Last July we published a very popular description the new Ritchey-Chrétien aplanatic compound telescope which is expected to give star images even superior to those of telescopes having paraboloidal mirrors. It was pointed out that the curves of aplanatic mirrors are not conic sections but are not too difficult for the experienced worker to create, once their zonal radii are known. Here, however, was the fly in the optical ointment-one must be almost an Einstein, we hinted, to calculate these curves; in fact, we inferred, the abstruseness of the necessary mathematics rendered the Ritchey-Chrétien telescope practically a secret.

As was anticipated, this negative suggestion, like the one on page 65 of "Amateur Telescope Making," acted as a challenge, which two of the regular readers of this department promptly took up. These were Professor Arthur Howe Carpenter of the Department of Metallurgy and Geology of the Armour Institute of Technology and president of the Amateur Telescope Makers of Chicago, also Alan R. Kirkham of the Amateur Telescope Makers and Astronomers of Tacoma and author of two chapters in "Amateur Telescope Making." As each seemed to have an identical objective we "introduced" them by mall.

For the next few weeks we were permitted to see the many letters which were almost daily exchanged between these two, each letter containing evidences of progress toward the solution of the aplanatic curves. Together these amateurs have "busted the 'secret' wide open" and-together they have now, at our request, prepared instructions for designing several types of aplanatic telescopes, which we shall present in three installments. After the process of laying out an aplanat has been described in abstract terms, the actual specifications (zonal radii, and so on) for three typical 12-inch aplanats will be given, in order that those who are not advanced workers and who do not care to follow the theory may also, if they wish, make aplanats. As the first installment goes to press both authors (also co-operating, Harold A. Lower of San Diego) are making 12-inch aplanats.

Well meant, even a bit "high-hattish," advice to the new beginner is to make at least one common Newtonian and one common (paraboloidal) compound telescope-itself advanced work-before attempting an aplanat, for the latter is advanced billiards. It is a kind of super-refinement whose very advantages over paraboloidal telescopes he will be likely to miss, even assuming that he can create its peculiar curves, until he has gained both a general telescope making and a general observing background and thus educated himself up to it. Otherwise, if he attempts it, he may wish he had never been born. The aplanat is an adventure, even to the professional-though a number of advanced amateurs are now at professional level in practical ability.

The following is by Messrs. Carpenter and Kirkham:

"ORDINARY types of reflecting telescopes even including those having paraboloidal mirrors-do not focus perfectly the light received from objects in oblique positions; the light from such objects spreads over a part of the field. The form of image given is shown in Figure 1. The image is wing-shaped and hairy, that is, it has 'coma.' The point of the image is directed toward the center of the field. Drawings were given of the images of stars at different distances from the center of the field in Newtonian telescopes as compared to aplanatic telescopes in SCIENTIFIC AMERICAN, July 1932. (The same drawing is again reproduced herewith.-Ed. )

"The cause of this aberration or coma may be seen from Figure 2, which is a vertical section of a paraboloidal mirror. The arrow represents the path of rays of light parallel to the axis. These come to a sharp focus at F. Thus, for objects parallel to the axis, the paraboloidal mirror gives a perfect image and leaves nothing to be desired. But the paths of three typical oblique rays are indicated by the broken lines reaching the mirror at the zones, P" P' and the center V. The rays reflected from P' and the center V come to a focus at F' on the opposite side of the axis, but not in the image plane. Rays from the outer zones-for example, at P"-do not pass through the secondary focus F' but, crossing the pencil at F", they reach the image plane at I". H. C. Plummer (Astronomical Journal, May 1898; Monthly Notices, Royal Astronomical Society, March 1902) shows that the points, P', F, and F' are points on a circle. This means that the image field of a paraboloidal mirror is the surface of a sphere; its radius of curvature is equal to one half of the focal length of the mirror. (Bell, "The Telescope," page 95.) These facts are usually ignored when testing the zones of paraboloidal mirrors at the center of curvature.

"The 'comatic image' is often shown as a series of circles tangent to the sides of an angle of 60 degrees, Figure 3. Actually it is quite a complicated series of curves. They were worked out and traced by Plummer, Crockett and others and were reproduced by Chrétien in his 26-page article on 'Aplanatic Telescopes,' in the French publication Revue 'Optique, January and February, 1922. Professor Ritchey states that this spread of light is sufficient to reduce by two magnitudes the light of faint objects near the edge of the field in large telescopes, and is an important consideration in the study of star clusters, faint nebulae, and planetary detail.

"This aberration is inherent in the paraboloidal curve and cannot be overcome by any form given to a single reflecting surface. K. Schwartzschild, in Proceedings of the Königlichen Gesellschaft der Wissenschaften of Gottingen, 1905-06, made an exhaustive study of this problem and derived curves for two compensating mirrors on the Gregorian plan, so combined as nearly to free the field' from the straying light up to two degrees or more from the center. His equations are in the form of a rapidly converging infinite series and are perfectly general, being applicable to any reflecting telescope having two mirrors. Abbé's sine condition and the fundamental concept of Hamilton that the paths of all rays through optical instruments must be of equal length, were taken as the basis of the investigation. Only thus could telescopes be stigmatic and aplanatic too. Through a beautiful mathematical analysis, Schwartzschild derived simple formulas which can be used by anyone to calculate two surfaces, compensated to give aplanatic images."

Messrs. Carpenter and Kirkham's explanation of the aplanatic telescope will be continued next month, and in the month following there will be especially calculated data from which those who do not wish to design their own aplanats can make one.

THE "Amateur Telescope Makers of Chicago" are planning big doings for the forthcoming national get-together of amateur telescope makers, which will be held at the Adler Planetarium in Chicago, from Wednesday, June 21 to Sunday, June 25. In the Planetarium there will be, not only during these few days but during the whole summer, a booth and shop devoted to amateur telescope makers, kept open by the members of the Chicago organization named, and this will serve as a kind of general headquarters of the amateur-a sort of "hang-out."

This will not be merely a fixed exhibit but an optical shop in actual use. There will be apparatus for tests of various kinds and at least two grinding machines, one designed by Zeiss and the other (so it is rumored), by the great inventor, Rube Goldberg. There will be apparatus for making small lenses, eyepieces, and so on; also a lathe. There will be polishing posts, not merely to look at, for someone will be there exercising mirrors on them. A fair-sized flock of telescopes made by Chicago amateurs will be on exhibit; likewise various mirrors, including a series of the new sputtered kind.

At the convention or get-together there will be but one day of formal meeting, to be announced later. This will be followed by a mixer. The secretary of the Amateur Telescope Makers of Chicago is William Callum, 1319 West 78 Street, Chicago. As the amateur telescope making movement has now reached large proportions the country over, a national organization of some kind is to be formed at this meeting. We have often been importuned during the past few years to attempt this ourselves, but have refused because we believed it would come spontaneously, and therefore actually be spontaneous, when the time was ripe.

RUSSELL W. PORTER writes that he expects to drive east from California for the national convention; John M. Pierce says he will drive to Chicago; Leo J. ScanIon of the Pittsburgh group says he will be there if he has to walk; your scribe, with some past experience as a hobo, will arrive quietly via the freight terminal. And every body will be poor but happy. This will not be a high-hat convention, so leave your dinner coat in mothballs. And now-everybody on to Chicago-let's make it a crusade if not a hunger march. Beat the tom-toms, gather in your clans and come.

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.