Now, [lambda] = 2 log (d squared/a squared) Hence the smaller we make the distance, d, between the wires, and the greater we make their diameter, a, the smaller becomes [lambda].  It is customary to call the value of [mu] for air, and copper, 1, but this is purely artificial and certainly not true.  It must be very much less than one in every medium, excepting the magnetic metals, so much so that in copper it may be neglected altogether, while in the air it does not matter what it is, for by the method of twisting one conductor round the other, the magnetization of the air space by the one current of the circuit rotating in one direction is exactly neutralized by that of the other element of the circuit rotating in the opposite direction.

Now, [beta], in two parallel conductors conveying currents of the same sense, that is flowing in the same direction, is retarding, Fig. 2, and is therefore a positive quantity, but when the currents flow in opposite directions, as in a metallic loop, Fig. 3, they tend to assist each other and are of a negative character.  Hence in a metallic telephone circuit we may neglect L in toto as I have done.

[Illustration:  Fig 2.]

[Illustration:  Fig. 3.]

I have never yet succeeded in tracing any evidence of electromagnetic inertia in long single copper wires, while in iron wires the value of L may certainly be taken at 0.005 henry per mile.

In short metallic circuits, say of lengths up to 100 miles, this negative quantity does not appear, but in the Paris-London circuit this helpful mutual action of opposite currents comes on in a peculiar way.  The presence of the cable introduces a large capacity practically in the center of the circuit.  The result is that we have in each branch of the circuit between the transmitter, say, at London and the cable at Dover, extra currents at the commencement of the operation, which, flowing in opposite directions, mutually react on each other, and practically prepare the way for the working currents.  The presence of these currents proved by the fact that when the cable is disconnected at Calais, as shown in Fig. 5, and telephones are inserted in series, as shown at D and D’, speech is as perfect between London and St. Margaret’s Bay as if the wires were connected across, or as if the circuit were through to Paris.  Their effect is precisely the same as though the capacity of the aerial section were reduced by a quantity, M, which is of the same dimension or character as K. Hence, our retardance equation becomes

R (K — M) = t

[Illustration:  Fig 4.]

[Illustration:  Fig 5.]