INTENSITY OF REFLECTED AND REFRACTED LIGHT. 



407 



9. We adopt the following notation in addition to that already used : 



«. /3 are the motions parallel to x and ?/ of a particle in the upper medium. 

 a, ft do. do. in the lower. 



I, R, T are the incident reflected and refracted vibrations. 

 I^ and 1j the corresponding normal motions. 



Occasionally 8x and 8y will be replaced by 



8 of cos (p + 5y sin (f) 



di/ cos (p — 8 a/ sin (p 

 respectively, when combined with a function depending on the incident wave, 

 and by 



8 a!' cos cp + 8^' siacp 



8 x'' sia (p — 8 y cos cp 



when combined with one which depends on the reflected wave. 



From the values of 8 x and 8p, it is clear that the axis of a/ is the line of 

 transmission at incidence, and that of of' at reflexion. The vahies of I, R, are in 

 general not required, but for the purpose of fixing the ideas, they may be con- 

 ceived to be as follows : 



I = a cos (ex +/y + ct) 



R = 6 cos{—ea;+/y + ct+g) 

 T = c cos («, X +/i/ + ot + k) 

 1, = Ae-^" cos(fy + ct + ri) 



If it should be thought that these values belong only to a particular case, I 

 would remark that, from the linearity of our equations, the results which we de- 

 duce for one circular function, are equally true, mutatis mutandis, of a series of 

 such functions. 



10. The values of «, ft »„ ft , deduced from the figure, are : 



a, = I — R sin^ + I, 

 /3 = (I + R) cos (p 

 a,= Tsm(p'+T, 

 13,= T cos cp' 

 The equations of motion in the upper mediimi are : 



!|- = 2 f<pr+-^(8x8c^ + 8p8i3)^8^^+Fcc 



= 2 (^(pr + ^SA 8«+-^^8x8y8^ 







= 2 (^cpr+i^8f^ 8^+2i^8x8,j8a 



