrily require ttie sarne precisiori as one for astrononiic,ll work). If a t the end óf
tliis siirrey tlic. slrl>,j~ct SL'CIIIS i i hit ~rristyt o t l i ~riflriiiriii, prrli:ilis tliis iric.:ins inrrvly t1i:it \ \ e hlii~iiltl turii t o Cli:ipter S I , 1';irt 1, "h.'S.hl.," ori "1M:iking Eycl>ic<~es" I1y I't~rtrr, ;iritl f;iitlifiilly r>;<.<.iit<.tht. ~iirliiriiii:iry ol>tic:il work tlirrc slir.c.ific(l. T?ycl)ircr Ieri\c.s :irc. coriili;~r:itilc. to rifli. scbol>cIi.riscs iii sim aiid iiretlio
l~ll;l~l:l: cl Tjrftr I?arol,l .l. T.oii~,~rrif San I>ii,i.n tulr~aco],~.Iii sii?ii 1 i ~ ) i < ~ tl!r .s l~ritli of fiir liiJlit ~ ' s ? / sis i r i ~ l i r < ,j«ldilil t trp. so flint n tt~1rscolitn h i , i r t 5' Iii~i!, i s /,i~iii/irr,'i~~(l iirto irhoi~t 1 8 " liii,~/fh. I ' h r i~irrii,rs t n t r s Ilint it i,, n/,,,> lisu,>o,' nrrd I I ~ I I I I ! ~othrr ,~/lr~ttifiq .sroj~~s ?!,ill, !V.Y,T li,,~l~l o ~ ~ , . Y ) J - . ~ ~ r, ,~, I~/ ~ i~ P ~ -~ ~ l ~1101 r r ~. ~ A -/ ~- o ?tlirm. I~~~~ i / l Iiu!r~Pl'rr,lip nr7rl.s. thin is o~ililri.lir~rth,'rp ia i i n ~~!ircrirr,. l\.lieli flirrt i.7 ii1irngF tkr :3,20'' ~ . ~ j r ( l <S. /t I~, v ~ L P( 1~1 L ' l h ~ri!ghl ¡S /1vr111~11,1,1, I I C I < I ~ J / P I I S cnii ?>o risr,ri s n f i v fncturilf] ir~iottiri!/. I:~solr.iiigpi"8,r'. i8 ,11x0 ~'erlirrrlliii d n y time. Iiiglit: Tlie l i . n~irl1,: i'rnn~Cn/~tniii',s scrtpt ii,ith 3.20" o b j ~ c t i v elells and changes of eyepiece giciny pozcurs «f . ~ 1 0 . 7 r2l. , .r25.6 and x32.6. Ilavirig beconle fainiliar witli the ;irt of rnt~kiiig poocl ryepiece lenses, tlie smnll aclirorriatic nbjrctive, e r r c t o r s and eyrliiece lensrs of tlie rifle hcope will prove a n ensy s t c p f o r w a r d not too (lifficiilt for tlie t i e ~ i n n i n g o~itician. Clark's article on "Small I.en\es," in tlie preseiit roliirne, especially his "Postscript o11 Objectircs," iirar t!ir riitl uf tliat article, will be uf g r c a t valuc t o
tlie riflc1ii;in wlio rri:iy wish t o rn:il<e :L rifle srope. Wliat IT:ivil:in.jt.ct-<;l:iss" iii "h.'l'.JI.," ~>;irticuliirlywliere he discusses "1'rnctic;il-SIii11)irig :iiid (;riiitling, Polisliiiig, 'I'rhtiiig ;ind Figuring," if closcly followrl;icrtlrie;ir tlie riflerri:iri wliererver he lies prone. 'l'liey tire used to extrinint. the target. S a k r , for example, tlie 13. ;ind 1,. clrcrilitive lit<.r;itiirr. .i spotter describecl in it Iias a .t5mrn. (;rl)out l'jíc") 0 . G . tind rri:igiiifictitioiis X 12, X 10.5, X P í i , X8íi.5. Ariottier is tiie te:irri ci1ptain.s Scope hli0wn iii Figure ti, ;it tiii rigiit-a ~iliotogr:r])li furriislird by I%:tiiscti and Loiiib. With tliis tlie team captain quickly picks u]) diff'erent targets.]
T E S T F O l t CONVICX SPIIEILES
R y J. 11. l i i s c .\inity\.illc, Loiig Ihlaii(1
Conrerniiic tlie ~ioliqliirip of conves sliliericnl siirfaces, Elliqon states in "Ani;iteilr 'I'rlc\colic JI;iliiiig," 'Xo rlliestiori of tlic.ir figure can iirisr ;tt tliis st:igc of tlie ~)roct.~~lr t o t < t it.' Profcshionul in:ikrri soiiietiiiics I v s t co~ivexs~)Iic~ric;rl surf;tcrs h y interferriice iiictlio(ls, r r f c r r i n g tlir coiivcz t o ;i st:~iiressed for a test for ~ O I I V C X~ C I I S ~ mliicli S w-oulci be :i'i s i ~ n p l eiis t l ~ i i tfor conc;ive mirrors, it ~v\.i)iil(l secrn tli:it siicli :I test, if nrnilnble, u ~ o u l dhe vcry usefol. 'I'herefore. tlie \vrit<.r p r o ~ ~ o wns test f o r conves sj)lieric:il surfaces reqiiirinp no aiisili:iry ol>tic:il siirf:icc, aiid orie xvhicli is simple a n d ns rigorous a s tlie iiiirror t e t :it ccriter of riirv:iture. If, for tlir. snlíe o f illustrtition, .ivr imagine n sy)liericnl surfnce consisting of onl!- ;L sliiii of silver of przictic:illy no thickness, wliicli woiild :it tlie s:inir tiroe rcrii:~iii optic:rlly triie ~vitlioiit siil)l)ort o n either side, oiie sicle w»uld 1)e a coiiveu niirror and t h e otlier n coiic;lve of tlie s:Lme r:iclius. 'i'lien, in orclrr t o t r s t tlic convez rnirror, orie wo111<1mrrely 1i:rve t o go arouricl t o tlie otlir-r sicle :inr:ictic:il optic;il siirf;ices a r e gener:illy forrned on gl;iss h u t if, irs in tlie c:ise o f conves
*
First publislied iii Scientific hiiir~ir*ari,Feh. 19:35, page 100
crritrr of curviitiire. 'l'li(. t c t is ripoi-oiis l)cc:iiisr it is rontliietrtl t o nll I~r:~<~tic.:il piir1~15t.scntirt.lywitliiri tlir licluicl iiic.diiiiri, ;iii<~r:itiirc.A vvry strong wor
infl:imrnnhle liqiiid tvliicli v:iporizcx~:it rooiii tc.mpcrntiire. Tlic worst rxplosioii dile lo clierriic:il silvering ~voiild he vcry iriild irirlc.rrl c o r n ~ n r e dwith tli:it diic t o L: g:illon of I~enzcnr ~)ropcí-lp viiporizccl arid ipnitetl i r 1 a closed ce1l:ir. Below is given n list of vnrions li(liiids :mcl tlieir r e f r a c l i \ e indices for the sotliurn lirie :tt p i v r ~ it ~ i r i ~ ~ r r ; i t i i r eHo\vever, s. tlie refractive indes usually dues iiot vary widely xvitli a sliglit chorige in tcrn1)criitiire. Castor oil Olive oil Niijol
Oils (cit 20. C.) 1.m Turpentinr 1.470 Kerosene 1.475 Acto oil
T w o refracting t e l ~ s c o p r s have heen rn;itle ~vitli kerosene a s the testing liquid and, although the ref. i n ~ l e xis orily 1.45, thcie i n s t r ~ i m e n t swere hotli siiccessfiil.
i l . t 0 C. ( V r r y lioisoiioiis if l,i,eatlied) (;lycc.riiic ((;ly(.crol) 1.172. :it 25" C. ( V W Y ~ I O ~ S O I I O I I it' V ) i r ( ~ : ~ t I i (i~ifl:~rrini:iIile) ~~l; T o l u c i i ~1.1!)5 ti1 -oo Carboii tet. -1.0 lierceiit, Etliylerit. hrorriidc 60 liercriit, 1.4989 :tt 28' Spoeirrl O i l s , í'r!lslrrl I ' l r . ~ r r(,?Oo ('.) 1l;ir.iol-P l . l..iíil. FVirolF l.kF2.5 l'riri~ol1 1.1Xli (l.
-
C,.
---
'I'lie tlircc liist-ii:ii.iid "spi.ci:il" oils ;irr (listril>i~trtl I)y St;,iieo nistril)iitors, Tlo~\-t.\t.r,Sii,jol, ; i i i "iriterri:il Iirliric:int," I C . 1 i r v . S Y , , S. . 1)riiig \v:iter \vliite ;iii(l r;isily ot)t;tiri:rl,le Io<:;ilIy, is ;i very goii(1 siil)htiliit(~fin. l~riiiiol-11. :iltIiorigli ~ i o tqiiit(- so liigli in rt~fr:ivtive ii~(Ivx. Soine rri:iy r;iise tlie ot>jectiori tlitit tliv clispersioii of tlic liquids mny not be cclii~il t o tli;it of tlie vrowii ,gl;iss. Of ctoiir\c, tcsstiiig iri solctcly, 1)iit tlir n r i t e r tivlieves tli:it tiitiiig ~vitli~vliitc. liplit is :iliotit ;rll ili:it is iiccess;iry ;iiid tlii rrfr:ictivr iiiclex c*rkioloitl.'I'lie riglit-li;riid clrti\viiig slio\rs tlie sct-iip. 'I'lic s~)lit~rii;il niirrt)r slioiil n r t l i ~ < it l , is riot 11ec(.51:1ry t o coristruct :I largt. optical flat or ;I I:irpe s1ilieric;rl iiiirror ~vlieii Iiiiil(1irip e roiii~)o~tn
' o i r ~ / o r1 %.T. ~V. RIchd:irn, 1I:rhtings-oii-EIiicIsori, N. B.: . Z , 15 niid O (Figiire 1) a r i ciirt1l)oiirtl (lisks witli '/;" lioles iit cciiter, covered nitli tiiifoil h;tririg >/," Iiolcs ;it cziiter. 1) ih :i tul)? 8" loiig--cross-liairs :it onr en& Iir:~' l Wiii
AT CENTER
imnge of E reflected from f:ice of prism ex;ietly ct>incident. This brings f:ices of prisrn squarr t o mirror ;isis :iiid ocii1:ir axis ;tiid insures rays converpirip on ocular beirig syrnrnrtriciil iibout ocular :ixis. Al1 parts sliould be securely claniped irito position to prevent movcment during edjustment. C ~ l l i n i n t ~ o n .B y Chas. U'. Eliason, Chicago, 111.: It would seem t o me tliat a really Iiigli order or prccision in :icljustrrierit is necessary for tlie use of tiigh-power oculars, :it 1ea.t. Tlie fielrl stop of ;L une-fiflli iricli eyepiere, for esample, is rnther less thiin orie-eigtith of nn inch in diameter, and tlic job is t o turn the nxial pcncil of tlie o l ~ j r c t i r e into tliis narrow opening. Since critica1 defiriitiori falls off so r:tpidly nway frorri the axis, this is exceedingly irriportarit, tind 1 I1ai.r thoiiglit tliat the sonietirnes (lisappointiiig perforriiaiice of arn:iteiir oli,jecti\.es is diir l o f:iiliire iii tliis regard. A gond mang of the h«oks on tlie sul>ject suggest checking the collimation by racliing out tkie cyepiecr and observing whetlier or not the out-of-fociis images a r e circul:rr. If this is done, ti moderately Iiigti-powrr cyepiece slioul
a onr-inrli ociil:ir gires rnr rernarkiihly ;~stigiri:iti(*irniigrs. Of course, the axis of tlic ti~tigiii:itisrri will rotatr if tlie Iie;itl iq iiiorectl. 'I'lie :ilirieiiierit of tlie lirisiri of tlie Ncwtorii:iri is n. nititter of sorne dificiilty. Accuriicy is irnl>ort:irit to pirforriiiiiice, Iio\vevcr, arid p:iiiis will be fiilly rel~tiicl ir1 l>(.tti.r (lefiriitioii. Tlie follo~ririg rnetlioroloiig:itionof tlic axis of the cyepiece :id:il>tcr irit~.rsects t h r iisis o f tlii L~lcscope tiib<,, i i r i t l iit riglit ;iiiplch Fitirieiits tlitrt (111 ~ i o tpcrriiit eiisy riiotioii iri i i I I rrcli~irecl clire(.tioii.; tire ;L sore tri:il to p:itience. i'ossil)ly tlir 11est iirr;in~enierit is tlie f;irniliar one of supl>ortiiig tlie prisrn by nieiiiis of foiir wehs terniinating ir1 slottecl Iioles
"TARGET' SLIPPED
.]
