60 



Mr. A. "Whitwell on the Lengths of the 



1. To find the lengths of the focal lines of a single 

 cylindrical surface. 



Fig. 1 represents an elevation and fig. 2 a plan of the 

 system of rays. The light is supposed to pass from left to 

 right and the index of refraction of the second medium = /j,. 



Distances measured to the right of o or o' are positive. The 

 axis of the cylindrical surface is vertical and the arc b, o, a, 

 represents the trace of the surface on the horizontal plane. 

 hi = o'a' = the semi-aperture parallel to the axis of the 



cylinder or the axial semi-aperture. 

 7* 2 = oa = ob = the semi-aperture at right angles to the 



axis of the cylinder or the tangential semi-aperture. 

 a'c' is the elevation and ac, be, the plans of two normals 



to the cylindrical surface. 

 r x = the radius of the surface. 



u = o'd' = the distance from o of the point in which the 

 incident rays cut the axis of x. 



(a) The line parallel to the axis of the cylinder ; this may 

 be called the axial focal line. 



Two incident rays symmetrical with respect to the piano 

 of fig. 1 are represented in elevation by the lines a'd' and 

 in plan by the lines ad, bd; the corresponding refracted rays 

 are represented in elevation by the line a 1 f g', and in plan 

 by the lines a eh and bek. 



The incident ray a'd', the refracted ray a'g', and the 

 normal a'c are all in one plane, and as was shown in the 



