Resistance alone does not affect the time constant.  It diminishes the intensity or strength of the currents only; but resistance, combined with electromagnetic inertia and with capacity, has a serious retarding effect on the rate of rise and fall of the currents.  They increase the time constant and introduce a slowness which may be called retardance, for they diminish the rate at which currents can be transmitted.  Now the retardance due to electromagnetic inertia increases directly with the amount of electromagnetic inertia present, but it diminishes with the amount of resistance of the conductor.  It is expressed by the ratio L/R while that due to capacity increases directly, both with the capacity and with the resistance, and it is expressed by the product, K R. The whole retardance, and, therefore, the speed of working the circuit or the clearness of speech, is given, by the equation

L
—–­ + K R = t
R

or L + K R squared = R t

Now in telegraphy we are not able altogether to eliminate L, but we can counteract it, and if we can make Rt = 0, then

L = — K R squared

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, [lambda].  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 [mu] for the conductor and by [mu]_{0} 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 [beta].  Combining these together we can represent the electromagnetic inertia of a metallic telephone circuit as

      L = [lambda] ([mu] + [mu]_{0}) dC/dt x [beta]