6 14 GENERAL THEORIES. 



The integrals of the two first equations are expressions of the 

 form 



F-/i(* 



The values of F and of G consist of two distinct parts. The 

 former does not change when we make successively = 0, /=0, 

 or z = V, and / = i ; it represents a plane wave which moves 

 parallel to the z axis with a velocity equal to V. The second 

 also represents a plane wave which moves in the opposite direction 

 with the same velocity. 



631. A magnetic disturbance in the form of a plane wave 

 produces then two plane waves moving on each side with the 

 same velocity. 



When G = 0, the magnetic force is parallel to the y axis and 



equal to - ; the electromotive force is parallel to the x axis 

 and its value is - . If we assume that the phenomena are iden- 



tical with those of light, the present case corresponds to a ray of 

 polarized light. The plane of polarization would coincide, either 

 with the plane of magnetic disturbance, or with the plane of 

 electrical disturbance which is perpendicular to it. 



If the original disturbance is periodic, and forms a simple 



vibration proportional to sin 271- , the same character will be met 



with in each of the planes parallel to the original wave, and the 

 wave-length of the phenomenon is the distance VT traversed by the 

 propagation of the motion during a single period. 



If the disturbance is circular, that is, if it may be figured by 

 a movable body which describes a circumference in a uniform 

 motion, the same character will be reproduced in the waves 

 propagated, and the planes passing through the radius and the 

 magnetic force, or the electrical displacement, are always perpen- 

 dicular to each other. This would be the case with a circularly 

 polarized ray of light. 



632. DISTRIBUTION OF THE ENERGIES. We have seen (120) 

 that in an electrified system, the energy of the medium for unit 

 volume is equal to half the product of the displacement by the 

 electrical force. In like manner, in the field of a system of 

 currents (570) the energy for unit volume is equal to the quotient 

 of the square of the induction by 



