28 Professor Airy on the Spherical Aberration 

 ,, 1 1 n nY d- 



1 n nY a- n-1 /I l\- /l , n + l\ a^ 



which, since 



1 n n-1 . M- 1 1 1 11 l,a-^_l^, a- A 

 s 





1 I a-yi nY a^ n—l /\ l\"/l , «+l\ "" 



whence iJM= S- ^ («-^) " ^ • ^^^ 



n- 1 



^■(i-^yc-^')^ 



which, putting for Y its value, and substituting for x in the term 



r + s .x — r .a — 61° 



^ ifi ^^ ' 



x + s.a+rl •*°'*' 

 gives RM=Z- ^{a-A) 



«2 I }^ «>' _L " - ^ /I , ll ■ 1 , M - 1 1 ll 1 ?< + 1 \ 



Vs ^ r/ yg ~ yj/ / n-l 1 \ y- 1 "-1 \] "" 



/I l\/l 1\ * V nr " njJ \nZ ns/l2' 



\s ^ Z)\r^ a) ^ 



