Now, [lambda] = 2 log (d²/a²) 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