Forced Vibrations of Electromagnetic Systems. 143 



cases, of which I shall give examples later, that the subse- 

 quent course of events does not so greatly complicate matters 

 as to render it impossible to go into 'details after the first 

 moment. On first starting the sheet, it becomes a sheet of 

 magnetic induction, whose lines coincide with the vortex lines 

 of impressed force. If /be the measure of the vorticity per 

 unit area, fl^fiv is the intensity of the magnetic force. In the 

 imaginary good conductor of no permittivity, this is zero, 

 owing to v being then assumed to be infinite. 



Notice that whilst the vorticity of e produces magnetic 

 induction, that of h. produces electric displacement, and whilst 

 in the former case E is made discontinuous at a plane of finite 

 vorticity, in the latter case it is H that is initially discon- 

 tinuous. 



11. True Nature of Diffusion in Conductors. — The process 

 of diffusion of magnetic induction in conductors appears to 

 be fundamentally one of repeated internal reflexions with 

 partial transmission. Thus, let a plane wave E 1 =/awH 1 

 moving in a nonconducting dielectric strike flush an ex- 

 ceedingly thin sheet of metal. Let E 2 =/avH 2 be the trans- 

 mitted wave in the dielectric on the other side, andE 3 = — /ivH 3 

 be the reflected wave. At the sheet we have 



Ei + E^Eg, (60) 



H 1 + H 3 =H 2 + 47rVE 2 , (61) 



if k Y be the conductivity of the sheet of thickness z. Therefore 

 E a_H 2 _ E 1 + E 3 _ 1 



E x H x E x l + 2Tr/ik 1 w' ' " " l } 



H is reflected positively and E negatively. A perfect con- 

 ducting barrier is a perfect reflector, it doubles the magnetic 

 force and destroys the electric force on the side containing 

 the incident wave, and transmits nothing. 



Take ^ = (1600) for copper, and p = 3x 10 10 centim. 

 Then we see that to attenuate the incident wave Hj to ^Hj 

 by transmission through the plate, requires 



z= (277/^)- = -JL x 10- 8 centim., . (63) 



07T 



which is a very small fraction of the wave-length of visible 

 light. The H disturbance is made fHj, the E reduced to 

 JEi on the transmission side. There is, however, persistence 

 of H, although there is dissipation of E. To produce dissi- 

 pation of H with persistence of E requires the plate to be a 

 magnetic, not an electric conductor. 



Now, imagine an immense number of such plates to be 



