CASSKGHAIN KKH.I-.rHMl WITH CORRECTED FIELD. 57 



In the same way, for tin- fir-t l.-ns ..(' the corrector, the subsequent normal scheme 

 ()',.. .O, is V, h'\ /'./' ={+'(>: , 7U-J68; - 1 '345856, +'980009}, which 



rivi-s for the first system. !>( \\.-.-n O 4 ...F 7 



Coeffificnt, q,. Coefficient, q 4 *. 



s +-65H4!)<; + -1898 1 7 



= + -479503 



* * 



+ 479503 



* * 



* * 



The preceding normal aclicnu- < > < >, is 



( g j, ; /-,/} = { + '141675, +3-326581 : -'208333, +2'1GGGG7}, 



wliich gives 



g* = + '020072, 2gk = - '059031, F = + '043403, 



gh = + '471294, gl + hk = - '386074, kl = '451388, 



A' = +11-066161, 2/i/= +14-415196, I 3 = +4'694446, 



so that with the values of grVy 4 + W.i, which are 



Coefficient, q 4 . Coefficient, q 4 . 



s =l - -006604 +'026897 



2 +'067934 



8 ..... * * 



we find the contributions of the first lens ()... F' 7 



Coefficient, q 4 . Coefficient, q 4 a . 



$,G = . . . . -'004143 + '000539,9 



^G = . . . . -'029340 +'012676,2 



S 3 G= .... +'906201 +'297642,1. . (32) 



With the values q 4 = +2'3734, q = +4'8325, the joint contribution of the two 

 lenses in respect to the terms q, q a would be, from these expressions, 



J,G= ...-'033578, J a G= ...-'356618, ^G = ... +2'136186. 



Hence if new values of ,, q 4 , q, are to satisfy the conditions exactly, these are 

 determined by the equations 



Coefficient, . Coefficient, q 4 . Coefficient, q 4 . Coefficient, q. Coefficient, q*. Constant. 



= -'158998 -'004143 +'000539,9 -'003424 -'000438,5 + '060587 



0= * -'029340 +'012676,2 -'023006 -'010587,6 +'369218 



0= * +'906201 +'297642,1 +'885540 -'255667,4 -2'009113 . (33) 



VOL. COXIII. A. I 



