tant, _t_, Fig. 1, which regulates the number of current
waves which can be transmitted through it per second. This is the time
the current takes to rise from zero to its working maximum, and the
time it takes to fall from this maximum to zero again, shown by the
shaded portions of the figure; the duration of the working current
being immaterial, and shown by the unshaded portion.

The most rapid form of quick telegraphy requires about 150 currents
per second, currents each of which must rise and fall in 1/150 of a
second, but for ordinary telephone speaking we must have about 1,500
currents per second, or the time which each current rises from zero to
its maximum intensity must not exceed 1/3000 part of a second. The
time constant of a telephone circuit should therefore not be less than
0.0003 second.

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