AVERAGING ONCE a year someone asks this department why telescope mirrors have to be so thick, and now comes an inquirer who reasons that if mirrors were thinner they would have just that much less weight to support and therefore wouldn't sag any more than thicker ones, also would adapt themselves to temperature changes more quickly.

This sent us to a remembered file of papers containing an article in the Journal of the Royal Astronomical Society of Canada, July-August 1935, in which Harold C. King, Calgary, Alberta, similarly contested the statement in "A.T.M.," page 75, that mirror disks could have thicknesses not less than "one eighth of their diameters, one sixth still better, and which was never rebutted. "Some dicta," he stated, "are grooved to be wrong by their supposed explanations. If there is anything illogical in the explanation there is probably something wrong with the whole proposition. Consider, for example, the dictum that the mirror of a reflecting telescope must be made of glass which has a thickness of at least one eighth of its diameter, and is said to be better if it is as thick as one sixth of its diameter. . . The reason given for this thickness, in the book 'Amateur Telescope Making,' is that if the mirror is made of glass having a less thickness in proportion to diameter than one eighth, will not keep its figure. That is, it will warp, the reason for the warping being that 'it will bend of its own weight.' Even supposing it to be true that thin mirrors are found to warp," he then continued, "the explanation that this is caused by its own weight is illogical on the face of it. It should be obvious that if the mirror is thin there is therefore less weight to warp it."

And so he made a thin mirror, 1/2" by 9-1/2", or a ratio of 1:19, and it gave excellent star images and suffered not the slightest change in figure-which does not, however, prove anything.

If the premise on which the above-described argument is based in sound logic, then we may continue on past the 1:19 ratio. If it is good for 1:19 why isn't it good for 1:29 or 1:39? Or 1:99? Why stop even there? Why not toss out the glass altogether and let the aluminum coating stand up alone? In this series of stages has any new principle entered in at any point? We see none.

This, therefore, is disproof by reductio ad absurdum, but just why does the thick mirror stand up and the thin one, weighing proportionately less, fall down? For answer, we need only look at an engineering treatise, in the section on strength of materials. Consider the mirror in two extreme positions-first, flat on its back, then on edge. Taking the first case, a cross-section of the mirror has its analog in a common floor beam having uniform loading, in this case the weight of the mirror disk itself. Various factors enter in and the analysis could be made complicated but there is no need of it. No need, either, to cite a flock of formulas. In Trautwine's "Engineer's Pocketbook" is the simple statement of principle that the strengths of beams having similar cross-sections are inversely proportional to their spans and directly proportional to their breadths and to the squares of their depths.

Now take the alternative case of the mirror when tipped up on edge. It is now a column and here the general relation involved is a proportion between the square of the height and the square of the width. Again the square.

This, then, is the plain answer-in principle, for circumstances sometimes will modify it in specific eases.

How, then, did the Calgary critic's 1:19 mirror get by? Probably because the 1:6 or even the 1:8 ratio contains a very large, healthy factor of safety and, many think, wisely so, just as is the case in most engineering structures wherever such is possible. And his 1:19 luckily lay within it-in this particular instance. It might always, or even often. Maybe three out of four, or even nine out of ten, mirrors would get by with a ratio of, say, 1:12. Maybe thereafter the tides would set in strongly against luck. These figures are based on no definite experimental data and are simply guesses.

The 1:19 that got by was probably pretty close to the edge of the cliff. It is fun to live dangerously. Therefore, try 'em as thin as you like-at your risk. But glass is cheaper than sweat and tears.

Commenting on the above comments, which were shown to him, R. W. Porter mentioned an experiment described in Comtes rendus, Vol. 186 (1928) page 311, by Professor André Couder of the Paris Observatory, a co-author of that excellent work "Lunettes et Télescopes," ("Refractors and Reflectors"), by Danjon et Couder, published 1935. "He took a Pyrex dish," Porter writes, "which was 7-1/2" in diameter and about 2" high, with walls only 1/2" thick, and parabolized the bottom of the dish. He then took it from a warm room out into the cold night and inserted it in his Newtonian telescope, and could see no change in definition with temperature change of 36 degrees F. This," Porter adds, "would be a good stunt for the amateurs to try out. A bar, if supported at its ends, sags twice as much as if the ends were clamped to some rigid body and that condition obtains in the experiment just described." Maybe because of this last this was not an extreme kind of experiment.

The 200" mirror has a thickness of 24", hence its ratio is approximately 1:8. Even then, it has an elaborate flotation system. Yet, from the single point of view of rapid temperature equalization, the 200" has a thickness-diameter ratio of 1:40! Its face is only 5" thick and no part of the honeycomb rib structure that supports that face (and is cast integral with it) is farther than 2-1/2" from the surrounding air. This is a true triumph.

AFTER the above was prepared, the following cognate discussion of a mirror of thin ratio, 1:13.8, came from C. S. Walton, 5975 W. 44th Ave., Wheatridge, Colorado, (one of the former Roof Prism Gang of wartime ATMs; he, with neighbor Anton Bohm, made 500 prisms of two-second roof-angle tolerance) .

"In June, 1941," he says, "Anton Bohm and the writer got the idea of trying to make a large mirror of glass much thinner than is usually prescribed. We got a piece of 1-1/4" plate glass, cut out a 17-1/4" disk with a biscuit cutter and completed a mirror which is at last mounted. In the intervening years after final figuring numerous Foucault, zonal, and Ronchi tests were made and no change from the original figure was detected. Now mounted, the mirror has good definition and no noticeable astigmatism."

