ON THE REFLEXION AND REFRACTION OF LIGHT. 263 



^ j , 



da? cfo 



dr 



dy dx 



(when 0? = 0) 



or since we may differentiate with respect to 

 fourth equations give 



, the first and 



in like manner, the second and third give 



^ ^/ 2 ~ ^ 2 dy* ' 



which, in consequence of the general equations (14) and (16), 

 become 



Hence, the equivalent of the four conditions relative to the 

 surface of junction may be written 



. M 



Ja? dii dx dy 



iJ e/ 



d(f) d^r d<f> t d^r t 



dy dx dy dx 



* (when# = 



(17). 



If we examine the expressions (13) and (15), we shall see 

 that the disturbances due to ^> and ( y are normal to the front of 

 the wave to which they belong, whilst those which are due to -v/r, 



