"CONCERNING the polishing of convex spherical surfaces, Ellison states in 'Amateur Telescope Making,' second and third editions, page 118, second paragraph, 'No question of their figure can arise at this stage of the proceedings, as it is impossible to test it.' Professional makers sometimes test convex spherical surfaces by interference methods, referring the convex to a standard concave. This method is hardly practical unless a number of similar convex lenses are to be made.

"Judging from the number of times the desire has been expressed for a test for convex lenses which would be as simple as that for concave mirrors, it would seem that such a test, if available, would be very l useful. Therefore, the writer proposes a test for convex spherical surfaces requiring no auxiliary optical surface, and one which is simple and as rigorous as the mirror test at center of curvature.

"If, for the sake of illustration, we imagine a spherical surface consisting of only a skin of silver of practically no thickness, which would at the same time remain optically true without support on either side, one side would be a convex mirror and the other a concave of the same radius. Then, in order to test the convex mirror, one would merely have to go around to the other side and test the concave at the center of curvature.

"However, practical optical surfaces are generally formed on glass but if, as in the case of convex spherical surfaces on lenses, we could again go around back of the convex and test it as a concave mirror at the center of curvature and that test would be the equivalent of a test of the convex surface.

"To do this, we make use of a simple principle employed for many years in inspecting optical glass, but to the writer's knowledge never applied in this manner. In examining optical glass for striae and general uniformity of index, when it is in crude broken chunks, it is placed in a large container having glass windows at either end. Liquid is introduced having the same refractive index as the glass and then, if the glass is homogeneous, one is able to look clear through the liquid and the chunk of optical glass, and the rays will suffer no deviation. In other words, we have optically eliminated the glass. Bell's 'The Telescope', page 61, gives an account of this method of inspecting optical glass.

"Figure 1 shows a sectional view of the set-up which allows us to test a convex as a concave by introducing a fluid equal in refractive index to that of the glass. The fluid optically eliminates the lens. Since the upper convex surface faces air, the light proceeding from the pinhole suffers a partial reflection and some of it returns to focus again adjacent to the pinhole and the test becomes merely that for a spherical mirror at center of curvature. The test is rigorous because it is conducted to all practical purposes entirely within the liquid medium, and the small amount of air between the eye and the window is too close to focus to be detrimental. Several solutions have come to the writer's attention as having about the refractive index of crown glass when near room temperature. Toluene [obtainable from dealers in chemicals; for example, Eimer and Amend, Third Avenue and 18 Street, New York City.-Ed.] seems to be the best commercially obtainable liquid, since it is homogeneous, and though inflammable does not have a low vaporization temperature. A very strong word of caution should be urged against the use of benzene or any other inflammable liquid which vaporizes at room temperature. The worst explosion due to chemical silvering would be very mild indeed compared with that due to a gallon of benzene properly vaporized and ignited in a closed cellar.

"Below is given a list of various liquids and their refractive indices for the sodium line at given temperatures. However, the refractive index usually does not vary widely with a slight change in temperature.

Aqueous Solutions (Sugar and Water)

Sugar-Refractive Index at 20 degrees C.

1.5001 at 16 percent water

1.5033 at 15 percent "

1.4951 at 18 percent "

Non-Aqueous Solutions

Carbon tetrachloride 1.460 at 25 degrees C.

Benzene 1.501 at 30 degrees C. (Dangerous)

Aniline 1.586 at 20 degrees C.

Glycerine (Glycerole) 1.474 at 25 degrees C.

Toluene 1.495 at 20 degrees C.

Carbon tet. 40 percent, Ethylene bromide 60 percent, 1.4989 at 25 degrees C.

Aqueous Salts

Pyradine 85 percent, H O 15 percent, 1.4960 at 15 degrees C.

NaC1 20, KCI at 80 percent, 1.500, 18 degrees C.

"Some may raise the objection that the dispersion of the liquids may not be equal to that of the crown glass. Of course, testing in sodium light would remove this objection completely, but the writer believes that testing with white light is about all that is necessary and the refractive index does not have to be exactly that of the crown. This has also been borne out by experiment.

"As a matter of convenience, a small prism may be used in place of the window, and the testing funnel mounted on a wall. This allows the observer to assume a comfortable posture looking horizontally instead of lying on his back as in Figure 1.

"This principle is also applicable to testing a convex hyperboloidal surface by using a small spherical mirror of scarcely larger dimensions than the convex hyperboloid. Figure 2 shows the set-up. The spherical mirror should be silvered and lacquered and the silver removed in the center, leaving a small transparent hole. Using this method it is not necessary to construct a large optical flat or a large spherical mirror when building a compound telescope of the Cassegrain type. However, it would be well to construct the small secondary hyperboloid of optical crown in order to insure freedom from striae."

THE test which Mr. King describes above has also been tried, previous to this publication, by J. H. White of Cranford, New Jersey, in making a 3-inch objective lens and later a 4-1/2 inch. Mr. White states that he finds it thoroughly practical. Besides the test described above (should it be called the King Test?), Mr. King has contributed another important advance to the telescope making art, having found a relatively simple way to render the Ronchi test quantitative without the use of mathematics, that is, by direct reading with apparatus. A description of this method will be found in the Journal of the Optical Society of America (Prince and Lemon Streets, Lancaster, Pennsylvania) for September, 1934 pages 250-252, and will be extracted here provided the amount of response appears to justify doing so.

AT our suggestion Leo J. Scanlon of Pittsburgh has kindly written down some of the hints he has accumulated while learning to work glass with metal tools, and here they are:

"Glass or Pyrex mirrors can be ground on iron tools if the tools are first machined to proper radius of curvature. The tools should be cast, either in iron or brass, and machined to curve. Do not use steel plate. Lead is not so desirable as iron or brass

"Iron tools may be rotated at a fairly high rate of speed-somewhere under 300 r.p.m., and the mirror may be rotated at the same speed on top, but I would not advise rotating anything larger than a 6-inch at this speed, while 50 or 60 r.p.m. is enough for a 10-inch. There is otherwise too much danger of breakage, if the mirror should stick to the lap and be whirled off.

"It is impossible to polish a lap on pitch at any of the above speeds, but flattened H.C.F. directly attached to the iron to polishes very rapidly and very well. [Some professionals are now using this method.--Ed.] The mirror may be finished by hand on pitch.

"The mirror may be whirled at the same speed as the iron tool; it may be held in the hands and slowly rotated first on one side of center and then the other while the tool revolved; or it may be ground as usual but on an iron tool. Any of these method will produce good results and they have all been tried here, some of them on mirrors up to 12-1/2 inches in diameter."

Mr. Scanlon did not mention that, while it is easy to make the concave metal tool on the lathe, the convex tool is not nearly so easy, as it cannot be made on a radius basis; also that H.C.F. may be attached to metal by warming the metal.

THE Amateur Telescope Makers of New York City, Lew Lojas, acting secretary, 1510 White Plains Road, Bronx, New York City, is the latest organization of amateurs Poor old tail-ender New York has a telescope makers' club at last!

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.