Three years ago this department urged Dr. Anderson to describe what was going on, also to state when the work would be finished. He wisely replied: "Dates I can not give yet," and he added, "I shall refuse to describe a job until it is completed, but you may be sure that my article will be in your hands within ten days of the completion of any one stage."

This promise was kept recently when the stage of bringing the surface to a sphere, preparatory to parabolizing and figuring, was completed. The account proves to be something of a now-it-can-be-told story, for there were troubles. Yet anyone who has ever made even a small telescope mirror could have predicted this - there always are troubles, some of them almost interminable; while in pioneering a mirror of unprecedented size, such as the 200", they were all the more expectable. Those that were encountered now turn out to have been even more puzzling than the best of the tales circulated orally by "Old General Rumor." Yet they were conquered and the project moves successfully toward completion-when? This still is unknowable-for a telescope mirror is finished when it is finished. Dr. Anderson's account, continued from last month, follows:

"Optical tests of the 200" mirror were at first made with the mirror tipped up so its optic axis was horizontal, using therefore only the one component of the supporting levers Later on, tests were made with the axis pointing about 4° above the horizon, so that both components of supporting force would be in action. In the later stages of figuring the mirror was made to rest on the supporting system while polishing was in progress.

"The first optical test of the mirror, in September 1938, revealed a fair spherical surface with some zonal and other errors, the chief of which was astigmatism. Measurement of the latter showed that the radius of curvature of a vertical plane was a millimeter or so shorter than that of a horizontal section. Rotation of the mirror about its axis in the testing position showed that the astigmatism did not rotate with it-in other words the radius of curvature in the vertical plane remained shorter in all positions of the mirror.

"More refined measures revealed another surprising fact-namely that at times the vertical astigmatism would have slightly different values in two orientations 180° apart. Running down the cause of this behavior required considerable time after it had been demonstrated to our satisfaction that the phenomena were real and not simply errors of measurement. A linear astigmatism of the order of 0.05", with a not very smooth mirror surface where errors of measurements would average 0.01" or 0.02", does not seem so very bad-and the 180° effect of about 0.01" might very well be considered accidental-as it was in fact until continued improvement in the figure reduced errors of setting to a few thousands of an inch. Anyway, both of these effects which had been noted in the early tests turned out to be real and correctable, though it must be confessed that it took a year or more to discover their nature and cause.

"The cause of the vertical astigmatism lies in the structure of the mirror itself, combined, of course, with the method of internal support. Suppose the mirror is tipped up so that its axis is horizontal. Its weight then is carried by the 36 levers whose points of contact are in the rib structure and something like four or five inches behind the continuous front of the mirror. Let us think of one of the hexagons (Figure 5), into which we divided the mirror in the previous discussion, as made up of two parts: first, the solid front curved plate and second, the ribs. The front plate is about twice as stiff in a vertical plane as the rib system is.

"If now the support point were located at the center of gravity (actually, on the axis of the 'pocket'), the half of our unit below the center of gravity would be in tension, so that it would stretch; while the part above would be in compression. Also, the deformation of the ribbed part would be twice as great as that of the solid front. If the undeformed front surface were a plane, it would, under this deformation, become slightly S-shaped vertically; that is, the upper half would be slightly convex, the lower slightly concave. Since, instead of a plane, we have a spherical surface in the undeformed condition, the deformed condition will consist in the addition of a very weak convex cylinder to the upper half and a similar concave cylinder to the lower half of the unit. Taking now the whole mirror, each of the 36 parts would be similarly deformed, but there would be no general deformation of the surface as a whole.

"Return now to the actual case. See Figure, 5. The supporting point is on the upper surface of the 'pocket' which lies some 6" or 6 1/2" above the center of gravity. The part A that becomes convex is therefore 6" shorter than the lower part near B, which becomes concave. So we may say that, on the whole, the unit is concave; and when we now add up the 36 parts we find, in addition to the local deformation of each unit, a general (net) vertical concavity of the whole surface, which is what has been observed. The diagrams of Figure 5 will perhaps aid in understanding this. The local deformations of each unit are of course present, but they are so very much smaller than the net deformation that, provided the latter is small, the former will be too small to be observed.

"If, in Figure 5, the support S could be located on line CG, curve AB would be symmetrical about CG, and the net curvature of AB would be zero.

