CASSEGRAIN REFLECTOR WITH CORRECTED FIELD. 33 



Thin tenses. 



The atarration coefficients for a single surface are given in the Memoir, p. 161 ; 

 i ff = (l-n) B 3 , *# = 0, r^/ = 0, V = ( I -n) B, SJi = 0, 3Ji = 0, 



,V = (l-n)(-l+n-n a )B a , <V = -n"(l-n)B, 3J = -n(l-n'), . . (5) 



where I have written e = 1 e, so that e = for a spherical surface, and = 1 for a 

 paraboloid. 



Both origins are at the surface, and 



g = l, h = 0, k = (n-1) B, / = n, ) = , n = ju_,/ix + ,. 



The case of the thin lens, with origins at its surface, is derived from this hy an 

 application of equations (17), p. 160. 

 Write 



then 



* nl ' " \ n 



&& = 0, ^ = 0, 



i^h = -kn = -<), SJi = 0, ^ = 0, 



V = ........... ... ...... .... (6) 



It may be mentioned that B, the curvature, is positive when the convex face is 

 presented to the ray. 



It seems unnecessary to give the algebra leading to these expressions in all cases. 

 It is quite straightforward, and that for <J,&, which is relatively long, may be taken 

 as a model. From the Memoir, p. 160, we have, taking <5,K to refer to the joint effect 

 of the two surfaces 



f + P3JV} + k{$/ 



VOL. CCXIII. A. F 



