Self-induction of Wires. 25 



making 



(2PZ) 4 (2PZ) 8 (2PZ) 12 



;=w,{i +J (M' + ^fF+- • • )}V» 



If we should regard the leakage as merely affecting the 

 amplitude of the current at the distant end of a line, we should 

 be overlooking an important thing, viz. its remarkable effect 

 in accelerating changes in the current, and thereby lessening 

 the distortion that a group of signals suffers in its transmission 

 along the line. If there is only a sufficient strength of 

 current received for signalling purposes, the signals can be far 

 more distinct and rapid than with perfect insulation, as I have 

 pointed out and illustrated in previous papers. Thus the 

 theoretical desideratum for an Atlantic cable is not high, but 

 low insulation, the lowest possible consistent with having 

 enough current to work with. Any practical difficulties in 

 the way form a separate question. 



Regarding this quickening effect, or partial abolition of elec- 

 trostatic retardation, I have (' Electrician,' Dec. 18, 1885, and 

 Jan. 1, 1886) pushed it to its extreme in the electromagnetic 

 scheme of Maxwell. In a medium whose conductivity varies 

 in any manner from point to point, possessed of dielectric 

 capacity which varies in the same manner, so that their ratio, 

 or the electrostatic time-constant, is everywhere the same, but 

 destitute of magnetic inertia (/a = 0, no magnetic energy), I 

 have shown that electrostatic retardation is entirely done away 

 with, except as regards imaginable preexisting electrification, 

 which subsides everywhere according to the common time- 

 constant, without true electric current, by the discharge of 

 every elementary condenser through its own resistance. This 

 being over, if any impressed force act, varying in any manner 

 in distribution and with the time, the corresponding current 

 will everywhere be the steady-flow distribution appropriate to 

 the impressed force at any moment, in spite of the electric 

 displacement and energy; and, on removal of the impressed 

 force, there will be instantaneous disappearance of the current 

 and the displacement. This seems impossible, but the same 

 theory applies to combinations of shunted condensers, arranged 

 in a suitable manner, as described in the paper referred to. 



Of course this extreme state of things is quite imaginary, 

 as we cannot really overlook the electromagnetic induction in 

 such a case. If we regard it as the limiting form of a real 

 problem, in which inertia occurs, to be afterwards made zero, 

 we find that the instantaneous subsidence of the electrostatic 

 problem becomes an oscillatory subsidence of infinite frequency 

 but finite time- constant, about the mean value zero ; which 