"Clearly the effect just discussed will be absent, or have zero value, when the axis of the mirror is vertical. As the mirror axis is tilted toward the horizon, the effect will vary as thee sine of the zenith distance. To correct it, a system of 12 gravity-operated 'squeeze levers' were applied, acting on the outer edge of the disk near the back, which when the axis of the mirror is horizontal, act so as to correct the error. Since their effect also varies as the sine of the zenith distance, the compensation will be correct in all positions of the axis.

"The second phenomenon mentioned above-that is, vertical astigmatism in two orientations 180° apart-is caused by a maladjustment of the supporting levers, and, like the one just discussed, is absent when the mirror faces the zenith. Let us again consider the mirror tipped up with axis horizontal, and assume that the supporting levers such as S, Figure 6, in the upper half are on the average so adjusted that their supporting points are somewhat in front of the center of gravity surface in the mirror, while those of the lower half are misplaced in the opposite direction. Reference to the same figure will make it clear that, in the assumed position, the radius of curvature in the vertical plane will be lengthened, while if the mirror is rotated 180°, the radius will be shortened by the same amount. Here the remedy is obvious.

"In order to test for astigmatism when the mirror faces the zenith, the arrangement shown in Figure 7 was employed. The light source and the knife-edge are, as usual, near CC. The plane mirrors MM, at 45°, are 8" in diameter. By rotating the large mirror the zone indicated by the dashed line may be tested for astigmatism. By adjusting the counter-weights of the 'lifting component' of the supporting levers, any observed small amount of astigmatism may be removed.

"The work of making the mirror surface a satisfactory sphere having a radius of curvature of 1335.7" was completed in August, 1941. Parabolizing by alternate fine grinding and polishing was started August 30, and is now very nearly completed 'in the rough', meaning thereby that the radii of zones are very close to the calculated values. The long work of smoothing and final figuring still remains to be done.

Testing will be done near the center of curvature, using a method worked out by Dr. F. E. Ross and the author. The method is new as far as we are aware; however, it would not surprise us if it should prove to be 95 'old as the hills'-for no complete search of the literature has so far been made. The method is shown in Figure 8. The lens L is so designed that, when the light source is placed at a point between its focus and the lens, the spherical aberration at its virtual conjugate focus is such that the conjugate focal points for different zones of the lens coincide with the 'centers of curvature' of the corresponding zones of the paraboloid. The light source is shown on the axis. To the right of the lens the rays travel along the normals to the paraboloid, whence they are returned along the normals and would converge to the source -but, by the aid of the half-silvered plate P, the returning light is brought to the knife-edge as shown. The source and knife-edge may be interchanged.

"The author wishes to express his deep appreciation of the assistance given him by Russell W. Porter in the preparation of this article."

EVER make a flat? Then you know the application of this verse, written by Anon Y. Muss:

An old man who lived in a cave
Knew how to make fringes behave.
If he moved his head closer,
And the fringes grew grosser,
He knew that the work was concave.

IF AS sometimes asserted, metal mirrors are inferior, optically, to mirrors of glass, they have certain special uses which justify them, and some like them anyway. Sidelight is thrown on their optical quality in a paper by Sydney J. Needs, Philadelphia, published in the "Transactions of the American Society of Mechanical Engineers" for May 1940, wherein he states that "there appears to be no metal which, when polished and examined even under low powers of the microscope, will present a surface of uniform appearance even remotely approaching that of well polished glass."

Needs is not an amateur telescope maker but an engineer who undertook an extended research on the influence of boundary films of lubricant in machine bearings, and performed his experiments between two circular metal flats. In order to prepare for these experiments he first had to learn, from scratch, how to make the flats used in it, and in this he was aided to some extent by "A. T. M." (The pun about "from scratch" was unpremeditated but any who have been through the mill would perhaps vote to leave it in.) Needs continues:

"The metal surfaces invariably contained pits or non-metallic inclusions, iron carbides or traces of manganese in the form of gray spots with well-defined but irregular edges. Experience finally seemed to indicate that the best surfaces were produced by high-speed tool steel or a high-chrome tool steel. The chrome steel is corrosion-resistant and will hold its shape over long periods of time but it warps badly during the hardening process and is somewhat difficult to polish."

FOR advanced amateurs who have followed the hobby for years, made many mirrors, also flats, there is defense work. Write us. Even for such, this is hard, tough, grisly-make no mistake - hence we frankly urge others not to aspire to it.

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.