MANY WOULD-BE AMATEUR TELESCOPE makers forego the sport of mirror making because they have no place to set up the conventional mirror-grinding pedestal. This, however, need not be an obstacle; mirrors have been ground on tables, in bathrooms, in jail, and even in a morgue on a marble slab between two corpses.

David P. Barcroft of Madera, Calif., has improvised from dime-store pans adequate equipment for grinding and polishing a mirror on a bench or almost anywhere. The drawings at the left in the illustration on the left contain an exploded view of the parts above the assembled dingbat. Barcroft attached the square baking pan to the bench with four blobs of pitch. He pitched the tool to a block of wood, centered this block in a common pie pan, poured plaster of Paris around it to half the depth of the pan and allowed it to set.

During grinding and polishing the upper pan may be rotated now and then. This is the equivalent of the conventional walking around the pedestal. When a tool is evenly supported, as with soft pitch on a highly rigid backing such as thick metal, there is little need to walk around the pedestal often. But when the backing is relatively flexible, as in the device described here, astigmatism due to uneven support of the tool may be ground into the mirror unless the tool is rotated a little at least once or twice a minute. Somewhat to Barcroft's surprise, continued use has not bent the light tinware of his assembly, nor does the pie pan with its cargo take off on the anticipated flight across the room.

To forestall rust Barcroft waxed the pans with paraffin. The addition of Dif, Oakite, Soilax, borax or cream of tartar to the water used should accomplish the same result. As a reservoir for the gunk he sometimes inserts a second and shallower square pan between the two already described.

The 14-inch length of two-by-six plank that forms its base may be clamped or screwed, overhanging, to a bench, table or other support. The pan is a special shallow layer-cake pan only five eighths of an inch deep, permitting the mirror to overhang it at the ends of the strokes. The central hole cut in it by McCartney is 2 5/8 inches in diameter and need not be perfectly round. The drawing describes the rest of the details. In the original the gasket is smaller than the mirror and is 1/32-inch thick.

During use the anticipated leakage from the felt-to-g]ass contact joint did not materialize; the device is well housebroken. An added point in its favor is the fact that the mirror and tool may be quickly exchanged, inverted or returned to normal position without fussing or preparation except for rinsing. Thus it is good equipment for the method of grinding and polishing in which, forgetting the gradual-approach and guessing-game method described in the treatises, the curve is excavated at the start to full ultimate depth of sagitta and maintained thereafter by working inverted half the time.

Commenting on the wooden handles, Roger Hayward, the illustrator of this department, urges the desirability of keeping the pitch-covered areas small. "When I made my first mirror many years ago I used a 3 1/2-inch-diameter wooden handle pitched to the back. After the mirror was figured and the handle knocked off, a bulge appeared in the figure where it had been. The pitch was also probably too hard." Similar instances have often been reported to this department. For pitching glass to handles your editor has always kept a special can of very soft pitch. With this even the 4 1/4-inch handle disk shown in Amateur Telescope Making, page 288, has never produced the often-described effect. The soft pitch may also be a little less likely to let go and leave the handle in the hand and the mirror fragments on the floor. However, a large handle blinds the lap during work. Many advanced amateurs and practically all professionals omit the handle altogether.

ROGER HAYWARD was invited to 1t contribute and illustrate his theory of the tiny pinhole in the Foucault test and to describe his favorite design for the testing equipment. He writes:

"When the Foucault test is used merely for detecting errors of figure in spherical mirrors there seems to be no lower limit to the size of the pinhole that may be used, provided there is enough light. When, however, the test is used for observing and measuring the figure of a paraboloid at its mean center of curvature, the story is quite different. W. F. A. Ellison describes in Amateur Telescope Making, page 84, an amateur who almost discarded a perfectly good mirror because he tested with too small a pinhole. A diagram of the light rays as they intersect in the vicinity of the focus of a paraboloid shows what the trouble is.

"The lower part of the drawing at the right shows the focus of a 6-inch paraboloid of 24-inch focal length when tested at its mean radius of curvature of 48 inches. The foci of the various zones are indicated. (The vertical and horizontal scales are different, but this does not affect the argument.) We must imagine that around each of the rays in the drawing there is a pencil of light the same size as the pinhole. The knife-edge is shown at the focus of the .866 zone, which the figure shows to be the point of sharpest focus. This corresponds to the circle of least confusion in astigmatic optics. If the pinhole used in the test is .006-inch in diameter, which is the size of this circle of least confusion, it will be clear that from one side of the mirror the pinhole will be completely obscured and from the other completely clear. The exact converse will be true at the .5 zone. The central figure above the diagram shows how this test should look, the maxima being the unobstructed pinhole and the minima being no light at all.

"At the upper left-hand part of the illustration a sketch shows the result of the use of a .004-inch pinhole. Two large patches appear, one completely black and the other of maximum brilliance. In neither of these patches will there be any apparent detail such as zones due to the polishing tools and other causes.

"These diagrams, which are constructed from the geometrical theory of optics, show the knife-edge at the .866 zone instead of the more usual .707 zone. This placing of the cutoff has the remarkable properties that the darkest and lightest parts of the focogram are at the margin and the half-radius points. The mirror therefore appears to be slightly concave instead of having the effect of flatness as when the cutoff is .707. (It may be of interest that .866 is the square root of divided by 2 and that the square root of 1/2 is .707.)

"If the mirror being tested were the usual 6-inch with 48-inch focal length, the smallest pinhole which should b used would be .0015-inch. A focogram with a .001-inch pinhole would have the same appearance as the .004-inch pin hole in the illustration.

"There is no good reason for striving for a tiny pinhole, since the cutoff is really formed between the knife-edge and the image of only one side of the pinhole. In fact the pinhole may be dispensed with altogether and a single knife-edge used for both the defining edge of the light source and the cutoff. At one point it forms a boundary of the light source and at another it intercepts its own reflected image. This arrangement is also much easier to clean than a pinhole."

Since the lamp and knife-edge move toward or away from the mirror as a unit, r²/2R is used in place of r²/R.

Suppliers and Organizations

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