390 



And again, O and O' would alone keep the potential at E, zero. 

 So would Oj and O' r 



O. 2 and O' 2 . 



&c. &c. 



Hence if we denote 2lkc by a, for brevity, the general solution is 



J ' 



where F(0) is an arbitrary function such that F(/) expresses the 

 potential sustained at O by the battery. 



" The corresponding solution of the equation 



, dv cFv , 

 kc-j- = T-2 hv 

 dt da? 



by which the effect of imperfect insulation may be taken into 

 account." 



Extract of Letter from Prof. Stokes to Prof. W. Thomson (dated 



Nov. 1854). 

 " In working out for myself various forms of the solution of the 



equation -n=-r-, under the conditions v=0 when t =0 from #=0 to 

 dt dor 



x=<x>; v=f(t), when #=0 from t=0 to t=ao , I found that the so- 

 lution with a single integral only (and there must necessarily be this 

 one) was got out most easily thus : 



" Let v be expanded in a definite integral of the form 



/00 



v= 1 iff (,a)sin axdx, 

 Jo 



which we know is possible. 