OVER ADAPTER TUBE,'_,/
in the \val1 of tlie telewope tiil>e. If tlie prism can also he rotated around tlic axis of tlie tube, the adjustinrritb a r e cornpletc. Tlir ~ x i s n iis first ceiitered witli respect to tlie telescope tube. This can be done witli siifficient accurticy by irie~isurrrricrit. I t is also iidjusted so tliat i t is roiiglily central to tlie adapter opeiiing, judged by looking through tlie eye eiid. A "target" is now prepared. h hole large enough t o fit siiugly over the insicie incl of the adiipter is cut from n white carci, nrid heavy black coriceiitric circlcs, nbout $&" apiirt, a r e ruled outside the cut-out "hull's-epe." Tliis card is slipperl over the iiiside encl of the adapter, f;rciiig tlic prisrn. (See Figure 2.) . If tlie cell cnd of tlie telrscol~e tube is now covered witli a dark cloth (the mirror Iiaririg beeri removed), it will be possihle t o see, on lookiiig into the adapter, a faint reflection of the t:irget in tlie iiearer sqztcirp face of the prism, (surface A, R, C,,D, in the drnwing). An eyepiece, lenses remored, should be slipped into the adnpter for this ~ ~ u r p o s c .Adjiistment of tlie prism is now made, so tliat the reflected system of circles is centered on tlie
arpuw<' fiicc of tlit. I)~¡HIII.'1'Iiis i q ~.:isily (Ion<' 1iy I I I O V ~ I I ~tlic prism iintil oiir of tlit. circlei is tiiiig(.rit to ;rll foiir ct1gt.s. Il'cir tlie II r<*ti('ctcd frorii tlic Ii!.l)otcrii~s(~sicle of tlit. 1)risrii. tVitli ii little .iiigglirig of tlie illiiiiiiii:~tioii, it \irill [lohhil)le to I<eep tlic reRt.ctetl circlrs of tlic t;irgct still iri view. Tlir :id,jiistiiic~riti\ iiow corii~~letril Iiy ~iiuriiigtlic prii.rii iip or tloxvn ttie :txris of tlit* tt.liscirpt. iiritil tlic iiii;igc. of ccII ciilctccl cliiiclily ;iticl tict*iir;rtc~Ip. I t i h tissiirried tli;it tlie tulle Ii;is bcv.ii liiie(l ii11 i i t rig!it :iriglrs to tlie clccliriatiori :ixis by tlit. usiiítl inctliocl, iiii(1 tli;it tlir optic;il 11tii.t~of clic tele\cop(. are iri tlirir proIwr rrlntiorislri~)~. Cori\itlt.r tlie follo~viiig tliCor(.iii: If two sl)li(.rcs :trr I)roiiglit tog(.ther so tli:it ;iny tlircc. poiiith uri one sl)lierr coiiici
C O L L I I \ . I A T I O N A N D hI1.J L I S T M E N T
27.5
tlie dcclination circle or it5 pointrr t o thv corrrct rc,i
SOlitli Nortli South Nort11 Tliv rovidr"te side iii crossiiig the riicritic:il systeiii 11:is been ac1justed t o its final setting anil tliere made secure ageinst accidental derangement. S h e rnetliod is as follons:
(1) On a concrete or other iuhst:intiaI floor, set instrument approximately leve1 ( 2 ) H.iisc pol,ir nxi\ .i~iproaimatclyto correct e l e ~ a t i o nfor latitude. ( 3 ) Set tele\cope tulle parallel Lo polar axis and directly abore it, and clamp both slow motioni.
( 4 ) Ad*jiist Iiour circle to retid V I liours, tind s r t it. (5) A
( 7 ) lte:i1)t'rit tlii process till tlir residu:il error ciidiciil;irityI)et\veen tlie liiie of s i ~ h tand the dec1iii:ition :lsis. IVliile tlit~v:iliie of tliis error cari he corriputed. it is perliaps more prartic:ihle t o t r p inserting ;i sliirri 1,etiverri oiir end of the s;i~)roximately wllat eiiiioilnt. Wlirii your hour circle rezidings finülly check, your circles ;rre correctly set. (15) Fin:illy, uritliout rlisturhing tlir tclescope, ndjust the levrl buhbles by their owii ac1,jiistinp screms (not by means of tlie iiistrument Icveling screws) t o tlie center of tlieir runh.
Wliile, witli re:<son~tl~le coiiifort and nhuiiclant liplit, me Iinve rni~cle practirally al1 rirccsstiry ad,jiistnieiits indoors tind witlioiit refercner to tlie stars, we hnve not thereby disregardecl astronoiiiy iri our process. Indoors or out, the force of pr:ivity has been oiir poirit of refererice. Sever;il points of corisider:~bIc irnportcin[*e rerriain to be mentioried, of wliicli all but oue are self e\-icleiit. h m o n g tliese, tlie leve1 bubbles niust be of fair qunlity :ind of a se~isitivityof about 60 secoiids of ;irc per clivision (iisiially 2 rnrn.); tlie mirror :ind prism (or tlie lens cell in the case of refr;tctors) rriust be eapnhle of prrrri;triirit :idjustrnrnt. T l ~ emanrier of s ~ t t i n gthe liiie of iiglit t o the n:r
smnll ~iiecesof 11r:iss ;iiiplr t o tlie two eiidc of tlir tc.lescopc tiihe. l'licsc. ;ingles ;irc c.irel1 ])rovide(l witli :I ~ ) e e pIiole iil)out $:{-' iii e'tiil)c, slioiil(l be hct p;iriillrl t o tlir liiie r ) f siglit 1)y settirig tlic cro?is-li:iirs 011 :I (listant street liplit, 1000 or more feet :iw;iy zinc1 liriiiig "1) tlie two perp siplith, h y higlitirig Lliroiigli tliriii oii tlic s:iiric ci1)jcct. If tlie <list;iiic(. l)rtweeii tlie liiie of tlie peeIi siglits :iiid tlir rriirror :mis is, say S", :iiioie iiirtliotl in:iy appenr corriplicated, it is reallp quite sinilile to c:irry oiit, ;iri
decliiiatioii tisis (3) Scttiiig holh circles correctly (4) Settirig our referencc lercl\ true. When tliis Iins been acconi~,lisliid,tlie inoiinting niay he .t:iken outcioors to pier or tripud, ;LS tlie c:ise niay l)c, :1ii(1 ~~~~~~~d u p readq- for oririitirig t« tlie meri(1inri. I f yoii kriow yoiir lonpitucle, wliicli c:tn rnost c o n ~ ~ n i e r i t lbe y read witli al1 iiecess;iry riccur;icy froiii a LT.S.G.8. i1u:icir:ingle slieet, :ind your wntch is ;id,juste
(oiir rlcclinatiori), k~iit \ve can siiy th:it O = rp 4- r . tlie letter r rrpr<.it-iitiiig tlie ;riigul:lr ~litiert~iicc I)rt\irr.t~riitlic :~ctii:il e1ev:ition of oiir po1:ir :ixis :irid tlic elev;itiori tlcsire(l. ~vliicliis oiir /a l'he rrsi11t:iiit sipn of tlie v:ilu<- of "e" \vil1 indic:ite mlirtlirr oiir :issiirnl,tion of tlie sigii of "e" litis I)ccri rorrect, or, iii otlier xvorclh, tliis corrcctioii slioiiltl 1)c :ipl,lictl witli its hipn clr:iiigr~l. i ' h r o r ! / : Iri tlic riplit 1i;iiiil ortaiit.
