442 Prof. Ch. V. Zenger on a new Spectroscope. 



mQO = am -\-ao = a+p, if a be the distance of the prism from the 

 mirror, and p its radius of curvature ; we then obtain : — 



— = 7 - 1 Tr> or i=(-+l) (»-l)». . (2) 



p (n—l)cQ \r J y ' v ' 



For the extreme red and violet rays we get ; — 



^ = (- +1 )(n h — 1)a), i h —i b = r- +\)(n h —n b ) G)p 



fe=(|+l)( n *-l)fi>, i-ri^ + lJA».». . (3) 



The triangle hlm } contains the angle yjr of the red and violet 

 rays after the reflection from the mirror ; and it measures the in- 

 crease of dispersion produced by the reflection from the cylin- 

 drical surface. 



If, therefore, yjr is known, the ratio between the angles <£ and 

 yfr gives the real increase of dispersion produced in that way. 



The angle hlm } , as an exterior angle of the triangle lm m, is 

 hlm l = (j) + 2i; and 2i being the exterior angle of the triangle 

 hlm lt we obtain:— 



^r + ^ + 2i = 2f„ 



, * r '+*=2(t 1 -t), 



1,-1 = ^—^- (4) 



Combining (3) 



and (4), 



2 



we get : — 







yjr + tj) 



2 



-6.+0- 



.Aw, 





* = 



= w . Aw, 







^ + <£ = 



•«e+>)- 



, Aw, 





^- 



■£■♦>> 



.Aw; 



(5) 



■f /2« ,\ 



J == t +1 ) • ( 6 ) 



To receive the spectrum on the surface of the mirror the 

 angle p must be sufficiently great ; it is given by the equation 



P = i-{r-co); . (7) 



p = i— (n — l)(o, 



