1897.] near the Foctis of a Telescope. 263 



while the second is 



^e 4 | \cos(ji-l)z-i8m(/i-l)A ~ 



(where .-f-±^) (5) 



The ratio of the first integral in (4) to the second is therefore of 



the order »/ , i.e. of the order — — , so that the first integral 



v z V z 



may be neglected. We have then approximately 



4 ~ )^/z~2' 



V^iS-'-'S-*)! 



=-i-«v /K s{ i(l - p - Q)+p - Q 



The rest of the integral (3) is of an order which has already been 

 neglected. Hence, by substituting the value of (3) in (2), we have 

 approximately 



giving 



V = \j« (*) + 4^1(1 -P- Q)cosfiz+(P - Q) sin fizl , 



Vi= \ + / K | (i ~ p ~ Q) sin ^ " (p " Q) cos ^4 ' 



or, since U x = sin fxz — V x , U., = V — cos /jlz, 