--
Tlie ellipsr represents the forcsliortcned circle wliich tlie rleclination axis a s a ceritrr. The c1ecliii;tLion nxis AS c:irries tlie uptic:il ;iais Si' ;it its oriter extremity X . F o r oor purl)ose, Si' is suiq)osrd t o he placed in ;i vertical po\ition :is inrlicntc.d. Tliis positioii is irril>ossihIc : ~ tlie t :ingle slio\i,n, and is 1)laced tliere only to facilitate tlie driiwing and permit visualiziiig t h e ronstruction triangle J ? ( ' S .A t tlie point where this relationsliip is ap~>licnt>le, iiariiely, wliere the decliriation axis is nearly Iiorizontal, tliis tri:inglr nenrly vanishes. Strictly, i t cari haie no arca except whcn tlie declination nxis is sliglitly :trv:iy from the n tlie two from horizontal nnd the opticnl axis vertical due to any d c r i ~ ~ l i oof pcrpcndirularity, arid this is ~v1i:lt we wisli to investigate. Draw tlie liorizontal P E to lie in :I vertical pl:iiie tliroiigh P,4, thus malring tlie aiiple Ef'A tlic angle of elev:rtion of tlie polar :rxis. Tliis plane will also ciit tlie circle clrscribed by tlie declinntion axis :it come di:iriieter J~.11. Tlie linc Al<, ~)eryiendiculart o PE, \vil1 tlien be vertical, and partillel t o the optic:il axis S T . Now, if through LY we pass a liorizontal plane, it will r u t A L a t B and
IZ \vil1 describe if rot:~tecl on tlie poliir iixis iibout '1
will lic riglit arigles. E A nt C. 'Slic :iriyIe , f T<S7,:¡S ~ r c l l:I< <,f('X :itid Ll('!<, l l i e :iriglr S A l l i ,wliicli wr 1i;irc I:il>iled 11, will bc. gircbii 1ij' tlie Iiour circlc, aiitl tlii. ;iiiple ( ' , l I : , rii:irkrd ili:, iiecc5ss:iry iri tlie sadclle, 9" long, of :in equ:itori:il wlirn iipori rercrs:il, tlie Iiriur circle iridicates :I dixre1i:incy of :
--
-
. O 0 &:$ti >: .'il.:392 = .00:32&
90° 11' and .00:12 1. X 9" n
-+
.O29", by wliicli arnount tlie satidlc end, whicli wns iiliperiiioit wliiri tiibc I\.;IS rerticiil, is too Iiigli. í'ollinirrti~igrc ('n,ssr~!/r(ti~iictn. T%y1I:irold A. I,»wcr, S;~iiDicpo, C;iliforni;i: Wlicii ;ciii;itciir trli.sci)l)c iii;rlccri g;itlicr to (tisci~is o1)tic;il ~iroI)lriris, orir frecluently lie;ii-s tlie statc.rricrit t1i:it ":i C:issegr:tirii;rn ~vill riot pcrforiri :IS well :is :L Scwtoiii:in." Tliis is seldo~n disputed, biit oiie clor\ riot oftrn 1ie;rr :iny csl>laii:ition of tlie' rctisoiis for tlie siir)p«sed inferiority of tlie Cnsscprnininn. \Vitli riiodcrn nietliods of testiiig, tliere is iio rcason for riot niiil:isicnlly n rri:itter of desipn, :ts it is almost impossible to obt:tin acciir:ite collinintion if tlie inountings of the optical 1i;irts a r e not firm, :inri yet c:ipahlr of delicate arljiistrnent. 1 liiire freqiieritly serii telescopes mhicli ivrre n r l l 1nount~c1, nnd with excellent «ptic:il surfnces, yet perforniaiice wiis not pood lieciiiise tlie prisrn rriounting wtis sliaky and e:isily jarred out of :idjustmerit. Cas\egr;iirii:ins frequently siiffer frnm tlii.: defect, and rriay also hnre a poorly ntl,ju\ted secondary rnirror wliich sliimmies a t tlie sliplitest jar. I t is not sorprisirig t o firid tliat tlie Cass Iias ;L bad reputation. All tlie opticnl p a r t ~of any telescope sliould be firrnly moiinte(1, and screw ad,iustrnents should be provicle(1 for centering :ind squ:iring t:n. Tlie secon(1:iry iiiirror, for cxample, slioultl tie suppo~teclby L: stiff spider, cap:rble of beinp :iccur;itcly centcred in tlie tiibr. The cell should be so mounted on tlie spider tliat it m;iy be tiltcd in iiriy direction for sqli;iring ori, :t~iclfirmly
lar-ked in position, wlicn oricr ;~tljii\tr(l. Fipiirr
-1. sliows $1 type of secoiiclary iiiiluiiting wlricli 1i:is givc.ii s:itisf:i<~torg-r<.siilts. \Vitli sliglit mo11ic1;it tlir otlirr ~ r i t l it i 11ibk 11:1rinp :i siii:~ll1101c i i i tlie center. IIi;ir~~ctric;illy o ~ ~ p o s i tthe e ryrpiere opeiiinp iii tlie telescope tubc we pl;rce :L tiirget, wliich rriay be ;t cliolk rri:irk, or a small bit of wliite p:iper. 'I'liis target is located
on the insidr of the telescope tube, opposite tlie eyepiece opening, and its position should be determined by very c n r ~ f u lmeasurernent. Having located tlie target, tlie riext stcp is to slip the sigliting tube itito the eyepiece mounting and sight through it a t the target. By ineans of shinls or ;idjusting screws, the eyepiece mountirig is ad.justed until the crosswirrs iri tlie sigliting tube a r e accurately ceritered on tlie target. This completes tlic adjustmerit of tlie eyepiece mouriting, and if it has been carefully done, i t will never need to be disturhed. Tf the main mirror is perforated, the adjustment of the eyepiece mount is a bit ensier, as al1 that we need do is tu stretch twn strings across the front of the telescope tube so that they cross in tlie exact center. Tlien these strings becoriie our target, the eyepie<+einounting is centered, and ad,justed until the cross-wires point a t the tm-o strings. The second step is t o place the spiders which will support secondary and prism (or diagonal) in position. Thesc spidcrs shoiild he adjusted by rneiisuring, until the center screw Iiole in e:icli syiicler disk is accurately centered iii tlie telescopc tube. Next, tlie prism is mourited oii its spider and lined up by means of the adJusting screws until tlie cross-wires in the sighting tube point directly a t the center of the prisni and tlie reflection of the
COI,I,IRlATION A N D A D J U S T M E N S
28 1
central screw Iiole ir1 tlir secondary spider clisk is seeii cx;ictly ceritered by tlie cross-wires. Ari acldition:tl checlí ori tliis ;icl.iii.itrnrrit is to siglit tliroiigli tlic criitrr scrt.xv Iiole of tlie srcon(1:iry h])i(l<.r. 'I'lie iiii;rpe of tlic eyepiece tiil)t* slioiilitlers were cnrefiilly loc;itrd, so tli:it tlrey are iri line, we ctiri sqii;ire u11 tlic ni:iin riiirror by iitl.justing it so t1i;it tlic legs of tlie seconi1:iry ;iiiil prism spiders a r e directly i r 1 line ~ 4 t htliei'r rcflectioiis in tlir riiiiiri rnirror. After iidjustirig tlie riiaiii rriirror in tliis way, we remove tlie sigliting tube, :ind look tliroupli tlie eycj~ieceriiouritirip, ;irid slioul(1 hee a niinibrr of coricentric circles. 'TJiese are tlie end of tlir teleseo~)itube, the priiriary arid seconclnry rnirrors, and tlie eyepiece tube, :inri their reflections frorn tlie two niirrors. In the ex:ict center, tlie reflection of tlie pupil of your eye sliould appear, nnd al1 of tliese circles shoiild be conceritric witli it. If not, tliey can be mnde so by sliglit tilting of the main riiirror. If tlie first ad,justiiierits Iiave been carefully dorie, squaring oii o€ tlie rnain niirror coriipletes the job, hut t o be quite certain t h a t everg tliing is right, tlie telescope should be poiiitecl a t ;i s t a r nnd the eyepiece racked slightly in nnd out of focus. If collimation is correct, when tlie star is in tlie center of tlic field, the out-offocus ring systern should appear circular, and of uniforrn width all aroutid. If it is elliptical, or tlie black spot is not well centered, tliere is a n error. I f the adjustrnerits hare tjeen carefully made, alinement mil1 probably be so nearly currect tlint it will reqiiire a fairly high power ociilar to cletect tlie error, but if tlie stor test sliows an error, very slight adjiistrnent of tlie prirnnry mirror sliould correct it. This method of collirnatinp a Cassegrainian may x e m to be a lot of trouble, but it docs not take long, and the improved performance will well repay the effort.
IJOZL~ to , I l a l i ~n Iliayonal for
a
S<~~ctonian
Wliilst tlie use of :L tot:illy rrflcctiiig ~irisinon a Newtoninri is permissihle. WP I I ~ I I SU~' :m (>pti<'i~l pli~nt.of c1liptic:tl coiitoiir if wr desire tlic vrry l ~ r s t rc>iilts. \':irioiis ~rrctlioossik)let o pick ul) :i piece o f gliiss wlrivli i.; optic;illg plaiie, aricl it is ccliitilly dificiilt t o cut a11 ellipse froni a good ol>Lical plane
without srriouq cletcrior;~tiori of tlie optical surfare. Thew tmo ohjcctions practic:illy determine tlic metlio(l., by wliich a perfect optical 1)l:tne uf elli]>tic:il contour rritiit he ~irocIuct=
slitle rest NR :iiitl Ilir rIriv<- iirriiiigrtl frorii ;il)~~v<-, so tlint :i forw:irrl riiovenient of tlic rcst docs iiot iift'rct tlit. tt.rision o f tlir tlriviiig ,rbi>r(l. Nrit1it.r a Iiigli sl)e(xd fol. tlie liitlie nor tlir prindirig \vlirtal is dcsirnhle; 20 r.l).ni. for tlic lt~tlie:iiiy tlir :ihr:c\ii.e. 'I'oo iniicli linstc~ will rc.siilt iii cliippinp of the gI:iss, :11irI ~~ossililyforcing it frorn its se:it. IVlieri fiiiisli<.<\ witli :i smootli cclgc, tlic tii~releclsliiift is lic:itrd, :iii
cllipse has n 1'4" minor nxis, then \ve reqiiire a glnss dislc 6" in dinmeter or tlieretibouts. This disk need not tic eclpecl, nnd it iriiist I i i ciit plie
otlier iiietlinelom, ;ilt<.rn:itcly. To t r s t for fl;itiiess, xrt. reclriire ;I siii:111 11lieric;il riiirror ;tl)out fi" in dianieter. 'I'lie r;itliiis of ciir\fatiirc of tliih ~ n i r r o r r c c l l ~ i r ~cor:si
TIieoretic:illy, the loriger tlie rndius of rurrntiirr, tlic grrater tlie acciiracy ol>t;~iii;il)le. Pr:ictic:iIly, for :i sni:ill fl:it, too great :i dist:iiice prc.veiit\ one seeirig tlie siirfnce of tlie fl:it inti!ri;itrly, ;iii(t diffr:ictioii effects :troiiri(l tlie edge of tlir flat tire sornewliat coiifusiiig. 60" r:tdius of ciirr;tturr is suitable for fliits o f I1/il" t o 2" riiinor nxis. h siiit;ible ;irrtingc~nrritfor te5ting is shown in Figure 3, :it riplit. Tlie splieric;~lrriirror is mourited in ;i circiilar rrcess in a block of xvciotl, wliicli is screwe\eis Iiorizoiitnl, in wliicli ciisr tlit. riid rierv will he circiil:ir. I t is tlieii corireriient t o provide a closc-fitting ninsk rrliicli hides tlie "surround." Alteriiatirely, tlie surround may be pnintcd witli rouge iind water, which quickly drirs. 'I'he ellipse is approxirnately fl;it wlien tlie focus, in a rertical plane, coincides with that in ii liorieontal pl;ine. To be more precise, find the focus moring the I
the grentest possihlc. ;ii.c.iiracy, wc. iircd :i prrfcctly circiiliir pinliolr, :ind an ordin:iry eyrl>icce. U'c prorretl t o estiriiiric tlic iiii;~geof Llir piiiliolr with thr ryepiece, ;iiid cxpziii(1 tlie iiii;tge un eitlier side of tlir heht fociis. Whcn the irri;igcs exl)iirid identic;illy oii hotli sitles of focus, tlir niirror is irn :icciirntr optical pliiiie, ;ind tlie c1e:irest (lrfiiiitiori of tlie ]>iriliole is oht:iiiietl. lliis rrietlio
image is elongated "liorizontnlly incide focus," ancl "verticnlly outsicle focus," tlie riiirror is c o ~ i r e r . A t tliii, st:tpc, it niay he interesting t o inquire whetlier this test can be used iri rriaking ':i cirrttl(tr optical 1)l:irie. l'lierc is orily orie differeiice, tlie cxpanded iniiigcs spreacl into iiii rlli/~tircrlform, conseqiient iil>«ri the angle a t wliicli tlie pliine is viewed. Ttie figures a, b, c, Figure 4, show what might
be abtninecl in the testing of a circiilnr plane, when perfect, a n d when closelq iip~~ro.ichirigperfection. The pinholc iin:ige i \ 5lionn in the center, the outside expanded image on tlie left, and the irisicle eapaiided image on tlie right. R e ~ e r t i i i gt o oiir original problrni. Having now obtained our accurate optical plane, it can be removed from tlie iron plute and clcanrrl. Tlie "surround" can be iised :igairi and :igain, with the aid of thin metal packiiigs to r;iisc theni to their original thickness, if found necessary. To mount tlie rllipticnl pl:ine a e require a sliort length of l)r;l\s tiihing, the interior dinrnetcr of whicli is a f r w thousandths greater tii.in tlie mirior axis of the mirror, a diiriension ahich can be accuratelp obtainrd. This
:uI)F is rrit ;it :in iiriplr of l.5", iii tlit. rii:iiiricr iiidic;itt.
the hrass tiibe slioiild fir\t hc nrinc;ilrcl hy licnting t o a red Iieat, niid plungi n g ir1 colil \\-:iter. r1ftc.r I)ericliiig, tlie proiigs can he rediicecl by filing to t i niiniiiiiirii, w f r , tiiid syiiirnetric;il contour. Fiiinlly, ;: hr:iss disk t« fit the tuhe, witli a proje<.ting scrrwecl stud (Figure 5, a t riglit) is fittid. A 450 hevel is fileil on tlie iniier edge in one spot, so tliat t l ~ e1il;ine mirror rests thcreon. Tliree screlvs a t 120".are used for fastening tlie disk in t h i tuhe, nnd tlie 4.5" bercl is carefully easecl aw;iy with tlie file, until, witli the tliree screws tiglilly hiririe, tliere is just a ~)ercelitihle"slialíe," eiisuriiig tliat tlie pliiiie is iivt riipprd. A cylin iind c , are ;irr:inged so tliat tliey can be indiridually screwed eitlicr forward «r R;~ckm~:trd. This ad,iusttiierit, aloiig with tlie possihility of rcvolring tlie plnne itself o11 tlie optical axis vf thc cell, will give al1 the adjustment required.
