398 



Mr. S. D. Chalmers. 



[Jan. 3, 



Thus, if the single system be corrected for spherical aberration and 

 curvature, the spherical aberration of the combined system is given by 

 J (cjb 4 + a 4 d 4 ). It is evident that this quantity will also be very small. 



These results can be extended to the case of rays which do not lie 

 wholly in one plane. It will be assumed that the image of the stop 

 formed by one member is perfect, the errors thus introduced being of 

 the same nature as those discussed before. 



Let PQ and B.S (fig. 3) be two diameters of the stop, their image 



PIG. 3. 



points in the plane 4 being p 4 q r 4 s 4 ; let parallel rays a and b pass 

 through p 4 and # 4 respectively, and let the axial plane parallel to them 

 cut plane 5 in OE; similarly parallel rays c and d pass through r 4 and 

 S 4 and are parallel to the axial plane which cuts 5 in OF. 



It being assumed that these pairs of rays intersect on the focal 

 plane 5, the rays a and b will intersect on OE, say at E, and similarly 



