1903.] The Theory of Symmetrical Optical Objectives. 271 



When the object is at oo, we can express the errors in terms of 

 those of the single system with a front stop. 

 Let the image due to the single system be at (4), then 



C 34 = B 34 = A 34 = A 12 , since A 31 + A 12 - = , and A 12 - = 0, 



Again 



2 4 _ 23 , 3 4 _ 2 H 34 _ 2 J 2 s 1 /TT ~n \ 

 2 2AT 2 074 SAM" CS + 4AM 1 ( 



K w - /8H 12 + D,, - 



^12 



therefore 



2 



n 2 



24 C 02 2 



_, K i 4 r K fiH ^ 



+ *** f ~ 7T- -I ^i2-p-Ui 2 + 'Di 2 - 

 J Ci 2 L 



When the object is at oo , 



D 



12 



* = c t { KM - j8H u + 1 2 DM } *, + (D 12 + A 12 ). 



From these expressions it is evident that the whole system will be 

 stigmatically corrected, if one component is so, and the additional 

 condition Di 2 + Ai 2 3 = is satisfied; the latter is the condition that 

 there should be no Distortion in the whole system. It is impossible, 

 under these conditions, to satisfy i = exactly ; but it may be shown 

 that in symmetrical objectives, whose aperture-ratio and field correspond 

 to those of modern Anastigmats, the combined effect of k and i will be 

 least when k = 0. If also e\ then e with sufficient approxi- 

 mation. 



u 2 



