58 



chianglng Aa, AjS, to their expressions (P*), and observing that the 

 general relation (a + Aa)* + ((B + A/S)* + (y + AyT = «* + /3* 

 + 7* = 1, gives here = 2 Ay + (Aa)* + (Aj8)* + (Ay)*, so that 

 the terms AaAy, AjSAy, Ay*, in the developments of 



[ - 1]- [ '■ '^l 



may be neglected, as being of the third dimension. And if, for fur- 

 ther abridgment, we put x, y, instead of A.r, Aj/, in the equations 

 (Q*) to denote the coordinates of the intersection of the near ray with 

 the plane of a'j/, that is, with the plane of aberration passing through 

 the principal focus, and denote the partial differential coefficients 



rr "PW 'i^w_ ^jv^ 

 1^' 1^' 343"' 3-3^ ' 



by Ay B, C, D, we shall have 

 and by elimination, 



1/' having the same meaning as before. 



(S«) 



(T-) 



