at a C(/lindrical Surjace, 57 



The power ot* impressino- convergence on a plane wave of 

 the diagonal strip of the lens is the same as the power of the 

 whole surface. A cylindrical lens can only properly be held 

 to have two powers, and it appears to me to be a mistake^ to 

 speak of the power of a cylindrical lens along a line making 



an angle (p with the axis as being — -^ sm'cj). 



If parallel light be allowed to fall on a cylindrical lens and 



a oround-olass screen be placed at a distance of from 



'^ ^ ^ /z, — 1 



the lens, then a line of images of the source of light, parallel 



to the axis of the cylinder, is seen on the screen. If a stop 



with a diagonal slit be now inserted and the screen be moved 



up close to the lens, a line of images out of focus, less intense 



than before^ and parallel to the slit is seen on the screen ; as 



the screen is moved away this line of images rotates and 



gradually becomes sharper, until when at length the screen 



reaches the distance the line of images is parallel to 



the axis of the cylinder and is perfectly sharp. This shows 

 that the slit has made no difference to the position of the 

 focus or to the power of the lens. As the screen moves 

 further back still, the line of images continues to rotate in 

 the same direction and gets more and more fuzzy or out of 

 focus. 



In a paper entitled '' On Astigmatic Lenses,'^ read before 

 this Society on Xovember 9th, 1900 *, Mr. R. J. Sowter makes 

 the same mistake, and speaks of the power of a cylindrical 

 lens in a direction OR making an angle with the axis of 

 the lens as Asin^^, where A is 'Hhe equatorial or focal power 

 of the lens."*^ He also speaks of the power of a piano-ellip- 

 soidal lens along a direction OR making an angle (f) with an 

 axis of the elliptic plane face of the lens as being =Acos^(/) 

 -i- B sin^<^, A and B being the two powers of the lens. 



My remarks apply as well to an ellipsoidal lens as to a 

 cylindrical. When the radiant-point is on an axis of an 

 ellipsoidal lens, the light produces two focal areas and tu o 

 caustics in the planes of maximum and minimum curvature. 

 A thin slice of the lens parallel to the direction OR will not 

 produce caustics, and the rays which pass through it will all 

 pass through the same focal areas as they would if the whole 



lens were employed. A screen placed at distances — or -^ 



would show the same sharp but less intense lines of images of 

 the source of light as when the whole lens was used. 



* Phil. Mao-. Feb. 1901. 



