38 THE MODERN KEFLEOTING TELESCOPE. 



the actual amount of glass which must be removed by the figuring tools in 

 parabolizing. 



CHAPTER XIV. 

 TESTING AND FIGURING CONVEX HYPERBOLOIDAL MIRRORS. 



The methods of figuring and rigorously testing convex hyperboloidal mirrors 

 are now so thoroughly developed that the reflecting telescope can be I'egai'ded as a 

 universal photographic telescope of the highest class, capable of giving, at the 

 focus of the paraboloidal mirror of large angular aperture, the finest photographs 

 now attainable of large and excessively faint objects such as the nebul* in general ; 

 while by the addition of a small convex mirror a great equivalent focal length 

 is obtained for the photography of bright celestial objects requiring large scale, 

 such as the moon, the planets, the dense globulai' star clusters, and the annular 

 and planetary nebulae. The convex mirror of course serves as an amplifier, and 

 possesses the great advantages over a lens used for this purpose that the perfect 

 achromatism and the high photographic efficiency of the reflector are letained, and 

 that the mechanical arrangements are very compact and economical. In oitlei- 

 to give perfect definition the convex mirror must be an hypei'boloidal one. 



The writer has recently made two convex miri-ors of different curvature, for 

 use with the 2-foot reflectoi-. These give equivalent focal lengths of 27 and 38 feet 

 respectively. 



Fig. 14 shows the arrangement of mirrors employed in the 2-foot reflector 

 when used as a Cassegrain ; a small diagonal plane mirror is used at m, to avoid 

 the necessity of a hole through the center of the large concave mirror. P is the 

 paraboloidal mirror, with its focus at /; H is the hyperboloidal mirror, the secondary 



Fig. 14. 



focus or magnified image produced by the combination being at JF; the point c is the 

 center of the hyperboloidal surface. Calling the distance fc^^p and the distance 



p' 

 cm + mF =^p', then — represents the amount of amplification introduced by the 



convex mirror. The radius of curvature R of the spherical surface to which the 



convex mirror is ground and polished preparatory to hyperbolizing is found with 



112 

 sufiicient accuracy for all practical purposes by the formula ^""r ^^'^''^e 



p'-p 



