The figuring or alteration of the curve from A to B and then through C1 to C2 is to be managed. It is evident that we want to flatten the edge of the mirror so as to increase the focus of that part, or to increase the curvature of the center and so to decrease the focus thereof. The latter is the method I adopted, acting on the advice of the same kind expert who enabled me to perfect my first mirror.
It will be seen that if the polisher has its square the same size all over, the curve will, at any rate if the pitch is fairly hard and the stroke not excessive, tend to retain its " A " figure, or even, as I found, to show increase of the curvature at the edge as compared with the center, so as to make the A figure more pro-nounced - i. e., the facets decrease in size uniformly from center to edge, and in consequence the work done by the rouge in abrading the glass in the center of the mirror is more than at the edge, with the result that the curvature in the center tends to increase relatively to that at the edge; or the mirror, in other wordsr passes from A to B and to C in succession.
Fig. 1 shows the polisher which up to to the present has been used. If now a series of inclined lines are drawn parallel to one another, as in the figure, starting from the edges of the central facet, and the pitch is cut away or trimmed off along those lines, we get a polisher like Fig. 2, which will produce the effect desired. The line along which the pitch is cut must be kept parallel, and a simple way of doing this is to use the instrument shown in Fig. 3. This simply consists of a frame of wood just wide enough to contain the polisher and rather more than twice the length, and deep enough to hold the crosspiece shown, clear of the surface of the polisher. By turning the polisher round on its center the crosspiece can be made to guide the chisel or trimming tool along the line of any inclination.
The amount of graduation should not be very great at first - as when once the figuring is commenced the alteration of figure is somewhat rapid - and it is of the utmost importance to spare no pains in constantly testing the curve as previously described. So long as no attempt is made to figure the mirror, and the facets-are consequently of uniform size, the testing may be performed every hour or so; but when once the polisher is graduated, and the focus of the center begins to shorten, testing should be carried out after every twenty minutes' work, or even oftener; towards the end, five minutes' polishing may make all the difference between success and failure.
I ought, to mention another method of measuring the focus of the different zones, as it was employed by Dr. Common for his great 5 ft. mirror of 28 ft. focus. He used, J think, 14 zones of different diameters, and each about an inch in breadth, and placed his testing apparatus in a sort of sentry-box 66 ft. away. Instead of using the screen, as above described, he measured the focus directly by focussing the image by means of an eyepiece. Of course the apparatus above described could be used in this way; but after trying the method I abandoned it on account of the great uncertainty about the focus of the central zone. The eye, mine at least, has such great power of accommodation for focus that the tube maybe moved a good deal without affecting the sharpness of the image - this is also due to the very sharp angle at which the central rays con-verge-alsomany eyepieces have considerable spherical aberration, which is different, of course, for central and marginal zones, and which confuse the readings and adds a fresh source of error comparable with the aberration we wish to measure.
For this reason, when testing finally int he telescope, it is most necessary to use the eyepiece with which most work is to be done. A power of about 300 for a 9 in. mirror, and the eyepiece should be the very best that can be got.
If alow-powere. p. is used in testing in thetelescope, the mirror, even if perfect, may show considerable under correction (class C or even B -i. e., elliptic or even spherical), which may quite disappear with the ordinary working power. This matters little in practical telescopic work, as low powers are not usually employed on objects requiring critical definition. My first 9 in. mirror shows signs of under correction with an ordinary Huyghenian of 60 diameters; but an e. p. from my Voightlander prism binoculars, giving a power of SO, shows no signs of error whatever.
It will be seen that I attach considerable importance to the final testing in the telescope. This, I suppose, can be omitted by experts who have had great practice in testing; but I think it is best to have a tube and rough mounting ready as soon as the focal length of mirror is accurately known.
While testing on a star in the telescope it is very im-portant to remember the distinction between the case of incident parallel rays (from a star) and of divergent rays (from a pinhole at the center of curvature). If the reader will look back to Chapter V, he will see that the appearance desired is that of Class B under the pinhole test.
There is no need whatever to silver the mirror when testing in the telescope; the flat should be silvered, but as a 9 in. unsilvered mirror gives enough light to show the companions to Polaris and Rigel, there is ample light from a 1st or 2nd mag. star.