Mr. J. Bridge on the Oblique Aberration of Lenses. 347 



y 2mn U + V r 2 



m 2 + m + l m 3 —m % + 



+ 







, o — ; — ( m + i »* 2 \ 



+ 2./*y + wrl + — ) 



\ r n } 



+ /?+?(»+ 1) J- 



Let u be the distance AQ along the axis of the focus of 



direct pencil of rays before incidence; v the distance Bq of the 

 focus of an indefinitely small central pencil of these rays after 

 refraction by the lens. Let planes perpendicular to the axis of 

 the lens be drawn through Q and q, and let b, c be the coordi- 

 nates in the directions of y, z of a point in the plane of Q 

 towards which a ray is proceeding before incidence ; v , \ the 

 point in the plane of q towards which the same ray proceeds 

 after refraction. Then 



_ y—b 



■■^-»m 



fi,= 





2* 



V z—v _ y— b 



2s 



u >ii m \r n)\ u +W l ' r ) 



*+-*& 



b III — 1 



u 2mn 



[p.y+^-fSy+^-S^+^j 



