which is the principle of the shunted condenser that has been introduced with such signal success in our post office service, and has virtually doubled the carrying capacity of our wires.
K R = t
This is done in telephony, and hence we obtain the law of retardance, or the law by which we can calculate the distance to which speech is possible. All my calculations for the London and Paris line were based on this law, which experience has shown it to be true.
How is electromagnetic inertia practically eliminated? First, by the use of two massive copper wires, and secondly by symmetrically revolving them around each other. Now L depends on the geometry of the circuit, that is, on the relative form and position of the different parts of the circuit, which is invariable for the same circuit, and is represented by a coefficient, λ. It depends also on the magnetic qualities of the conductors employed and of the space embraced by the circuit. This specific magnetic capacity is a variable quantity, and is indicated by μ for the conductor and by μ0 for air. It depends also on the rate at which currents rise and fall, and this is indicated by the differential coefficient dC / dt. It depends finally on the number of lines of force due to its own current which cut the conductor in the proper direction; this is indicated by β. Combining these together we can represent the electromagnetic inertia of a metallic telephone circuit as
L = λ (μ + μ0) dC/dt × β
Now,
λ = 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 λ. It is customary to call the value of μ 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, β, 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.
