ON THE REFLEXION AND REFRACTION OF LIGHT. 285 



u t and v, the disturbances in the lower medium being expressed 

 by similar formulae in <^> / and ty r 



The two last equations of (17) give, since 



q 7 



A& = - = -, 

 9, % 



< and <, being accented for a moment to distinguish between 

 the particular values belonging to the plane (yz) and their more 

 general values 



= 6*' and < = 



The correctness of these values will be evident on referring to 

 the Memoir, formulae (20), (21), and recollecting that 



7 ' ' 



o = a = a t . 

 Hence the first equation gives, since x 0, 



j^ +1)(#) ; = ^_^ = _ (/ ,^ 1) ^. 

 dy dy ' dy 



ind cf)'--- 

 dy ' ^(^ 2 +l) %* 



Also the second equation may be written, 



And since we may differentiate or integrate the equations 

 (17) relative to any variable except a?, we get for the con- 

 ditions requisite to complete the determination of -^ and ^ y , 



2 -I) 2 ^ 2 >|r y Mwhena; = 0) ..... (29). 



Or neglecting the term which is insensible except for highly 

 refracting substances, 