Walton continues: "Mr. R. E. Glover, supplied some mathematical data and remarks on thin-mirror practicability. 'If this disk,' he stated, 'were supported in a horizontal plane by a rim under the outer edge, its own weight of 23.3 pounds would deflect the center of the disk 0.000,025,3" downward. It is estimated that, if the disk were pressed against the polishing lap with a force of 20 pounds, transmitted to it through a handle 4" in diameter such as was used (Figure 1), the deflection would be 0.000,023,4", based on the assumption that the pressures were applied uniformly by handle and lap. Both of these deflections are large enough to have an effect on the corrections, since they equal about one fifth of the modification necessary to parabolize the mirror. They are small enough so that, with care in the design of the mirror support and, before that, of the polishing handle, they should permit a disk of these dimensions to be used successfully.'

"The handle we therefore devised," Walton continues "adhered to the mirror at six points located on the 70 percent zone-that is, at two pitched on points on each of the three pieces shown in Figure 1. The mirror was worked face down and the illustration shows it on its lap atop an oil drum.

"Tony Bohm and I were after quick results so he did the roughing out with his sandblasting equipment [Runs a gravestone works.-Adv.-Ed.] and then an old coarse-grit Carbo wheel used on its side by hand, with plenty of Carbo grains, brought it to rough curvature in a hurry.

"We made a concrete tool having approximate curvature and stuck glass facets on it with pitch. It turned out to be a fast cutter and did not seize easily in the fine-grinding stage. Clifford Crowe chauffered the mirror around on the lap for about 23 hours and I took a dozen spells of about three minutes each at figuring, mostly with a small polisher, as the big mirror did not respond to overhang strokes for parabolization.

"The mirror is mounted in a hexagonal, l/4" plywood tube, on a 27point flotation system very closely following Hindle's chapter in 'A.T.M.' It is rather critical on focus, being f/5, and images deteriorate rapidly toward the edge of the field, but the drive holds objects in the center and thus this deterioration is of little inconvenience. We are inclined to think the wooden tube is better than other kinds we have used, from the point of view of image steadiness.

"For any such telescope I strongly recommend designing the tube saddle so that the tube, or else the whole upper end of the tube, will rotate, a method that pays out richly in comfort of observing at the eyepiece, which may thus at all times be used in a horizontal position."

WALTON mentioned the fact that his tool, built of a mosaic of plate glass pieces stuck to a background, did not easily seize to the mirror. This is an example of the "broken" type of tool described by Ferson in the chapter on "Prisms, Flats, Mirrors," in printings of "A.T.M.A." issued since June 1944. Figure 2 shows a tool facetted by sandblasting after a couple of stages of coarse grinding. This, Walton writes, is the tool he used in making a Schmidt. He points out that this tool, and the mirror also, shows considerable transparency because fine grinding could be carried on as far as desired without fear of seizing, thanks to the breaks.

While the broken type of tool is not new-professionals often use it-Ferson, in making many scores of blocks of prisms cemented in blocks (thus, essentially flats) during the war, greatly developed its working philosophy. In "A.T.M.A." he points out its superiorities, in a clear train of reasoning with which experience checked fully. Turned I edge had resulted from grinding with too much water; necessary, however, to avoid seizing. If now the wets could be dried up really to refusal of the work to move further, he found there would be no turned edge. And if the tool were channeled, the wets could be thus dried up-safely without risk of sticking. As a by-product, the fine grit cut faster and pits were less troublesome-the whole story is too long to develop here in closer detail.

Your scribe has subsequently used a tool much like the broken one described by Walton-glass facets pitched to an iron disk. It worked fully as described by Ferson but scratched badly -until the edges of all the facets were chamfered, and thereafter it scratched not at all. Another tool was given integral facets by grinding them in with the edge of a thick piece of copper against a straightedge clamped on, using Carbo. Time, ten minutes a channel (say, 1/16" deep) and it paid fine dividends: not a seizure in a shipload. You could lift the mirror off without any effort at all, at any time.

EXUENT pencil mark test was the verdict reached in these columns last January, on evidence that this otherwise useful test, described in "A.T.M.," page 288 (draw pencil marks across the fine-ground tool and mirror and rub the two together dry), sometimes leaves scratches or gouges, possibly by molecular, glass-to-glass cohesion and grabbing and probably not, as several have suggested, by grit in the pencil since the disks are first rubbed clean with the hand. Such piteous pleas in extenuation of this Jekyl-and-Hyde accused were received that the sentence is suspended. But a warning-"The above-described test may cause scratches"-will be inserted in "A.TM.," page 289, line 2, and the suspect watched further.

Fred B. Ferson, Ferson Optical Co., Biloxi, Miss., advises us how the pencil test is made in his plant without rubbing dry disks together. "We merely lift off the mirror and draw two lines across its face. Without bothering to wash it we brush on a little more emery and grind half a minute or so. On any zones not in contact the marks will show through the back of the glass if clear and, if not, wetting it will make it so. Incidentally," Ferson adds, "emery does not stick mirrors; that fault lies largely with Carbo."

FOR WORKING 16" mirrors, now becoming the mode, a modified Draper machine is suggested, sub-diameter tool on top. An article describing the basics of stroke length, stroke offset, stroke de-centering, and the respective effects on the curve, is in preparation. For the machine, see Strong's famous book, Figure 10.

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