[Erir~on's NOTI:: Thc rlii~ptrr wliicli folloms is n rolli~tioii of v:~rioiis amatriirs' cslit~ric.iicc.s--a hort o f "te4ti1rioriiiil n~~eti~ig"--riiiidC111) frotn descriptivc Irttcr5 rccei\.e<.irig ratlier es~iciisi\,e. Iri acltlitiori to tlie inetliotls wtiicli folloa., tlie rc;i
FJGCRE 1
C i r r l r s oli tlrp S?" r ~ ! l r r t o r of t h .~l I r J > o ~ ~ a l dO h l i ~ r i ~ a t o ) l i~~', o ~ o s hirilt , bg f a r n f r niiil Sii,a.siy (slioii.i,tg D r . Si,,a.srj,). L ' i . i , r i h12rr flrr r.ir,,lr.\ U I . P I I O I m i l i i l t r l ! , iliridr,
refer t o the niethod described by Porter, in tlie chapter on design of mountingq, also in tlie chapter oii "Wrinkles," in "A.T.RI " Sornetirne\ isolnted \i,orhers are in douht regarding the necesqnry clo\enes\ or fincnrss ot iubdi\isi«ri uliicli the 5etting circle5 of a telescope sliould be piuen, anc1 woncler whether such coarse subdi\isions as 360 interral\ on the declination circle and 144 intervals (each one 2 % " ) on tlie K.A. circle
is firic crioiigli for n grroil tcles<~olic.Otliers Iizivr eriolleys, ancl n pin fits into tlirse liolcs. Tlie pin fits tiplit :iricl tliere is no lost motion. By iiir:ins of n r e r y criide trial 1 found tli;it this hrarl is fairly accurntely gradu:itt.(l, easily witliin a tentli of :i degree. TiTitli tliis 1 c1;iirip tlie circle iii a foiir-jnm cliiick, arid place a sh:irli tool sterl scratcli piii iii tlie cornpounrl. By rncaris of this set-iip 1 cari e:isily, nn
1 first foiinil tlie centcr tiritl riinrlir
:L circlr :il)oiit '/," frorii tlie eclge, sli:irl, ct~iitcrpriiic'lr. 'l'licii 1 ~ii:irkc~
of
:i
hy nir:ins of
oiit the center of tlie disk, moiintecl it on a snw nrbor nnd set it u p in a smnll polishinp latlie. By settiiig t i sm:ill tool-rest tiglitly u p npninst tlie clislí, ;ind 3vorking undrr :i reacling gl:iss, ;i fnirly goocl joh of scratchirip the division ni:irks w:is'doiie witli L: scriber. n r . S. 11. S h ~ i b no.,: , 707, R i c R r ~ ~ o n dT'cr.: , 1 got n hig panel of ply-wood ancl m;i
thr rnoiiiitiiip i.; attainrcl. It is iriucli ~ n s i r rt o iri;ikr n poocl circle thnn t o pI;icc tlie ;iscs of tlic telcscope pnrnllel t o tlie eartli's ;ixis ;triiit tlir siiiiie priiicil>lr coultl l)c ;i
the front nntl Incilorr(.d. 1 iisel;tckcricil. I t should be a i clohc' to tlic sc:ile iis pohsit)le, ir] orclrr to ayoid ~jiir:rlliis. S o t e that the 1)iico sidc of tlie sr:ile iiiust be iirst L o the l;iiiip, ;ind tlint tlie base of tlie iiiinier:ils rriust be townrd tlie edge, a s tlir mirror iiircrts. Tlie 1:lrnp is ;I 3-volt flasliliglit glot~e~vorkingon nne cell, t o gire a f:iint light. Tlie hocket aiid oiie sirle of tlir switch :trc "grounded" oii tlie irioiiiiting. Tliis scale is ileliglitful to use. Tlie divisions are seen r e r y cleirrly, yet t h r eye is not daszled as wlien using u flasliliglit. E . iV. lt'!ycTa>; D.D.S., Croton Falls, N . Y . : 1 obtnined from one of the manlifacturcrs of gears an iron spur gear of 9" pitcli di;imeter, having 180 teetli, for about $3, ancl mountecl tliis Iiorizontally on a stand or tahle, so that it w«ul(l r « t : ~ t eon a vertical stiih shaft. 0ii top of tlic pear 1 ;rttnclied a circu1:ir w-r>oderit;il>lr to hold tlie annular flnt riiig of slieet rrietal wliich was to be riiarked. Rbore this, on 21 separate siipport, 1 riiouiited tlie riiarking tool, n-liich \vas made frotii a n olcl file grouiid t o a poiiit. Tliis ran in a guide, ir1 orcler to obtain rriarks of the rlesired length. Tlie guidc was provided witli tootlied steps, in o r c l ~ r t o perniit ninkirig markh of cliffererit lengths. To rotate tlie gear arcuratcly 1 d u g oiit of :i jurik pile :in old screw wliich served (mcll enougli) as a worm* and, by rot:iting tliis worm through nny dcsired part of ;i circle the trick \vas turned. (Dr. Rydcr rriclosecl a prii sketch, Figure 3, \vil11 tlic. statement thnt, ~vlicrigraduatiiig
* I'rc*uiiinbls a \voirii used Eor layiug out setting rircles ouglit to be termed an angle\i.orin.-b:d.
c i r c l t - i , iti-rn I I I C ~ ~ S I I ~ I 'rS~ i i l s t I w t i ~ l < t j n t i > ( L S C ' I ~ I ~ C tllt. ~ : ~ r r u I o ~h ~i r ihc ,e close c o n c e r i t r i c t i o n i s rc.cliiirc(1.--l
.Ls ilr~sr.i.ihu1111; J í r . S ~ ~ r i ~ i l o "Tlrc ~ i . )~liotogriilili iit t l i r 11'jt s l i o i i , ~luff . t o viglit; t h ~I i r n < l s f o i . k i,f tlie Lirfhrp ir.,, i i r e ,iiriri!/ (20'' sli.irr!/-tlrr,tr i <.o11111 g I,r ziswl rr,itlt .\,~inlli,r t u o o < l i . ~ i g tliu l i i ryrrrili,i!/ l a f l r e ( s i z e ?~h.i~nll!/iib tliu ,slio,i o j iin a u i n t ~ i i r ) 188 co1il11 !,are 11nt-d a b u t i t m ,, L C O « ~ I , ~I Ll i ~ hiilid t , a 2 2 ' 2 ' ' / ~ ~ i g (ofh s t e r l t a l ) r ' r n c l i !i~" ~ r i o r i i of ~ c k i < . b tcoirlil c o r r c o j , o ~ i < lt v o ~ ~ l i , is held firnily o n t h r rsari(ir1.1 hrttcu,,ri r p ~ i l r r , s i ~ it h r Intli,,. a > i < l %,S ?i ~ ~ p,shriti,~i v i n t h r l u i t - l i n ~ i i lp i i ~ f i l r r , olil, at f r o r i t u ~ i d o l i r o t r r n r of I h r l n l l i ~ ,Iirild d o i c n t h r p i r e t , o j í c r i g l ~ ii'oli i c h i c h 1ir.t.s lis e I n t h < ~s,to1,. I t in b < ~ t i , . ~ ~t rb?i is strip a n , l thi, I i . n i ~ r l i l i g clirrirrgr of tlie l a f l i u t h a t t l i r olisuri.pr i ~ i x e r t st h r d i l f r r p r i t S ~ Z P I I11iri.s ~u1tif.h ~ . o ~ i f r t S Pj1ill.s a r e 711 t k u Iirtir
but not o u t the
h n v i n p acrrss to a c l i v i < l i r i g head o r a r r i a s t r r genr witli \'liicli t o lay d i v i s i o n s , i t \ v a s d e c i d e c l to a t t e r n p t t l i e work iii a 20", s m i i i g lathr, r n a k i n p t h r d i v i d i n g Iiead i ~ u r s e l v e s . A c c o r d i r i g l y we p u r c l i a s r t l a ti' s t e i l tape i n a l i n r d w w r e store, ari
A disli of wciiirl, roiiglily oct;ipoii;il, 16" tlcross tlie cSorriers, w;is seri.weil t o tlie f ; i c ~pl;itc of tlie Iiitlic, :~iiil turiied tloivii iiritil tlie 3.5'' tiipt. just rriet ;~roiiiiiltlir circuriifcrt.iict', wlicXr?iilioiisr~\.rr;ilhrii;tll Iiolcs wcrc ~iiiii('licdi i i tlir t;il)e aiid it \v;is fastciictl to tlie ~icri~ilicry cif tlir wootlcii tlislc \vitli wirr ;iiid screws (Figiire 4, :it left). SIiis g a r r i i \ 61 liirge circle, cliritlctl,wlirre it ~voul(lnot intrrfcrc
F I G C ~ I3E " T l i i s s1ii1w.s f l i ~cirr.1~ b ~ i i i g gi.nrlr11it1~~1.i'liu trni.rlilig r n r i . i n ! ~ r of tlie I u t h r i s ~ i i o r r , i lV!/ liniie ~ ~ , i lr.i'u.\.s-trairs h i~istnll,,,l. 1111 p , i l l i i i ~ 1 1 1 ~l>r,li, t h p r,'l!olr~ ~rir<'lrn. Y S ti^ o I I o t i i r t 1 1 . 1 , d r < , r > ~ r , iiht 1c~)it<11m~d o,f t b r ~ i t z > , t h r rO! ili,.i.vioil.s, niid tl,r )ir>, o j rorrf,<.t tecliiri~i ur sltort."
witli tlie worliing of tlie 1;itlie iincl, on hriiiginp one of tlie 1L9" dirisions t o tlic cros+li;~irs, corisitlered tliis part of tlie operatioii 1)rep:ired for work (Figure 5). 'I'lie disk o f sterl, 1/2" tliich, to be gredunted (Figure 4, a t riplit) wns placeil hel\veen centrrs nf tlir latlir on i i ~iiaridrel, ilriren hy a lathe dog iii rrted iiitii a Iiole in tlie grac1u;ited dislr. Tliis provided ari inflexible connectiori betwcen the disk to be graduated, and our home-made dividing lieacl. Tlie lathe \vas driven iit ordinary speed long enough tto take a light ciit frorn Ilie face of tlie work, in order t o true it with the maiidrel. Tlic bearings on tlie lieüdstoclc spindle were tiglitened to tlie poiiit where it re-
qiiirrrl ii s l i ~ l i tjrrl.; of tlir tlriviiig l)elt t o iiiovv tlic iliri(1irig lic;i
. I t t l i u l i f f i v n S/irinnfi~~I~l ~ Y I J EnioicntOir<,lrs?iin11<,1l l o tirc <,orrrct ~iigle. l ' i i u riglit-li , o l o r i1iil.e.
