466 Induction of Currents in Continuous Media [OH. xv 



534. If we differentiate these three equations with respect to x, y, z 

 respectively and add, we obtain 



3u + Sv to 



dx dy dz 



of which the meaning (cf. 375, equation (311)) is that no electricity is 

 destroyed or created or allowed to accumulate in the conductor. 



The interpretation of this result is not that it is a physical impossibility for electricity 

 to accumulate in a conductor, but that the assumptions upon which we are working are 

 not sufficiently general to cover cases in which there is such an accumulation of electricity. 

 It is easy to see directly how this has come about. The supposition underlying our 

 equations is that the work done in taking a unit pole round a circuit is equal to 4?r times 

 the total current flow through the circuit. It is only when equation (476) is satisfied by 

 the current components that the expression ' total flow through a circuit ' has a definite 

 significance : the current flow across every area bounded by the circuit must be the same. 

 We shall see later how the equations must be modified to cover the case of an electric 

 flow in which the condition is not satisfied. For the present we proceed upon the sup- 

 position that the condition is satisfied. 



Currents in homogeneous media. 



535. Let us now suppose that we are considering the currents in a 

 homogeneous non-magnetised medium. We write 



a = /JLOL, etc., X = ru, etc., 



in which /* and r are constant. The systems of equations of 529 and 534 

 now become 



da w dv 



Differentiating equation (478) with respect to the time, we obtain 

 du d 



$(&u.&u.&u\ d_fdu dv dw 

 T + + + + 



in virtue of equation (476). 



Similar equations are satisfied by the other current-components, so that 

 we have the system of differential equations 



