530 The Electromagnetic Theory of Light [CH. xvm 



with that found by Fresnel to represent the results of experiment. It can be 

 shewn that the corresponding wave-surface is the well-known Fresnel wave- 

 surface, and all the geometrical phenomena of the propagation of light in a 

 crystalline medium follow directly. For the development of this part of the 

 theory, the reader is referred to books on physical optics. 



Assuming that a, j3, 7 as well as X, Y, Z are proportional to the exponen- 

 tial (593), the original system of equations become 



^ X = my nft, etc (594), 



o 



~~a. = mZnY, etc (595). 



If we multiply the three equations of system (594) by I, m, n respectively 

 and add, we obtain 



while a similar treatment of equations (592) gives 



lcL + m@+ny = Q (597). 



From equation (596) we see that the electric polarisation is in the wave- 

 front. From equation (597), the magnetic force also is in the wave-front. 



From this point onwards the development of the subject is the same on 

 the electromagnetic as on any other theory of light. 



MECHANICAL ACTION. 

 Energy in Light-waves. 



611. For a wave of light propagated along the axis of Ox, and having 

 the electric force parallel to Oy, we have (cf. 592) the solution 

 X=Z=0; Y=Y cos K (x-at), 

 a. = y9 = 0; 7 = y cos K (x at), 



and this satisfies all the electromagnetic equations, provided the ratio of 70 to 

 F is given by 



7o Ka C /K 



The energy per unit volume at the point x is seen to be 



~(KY* + rf) = (KY* + f J , y( ?) C os* f c(a ; -at) ...... (599). 



From equation (598) we see that the electric energy is equal to the mag- 

 netic at every point of the wave. The average energy per unit volume, 

 obtained by averaging expression (599) with respect either to x or to t, 



_ 



8?r STT 



