Mr. R. J. Sowter on Astigmatic Lenses. 



241 



at right angles is equal to the sum of the minor and major 

 powers, L e. A + B. 



The cornea of an eye affected by corneal astigmatism may 

 be taken as an illustration of an ellipsoidal lens, for the curve 

 of equal thickness or natural aperture for the asymmetrical 

 corneal surface is an ellipse. 



For a spherical lens, which is a particular form of ellip- 

 soidal lens, the natural aperture is a circle, the powers are 

 equal in all directions, there is a focus and no focal interval. 



A cylindrical lens is a particular form of ellipsoidal lens, 

 it produces only one real focal line and has an infinite focal 

 interval. 



For a cylindrical lens the natural aperture is an infinitely 

 lono- rectangle, fig. 1 a, and the lens power in any direction 

 is oiven by the inverse square of the radius vector. 



Thus if A is the equatorial or focal power of the lens and 



OA = a, then A= -=. 

 7 a* 



Also 



-p 1 cos 2 $ . 

 K=-s= — r- [ - = Acos 2 <f). 



It is evident then that an ellipsoidal lens may be repre- 



