THE MODERN REFLECTING TELESCOPE. 



39 



For example, let the focal length of the paraboloidal mirror P, Fig. 14, be ten 

 feet; let fc = p — 2 ft. and cm + mF — p' = 8 ft. Here-^ = 4 ; the image of 

 the moon or othei- celestial object produced at F is therefore four times larger in 

 diameter than it would be at f, the focus of the paraboloid ; and R = , ^ = 64 



inches. 



The method of testing the convex mirror while hyperbolizing it is shown 

 in Fig. 15. The illuminated pinhole is placed very near the axis at F. The diverg- 



PARABOLOIOAL 



PLANE 



.„=.:iv^::-:::: 



Fig. 15. UlAURAM iLLUSlKAlUNli TESIINU Ot HVI'tkbOLUlUAI. MlKROK. 



ing cone of light strikes the small plane mirror, then the convex, then the lar'-^e 

 paraboloid, whence if all of the mirrors are finished and are well adjusted or coUi- 

 mated, the light is reflected in a parallel beam to the large plane ; returning, the rays 

 are brought to a focus very near the axis of figure and in the plane of the illuminated 

 pinhole. All of the mirrors except the convex one are silvered. The convex spheri- 

 cal sui'face with radius of curvatuj'e R, as above described, when viewed with the 

 knife-edge test from the point F, presents the same geiiei-al appearance of a smoothly 

 curved surface of revolution, in strong light and shade, which a paraboloidal surface 

 presents when similarly viewed from its center of curvature (see Fig. 8, p. 3;^). 

 All that is necessaiy to produce the hyperboloidal surface is to soften down, with 

 suitable polishing tools, the apparent broad protuberant zone between the center 

 and edge, until the mirror, as seen from F, appears perfectly flat; i.e., until the 

 illuminated surface is seen to (hirken with absolute uniformity all over when the 

 knife-edge is moved across the focus. This hyperbolizing may be done with small 

 local oi' figuring tools, or with a full-size tool so trimmed as to give an excess 

 of action on the broad zone a, or (what is usually best) by a condiination of 

 the use of both kinds of tools. 



As in the case of the paraboloid, it is neces.sary in this test that all of the 

 miri'ors be lined up or collimated with care; otherwise the surface of the convex 

 mirror will not appear as a surface of revolution, and cannot be pi'operly tested. 

 The axes of the paraboloid and hypei-boloid must coincide, and the face of the 

 lai'fe plane miri'or must be at right angles to these axes. These adjustments are 

 made by means of an extension of the method of collimation described in the pre- 

 ceding chaptei-, p. 35. First the paraboloidal mirror is adjusted so that its axis 

 intersects the hypei'boloid at its exact center or vertex ; in making this adjustment 

 fine threads are stretched diametrically across the cell of the convex mirror, this 



