4 is from the fine equatorial at Johns Hopkins University, designed by Professor Hastings and executed by Brashear. The objective was designed with special reference to minimizing the spherical aberration not only for one chosen wave length but for all others, has the flint lens ahead, aperture 9.4 inches, focal length 142 inches, and the lenses separated by ¼ inch in the final adjustment of the corrections. 5 is from the Potsdam equatorial by Grubb, 8.5 inches aperture 124 inches focus. The great similarity of the color curves is evident at a glance, the differences due to variations in the glass being on the whole much less significant than those resulting from the adjustment for power. Really very little can be done to the color correction without going to the new special glasses, the use of which involves other difficulties, and leaves the matter of adjustment for power quite in the air, to be brought down by special eye pieces. Now and then a melting of glass has a run of dispersion somewhat more favorable than usual, but there is small chance of getting large discs of special characteristics, and the maker has to take his chance, minute differences in chromatic quality being far less important than uniformity and good annealing. Regarding the aberrations of mirrors something has been said in Chap. I, but it may be well here to show the practical side of the matter by a few simple illustrations. Figure 64 shows the simplest form of concave mirror—a spherical surface, in this instance of 90° aperture, the better to show its properties. If light proceeded radially outward from _C_, the center of curvature of the surface, evidently any ray would strike the surface perpendicularly as at _a_ and would be turned squarely back upon itself, passing again through the center of curvature as indicated in the figure. A ray, however, proceeding parallel to the axis and striking the surface as at _bb_ will be deflected by twice the angle of incidence as is the case with all reflected rays. But this angle is measured by the radius _Cb_ from the center of curvature and the reflected ray makes an angle _CbF_ with the radius, equal to _FCb_. For points very near the axis _bF_, therefore, equals _FC_, and substantially also equals _cF_. Thus rays near the axis and parallel to it meet at _F_ the focus half, way from _c_ to _C_. The equivalent focal length of a spherical concave mirror of small aperture is therefore half its radius of curvature. [Illustration: FIG. 64.—Reflection from Concave Spherical Mirror.]