and Resistance of Straight Conductors, • 387 



these equations may be written 



dT 



f-°-4<4)-§> 



Moreover, if E denote u the electromotive force due to other 

 causes than the induction of the current upon itself," 



I ~~ dt 



To apply this to periodic currents following the harmonic 



law, where all the functions are proportional to e ipt , we may 



dT 

 replace d/dt by ip. Hence, eliminating -^-, we get 



1 EC ~ P + fid?*/*) 



interpret (15), we have to separate the real and imagi- 

 parts of </>/<//. Now if x be small, we get in ascending 



To 

 nary 

 powers of x by ordinary division, 



<f>{x) 1 1 1 2 1 3 1 4 13 § ,-.n\ 



so that 



+ i{\ P ^-y^ + ^ P ^-...}. . en) 



Thus, if we write 



E = R'C + i j pL'C, (18) 



we find 



r'=k{ i + ^/«y- jL AV+. . . } 



_ ( l P 2 v i /«V , I HON 



=R 1 1+ i2^r-T8oT{r + -"j' • • • (19) 

 "-*{ a+mQ - ii*y+ lo^" 4 - •) } 



= l|A+^^-48-B^ + 8640^ :••;/' (20) 



* For the case /a=1, (19) and (20) follow readily from Maxwell's 

 equation (18) § 690. 



2E2 



