26 Professor Airy on the Spherical Aberration 



y-l ly y'l n + l \ \b r/ a' 



\a r' 



n-l 



or putting X for ^—^ 



nr na 



taking the reciprocal. 



It is now necessary to find an expression for RD. 

 Now DP = — ;— . —J— a ; 



Twn . /f 12 x-r\ .a-hX ) x-r.a— 61" a' 



^ t a + r| .0^ ' a + rl . o'^ 2 



.-. KP (putting t for the thickness of the lens) 



= x-\-s—t- 



x—r.a-Vf 



As before, the terms depending on t may be neglected ; 



.-. KP-X + S ,„ , . - ; 



o + rl .6' 2' 

 . . KD = ^{KP' + DP-) 



/( ,o x + s.x—r .a — b\' „ , x-r\ .a-b\' ) 



V t a + r\ .b- a + r\\b- ) 



,2 r-{-s .x—r .a-b 

 I. a 



x—r.a-b\ A 



7- + S. x-r.«— 6|- a- 



