1880.] and Befraction of light. 331 



Let I, m, n; l^, m^, n^; I', m, n be the direction cosines of the 

 normals to the incident reflected and refracted waves respectively. 



a, /3, y; a^, /3^, j^; a, ^', j the direction cosines of the directions 

 of vibration in these waves, k, k^, k the amplitudes, V, V the 

 velocities in the two media. 



Then we may represent the disturbances by 

 j,flx + mi/ + nz 



U = (XKJ ( • t 



V 



, ,„fl'x + 7711/ + n'z 



, , , .fix -\-77fiy ->r7%Z \ 



U=0. Kf^ p tj 



The equation u = u' when cc = gives 



.fmy + nz \ , ^fm,y+77,z \ 



m y + n z 



Whence 



n _n^ _ 7i' 



and CLK + cfjATj ='xic .\ 



Similarly /3« + ^S^^:, = /3V > (4). 



7/c + 7^/Cj = 7V J 



And equation (2) gives, 



dw dw dv dv 

 dt dt dt dt 



+ 0K \y{W- m-x) K + {1^/3^ - m^oi^K^) - — (Z'yS' - m'aV) [ . 



Now let the intersection of the incident wave-front and the 

 plane ic = be taken as axis of y, 



m = 0, therefore m^ = m' = 0. 



