308 Maxwell. 



Maxwell further assumed that the current thus produced 

 interacts dynamically with the luminous motion in such a 

 manner that the kinetic energy of the medium contains a 

 term proportional to the scalar product of e and curl de/30. 

 The total kinetic energy of the medium may therefore be 

 written 



\p& + Jcr (e . curl 9e/a0), 



where p denotes the density of the medium, and cr denotes a 

 constant which measures the capacity of the medium to rotate 

 the plane of polarization of light in a magnetic field. 



The equation of motion may now be derived as in the 

 elastic- solid theories of light : it is 



32 



pe = % V 2 e - o- r - curl e. 

 ot cu 



When the light is transmitted in the direction of the lines 

 of force, and the axis of x is taken parallel to this direction, 

 the equation reduces to 



and these equations, as we have seen,* furnish an explanation 

 of Faraday's phenomenon. 



It may be remarked that the term 



J(T (e . curl 9e/80) 



in the kinetic energy may by partial integration be transformed 

 into a term 



Jo- (curie. 9e/90),t 



together with surface-terms ; or, again, into 



- Jo- (curl e . 8e/80), 



together with surf ace- terms. These different forms all yield 

 * Cf. p. 215. 



f This form was suggested by Fitz Gerald six years later, Phil. Trans., 1880, 

 p. 691 : Fitz Gerald's Scientific Writings, p. 45. 



