1891.] vibrating electrical system, and its radiation. 171 



we have 



d J _ db da 

 dx dx dy 



= — 4f7T/MU. 



Hence defining FGH by the formula 



F, G, H = j—fi(u, v, w), 



we annul J, since 



du dv dw _ 

 dx dy dz 



owing to the absence of condensation. 



The components of electric force are 



dF dV 

 r ~~ dt dx' ¥ — ■»-« — ■» 



where V is a function whose presence is necessitated by the fact 

 that the currents must be circuital ; it must enter in this form in 

 order that it may produce no result on integration round a circuit, 

 and it is completely determined by the conditions of any special 

 problem. The fact that V must be a single-valued function so as 

 to give a null result on integrating round a circuit shows that it may 

 be expressed as the potential of an electrostatic distribution ; thus 

 its introduction into the equations is accounted for consistently 

 with ordinary electrical ideas. 



In a dielectric the total current uviv is the displacement current 

 in the dielectric, so that 



K d 



(u, v ^ w ) = ^ Tr j t ( p > Q> R )- 



In a conductor the displacement current is evanescent com- 

 pared with the current conducted according to Ohm's law, so that 



a (u, v, w) = (P, Q, R), 



where a is the specific resistance of the medium. 



Also, by definition above, 



V 2 (F, G,H) = - 47r/i (u, v, w). 



Thus in a dielectric the equations of propagation of the vector 

 FGH are of the type 



fiK df dxdt ' 



