Self-induction of Wires, 81 



And o v_i 



S = c('21og^) (2/) 



Their product, when in the same units, is v -2 , the reciprocal 

 of the square of the speed of undissipated waves through the 

 dielectric. The two variables, potential difference and cur- 

 rent, fully define the state of the wires, except as regards the 

 diffusion effect in them, of course, and an effect due to outward 

 propagation into the unbounded dielectric from the seat of 

 impressed force, which is made insignificant by the limitation 

 of the magnetic field (in sensible intensity) due to the nearness 

 of the wires as compared with their length. To L has to be 

 added a variable quantity, whose greatest value is J ^ + -J fi 2 , 

 if fi Y and //, 2 are the inductivities of the wires, to obtain the 

 complete inductance per unit length. 



So far, then, there is a perfect correspondence between the 

 double-tube and the double-wire problem. But when we pro- 

 ceed to make allowance for the presence of neighbouring con- 

 ductors, as, for instance, the earth, although there is a formal 

 resemblance between the results in the two cases, when the 

 proper values are given to the constants concerned, yet the fact 

 that in one case the outer conductor encloses the inner, whilst in 

 the other this is not so, causes practical differences to exist. 

 For example, there are two constants of capacity concerned 

 in the concentric tube case, that of the dielectric between 

 them, and. that of the dielectric outside the outer tube. But 

 in the case of looped wires there are three, which may be 

 chosen to be the capacity of each wire with respect to earth 

 including the other wire, and a coefficient of mutual capacity. 

 There are, similarly, three constants of inductance, and two of 

 resistance, and at least two of leakage, viz. from each wire to 

 earth, with a possible third direct from wire to wire. This is 

 when the wires are treated in a quite general matter, and 

 arbitrarily operated upon ; so that there must be four elec- 

 trical variables, viz. two currents and two potential-differences. 

 I have somewhat developed this matter in my paper " On 

 Induction between Parallel Wires"*; and as regards the 

 values of the constants of capacity concerned, in my paper 

 " On the Electrostatic Capacity of Suspended Wires " f. As 

 may be expected, the solutions tend to become very complex, 

 except in certain simple cases. If, then, we can abolish this 

 complexity, and treat the double wire as if it were a single 

 one, having special electrical constants, we make a very im- 

 portant improvement. I have at present to point out certain 



* Journal S. T. E. and E., vol. ix. p. 427. f Ibid. vol. ix. p. 115. 

 Phil. Mag. S. 5. Vol. 24. No. 146. July 1887. G 