in,q
and X'' lonp. This deptli w;is ;~tiopti
sliort :iiid I ~ i i prlivisioiis, :iiitl iii'i<~rtiori11f tlit. 1ir(>1icZrtliirkness of stop in tliy rrohs slicle of tlie I;itlie sooii bcc:iriit. t~iitorn:itic. ()rice ;iroiiii i i i c ~tlie 1)ro1)er rleptli of cut W:IS rleterriiined ;it tlie I>t3giiiriiiig. \VIi<.ii tlie gr:idu:itiori w:is coriil)lcter
open space, striick tlic clic and rehounded, it alwaq-S fell hack t o one side or :iiiotlicr, iiistr:itl o f ;igtriii strikiiip tlir dic. 1Ieiice tlie blo~vs\vere : i I I ec1u:rl. Tn Iiolrl tlie clir ;I stick »f wrotl wtis tittnchetl r:idi;illy t n tlir centcr of the circlc, aiicl its 11ase :111(1 ii verticid holc (.jig) WIIS bored a t its outer eiid. 'Pliis permittecl sxvingiiig tlie clie t o ench new positiori, :rlso placing it accur;itely ir-iit*re tlir nuiiilier \tr:ih w7:inted. Wlirn tlie edgc of tlie clc6liii;ition circle (Figure 6, Icft-linncl plioto) w:is grnrlu:ited, tlie s:irrie set-up tvai iisecl. 1nste;trl rif :ittnchiiig ;i stop to tlir cross-slide, Iio\verc.r, it w;is ~>laccd«TI tlie m:~y.; of tlie l;itlie, aiicl tlir entire carrizige nii)rr(l h y riietiris of tlie I:irge \vlieel 1i:iiidle intericle(1 for t1i:it piir1)ose. We foiiii r o g r e i son tlir second circle t o be pr:tdii:itecl. TIiis tirne. Iiowever, tlir,)irgIi 1;ick of coiicentr:ition. nii extra in;irk >vas insrrtecl wlierc it n:ii iiot rccluirerl, ;irid the error wns not disc«vrrr*d iiritil tlie groc1u:ition w:is :ilmost cornplcte. Then to our clingriii, tve foiiii K S C I I ~ C of otliers is distractirig, tiiid irie\-ittibly leacis to error. IVitli tlie method zibore oiitlined, ve fr)uri
Iialf ilrgrct~s, Ibiit (Ioiil)tc
of tlie Cincinnnti llilling 3I;iciiiiie Conil);iiiy, \liom.; lio\v tliew ~ r o r k . 'I'lie handle iit tlir riglit Ii;is ti spriiig piii tli;il siiito Iiolc.\ evciily sl)iiccd : r i 1 c r l r i r : l . 'l'liroiigli Ilic Fr;irs shoivri i r i st.c.tioii it :ictii;~tes t i ~vorni;tnd tvorrii \vi.licil, tlic ~ r o r l i11t.irig ;1tt;iclic.t1to tlie sli;ift of tlie 1;ittc.r. Sucli rigs cost wt.11 "1) iiito tlic Iiiindiuiii-pricccl rii13tor r a r . Most ;irnateurs arc lucky eren t o get kr look a t onc, like a ctit aritl a hing. onei can he Iri adtlition t o tliese niid siniil:ir 'diriding Iieads-simpler liad for considernhly less irionry hut r r e n tlien not clie:ip-there are sorne re:~lly ritzy onei called diriding erigines wkiicli it is wortli wliile at least t o know about, even if tliry re quite beyoncl tlie riioori. T11e one shoivii in Figure 9, in both front anii rear view, \vas made by an arnirteur tclcscope maker, Varcl B. IVnllnce r f tlie Vnrd I,:iboratorirs, P;c~:ideii:i. Ctiliforniathoupli Iie built it ni:iinly for nnother purpose, tlie coniiiiercitil ~ ~ r o d u c t i o n of protr:ictors. He cfescrit~es it thus: "The t;ihie of tlie eiiF ie is a little riiore than 1%'' in dinrneter nn(I Iias 360 teeth c u t on tlie e c i ~ i . Tlie t:~bleis split tliroiigli tlie center line cif the teclh, so th:it the upper hnlf may be rotatetl with respect to tlie lower half. A f t e r tlie teeth were Iiobbrd (ir1 t h r Astrophysics sliop a t 'Cal Tech') the two halvrs of thc Fear ivere cliiftrd :incl I t i p ~ ~ c 14.4 < l tiriies in different positioris.
'rlir ultiiii;itc rrsiilt 1v;is tlitit tlicre is no \.ihiblr crrcir iii tlie tt~.tli iii :iny liosition \i-lit.ii viewe(l tliroiigli :L g1:iss. "/\t tlir Icft-linntl si
lowcre(1 to t:il<e tliiclc or Lliiii ~ r o r k . 011101) i ~ f;iII tlitit it is al50 iieccss;iry to he able t o rot;ite the tr:it.elet so tlint Iirrel or rveri c!-lini1ric;il worlc iii;iy he done. Witli tlie li!.dr:iulic sytern, ti11 tlii9 is :iccoiii~,lislic
are oiily ;il)oiit oric seeoiitl of tire :iiitl iri soirle c;ihes even ICSS. Tliis is tlii~iit i ~iiilli~~iitli of t i (.irelc. fI:~viiig iri;i(I(. tlit~wfliglits ir~totlic. tmni~i?-rr:iii, ~ v cretiirri t11 e;irtli lowly Ivvcl 11f tlie :iver:igc :iiri;itc.iir, \vlio srltloiri ciiri fiiitl 10,000 ccrith, s p e i k of $10,000, for :I circlf
hetter ;it tlie not t o iiiiie1i
Iie mil1 he lilícly to xr;int to I:iy oiit. Tlie fiin Ii!. liiis i r i ~il;rniiiiig,buildirig iiritl \\7:itcliiiig Iiis "p:itciit cliiiy1j:it" worl, will rc'lxiy tl1:it rniic.li r>iitliry. 'l'lii 1cttr.r~n.liic,li fiillon. slioiv IIOW tlvo :ini;it<*~irs rii:~d(. ' , / ! O an
.l. 11'. .loliiiso~i,C'h/ctlroti. S ~ b r c r x k c t : IIcrc.witli is ;L sketcli of n little device wIir11 1 l t r f o i l l ~ c l f i l . Aiiy grtiuld be I~lochr
for the worm, tiiicl for w:isher\ k)etmceri ruhbirig siirf:ices, \r«ii1<1 prob:ihly riiahe f o r siiiootlier oper:ition, tliis is not necessary and the ni:iltcr is iiiost likely to iiw ~ r l i a t e r c rcoines to 1i:iiid. Tlic coiitrir:iiice consists pf (1, see Figure 12) :in axle witli one cnd tapered to fit tlie lit.acl-stocli sliin
In pr;icticc tlie circlr is 11(.1<1in tlir chii<.lc 1iy liolting it to n block of stecl or on ;III crtrtr f:icr ~il;itc, aiicl tiiriir(1 triit. :ititl polislii ot~viiius. l'lic lo01 sliocilositioii it is 1,icllutl a c r o ~ s
SECTlON A-A
ASSEMBLED
tHUCK
HOLDING WORK
F I G V R E1 2 nctniis nf t h c J O ~ ~ I I P 111a~hii16'. OII « S < l r n v , n by J . F . O d ~ n b a c hfron? rough s k ~ f c h r si i i t l i e m a k u r ' s d u s c r i l r t i c e I ~ f t u r .
tlie work. Tlint is, i\.ith nrgativc cleiirnnri. 1 hacl plenned t o use :i t1i;imond point ~ ) u s l tool. i something lil
x,
so 1 postponccl tlint. Tlii tool iirtii:illy iisrtl \v;is \irnilar to :i tlirc;icIing tool \lut re\-rrscd :iiicl w:is pitlled, % ;tiitl %'. Tlie varri;igc* is Iooseiii.(l .\o :is 111 iiio\t. frrrly :iiitl ;i f,-\\, iriiiiiitr\' ~ i ~ i ~ c t i c r sliows tlie riglit prrhsurr to give tkic. rf~cliiirt.tlrleptli of rii:irli. 'l'lir iitbg:itive cletir;tnie of tlie tool prrverits aiiy teritleiicy tci dig i i i :irid iri;il;c :I rougti jiric twicLry 1):ipc.r \\-liile tlic circle mnrl<. 'I'lie sliglit I~iirrsciiii hr. rcriiovv(1 P ih oli tlie latlit.. Ilo\vvv<.r, tlir 1ll:l~)ih~vill1101<111l;ick g r e ; ~ ~ t(:~ I I \.isil~ility) lietter if iiot siii~otlit'd." :ind [151>rron'sS(~1.1:: A i f t c r tlie 1)rccetliiip tlvscriptioii lizitl I~eeiil>rcl):~rc
d i i
i,it~rliri,tiitionof
.loh?ison'n
drnl,,inrf, rlii,ir
hii R~rss,,il1T.
Prirto~. It
e,nn
« T I tldr !;,.S/ 01' .s)lili~ { l ~ i i rrrllr,,~il~t.. S i ~ r ? ' o ~ ~ ~ ! ~ It h i ir~ !(Irrrr!,i~~fl, / j o y rollt.~nic,,ii.p ~ T L~<,j),.oi, ¡.S a r?ri>l>i>~!, ~iru"r31<, i i i r i ( 1 ~ iclipn
Iinscfl
i 1 7 P . ,L nu~i-('fr~n~clrrticr, PI.~o).s.
c l u s e o.tir
u/
tlic
sp
qilite
l~irgf,, Ilio#rgh
equipineiit hecauce tlic clirisiorii: on the rirrles ~>rorliicedslio~r-rdprrioclic inequalities-ser tlie first rubl>irip, tlie one \r.liicli surrr~iin
To liis lirevioiis descriptians, Mr. Jolinson nccordirigly has added tlie :otlic*il xvliicli folltrxvs. 1 A 1)ruiii.c. woriii-gear-40 tcetli, l ( i pitcli-was bouglit a t $1.50 nnil xvitli it a iinrrii tlie ('liic;igo (;elir Works. 'rlit. siil)l)ort for tlii. \voriii 7v;is clizingril frorii tlie f;ice plzite ti) tlie 1:itlie becl, tlie t ~ v oI>c.;iriiigs giviiig :itlded rigidity antl tlie face pl;ite hring relr;iscil for Iiol
but 1 used the indesiiig hrnrl t o grndu:ite its oxvn
xc
o.
1/100 Dial
1.111
rev.
2.222
"
3.333 4.444 5.555 6.666
"
7.777 8.888 9.999
"
" " "
" (10 rev.)
