WHILE A LARGE MAJORITY of amateur telescope makers today are of the genus American, subgenus North and species Yankee, the hobby also has taken root the world over. From time to time we have published here the descriptions of telescopes made by amateurs in India, and Figure 1 shows one more of these. Kamalesh Roy, of Lhasa Villa, 80 Park St., Calcutta India, is the maker and this reflector has a 7" mirror of focal ratio 9. Roy made two such mirrors, one for himself and one for the University of Dacca, Bengal. He says that, fortunately, Prof. M. N. Saha, F.R.S., at Calcutta University, took interest in his work and encouraged him to build the mounting at the University's workshop. Prof. Saha (pronounced "shah") is an astrophysicist of worldwide note. The telescope is mounted on the roof of the University Science College Building.

A series on telescope making, by Roy, appeared in the November and subsequent numbers of the Calcutta magazine Science and Culture, where his connection with the Palit Laboratory of Physics at the Calcutta University College of Science is mentioned.

When his telescope was completed, Roy took one of the discarded tools, of thin 1/2" glass, ground it to f/4.3 and made of this the primary for a Cassegrainian telescope. Performance was not very good, and Roy therefore asks just how far one can safely go with the thickness-to-diameter ratio of glass mirror disks. Answer is difficult and not sharply definitive for individual cases, or even for general cases. That is, while a ratio of 1 to 8 is usually recommended (sometimes even 1 to 6 ), this includes a rather liberal factor of safety. But if the worker is willing to gamble, he may run his ratio along to 1 to 10 or 1 to 12 with fair chances of good results. It has even turned out satisfactory at ratios like 1 to 20, but this is much like skating on thinner and thinner ice. If only every disk of glass were identical with every other disk of glass, and if every telescope maker were identical with every other telescope maker, we probably could refine the matter to a definite limiting place.

Thus, nobody can give a set answer to this question. If you're a born gambler try a 1:50! Such a disk probably would be useless, yet who would dare dogmatize, even here, without hedging? One piece of glass out of a dozen, at 1:50, might miraculously stand up. Some born gambler with sporting instincts and lots of time on his hands may want to see just how far he can pursue fate by making thinner and thinner mirrors till he thus receives as much punishment as he can endure.

CLUBS of amateur telescope makers and astronomers in various centers have from time to time started 20"

reflecting telescopes as group projects but none of these projects ever has been reported as completed. Evidently an individual can start a 20" after a club does, yet finish before it-William Buchele of Toledo, for example, whose 20" was described here in October 1939, and who went straight through the work without taking time out to differ with himself. Now the Northwest Amateur Astronomical Society of Detroit has tackled a 20" and we predict that Detroit will finish it. A. J. Walrath, 14024 Archdale Ave. Detroit, Mich, sends the photo in Figure 2 and says it is the 20" Pyrex disk after being trued up and with a groove ground in the edge for a locking ring. "A spiral spring, adjustable in tension, will be attached to this ring," he explains, "and by this arrangement the pressure of the mirror on the tool can be adjusted as grinding and polishing conditions require. In the illustration a sub-diameter tool, rotating at 40 R.P.M., is shown. This is used for rough grinding. The mirror, when completed, will be an f/7.

YOU want to get out of grinding and polishing your mirror by hand, yet if you also want to get out of building an elaborate machine to do the same job of work, you can without very much trouble throw together a sort of demi-machine. That is what James L. Russell, an attorney at law, Chester-twelfth Building, Cleveland, Ohio did, as Figures 3 and 4 show. He calls it his "Man Friday" and says it takes the "swets" out of the grinding wets.

Lower half is a board swiveled over a shelf on a vertical bolt (the lower end is discernible in Figure 3). The tool is held between wooden end pieces attached to this board.

Upper half is a pear-shaped piece of wood (to afford access to the mirror disk to rotate it occasionally) with a central hole to drop over the handle of the mirror. This part is actuated by a horizontal pitman driven from a lathe or what-have-you.

In Figure 3 the upper, or horizontally reciprocating, half is shown lifted off the mirror and tipped up on edge above the mirror button. The fork-shaped object to right is a guide standing on its own loose base. Through this guide the pitman runs, and when in use it is clamped to the shelf with a C-clamp and shifted sidewise if side strokes are temporarily desired.

The pitman is hinged on a bolt and crosspiece over the mirror (Figure 4), but it will be better if these are kept considerably lower than those shown, since a high point of application of effort tends to tip the mirror and cause turned edge.

The tool should be rotated now and then by hand-not very important in earlier stages of grinding-and the mirror may be turned when desired, simply by giving it a turn by hand while you sit and watch the slave do your drudgery, as you feed the Carbo to it and struggle to keep awake. Possibly the latter also would take care of itself automatically if you were to attach sandpaper to the pitman, then do your nodding with your nose over it. [For this latter brilliant contribution your scribe does not, however, take credit since a friend's dog really furnished the germ of the idea. Like many another mutt, old "Tote" enjoyed the winter warmth of a kitchen stove and, if the oven door were left open, would stand and insert his entire head well into the oven and soak up heat. Soon he would drowse and then his head would gradually sink. Finally his wet nose would touch the oven floor and there would be a hiss of steam and Tote's head would jerk suddenly upward, whacking the top. But he would not withdraw-the place was just too good. So the cycle would begin again: sink, hiss, jump, sink, hiss, jump, at about one stroke per minute. Two lads your scribe and his chum-slandered the dog by calling him a poor old fool, but this scientific canine was only trying his best to give them the inspiration for an interval timer.]

ALL of the above was light, easy A reading, so put on your workin' pants for the following, which isn't.

