24 THE MODERN REFLECTING TELESCOPE. 



unsilvered surface is surprisingly great, a much more brilliant " artificial star " tlian 

 that given by the oil lamp is i-equired for the greatest refinement and accuracy 

 with the knife-edge test, especially in the cases of plane, pai'aboloidal, and hyper- 

 boloidal mirrors, in which there are two reflections from the unsilvei'ed surface. It 

 might be supposed that a larger pinhole could be used, and thus a more brilliant 

 illumination of the mirror surface secured ; but a large pinhole allows an a})parent 

 diffusion of light over the mirror surface, which obliterates all the more delicate 

 contrasts of illumination due to minute iiregularities of surface. With feeble 

 illumination of the surface the eye is entirely unable to detect slight contrasts, 

 which with brilliant illumination become sti'ong and unmistakable. When the 

 knife-edge test is used with an extremely small pinhole of between -j^-^- and -g-J-g- 

 inch in diameter, illuminated by acetylene or (what is much better) oxy-hydi-ogen 

 or electric-arc light, minute zonal irregularities are strongly and brilliantly shown, 

 which are entirely invisible with large pinhole or insufficient illumination. With 

 the arrangement of lens and diagonal prism (Fig. 1) either of the sources of light 

 named can be used without difficulty ; disturbances of the air from their heat 

 should be prevented by placing the light behind a partition with a window of thin 

 plate glass. 



With the best conditions of apparatus Just described, the degree of accuracy to 

 be attained with the knife-edge test is sur[)rising. With a mirror of 2 feet aperture 

 and 50 feet radius of curvature, the plane of the center of curvature can be easily 

 located to within y^^ inch, and with care to within half of that amount. With the 

 dimensions given, a change of ^^ inch in the radius of curvature corresponds to 

 a change of — ! inch in the depth of the curve of tlie mirror surface. There can 



° .'iOO.OOO . . \ 



be no doubt that zonal irregularities of surface of half of this amount are readily 

 recognized. 



We are now ready to consider the finishing of a spherical miri'or. As before 

 stated, a continuation of the use of the full-size polishing tool tends toward the 

 gradual elimination of zonal irregularities. This work is often slow and laborious, 

 however, for when the mirror becomes nearly finished, so that any zones, when 

 seen with the knife-edge test, appeal- as extremely slight elevations or depressions, 

 the improvement becomes exceedingly slow. The woi'k may be facilitated by the 

 local use of very small polishing tools upon protuberant zones. These tools are 

 usually from 2 to 4 inches in diameter, and consist of squares of rosin upon a basis 

 of brass ; their faces are waxed and cold-pressed, and the squai-es around their 

 edges are tiimmed in order to soften or blend the action of the edges ; small local 

 tools with their surfaces trimmed as shown in Fig. 13 (in which the shaded parts 

 represent the i-osin) ai'e excellent for the purpose. These local tools are used as fol- 

 lows : the positions and width of any pi'otuberant zones are carefully determined by 

 the knife-edge test, and the glass is replaced on the rotating turntable ; stationaiy 

 pointers are clamped to the machine, and ovei'hang the glass so as to indicate the 

 exact positions of the zones ; the surface is painted all over with louge and water, 

 and the optician works the small tools on the high zones by hand ; the rubbing 

 is done on each zone duiing several revolutions of the glass, the length and direc- 



