432 Mr. 0. Heaviside on the 



ance of the line ; R being the constant that R " becomes with 

 p = 0. We may therefore write (166a) thus : — 



C= Cedz+mp-t fedz . eP*+(- \pl 2 ^-\ 

 Jo(/*Jl Jo{fe)edz ^ 



where the first term is C , the finally reached current ; the 

 following summation, extending over the p's belonging to 

 f=0, is its expansion, and therefore cancels the first term at 

 the first moment ; and the third part is a double summation, 

 extending over all the fs except /=0, each /term having its 

 following infinite series of p terms. This quantity in the 

 second line is zero initially as well as finally. If there were 

 no elastic displacement permitted (S = 0), the solution would 

 be represented by the first line of (172a), for we should then 

 have C independent of z y and 



..o Jo 



2 

 i/0 



for the differential equation of C, whose solution is plainly 

 given by the first line. The part in the second line of (172a) 

 is therefore entirely due to the combined action of the electro- 

 static and electromagnetic induction. 



When the impressed force is entirely at z = l, and of such 

 strength as to produce the steady current C , and if we take 

 Ro" = B, + Ljp, where R, and L are constants, there will be only 

 two p's to each/, given by/ 2 = — S p(R + Lp). The subsi- 

 dence from the steady state, on removal of the impressed 

 force, is represented by 



^ RCp 3 x {fz) fz 

 *R + 2LpJ (/Q S oi > ' 



where the summations range over the p/s, not counting the 

 p> = — R/L whose term is exhibited separately ; there is no 

 corresponding V term. A comparatively simple solution of 

 this nature may be of course independently obtained in a 

 more elementary manner. On the other hand, great power is 

 gained by the use of more advanced symbolical methods, 



