594 A DYNAMICAL THEORY OP THE ELECTROMAGNETIC FIELD. 



The correction for the eight nearest wires is 



+ 0-0236. 

 For the sixteen in the next row + 0'00083. 



These corrections being multiplied by the length of wire and added to the 

 former result, give the true value of L, considered as the measure of the 

 potential of the coil on itself for unit current in the wire when that current 

 has been established for some time, and is uniformly distributed through the 

 section of the wire. 



(115) But at the commencement of a current and during its variation the 

 current is not uniform throughout the section of the wire, because the induc- 

 tive action between different portions of the current tends to make the current 

 stronger at one part of the section than at another. When a uniform electro- 

 motive force P arising from any cause acts on a cylindrical wire of specific 



resistance p, we have 



dF 



where F is got from the equation 



d*F 1 dF 



r being the distance from the axis of the cylinder. 



Let one term of the value of F be of the form Tr n , where T is a 

 function of the time, then the term of p which produced it is of the form 



4 TT -p. 

 Hence if we write 



p I 1* . 2' ofa 1 

 ' 1 d'T 



The total counter current of self-induction at any point is 

 IP \ 1 , . air cW . . uV 1 



P 



f 



from ( = to t = oo . 



