THE MODERN REFLECTING TELESCOPE. 37 



face, leaving the outermost zone uneliauged (see Fig. 10). There are two distinct 

 methods of accomplishing this : (1) by the use of full-size polishing tools, the losin 

 surfaces of which ai'e cut away in such a manner as to give a large excess of polish- 

 ing surface near the central parts of the tool; (2) hy the use of small polishing or 

 figuring tools worked chiefly upon the central parts of the mirror, and less and less 

 upon the zones towaid the edge. 



(1) Pamholizing with FuUSize Tools. The rosin surface can be trimmed 

 in a variety of ways to give a great excess of action on the central parts of the 

 miri'or. Fig. 13 shows one of the best forms of tool for this purpose, the shaded 

 parts I'epresenting the I'osin surface, coated with wax. The form of the edges of 

 the rosiu-covei'ed areas can be altered as desired, and thus the amount of action on 

 any zone can be in some measure controlled. Length of sti'oke and amount of side- 

 throw are also very imp)ortant factors in controlling the figure of the mii'i'oi-. Tools 

 of this kind serve admirably in parabolizing mirrors up to 36 or 40 inches in diam- 

 eter, when the angular apei'ture is not very great. 



(2) Parabolizing with One-Third-Size and Smaller Tools. In the case of 

 very large miri'oi's, when full-size tools are almost unmanageably heavy, and in the 

 case of mirrors of great angular apertui'e, in which the departure fi'om a sphei'ical 

 surface is great and is effected with difficulty with full-size tools, one-third-size and 

 smaller figuring tools may be used. The machine should invariably be employed 

 in this work, the ti'ansverse slide being used to place the tool in succession upon 

 the various zones. In ordei' to preserve the suiface of revolution the setting of the 

 transverse slide should be changed only at the end of one or more complete revolu- 

 tions of the glass. The i-osin S(iuares of the small tools should be somewhat softer 

 than usual, so that the surfaces of the tools can accommodate themselves slowly to 

 the slightly different curvatures of the successive zones. The squares around the 

 edges of the tools should be ti-immed, as before described, in order to soften the 

 action of the edges. The mirror should be tested very often, and the utmost care 

 taken to keep the apparent curve of the surface, as seen with the knife-edge test, a 

 smooth one, /. t., free from small zonal irregularities, at all stages of the parabol- 

 izing; this is not extremely difficult when the optician has become experienced in 

 the use of the transverse slide. 



The inirroi- of the 2-foot reflector of the Yerkes Observatory, which has a focal 

 length of only 93 inches, was parabolized in this way by the writer. Two small 

 tools were used, of 6 and 8 inches diameter respectively. The actual difference of 

 depth, at the center or vertex of thismiri'or, between the paraboloid and the nearest 

 spherical surface is almost exactly 0.0004 inch. This difference is unusually large 

 in this case, on account of the exceptionally great ratio of aperture to focal length. 

 This difference varies, in different mirrors, as the fourth power of the diameter of 

 the mirrors, and inversely as the cube of the focal length. In the case of Lord 

 Rosse's great mirror, in which the ajierture is 6 feet and the focal length 54 feet 

 (ratio 1 to 9) the corresponding diff'ei'ence at the center is only 0.0001 inch, very 

 nearly. In the case of the 5-foot mirror of the Yerkes Observatory, of 25 feet focal 

 length, the correspouding difference is about 0.C006 inch. This gives some idea of 



