THE THEORY OF OPTICAL INSTRUMENTS. 



443 



H 



W for the primary image ............ (24), 



p7H -- p-,= U+ W for the secondary image ........... (25). 



we find 



The condition of distinctness is U=Q. 



That the image of a flat object may be flat as well as distinct, 



U=0 and TF=0 (26). 



Form of the CJiaracteristic Function for a Spherical Refracting Surface. 



Let the planes of reference pass through the p/ 



principal foci. 



Let BC=s be the radius, then 



AJ}_ /M T)A . W 



.ii J.7 j j^yj-2 ~~ 



Li, , ~ r*i /* ~~ /^l 



II n 



If the co-ordinates of P, are a lt b l} -, 



P7 P'z^ 



1 ^2> ^2> ~ > 



P a, 6, z, 

 and if P l P = r l and PP s = r 2 , then 



F- /*!, 



under the condition that F is stationary with respect to variations of a and 

 b, when 



This gives the following values of a arid b : 



6 = 6, + b, + XA + XA + &c., 



when 



X, = 



X, = 



* /*! 



a,* 



562 