Work 0. 1/36 or 10" 1/18 or 20" 1/12 or 30" 1/9 or 40" 5/'36 or 50" 1 / 6 or 60" 7/36 or 70" 2 / 9 or 80" 1 , 4 or 90"
Tlieri relwcit. rsiiip tliis ti:, :i di:il \TI. c:in gr;itlii:ite in fiill (Ieprcrs by ttirniiip it l/g, or we cari get five riiinutes of tirrie by tiirriirig it .3.56.-5(17 J1cccr.s Strest. [F:III.I.OR'sNOTI.: For tlieor~ticiil~ l i i t ion ~ circles, see c1i:iptt.r ori "'TIic Ilirie li;icl t>y tiickirig a circle of c;~ríll)o:ircl a t its ceiiter t o L: I)o:~r(l. Pl;ice a refrreiice rii:irk (rrl>ret.titirig the cutter) on tlie hocircl a(1,j:iceiit to tlie edpe of tlie circlt. :irid rri;irl; tlie 11vril)liery of tlir cir<,le in
By II.\KoT.DA . LCJWFR Snii I>icgo, ('nliforiiin
Tlic prohlem of driving :in e- p:irticiil:lr telescope, reqiiires :i krio~vlet. thc coninion iniliressioii tli:it if \ve drive aii equtitorially mouiitrc' tcle.;copc :it esnctly tlie sic1cre:il rate, it will follow tlie stars perfectly. Acttitilly, tliis is only :ipproxirnately true. Refraction stiifts the positiiori of tlie sttirs by nn :rriioiirit tli;it raries witli tlie eenitli distante. Tliis sliift iii tlie n~ipiirentpositiori of n s t a r :rffects hotli the riplit nscension and tlie liotopral)liy, proricled the cxposures were fairly sliort. If a e assiirne tli:it tlie poltir axis of tlie telesco~)eis :idjiisted parallel to tlie :txis of tlie eartli, Llie clo'ck r:ite whirh \vil1 be requirecl t o follow :in equatorial s t a r a t thc meridinn is slower tlinn the sidere:il r:ite by 1 secoiid per Iiour, or 2.4 sccorids pcr d:iy. A t various hoiir :triples e:ist or west of ttie rneridian, tlie clock niust be sloner tlian the sidereal rate by the following amounts. 3 4 1 2 Zlour anple O 1.3s 2.0s 4.0s 1.0s 1.1s 1,osirig rate Tlie :+djustment of tlie polar axis tias some effect on the clock rate, as well a s on tlic sliift of :i stilr in rate the clock t o lose ahout 25 scconds per day on siderral tirne. The additional changes needed t o follon :i s t a r acciirt~tely in any p a r t of the sky can best be made by careful hand puiding. To a d j u s t the polar axis so that it points t o the refracted pole is not difficult, but it can best be done by photograpliic niethods. First, the tele-
scopc. is ;i l ) l ~ r i ~ i t~1iurii:il ; i r ~ - tr:iils \vliicli ;(re 1irotliicecl \vlicri tlic clock is stoplieore pele Triiils poiiit riglit Trtiils point l r f t Asis poirits belolv pole I f the triiils riin diagonnlly, corrertion is requirecl hotli iri ;iltitude :ind Llie direction o f tlie error, \ve ailjiist tlir polar azirniith. After detrri~ii~iiiig axis sliglitly, ;iri
ioiig esl,osiirrs, iiiicl wliile tiie sicl(.rcal riite is iiot rxactiy wI1:it \ve need, i t is so iieiir t o it tli;~ttlie liibor uf giiicliiig i s n o t greait. r \ i i u oiitfit \vliicli is iritriirrors sucli :is iii:ry be caiisecl by ;L (Iriiiil<eii worrii, or gc:irs \vliicli [lo iiot iiiesli 1)tarfectly. Ilrvel or spiir ge:irs, if i i r t l , hlioii1<1 riot l ~ eloc;tted rie;rr tlie slow speed entl of tlie drive, otlic.r~visc tlicre iiiiiy 1)r :i sliglit irrcgiil:rrity i r i tlic clrire erery tirne i~ tooth eiip:rges. M'e Iiiicl oiit. e-ilicrieiice ~ r i t l itliis trouk~le. Slie iri:iin rroriii slitift of our tclcscopr \vas driveii by a ptrir of hevel getirs, tiiid wliile tlie clrive seeiiir
\vil1 nlso nfford ;in opl>ortiiiiity for tlie riglit :iscension tlial to hc rn;ide rrii~\~;il~le. b'rictiori ~vitlitlie liiib o f tlic xroriii ~vlieel \vil1 drivc tliis c foiiiid 1)y setting t o t h r propcr dccliiiiition, tli
Fic:rici..
1
L r f t . C . O . C l i a p ~ ~ i ( rv,itli n hi* atlinll t<,les<'o,ir. (1rii.pli TI!/ 1 0 ) n/nt.t,r i./o<-lt ~ , I , ~ I ~ , , I l i lÍi!,/,t: A c/~,.s,~-ir,, of 1 1 , ~ dri1.r alrori.i~ lrt Hit, l r f t . T l i r p h o r i o g r n ~ ~ hs p r i ~ i !lici; ~ buti in
polar axis iricliciites tlie riglit kcension of tlie rcl ivitli ~ ) l ; t i i i I~e:iririgs, a Kv I1.P. riiotor is a s:ifcr het th:iii oiie of the srn:ill rlcctric clock inotorsl F o r sriiall pcirtable telesco~ies,or instrriirients of modrr;ite sizc T\-hicli are lucatecl ~ r h e r eelectricr Iiowrr is not availahlc, an ordiiiary alarni cloclí m;iy be used :is ii clrivc. As tlie :il;irni clock will iiot have power enouph t o drire tlie telesrol)e, :i phonogr;ipli sllring is iisecl for this piirposc.. arid tlie clock merely regul;ites the spccd. Aii rxcellrrit rs:ciriple of this iiiexpensive drive is ahown iri Figure 1. Tliis was constructed by C. C. Cliapninii, 3715
F;~iriiioiint I3lvci., Rirersiclc, Cnlifornia.
Mr. CIia1irn:iii ~lcsrrihcs the drive
as f
"'l'lie d o c k is a clieap :ilariri clock, mitli nll tlic 1i:irts iiot iise(1, (al;~rrn petrrs, li;incls, ciise, t*tc,.)
Fi<;ii:i< 2 A f n i ~ n t i n gof P r ~ n c o t t ' sport«hle t c l r s c o l ~ p lits<'lf II
(':iliforriia. I t i% n r r r y ritaat ,jol), ;iii(l tli<. perforiii;iriee is :iII tli:it coiild he tlrsirctl. 'I'lir 's<.o]>efollo~rstlie ht:irs riicc*ly, :iiitl iio tr;icc. of vibriition from tliv clrive eoiiltl I>e tiotice
froln
B ! I I O I 7.. L Grni.~.s' 7jict(r~111<111~ < 1 ~ i l ' ~ - p l . n r > f t!t(it 11. g o n d d r i i . ~( Y I I ~ ~ I Pwlrrde 71nrts ,,ich.<,(l 1'1) rrt tlie secolid Irn,i
turn rotates in tlie jiolar ;ixis hoiising. This tube Iias a 5" clriim ;it tlie 1owc.r crid, over wtiicli a strnnded mire cahle (:iirpl;iric coiitrol <.;il~lr)~);i'seh, 1n;iliing 1Y2 cornplete tiirns. Tlie clock, :in old ;~liirm cloclí, 1i;is tlie spring rcriiowd :irid :r 1%" (Iriini fitted, u~itli tlie cnblr pns,sinp :irociiztI it .sest~r:~l turiis iind f:istene:inStrcrt, 1.0s Angeles, California. J l r . Graves used an olcl Dicta~>h«nc,with :I gorernor controlled motor. h 288-tooth worm wheel on the polar üxis, and a 5-to-1 berel gear wliicli clrires the main worm, are tlie only gearing not sliown in tlie illustr~ition (Figure :3). Tlie lürge berel grnr on tlie riinin n-orm shaft is clamped to tlie worm sliiifl by a niit wliicli can be quickly loosenrd when it is desired t o turri tliis sliaft by hancl, for adjiistment in right :iscensioii.
(Figiiic 4, riglit) tr:i\el\ t o coriiniiit:~tor
mut;itor from tlint pnir of rn,ipriits .irid rontliictetl to tlie other pair tlirough the otlier tirush-cin~l so on. Wlien 5uficient speecl i \ att:iiiied t o raise the go\ernor weipiit\, their molement cause3 tlir coniniut:itor t o rotnte forwnrd sliglitly, cuttirip off tlic curreiit sooner and drcrt. ising the speed. A t e r y slight rise of tlie gorernor meights cause5 suficient iottition of the corn-
mut;ilor to givc vcry closi spcetl rcpulntioii. ( 1 1i:ivi kept :L strir ni1 a kriife-(.dpc for :I c«niidrr;iI)le tirne.) "'i'lii pliotogr;ipli (Figiirr 4, left) sliows tlir u.«rrn r(.tliictiori g c ~ i r :itt:icliecl clirt~ctlyt o tlii clo<*k,for purpnses of illiistr;itioii. 'I'lii.; is iiiiiirr<.rt. Iri orclcr t o kill vi1,r:itiori ori liplit iriorintiiigs, tliv ricliiction gcX:ir slioiilr att:iclicd to tlie tclrscope riioiiriting, the drive h<~irigfrorn iriotor s1i;ift to rrcliiction gc:ir slinft tliroiigli ;L 'Itttlie tlog,' tlrc. clock itself rcstirig iiliori ;t cushioii of il)ongc ruhhcr. "C'oinriiut;itor segriients slio~vrisli;i
FIGLI~F: 5 and ttirirlg diagrnm of t h ~Jforrp drirp. A . B , rtr., ?nngnrtx. B , H , armatiira se
"hí:ipnet arid nrmntiire sections :*re cut frorn slieet irori witli siiip\, varnislied mith sticllnc, insulated witli p p e r betwecn cacli Iayer and tlien baked, forniing a solid piece. "l$nse, top aiid pillars were made of lvood; hrass woiild be better. "Arm:iture sections are mountecl in slots sawed ir1 a wooden spool, as shown. Tlicy or tlie iriagnets rnust not be surrounded by an electricnl conductor if yoti cvcr wisli to iise ;ilternating currerit. "Wire: Ten layers of No. 22 copper magiiet wire, for G volts. "Fipurv 5 sliows tlie relatire position of magnets, arrnaturc sectionh, commutator, hruslies, aiid miririg cliagr:irn. I t will hr noted that tlie rnagnets ctrc placed 45" :rpart, thus making four
"Figiire 5 nlso slio\vs liow tlic coriimiit:itor is rotatr(1 sliplitly by tlie risirig of tlir governnr wciiglits, tlirocigli tlie link :i<.tioii. "Sperd ac1,jiihtrrirnt is ob1:iirit.d liy iiicre:rsiii~ or tI<.cre;isiiig tlic. cffective lriigtii of tlie govcriior :iriris; fiii;il :id~jiistriiriit by sliglit rotiitioii of tlie brusli ctirriag~. Specd obttiincd witli sizc sliowri i i i diiigriirii is í~lioiit 160 r.p.m.; witli goverrior arrris ',<"shorter it is tibout 180 r.1i.m. 'l'li~one sliown in tlie l~liotogr;i~ili riins 200 r.p.rr1. " S ~ i w < lis cleterininecl by a strolioscoyic* diik liglite(1 liy :L iirori glow I:c~rip. 'l'lie nurnlier of t tlie corniiiirt;itor, mliicli is, of course, frce to rot;ite." Slynchrono~ts ~ r i o t o rdrizqi,s: \Vciglit tlrivcs, coritrollc(1 l)y :I coriic:il pendulurn, Ii;ive f o r rii;iny ye:irs Iieeii tlie iisii;il riirtliotl of (Irivirig trlrsrolirs in 1;irge obserratories, but receiitly tliere 1i:is licvn :L trericl to~r.:trably be rnucli too costly for tlie average ainateur. Hoxvever, tlic frccliiericy control of rnost of the large power systerris is quite goocl, arid in rriost cases woulcl be ;is ;iccurate a s any conical peniliiluni d r i r e wliicli could. be constructecl by arnateurs. Since tlie introduction of electric clocks for use in tlie honie, the frequency of most power systerns li;is beeii repulatecl to give standorcl tirrie. S o w tliis complicates matters a bit, as n e need sidereal tirne, or a close approximation to it, for o u r telescope drire. Quite a number of different gear trainq have been morkecl oiit whirh will enable one t o iise n synchronoiis motor, nncl still drivc thc tele5cope a t about the sidereal rate. The selection of a suitable gear trairi is a rnatter
of individir:il prrfcrriicr. Silriic ;iiii:iic~itrs llavr. liol~l)(.d011t iiTorin ivlirels 11y Clie iihe of ;I t:ip iiiouiiteI:iss., :tritl 'i'kic Cliic;ipo (ic:ir Worhs, 771 We\t J ; ~ c l í o r i15uolev;lrcl, C'liic;rpo, Ill., list 100-tootli lvorrii wlirels, ~vliicli iri suittible sizcxs ;irt. s;itihfiictory for tlie rii:iiri ivorrii ~vlierl oii ttie 1)olitr :isis. Tf oiie m;iiits ;t i i i ; i i i i wr-cirrii irdice1 ivitli iiiore teetli tli;iri tliis, tlie Lee Jlfg. Co., Il.269 Surtlilit\\ii iivr., I)t.troit, Alicli., c;iii siiliply ivoriii n-lirels of 359 aiicl 8íi0 teetli. 0iir of ~ J I C e;iiie\t \v;iys of rii;ikiiig tlie cli;irige froiii st;iiielic.ve. I t doci iiot reqiiire h i niatliematic;il geriius arid a. sliile rule. Oii tlic, coiitr:iry, oiily tlie siriipiest aritlirrietic is neecled. l i s :tri cs:irriplt~ of liii
50-cyrle, tlieii w r niiist iisc. ;i 100-tootli \ioriii pr;ir for tlii first slep i r i the rccliictir~ii frorii 1111. irlutor sli;tft, instr;t ~ ) k~iit ~ l l , soiiic :irc. tiesigrit*tl to riiri orily ir1 orie clirectioii, 1 1 it i.; Ii<.ltcr tri <*lithcl< rot:ltioii first. Spir:il getirs c;in
A I ~ .prnr11111~ of t h ~?tivit. i.oi~l)jn?trlt.xig~i u ~ h i c h is r ~ o s s i h l r . ~ c i t h nn vlrctric d o c k ~irotor. S)".i~i~fi~lrl l ! i ) i u j i i r i t ¿ ~ i t i ~ i ! ] . I I " , birilt b ! ~Lrii .l. Setinlon. Y'hp motor is n 1400 r.l,.i~z.,s!,~r~~lii.r~~~o,i.v, ivitli t i ~ o?i~,litrtivriitnits- ,111 horrs~11i n n n j n l i joi' cooliny. l ' h e poinr gelir is strvl ?n~lrrlb0.r 3 l; " X 6" X 6 " , t?if~liiding r i i i < l i,s l,ro~~
he obtninrd in quite :i rnriety of sizes nncl rntios, a n d they are quite useful for getting >iroiinrricl is recommrrided for use willi Iiravy t e l r r r o ~ i i s\vliicli are ecluip~>cdxritli plain beariiips. Tliis motor operatri. at 1800 r.p.iii., ~rlieriusecl on 60-cycle currrnt. A much smaller and lehs expensire synchronous motor, which still is
powerfiil eri~~iigli for iii.struriiciit~ 111) t t ~15", can l ~ eobtained frorri Aiidrews Hardw;ire ~iricl Met:il C o . , 334 Soutli M;iiri St., 1,os Angeles, Cal. Tlicse niotors opt.r;ite a t 2.tOO r.p.iii. oii ti0 cyclcs. Iriiliiiries slioiiltl Iic ;iept., Aiidrews Ilartlware Co., ;iiicl sliould refer t o tlie "Aiidrews Hardw:~rc S11eci;il Syiic1iroriou.s Jlvtor for telesco1)e drive." Tlie W;irrcii Tcleclirori Co., Aslil:iiid, JInbs., ~rianuf;ictiire syiiclironous
Fracitz
7
A 9" t ~ l c . s < . « , 7,irilt ~ , ~ b.11 n r . Zi. P a g ? Bnilry, of Ilii.6,rsirlp. Cnlifoi'riirr. . l i l í l r r l ~ . s l f l r r < l i t , a r s!/~ichroriotrx ~ ? t ~ o l o rusrrl fiir d i - i r c . íiiii<Eiriy ir^ 1í.d. is ~.uritrnllrít b y nioi-rriy t l i r ~ i ~ r i ir ~ o ri l t i t a ~ i g u r i tt o ttie u80i'in w h e e l . ,\ole s ] i r . o i ~f o r f u k i r w I ¿ P nlaek u n soc,?ri tlrruads.
