VARIABLE STATE IN A CYLINDRICAL CONDUCTOR. 215 



capacity, as in the phenomena of statical electricity, or of the 

 permanent state that is to say, that the new charge is entirely on 

 the surface, 



If a 2 = 7/0, the equation becomes 



If the loss by the surface may be neglected, the coefficient fP is 

 zero, and we have 



We may observe, moreover, that if the loss is not zero, we 



may put 



equation (i) takes the form of equation (2) and becomes 



In both cases, the potential V is a function of x and of *, 

 which tends to become a simple function of # when the time 

 increases. 



The general integral of this equation has been given by Fourier 

 under several forms. 



If we consider a wire of length /, originally in the neutral state, 

 one of whose ends is in connection with the earth, while the other 

 end is suddenly raised to potential V , and then kept at this electrical 

 level, the general value of the potential at the distance x from the 



