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XXI. On Ellipsoidal Lenses. 

 By R. J. Sowter, B.Sc, A.R.C.Sc* 



rj^HlS note extends the treatment of thin ellipsoidal or 

 J- astigmatic lenses by the author's method f , and gives a 

 simple solution for complex problems of the following 

 types : — " To determine the astigmatic pencil, after refrac- 

 tion of an astigmatic pencil by an ellipsoidal lens." And 

 " to find the ellipsoidal lens equivalent to two cylindrical lenses 

 placed a definite distance apart, with their axes inclined at 

 any angle." The method of treatment can be applied to 

 crossed ellipsoidal lenses, in contact, or separated, and is 

 applicable in general to astigmatic pencils. 



It has been shown by Prof. S. P. Thompson J, and by the 

 author independently, that for obliqnely-crossed cylindrical 

 lenses an important double-angled parallelogram of powers 

 can be constructed. This parallelogram is associated 

 with the resolution of a lens-power P into the two powers 

 P cos 2 0, P sin 2 0, at right angles. It is here " generalized/' 



Ffr. 1. 



If an astigmatic pencil having two focal lines at distances 

 u v from an ellipsoidal lens of focal powers A, B is refracted 

 by the lens, which is further defined in position with respect 



* Communicated by the Physical Society: read April 14, 1905. 

 t " On Astigmatic Lenses," Proc. Phys. Soc. vol. xvii. 

 X Proc. Phys. Soc. vol. xvi., and Phil. Mag. March 1900, 



