19 



ix iu 



+ 2 



3a 3u 



3a 3j^ 

 + "^ 3z Sz • 



3a 3m , 

 + 3^ J^ "^ 



3a 3m 



3a 3m 



Jy 3x ' 



„,. ... 3a 3« 

 + 3^37 ■•■ Iz"^' 



(V) 



3a 3m 



**" E" 3.T 



3a 3m 

 3x 32 



Tlie equations marked (C/), contain the laws of reflexion and 

 refraction, ordinary and extraordinary ; since, when put by means of 

 (C) under the form 



(W) 



and combined with the relation ccl ■\- fil -\- yl ■= 1, they suffice to 

 determine, for any given forms of the functions t;, , v^, and for any 

 given directions of the incident ray and of the tangent plane to the 

 reflecting or refracting surface, the cosines a^ , ^2 , y^ j of the angles 

 which the reflected or refracted ray makes with the axes of coordi- 

 nates, and the value of the multiplier X ; observing that the ratio 



•■ (I) +^. (!)+'■© 



9 % 



