Maxwell. 281 



the constant fi be supposed to have the value unity, the 

 equations may be written 



div H = 0, 



c, 2 curl H = E, 

 - curl E = H. 

 Eliminating E, we see* that H satisfies the equations 



jdivH = 0, 







But these are precisely the equations which the light- vector 

 satisfies in a medium in which the velocity of propagation is c^ : 

 it follows that disturbances are propagated through the model 

 by waves which are similar to waves of light, the magnetic 

 (and similarly the electric) vector being in the wave-front. 

 For a plane-polarized wave propagated parallel to the axis of z, 

 the equations reduce to 



2 y = x 2 *^y y 



" Cl dz '"' dt' Cl ~dz '' dt' dz dt' dz 



whence we have 



= E x - c\S x = E 



these equations show that the electric and magnetic vectors are 

 at right angles to each other. 



The question now arises as to the magnitude of the constant 

 Cj.f This may be determined by comparing different expressions 

 for the energy of an electrostatic field. The work done by an 

 electromotive force E in producing a displacement D is 



fD 



E . dD or JED 



o 



per unit volume, since E is proportional to D. But if it be 

 assumed that the energy of an electrostatic field is resident in 

 the dielectric, the amount of energy per unit volume may be 



* For if a denote any vector, we have identically 



V-a -f grad div a + curl curl a = 0. 



t For criticisms on the procedure by which Maxwell determined the velocity of 

 propagation of disturbance, cf. P. Duhem, Les Theories Electriqv.es de J. Clerk 

 Maxwell, Paris, 1902. 



