APPLICATION OF FOURIER'S FORMULAS. 213 



CHAPTER II. 



VARIABLE STATE. 



223. APPLICATION OF FOURIER'S FORMULAS. The problem of 

 the propagation of electricity in a conductor when the permanent 

 state has not been obtained as, for instance, when a battery is 

 discharged through a wire offers great difficulties. 



The flow of electricity which penetrates into a volume-element is 

 not zero, since the charge varies with the time; but it cannot be 

 asserted, a priori, whether the internal density varies, or, indeed, 

 whether it still remains zero, and the increase of charge takes place 

 only on the surface. 



In the absence of adequate experimental data, the simplest idea 

 is to pursue the analogy between the propagation of heat and that of 

 electricity, and to try to apply Fourier's formula to the variable state 

 of conductors. This is to assume implicitly that the flow of electricity 

 at each point, is proportional to the electrical force at this point, or to 

 the differential of the potential of all the acting masses. This 

 proposition seems natural enough, if it is the case that the electrical 

 forces really act at a distance and in an instantaneous manner, as is 

 readily admitted in the case of universal attraction ; but if, on the 

 contrary, electrical actions are transmitted through the intervention 

 of a medium, in virtue of what we have called the electrical elasticity 

 of this medium, it is necessary to assume that the state of electrical 

 tension (99, 126) is set up from layer to layer. A physical effort of 

 this kind must necessarily require a finite time, however small this 

 may be. This question of time, which does not affect problems of 

 equilibrium in the permanent state, may have a preponderating 

 influence in the phenomena of the variable state. 



In other words, we may assume that the electrical force is 

 propagated with an extremely great, but not infinite velocity, or else 

 that the potential of an electrical mass is itself propagated with a 

 finite velocity. 



