64 Mr. A. Whitwell on the Lengths of the 



Now 



1 1 /*-l 

 - + - = 



U l\ 



1 



^ 



r 3 



-2 and _ 1 + L = ( ^_ 1) (1_I). 



nd ^.J^Y 



^3 \ n / 



or 



', 



(^)- 



.*. the length of the tangential focal line of a sphero- 

 cylindrical lens = the tangential aperture x distance of 

 the line from the lens x glass to air power of the 

 cylindrical surface. 

 The results in 2 of course apply to a piano-cylindrical lens. 



3. To find the lengths of the focal lines of two piano-cylindrical 

 lenses in contact } the axes being crossed at right angles. 



Fig. 5 is an end elevation of the system of rays looking 

 in the direction of propagation of the light, that is from 

 left to right, and fig. 6 is a front elevation. The axis of the 

 first lens is vertical and its focal length = f x . The axis of 

 the second lens is horizontal and its focal length = f 2 . 

 The semi-apertures are 7i t and h 2 as before. Two rays, 

 symmetrical with respect to the plane of fig. 6, incident at 

 a'b' after refraction by the first lens will intersect at the 



point c' at a distance from the lenses = o'v = v x and at a 

 distance from the axis of x = c'v' = ■— . 



The second lens will bend these rays downwards to the 

 position a'd', I'd'. The deviation c'd' will be = ^ since 



h ^ 2 



-j is the deviation per unit of length along the axis of x. 



