in Relation to the Coma of Optical Systems. 361 



where OOi is at right angles to the plane yz. The ray 00! 

 meets the xz plane in \ Y and the image plane in J x . 



Fisr. 2. 



Then 



OO x PN IliQN, Tf 



/i ^ p =/j, 2 — ^ — (equation 1L. above) 



but when 00 x is not large, 



PN PN . ^ 



QN QN 



Q I - = qr = smA. 



Hence 



II, = 00,^ 



sin B 



/a sin A 

 But if there be spherical aberration present, 



JJ\ _ QJ _ NJm 

 Hi " QI " NJ ■ 



and we have 



/^osinB N,!^ 



JJj = 00, 



/* sin A * N X I ' 



if KKj be the ideal value of the image JJ X — KKi = Coma ; 

 and we have 



i_ OOj/^smB y,K \ / OO^psinB \ 

 i^VKK! p sin A* NJ i /"VKK 1 yusinA V 



KI / OO 1 _/£ sinB\ 

 + N 1 I\KK 1 ~~ fi sinAf 



or 



Coma KI _ /_00_, /* sin B _ \ 

 KKj ^"VKK, /^sinA V' 



provided the product of the -^w- and ^-y may be neglected. 



