346 Mr. J. Bridge on the Oblique Aberration of Lenses. 



and 



i, v ./M m— 1 y\ 



\m ??i r/ 2 V?" s/ 

 Substituting for ij 2 and ~2, 



u.= u,'m — (m — 1)- + (/i + ?« — 1. — ) 



^' s m s \ r / 



m-1 /1 l\y 2 + 

 " ' 2m \ r s / s 



2 + z* 



y jm-Vf /l , 1A .y a 



r 2m V r s / 



By substituting for /// and v', and collecting, this becomes 



jn-ir, „ Jm .m—\ 2m 2 — 2m + l m 2 — m + l\ 



m— IT, „ c „Ym 3 -2m 2 + m + l 3m 3 -5m 2 + 2m 



+ y '-&d> +Z) \ ? rh 



3m 3 — 4m 2 + 2m — 1 m 3 — ?« 2 + m\ 



+ ^ 7 3 / 



_, ,/m 2 — m — 1 2m 2 — m— 1 m 2 \ 



For write — , then 



^+^)l+== i -'(F-l-)("+ s =i-f) 