clock inotors which Ii;ive been used succes.;fully for d r i ~ i i i g telescopes of iriodrrate size. Tlie ordinary Telecliroii rriotor wliicli is iised in rnost sinall clocks is not suituble for telescope drireh, hut a Itirger a n d morc po\verfiil iiiotor, Type C2M, is available. Tlie TJ-11e C2M Telecliron ik ratcd ;it 12 wntts, arirl drvelops :r torque of 2.0 iiieh-pounds, at 1 r.p.rn. The 1-Iarisen Mfg. Co., Princeton, Ind., also nianufncture a smnll sj'nchronous cloclc motor wliirli should be suitable for driring a telescope of moderate sizc. Data rrg;irding the torque of these inotors is not a t haiid, hut tlie motor seenis to tiare n surprising ;imount of porver, corisideririg its small size. Shese motors are self-starting, and havc a built-iii gcar hox which reduces the speed t o 1 r.p.in.
Tlie I3arber-Colemari C'o., Iiockford, 111.. can supply rnotors u~hieli are quite siriiil:ir t o tlir Andrews fI:ir(lw;trr riiotiirh. N o
FIGURE 8 L r f t : S g n r h r o r i o ~ ~ms o t o r d r i v r , w i t h ~ n r i n b l er n t i o frirtion clriiv f o r s n ~ e d c o n t r o l . Htiilt b y C h n s . d . Lozrw- niid H a r o l d d . I , o I L ' P ~ Ti!? f1rii.e is ~ n o l c n t r d . O ~ a L base u~hiclr i s spparntu frorn t h r tc,l~,scopr,nnd is fiontrd o i l r u h h e r , iit orrler to p r r v r n t ? i f ) r i i f i n n . K i y h t : J f @ t h o d o j m o u n t i t i y t h p frir'tir~n (lisk. A70tp tlle r u b b e r c o u p l i n g , u~hiclip r e i e n t s ribrrrtion frorr~ beiiiy t r n n s m i t f e d t o tlle teluscope.
and Robert R. McMath Iiave developed Telecliron drives for severol telescopes, and have used them for the verp exacting work of celestial photography. These drives use two 12-watt 'relechron rnotors, and have prored powerful enoupli t o handle a telescope which, with the extra camera equipmetit, weighs over 1000 pounds. The first of tlie McMath Telecliron drives was equipped u~itli :i gear train which used a 365- and a 366-tooth spur gear for making the change from standard to sidereal time. The error involved in the use of thcse gears amounts t o less than ?/í0 second per hour from sidereal time, aria is
less tli;iii thc. : ~ r r r ; i g r e r r o r ir1 tlit. fre(1iiency of the alternating ciirrent on rnost 11o\vcr syst(:iii\. I t is rcported tli:rt tliis (Irive sliowed no d r i f t in riglit nsct~iisiciii(liiriiig tlie prriod of trii Iioiir. C. ('. C'Ii;~l)rri:iri :in11 11. 1';ige I%;iiIey, o f Itiversicle, C;iIiforrii;i, 11:ire ec~iiippc(l scri.r;il telc.scoliis witli syiiclirorioos motnr íIrivc.i, iisiiig hrii:ill motor.. olit;riiietl frorii tlie Aritlrewi I I a r < l w ; ~ r eCo. Tliesc tclrsciipe.; r;iiigr froin 9" t o 15" i r i po\vcrfiil ( F i g u r e 7 ) . 01ic nietliocl of ~ivoiding tlie use of special gears in in;ikiiig tlie cliniigc froiri stariíl;ird t o siniits orily r o t ; ~ r ymotion t o the worni sliaft. Change in tlie rtitio of tlir tlrire is accoriiplished by nioving the motor axially ori sliding wiiys siriiiliir t o tlie croi\-feed of a Iathe, by rneans of a screw wliicli is tiirricd by a flcxililr sli:itt. Moriiig tlie roller riearer t o tlie center of tlie clisk s ~ x e c l \ u p tlie telescope; rnorinp it t h e other way s1ou.s tlie rate. '1s the flcxil)le sli;ift is long eiiougli t o I>e ~vitliin e:isy reacli, regnrílless of tlir positiori of tlie ryepiece, tiiis enables one t o guide in right asceiisiori. 'rlie control i\ not critical, arid one niay tiirn t h e flexible sliaft 1i:rlf i i t u r n o r so ;it A t i i ~ i e\vitIi«ut a st:ir juriipirig uff of tlie cross-\vires. A l s tlir hperd nf tliis ( l r i w delrencis on tlie positiori
t ~ c k l etlie rn;iii> probleini wliicli are encouritrrrcl iri t11c hiiilding of n good clork tlri\ P. Additional informati011 on this subject niiiy be fouiid iii tlie following publicatioris. "A h1:iiiii;il of Cele5ti;il PIiotogr:ipli~," by Edrinrd S. King. "Tlie l'elescope," by- 1.oui.; Rell. l'ol~ulrtr ~ l s t r u r r o r t ~ yOctuber, , 19'30 (Illchlntli, "Jlc3lath-IIulbert Telechron Drik ing Clock"-6 pp.). ZJul>licntion.s of thr l'~iiz~rrait!/ of Jlichignn, Vol. 4, 3 0 . 4. i ' l i ~ l
[EDITOR'S SOTE: 7'11~n i i t t t ~ r i r i the ~ > r c c r ~ l i i chaptrr ig is :rimrtl nt ,r;ige ;ini:itriir ~vitli CIII :~vcr:ige-si;r.ecl telescopr, I>ut :i hiri;iller iiiiiiib~~r ; i t e i i r ~ - i s ~ ~ ~ c i ; iriow l I ~ tli:it largrr nn
FI(.CRE1 D r i r p f o r t i t v tpl~nrope shousn In Ftgtare 2, D r l l ~ r ,of I T a ~ l ~ t n y / » ~ ~C n,
m t ~ d eb q d l n r i Gce
and C. Cnrrrl
In cn\es wliere outsitle power i\ a5ailable but poorl) ~jnc~iroriizrtl,atterition i? ralled to the frequency c o n t r o l l ~ ddrive dereloped at t h e 3l.lc.M athHI~ l h e r tObservatory, wliicli is cntircly independent of the system frequcIncy
320
I> H I \' IZ S F O li 1 . h l t G 13 lt 'T F. I , I C S C'O I ' R S
;tiit~tli i i tlic, I'cchlicrcfiona of thc Oi~~~i-~,/t/r,i.!/ of the l'niz~rrsilg uf ~ ~ I i c l i i ~ ~ Vol. r i ~ i\., . No. 10.1 .ll(oiut, *V. Ir.: 'I'liiq clrivt. (liyiir(.s 1 ;iii O I ~ C .tlir ~ S clo(.li ~1rir.r. 'l'lie gr:iriiig froiii tlie iiiotor to tlit* 1)ol;ir ;ixi\ i\ a s
I ~
fnllo\vs: 1:400, I:N, 41:69, nnd 1 :180. Tlie 1:LOO iinit is n storlc sl>ectl retliicer is tIiro11g11;I STII~III (litYcrci~ti:~l. cont:iininp t\!-« worni gr;irs. Tlir 1 :8 reclt~(~tiori r l scc«iiy The G r a n t Gear Works for $:3ti.00. A third motor is connected t o t h e d r i r i n g worm through 1 : 1 2 recluctiori
~ e a r i n g . Wlicri tliis motor is st:irted, a sm;ill ni:ipnc.tic* cliitcli. clc;trly ?>11o\v11 in Fipiirr 1, rubleriiof liaving ;i clock dri\.tb :~rid sio\v iliotiori :liso. Tlie s l o ~ viiiotiori liere ii5ed i \ 2" per minutc, \\-hile tIi(.
SPUR
GEARSMOVNTEDIN WOR?
1 NTLRNAL GEAR
FAC t
TUREE SE.TS OF
To
TNESL G ~ A R $-
CEARBO
6EAP.
BOX-
IYTERNAL A N D 41 TOOTH SPUR
BRONZC PIECEMOUNTED
iY
GEAR FACE CARR~ES THREE. OF
.
