30 Professor Airy on the Sjfherical Aberration 



If NL, the breadth of the first image, be called /3, OM, the breadth of 

 the second, /3', then 



a—b i , \ ^ 



^=^^^^A{e-g)a, or a=^j^-^y 



and ^'= ^ (e-g) ■ a, or a= YJ^^Z^g) ' 

 Substituting these values for a, 



f /n + 2 , 2n + 2 — — , 2W + 2 J ny \) /3^ 



/ /n+2 . 2M + 2 —— 2M + 2 ^ ,^ ny- M /3" 

 {e-gf\ n 71 ° n ° 4(w— l)-/j 2 



We shall denote the quantity 



/ /« + 2 . 2« + 2 2W+2 , 2 , ny \ 



(e-^)2 V n n * n * 4(n— l)v 



/• 

 bv the letter V, and shall put ?7 for -i. + F: hence, we have 

 •' n 



z^Z-^A"- A)-Z' .7::^ .v.'-. 

 .= S-|(.-^)-f.t/.f, 



