Prof. Ch. V. Zenger on a neiv Spectroscope. 443 



p-g+l)(»-l)«-(»-l)«! 



If/ be the focal length of the mirror, we have 



P / A 2 l 



2=f^ nd p=f 



and we finally obtain : — the angle of dispersion 



<l> = G).&n; (I.) 



the angle of reflection 



i=z (w +1 ) (B ~ 1)a,j ■ • • • ( n o 



the difference of the angles of reflection for the extreme red and 

 violet rays 



Ai=(^ + l)«».A», .... (III.) 

 the increase of dispersion being 



J=(«/+i) (iv._) 



The angle of aperture required for the reflecting surface of 

 the mirror becomes 



S=^(n-l)a> (V.) 



The equations (I.) to (V.) give all the dimensions for the 

 construction of the spectroscope itself. 



Suppose the prism to be of crown glass, flint glass, sulphide 

 of carbon, or ice-spar, we obtain : — 



Crown glass. CS 2 . Flint glass. Ice-spar. 



n h . . 1-5447 1-7025 1-6711 1-6833 

 n b . . 1-5243 1-6182 1*6277 1'6531 



An . . 0-0204 0-0843 0-0434 0-0302 



If the increase of the angle of dispersion be <£, or tJt = <£=21, 

 the focal length of the mirror /= 2 centims., j» = 4 centims., then 



the distance is a — 40 centims. ; -„ — 20 ; and the other values may 



be calculated as follows : 



— 







Crown glass. 



cs 2 . 



Flint glass. 



Ice-spar. 



<j> . . 0-0204 co 



0-0843 co 



0-0434&) 



0-0302 » 



yjr . . 0-4284o> 



l-7703o) 



0-9114&) 



0-6342 w 



At . . 0-2244O 



0-9273o> 



0-4774&) 



0-3322ft) 



S . . 5-243ft> 



7-025&) 



6-711&) 



6-531ft) 



