CASSEGRAIN REFLECTOR WITH CORRECTED FIELD. 47 



Write 



O,O 4 = <*3, O 4 O. = d 4 , 



PA = "i, 0,P s = 7i 3 ; P,0 4 = v,, 4 P 6 = u & ; fi. = v tt O.P 7 = u lt 

 also 



F,), x 4 = l- 



then we have the equations 



0, 



XjVjttj = 0, 



= 0; 



and the linear magnification is equal to 



-(ttj/W, ).(,/'') (W"*)- 



Varying the system with respect to 1/n, the refractive index, and making a 

 condition that v,, M 7 , and the magnification are unchanged, we have 



= 0, 

 = 0, 



and 



/M 6 Arj/t's = ; 



eliminate A?< 3 , Ac & and this gives 



Ai, (!/,+ !/,) 

 eliminate Av 3 , A7< 6 and we have the two equations 



A-c, 

 finally 



or .... (23) 



thus, knowing c 3 , fi 6 , r,, and choosing, say, * we determine in succession , the value 

 of the ratio, Ug, 6 , x 4 , v a , 7 , x a . But this choice and order is open to modification. 

 For example, if we take, as on a subsequent page, 



t= +'9261, dj= -K01G94, tt3=+r6000, x 4 =+l'4286, 