TREND away from prisms and toward flats for diagonals in reflecting telescopes is growing. In "ATMA," page 282, Hindle urges flats for best results. In the October, 1940, number, Wates discusses the subject favorably to flats, and now H. H. Selby, author of the chapter on flat making, in "ATMA," quantitatively investigates errors caused by prisms, giving us something definite that we can lay hold of and showing how damaging prisms can be in some cases. "Every now and then," he writes, "someone asks me why I use diagonals instead of prisms; or remarks, 'That RFT worked fine till I put in my diagonal eyepiece'; or says, 'This plate from my Newtonian is fuzzy, yet you checked my mirror and said it was OK."' Here is Selby's analysis, and let not those grimacing goblins, the complicated formulas in it, scare you a bit, since they turn out, on closer examination, to require nothing worse than substituting some known values for symbols and then doing some common arithmetic. Selby writes:

If even a perfect prism is used to deflect the rays from a perfect paraboloid to the side of the telescope tube, the correction of the mirror will be adversely affected and the telescope will perform as if the mirror were over-corrected for axial spherical and axial chromatic aberrations. Also, some chromatic variation of axial spherical correction will be introduced. These effects are slight however, in the average case. Because the effects of prisms on the performance of telescopes have been the subject of many discussions with TNs, formulas for computing these effects are given here for reference.

Spherical aberration: In Figure 5, a marginal ray is shown reflected from the mirror to the original focus, Fo. When glass is interposed, the ray is refracted and reaches the axis, Fm. The error introduced by this refraction will be a function of the following variables:

R = radius of curvature of center of mirror

R_r = radius of curvature of edge zone of mirror

r = radius of mirror

T = thickness of glass equivalent to the prism used, which equals side of cathetus face

n = Refractive index of prism. No subscript indicates that n is for a wavelength of 5893 A.U.

By substituting the proper values of any specific example in the following equation, the distance F_o F_m which computers call sph for spherical aberration, can be found for any color of light.

This equation may mean more if examples are given; hence two examples at the extremes of normal use are chosen, so that practically all cases will lie between.

I, a 6", f/8 mirror with a 1 1/2 " prism.

Constants:

Rr = 96.047

r = 3

T = 1.50

n = 1.550

II, a 12", f/2.5 mirror with a 4" prism.

Constants:

Rr = 60.300

r = 6

T = 4.00

n = 1.550

In Case I, sph = 0.0012". Since the r²/R correction is 0.047", sph is insignificant.

In Case II, sph = 0.0302". This is 10 percent of the r²/R correction of 0.3000" and is more than sufficient to ruin the image.

Chromatic aberration: This aberration is computed quite simply within 0.0005", thus:

where n_c = refractive index for red at 6563 A.U.

n_g = refractive index for blue at 4359 A.U.

The size of the blurred patch due to chromatism is given by

For comparison, the diameter of the central diffraction disk of a perfect mirror, without prism, is found by

where) = wavelength of light, or 0.00002". A glass frequently used for high-grade telescope prisms is a borate crown in which n_c = 1.514 and n_g = 1.526.

In Case I, chr = .0077", () chr = .00048", D =.00039" and the image is only very slightly affected.

In Case II, chr = .0200", chr = 0040", D = .00013".

Here, the image is enlarged to 30 times normal and results are very seriously impaired.

Chromatic difference of spherical aberration: This error is the least of three axial aberrations introduced by a prism. (The lateral, or Seidel, errors which are functions of the position of the prism and the angle of incidence are not considered because nothing can be done in figuring a mirror eliminate them while maintaining a sharp central image.) However, if a mirror is to be used for different colors, for different purposes, such as a mirror tested visually and used later for infra-red or ultra-violet photography, this aberration might well be considered with very large jobs. The equation is

where n = index of prism for shorter wavelength and n the index for longer wavelength.

Compensating for prism: The preceding equations will allow the builder to find the errors which given prism of good quality will introduce when used with his telescope. The spherical aberration can eliminated in the figuring but chromatic error cannot, while chromatic difference of spherical aberration can be considered in special cases. If the introduction of a suitable prism would blur the image chromatically more than an allowed tolerance, the prism should be discarded in favor of a flat. If not, the mirror should be figured to a definite amount of under-correction less than r2/2R in order to have a sharp image. To do this, it is necessary to know the spherical aberration of an uncorrected mirror of the same constants as the mirror to be used. This is given by

The proper radius of the equivalent sphere is that of the paraboloid at the edge, or R = R_o + r²/2R .

Then the proper correction to give the mirror, instead of the usual r²/2R, will be - 2 ( F + sph). In Case I,

R = 96.047

r =3

sph = +.00120

F = -0.02341"

r²/2R = .04683

Proper correction = .0444".

In Case II,

R = 60.300

r = 6

sph = +.03021

F = -0.15000

r²/2R = 0.30000

Proper correction = .2396"

End of Selby's contribution, which ought to have the effect of raising the standards of telescope making.

Readers wishing the mathematics behind his formulas may obtain it by asking.

To avoid unnecessarily worrying the very beginner, the lesser effects due to prism error probably will not be likely often to exceed those due to inexperience in mirror making; they may even help compensate the latter in some instances. For second and subsequent telescopes the worker may to good advantage work out the extent of the prism factor and allow for it if it is found appreciable.

In case Selby's statement that the glass thickness, T, (Figure 1) in a prism equals the width of its cathetus (shorter) face seems puzzling, note Figure 6. The light path, a + b, within the prism, is of equal length no matter where the ray strikes it and, the reflection at the back not entering into this particular consideration, the prism therefore equates with a simple, plane-parallel slab of glass, as shown.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.