Maxwell. 289 



and similarly the equation 



E = 47rcO>/6 



is replaced by 



E = 4;r (c?D. xt c?D y , cjD z \ 



The other equations are the same as in isotropic media ; so that 



the propagation of disturbance is readily seen to depend on the 



equation 



(/i J? ft.ffy, H Z H Z } = - curl [c, 2 (curl 5),, tf(cuilH} y , Ca 2 ( curl -#)*) 



Now, if jui, ju 2 , A*3 are supposed equal to each other, this 

 equation is the same as the equation of motion of MacCullagh's 

 aether in crystalline media,* the magnetic force H corresponding 

 to MacCullagh's elastic displacement ; and we may therefore 

 immediately infer that Maxwell's electromagnetic equations 

 yield a satisfactory theory of the propagation of light in 

 crystals, provided it is assumed that the magnetic permeability 

 is (for optical purposes) the same in all directions, and pro- 

 vided the plane of polarization is identified with the plane 

 which contains the magnetic vector. It is readily shown that 

 the direction of the ray is at right angles to the magnetic 

 vector and the electric force, and that the wave-front is the 

 plane of the magnetic vector and the electric displacement.f 



After this Maxwell proceeded to investigate the propagation 

 of light in metals. The difference between metals and dielectrics, 

 so far as electricity is concerned, is that the former are con- 

 ductors ; and it was therefore natural to seek the cause of the 

 optical properties of metals in their ohmic conductivity. This 

 idea at once suggested a physical reason for the opacity of 

 metals namely, that within a metal the energy of the light 

 vibrations is converted into Joulian heat in the same way as 

 the energy of ordinary electric currents. 



* Cf. pp. 154 et sqq. 



f In the memoir of 1864 Maxwell left open the choice between the above theory 

 and that which is obtained by assuming that in crystals the specific inductive 

 rapacity is (for optical purposes) the same in all directions, while the magnetic 

 permeability is aeolotropic. In the latcer case the plane of polarization must be 

 identified with the plane which contains the electric displacement. Nine years 

 later, in his Treatise ( 794), Maxwell definitely adopted the former alternative. 



U 



