Mr. J. Bridge on the Oblique Aberration of Lenses. 

 where 

 A= 



349 



B = 





+ 



2?n 2 + ?w 3m + 2 



ru 

 m? 2m + 1 

 n 



+ 



+ — 

 n 2 



r n u 



The expressions in [ ] are symmetrical with respect to y and z, 

 so that the expression for - is found by writing c and z for b 



and y outside these brackets. 



Putting c=0, that is, supposing the ray, when incident, to 

 be proceeding to a point of the plane of Q where it is cut by the 

 plane of xz, we have 



V__b_ b t /m — l 1 \ 

 v u u m\ r u ) 



[A(j,«+.-) + 8B 8 J! + ( m+ l)^]. 





m — 1 



2mn 



It is obvious that when b = 0, c = 0, the above gives the ex- 

 pression for the aberration in the same form as that in Encyc. 

 Britt., art. Telescope*. I have found that form more convenient 

 for the calculation of a large number of cases than those in Cod- 

 dington. 



It is satisfactory to find that these expressions very easily yield 

 those for particular cases as found in Coddington and elsewhere, 

 as follows : — 



Primary and secondary foci of a small centrical oblique pencil. 



For the primary focus, that is, for rays incident in the axis of 

 y (c being supposed =0), 



MK the plane perpendicular to the axis at the focus for a 

 * Clairnut is, I find, the author of this form. 



