444 THE THEORY OF OPTICAL INSTRUMENTS. 



whence we get, as the value of V to terms of the fourth order, 



' + M.') (.. + &&) (a, 1 + 6,') 

 ')(.' + M(. f + ^) 



fl(tf+V)(A+W 



f n 

 M 



'e the coefficients in the general equations (18), (19), (2<>), (2), (-2:]) are 

 as follows : 



a=o, s=*^, 6=0 , 



