444 Prof. Ch. V. Zeuger on a new Spectroscope. 



It is obvious that ice-spar has the advantage of not absorbing- 

 large portions of the extreme red and violet rays, not refracting 

 so much as flint glass or bisulphide of carbon, while yet its dis- 

 persion is nearly as much as that of flint glass; it requires 

 therefore not so large an aperture of the mirror as flint glass or 

 bisulphide of carbon. 



Supposing the angle of the prism to be 10°, we obtain : — 



<f> = 0-302, 

 yfr = 6-342, 

 Az = 3-322, 

 S =65-31. 

 For 20°:— 



<f> = 6-604, 

 ^ = 12-684, 

 At = 6-644, 

 S =130-62. 



For more than 30° the reflecting mirror cannot give the whole 

 spectrum at once, unless it has an aperture of 195°'93 ; and then 

 it would reflect the rays on both sides of the prism, instead of 

 only one as shown in the diagram. 



In the case of the angle co being 10°, the refracting angle of 

 the prism should be nearly 211°, or three prisms must be used 

 of 60°- 70° to get the same dispersive power in a common spec- 

 troscope. 



If the angle be 20°, six prisms of 60°-70° nearly should be 

 used to get the same effect, and so on. 



If the angle of incidence be not equal to zero, the dispersion 

 increases to, very approximately, 



(7b sin % \ 

 1+ 2 Jcokn, 



and the preceding equations become : — 



, /, n 2 sin 2 i\ A /T . 



</> = (!+ — i — j.o.An, (I.) 



• /a i\/-i ft 2 sin 2 A A /¥T . 



^ V )( "2~/' "' " ( ] 



A- ( a . n\/\ . ft 2 sin 2 Z\ . /TTTS 



Al= \2f +l )\ l +~~2~~) CO ' An ' ' (IIL) 

 There is a practical difficulty in getting exactly cylindrical sur- 

 faces ; but it is possible to use spherical surfaces instead, if only 

 a narrow zone of the middle part of a convex or concave silvered 

 glass mirror be used. All the formula; quoted above may be 

 applied to it, and the dispersion augmented without fear of mar- 

 ring the exactness and definition of vision. 



