A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 595 



When t = 0, p = 0, .: = P, = o, &c. 



t / 





rrom = to = oo . 



Wlien t = 0, p = throughout the section, .-. (*) = P, K^ =0, &c. 



\ dt /o \ dt /o 



When<=oo,_p = .-. K =0, t =0,&c. 



Also if Z be the length of the wire, and R its resistance, 



and if C be the current when established in the wire, C=-fr. 



M 



The total counter current may be written 

 7 7 



Now if the current instead of being variable from the centre to the cir- 

 cumference of the section of the wire had been the same throughout, the value 

 of F would have been 



where y is the current in the wire at any instant, and the total counter 

 current would have been 



/7 



J J 



Hence L = U 



or the value of L which must be used in calculating the self-induction of a 

 wire for variable currents is less than that which is deduced from the suppo- 

 sition of the current being constant throughout the section of the wire by 



752 