SE
PUNETPRY GEARS -
¡Ira!viiig
WORM &BEVLIL GEARS70 MOTOR s w e i~t ~ m r r 1 S i z , l , j
by liussell \V. I'urtrr, iiftcr Al;rii (;re
fnrt rriotion is 1 revolutiori Iier rriiriute. Tlie clock e r r o r is 1.76 aecontls p r r sidcrciil day. \I'itli tlie rsrcption of tlie Ifi-pit<,h spiir gc;irs ;ind d r i r e ge;ir, al1 tlir pears in tlie drivrs a r e stock, 2-t-pitch hr:iss pears. The cloclí is nioii~itcclin srlf-alining ball be;iriiigs tina :id,justnient is provided f o r tlie large spurs : ~ n d the miiiii cirive grtir. Tlie iise of hall beariiigs does away with objcction:ible rnd-ploy iii t h r rntiin n o r m s1i:ift. Al1 pears in the clock exccpt t h e 400:l speed reducer (a Roston Gear IVorks ~ v o d u c t ) cnmr from Grtint Ge:ir lTTorks. The synchronoiis motor is í i $o H.P. \Vestingliouse. The two srn:lll motors :ire series motors «f i,,, nnrl ?:<;, 1I.P. Tlie relays u\r
rnotioris, ~~articiil:irly fiir 11Iirit~i~r:il)liy, iii t1i:it t1ic.y e. l'lic followiiig is :i list of grtir riitiiis for ol~t:iiiiiiigsirehciit <.lose ;~l)11ro'tirii:itioiisti) tlic. fr:ictiori H ( i . 1 , 0 0 . 0 0 src. sol:ir (1:iy -.-. - ;iii
--
Error in
Sec. per day 1.45 C a n I>eobtained in brass stock gears.
369 368
9 X 41 8 X 46
- -
+ 1.76 (ratio used in this clock)
Ilohtoii (;viir \Vorkr; c:irri(ls i i i stoclí ?O pitcli "<~h:iiigepe:ir.;" in aiiy niirnber of tectli, frorn 20 to 120. Prictas are froiii $.i5 to $1.83 (1985). Tlie bore is X'', ftice Y8'' :irid no Iiubs. 'I'lieir bore is cut mitli double %" keyways.-1Vest ¡'oi11t, E . 1.. B y .losrpli E . Hoc.lii~r, ('hicriyo, Illinoia: 'I'lie reqiiirernents of this clock drive (Figure 4) were to drive my 14" reflector (Figure S), tlie n i o ~ i n g parts of wliicli ~veigli-1.00 pounds, witli siifficient :tccur:icy for loiig exposiire ;is tlicse esposiire\ woul(1 run to 8 hours or riiore, a I ~ l ~ o t o g r a p l ~ Iriasiiiucli y. drive liaring a rriiiiirriurri of rrieclinnical errors, :is well as relial~ility and sniootliness of operation, wgts requirccl. Therefore, ;i [ ~ o l ~ :ixis ir worrii gear li~iringa large iiurriber of t x t h was clioseri iri order t o secure sufficirnt accuracy, anci a sprci;il attcrript w:is rnade t o provide a strong ;ind rigid support for tlir rnt-cIi;rni\rii, ~vell-rriounted ; ~ n dclose-fitting braring\, with gears, sliafts, etc., of :iinple proportioris t o oid flexures aiid \ ibration. All the gear\, except tlie worrns, :ire of bronze; the sliafts and worrns are
L > l L I \ ' E S FOIL 1 , A I t C ; E l t ' 1 ' R I . E S C O I ' H S
;?A:<
staiiiles\ steel, ahile tlie t~enrings ure plioslilior bronze. TIie shafting uwd is of tlie t ~ p etli.it roirir\ groiiiitl t o size. Tlic ge;tr reciiig tlie 1,irge 25" gear on tlie polar ,ixi\. Tlie g e ~ r i n g
FIOCRE 4 D r i w f o r t h r trlrnrol,r S I I ~ L I ~ TinL F i g t ~ r5 ~, mnde b$/ Joseph E . Boehn? of Chir a g a unrl n ~ u ~ ~ r iir1 t ~ ,111 r l ~ l > , v c r ~ a t111 o ~Lah-P . ~ G e ~ i e v a ,W i s ~ u n s i n .
was first c:~lculatet:iinc.d for tiutli stell:tr tiiiie :~ri
less steel worm, by the D. O. J a m r s Mfg. Co., Cliicago, ;ifter s~ver:il miclely rarying quotatiori\ liad been receivccl from vürious concerns (Cost, 10:-33,worm gcur $23, worrn $ 7 ) . Since the large gear is rigidly fastened t o tlie polar axis shaft, n haiid crank uf 5" radius a t one end of tlie 7jx" iiiain woriii shaft provides for fast inotion in 1I.A. 'I'his shnft also carries a clutch, as well as the 144-tooth, 24-piteh worm gear. This gear is free t o idle about the shaft when the clutch is disengaged. The clutch is a multi-toothed, disengageable spline, formed by a -56-tooth, 32 pitch, ririg gear ri~eshing with a spur gear of tlie sanie size. Tlie ring gear 1s attached to the 144-tooth gear while the spur gear revolves with the
niain worni sli;ift. liut c:iri l)e sliiftcd \)y li;iri(l tu (1iserig:igt~tlic two gcars wheri drsired. L\ sriiiill cltinil) \cre\r Iiolils tlie petirs citlicr iii or out iif iiichli. Tliis cliilcli is siinple, iiies~~eiisirc~ iinrl foolproof. 1 l i t * :,í;,) 11.1'. l~:ill-I~c~i~ring syr~chror~ous rriotor is ~iiouiitc~l ori s11011gcriihlier to rt.tliicr ribr:itiori. Tliv \vorrri for tlie -45-tootli, :I>l>itdi, rctluctioii g c t r is nioiiritc.il tlircctly oii tlic motor slinft. This little iiiotor 1i;iii~11estlit- .l.OO]'ly iririre. mliile a l)lionogr;i~>li riiotcir pror<.d tilo wi~;ck. JZ spceitil 1iiii:ir drix ing rate is 1)rorier:itiiig tliroupli a 20-to-1 Trorin rrduction, rotiites tlie piiiioii frariie. Tlie 20-tooth \rorni gc;ir i\ attnchecl to tlie pinion frarne, nliile tlie xvorni is coupled to the niotor. i'his worni :LISO svrre'r t o loclí tlie pinion frarne in a fised position ~vlieiitlie slow niotor is not bciiig used. A11 gears a r e 32-pitcli. This slow rnotion unit lias proved cxtrerriely eficirnt and coiireiiient t o use. Operated a t twice tlie synchronous driving ratc, it girc-s vcry fine driving control for photograpliic or similar use. For random visual use a Iiiglier operatiiig speed woiild be niore suitnble. She hase for tlie drire meclianisrn is of welded angle iron, arid wcighs 75 pouricls, inc-luding the Iiusky hearing supports. Bearings are "Bunting" phosplior bronze he~iring biistiings, which were first closely fitted to their respective sli;tfts. SIirn-ttie shafts still in place-tlie busliings were properly positionecl :ind sol(lerec1 tu tiieir support posts. Cxtting oil grooves antl a little ruiiriing-in cornpleted the job. These bearings are inexpensive and efficient. The entire drire mech;inihm, incliiding the large polar axis gear, is protected by ;t dust- and oil-tiglit metal housing having a removable iiispection corrr. Tlii ge:irs :ind betirings operate in a constant batli of oil. IIeavy oil, siich as fluirl-type :iiitorriol)ile traiisrriission oil, has been found t o be the most s:itisf:ictory~ giririg quiet arid smooth ol>eration.-3211 X. Sen~inaryA v e . ,
l
[KIII~~OH'S YOTE: Tli<)rI~:il)f('rwliic*l~follo\v\rs is n corriposite of sevrr:il :iin;ittxiir%'csprrieiiit. ~vitliIi:iir
It Iias plenty of pov-cr, ancl its spied can b r ;iccurately controlled. A 1 : ~ r ~ e double-spring niotor wns :iccorciingly bouglit, :lnd the following alter:itionc made. Tlie povernor weiglits were taken off arid were repl;iced by lienrier ones made frorn ~ ~ i e c eof s hriiss rod %'' di;inietcr by X'' long. Tliis, with a norm:il setting of tlie spercl repulator, allowecl tlie riiotor t o run steadily at about oiie tliird of its usual speecl, ;ind t o keep poiiip f»r ;iboiit 25 ~riiniitesa t one wind. Tliese oversize areiplits are shown riear tlie riglit, in Figiire 1. l'he s p r r d repulator ~i-n\fitted witli a sensitive screw acljusting device.
'Tliis <'orisi\ts of :I siri:ill 11r:i.s tiloclc ~ < ~ r e í v (ti? > iri(llc. \Vitli tlie riiotor >lowccl
/'
SP~NDLE
3 R.P.M.
i
TVR~ABE SPINDLE
PEEY
vl(;L'~l;3
riglit speecl for a 180-tooth wlirrl oii tlir poltir nsis. I t is only nrceswry to choohe tlir riglit ivorrri rntio to siiit rrioiintirigs Iiiiviiig a different riiimber of teetli on tlir pol;tr gear. I'lie (Irit-e froiii tlie ivorrii mlierl ori the clock is taken thrniiph n kind of in Figure 2, a l tlie right, and then tlirough k i pair of hevel ~ l u t < ~ Islioívri i, wheels to tlie tnngeiit screív. Tlit. cliitch is sirriply a kind of sleeve fittcd with a set screw. \Vlieii tlie scrcw is loosriierl tlie clock drive is not triinsmittecl, aiid tlie slow iriotion caii be worlic(1 by hnnd. F o r s~nnllacljustrrients in R. A., mlien usiiig higli poívers, tlie clutch is just cased open a. bit until tlie heavrnly horly Iiris cauglit iip, ur tlie speeding-up cord is pulled iintil the motor has cauglit up, as the case may be. Tliese two gadgets may be left out if tlie rrliiatorial is fittccl with :t separate slow motion in R. A., independent of tlie clock (1rive.-S3 1T'iilihrrm r i v r n u e . G r o ~ g e3Iuigh
o f tlit prdest:il (li'igiirc 3, :it tlic* riplit). l'liis tr:iiri (1rivt.i :i tlriiiii :iroiiiid \vliicti oric. ericl of 11 11c.lt i \ ~voiiricl. 'I'lie t)(.lt gocs o \ c r tlic. 111111i.yori tlie 1)ol;rr :txis ;irid is Iiej~tt:iiit I I iiic;iiis ~ of ;i \vt*iglit a i i i i t otlirr t~ri
turris, tlie hclt i q iiii~voiirid.c;iiisiiip tlir ~v\.c.iglitt o tlrop slo\vly :irid rotlite tlie pulley, ~vliicliis coiiiicctctl 1)y iiiitcr gct:irs to tlir 11ol:ir ; i s i \ hli:tft. il l(ctc*r cbo,nniittiic.trtiott: 'l'liv ilrive sliomii iri tlie 111itit~igr:i~~li (1:igiuc S) 1i:is 1)rrii irigiiii~;itisf:ictory. ~\Itlioiigli tl~i,
WASHER
satisf:ietorily witliout heiiig Lold of tlie grief tliat c:iiiir 1 ~ - f o r e . Hence tlie inclu\ioii o f tlotti iterris rvitli rep:trd t« tliis tfrivt..-Rrl.]. First, T coiiI(1 not get it to run propcrly niorr tlitiri eight iiiiniitrs \vitliout rea,iridiiig, \vliicli \vos U nuisnnce. Secoridly, beiiig rriouiited in tlie htise of rriy tele\colie, it sliook everytliirig wlien 1 rewouri:icks could, of course, be overcurrie by uiirig :I 1:rrper sprinp nnd niounting tlie eritire system on :i separate liase. The essentinl ndrantage of this drive lies in tlic metliod of trnnsmitting powcr t o tlie polar :i>iis. It requires less power in tlie spring motor, bec;iuse most of tlie ~vorh-of turnirig tlie polar aixis is clorie by tlie xx-eiglit. Theii, again, the whole clockwork ran easili be rnoririted a t anq- di\tence from the telescope proper, by lengtlieiiing tlie helt, tliereby e1iiniii;rting vihration.