44 Lord Rayleigh's Investigations in Optics. 



r' — r, s r = s. The aberration then varies as 7, and cannot 



vanish. u v 



If the lenses be of the same curva- Fig. is, 



ture and be turned opposite ways a ^ 



(fig. 18),/= -s, /= -r: The aber- Jj ^ . 



ration is proportional to // ^ 



c ^ ,+ <;-7) +2 ^ ,+c )G + s -) ; 



or, on substitution of the approximate value of 7 ? 



where, as before, 



, 11 cos d>' 



a ■=■ — • 



COS0 



Thus the combination is aplanatic, independently of the value 

 of u y if 



i^l=p£L (16) 



By supposing the light to be parallel between the lenses, we 

 obtain (13) as a particular case of (16). 



We will next investigate the aberration in the case of a 

 prism with flat faces on which divergent or convergent light 

 falls at the angle of minimum deviation. 



From (4), with notation similar to that employed above, 



fc-*£*)-'S(' :s £*> • • • <"> 



and 



y':y = u' + l: u f , (19) 



I denoting the length of the path of the axis of the pencil 

 within the prism. 

 If y be neglected, 



whence 



c 2 _ ftc 12 iic' 2 _ c 2 



u u' u' + l~ v' 



. . (20) 



V u f + l 

 u v! J 



• • (21) 



