522 



On Skew Refraction through a Lens, etc. 



For the 0° ray this is 



1 



mT 

 d6*n' ' 



and for the 180° ray 



1 



We have 



d m' 



leu 



1 dm' 

 n' TO 



n 2 dO 



m an 



d 2 m 



the &c. consisting of terms which vanish at 0' and 180\ We thus 

 obtain at 0°, z = 8*554, and at 180°, z = 3'530. 



As the curves are symmetrical about the axis of //, the first differential 

 coefficient of y that does not vanish must be of even order. It is 

 accordingly of the fourth order at the two points thus determined ; 

 and the curve is sensibly straight for a considerable distance. 



If, instead of sections of constant z, we take sections of constant f 

 through these two points, the conclusions remain true ; for, by Meunier's 

 theorem, the radii of curvature in the two sections are in a finite ratio. 

 From the above values of z, together with the equations of the rays, 

 Ave can deduce the values of y, and then transform to ?/ (. We thus 



find— 



for e = o c , i =11-94, 



for = 180\ C = 4-86, 



results which are illustrated by the sections for 



i = 12, C = 4, and { = 6, in Plate 9. 



