34 



THE MODERN REFLECTING TELESCOPE. 



PARAeOLOIOAL 



Fig. 9. Testing a Paraboloidal Mirror ai its Focus. 



If F be the desired focal length of the paraboloidal minor whose serai-diameter 

 is R, then the spherical surface which is fine-grouud and fully polished preparatory 



R2 



to parabolizing should have a radius of curvature of 2F -|- -—^. This is because 



parabolizing is done by shortening the radii of curvature of all the inner zones of a 

 mirror, leaving the outermost zone unchanged, as shown in Fig. 10 ; this is a far 

 easier and better method in pi-actice than to leave the central parts of the miiTor 



Fig. 10. 



Ku;. II. 



unchanged, and to lengthen the radii of curvature of all of the outer zones, as shown 

 in Fig. 11. 



Let us now suppose that the concave mii-ror shown in Fig. 9 is a spliei'ical one 



R2 



with radius of curvature 2F + — -, where R is tlie serai-diaraeter, and F is the 



4 F 



distance cm -\- mf\ from the center of the mirror surface to the plane of the pin- 

 hole and knife-edge. If the spherical surface be now viewed from the point /'with 

 the knife-edge test, it will appear to stand out in relief, in strong light and shade, 



Fig. 12. 



as a surface of revolution whose section is that shown in Fig. 12, the height of the 

 protuberant center depending upon the angular aperture of the mirror. The reason 

 for this appearance is readily seen by refei'ence to Fig. 10. To change the spherical 

 surface to a paraboloid, the protubei-ant center nuist be I'emoved by the use of 

 suitable polishing tools, until the surface, as seen with the knife-edge test from the 

 pointy, appears perfectly flat, /. e., the illuminated surface darkens with perfect 



