6*2 Mr. A. Whitwell on the Lengths of th 



But v 2 = fjbu and — — - = a( — — — Y 



By eliminating u we find 



v — ^^ 



?' 2 (yCt — 1)4" ^'l 



and substituting this value of t^ in (2) we get 



L = A 





or 



/,= 



/l ' 



that is the length of the tangential focal line 



= the tangential aperture x distance of the line from the 

 surface x power of the surface. 



2. To find the lengths of the focal lines of a 

 sphero-cylindrical lens. 



Figs. 3 and 4 represent an elevation and a plan of the 

 incident and refracted rays at the second or spherical surface, 

 the corresponding rays at the first or cylindrical surface 

 being represented in figs. 1 and 2. 



Let q q' be the centre of the spherical surface the radius 



of which = — r 2 . 



(a) The axial focal line. 



The two symmetrical rays, represented in elevation by the 

 line a'f\ which were the refracted rays at the cylindrical 

 surface, are now the incident rays. After being refracted at 



