80 Mr. 0. Heaviside on the 



and the inductance is the sum of that of the dielectric, inner, 

 and outer conductors. Another remarkable peculiarity is, 

 that equal impressed forces, similarly directed in the two con- 

 ductors at corresponding places, can do nothing ; from which 

 it follows that the effective impressed force may, like the 

 effective resistance, be divided between the conductors in any 

 proportion we please. 



In Part IV., having in view the rapidly extending use of 

 metallic circuits of double wires looped, excluding the earth, 

 consequent upon the development of telephonic communi- 

 cation in a manner to eliminate inductive interferences, I 

 extended the above-described method to a looped circuit con- 

 sisting of a pair of parallel wires. So far as propagation 

 into the wires is concerned, it is merely necessary that they 

 should not be too close to one another to allow of the appli- 

 cation of the J and J 1 functions to them separately. Now 

 suspended wires are usually of iron, and are not set too close, 

 so that the application is justified. On the other hand, buried 

 twin wires, though very near one another, are of copper, and. 

 also considerably smaller than the iron suspended wires ; so 

 that the diffusion effect, though not so well representable 

 by the above-named functions, is made insignificant. Dis- 

 missing, as before, this question of inward propagation, we 

 have, just as in the tubular case, two electrical variables and 

 three constants, viz. the potential difference of the wires, the 

 current in each, and the effective resistance, capacity, and 

 inductance. 



First of all, let the wires be alone in an infinite dielectric. 

 Then we have similar results to these concerning the double- 

 tube. The effective resistance, which is the sum of the 

 resistances of the wires, may be divided between them in any 

 proportions ; and so may be the effective impressed force. 

 The effective capacity is that of the condenser, consisting of 

 the dielectric bounded by the two wires, the surface of one 

 being the positive, and that of the other the negative coating. 

 Or, in another form, the effective capacity is the reciprocal of 

 the elastance from one wire to the other. In the standard 

 medium, this elastance is, in electrostatic units, the same as 

 the inductance, of the dielectric, in electromagnetic units. 

 Thus, 



L =2/ilogSk, (1/) 



r x r 2 



if r x and r 2 be the radii of the wires, and r n their distance 

 apart (between axes), and fju the inductivity of the dielectric. 



