York, which will receive electricity, and give out mechanical work.
Now this machine, which may be called the motor, produces a back
electromotive force, and the mechanical power given out is proportional
to the back electromotive force multiplied into the current. The
current, which is, of course, the same at Niagara as at New York, is
proportional to the difference of the two electromotive forces, and the
heat wasted is proportional to the square of the current. You see, from
the last table, that we have the simple proportion: power utilized is
to power wasted, as the back electromotive force of the motor is to the
difference between electromotive forces of generator and motor. This
reason is very shortly and yet very exactly given as follows:

Let electromotive force of generator be E; of motor F. Let total
resistance of circuit be R. Then if we call P the horse-power received
by the generator at Niagara, Q, the horse-power given out by motor
at New York, that is, utilized; H, the horse-power wasted as heat in
machines and circuit; C, the current flowing through the circuit:

C=(E-F) / R

P=E(E-F) / (746 R)

Q=F(E-F) / (746 R)

H=(E-F)_2 / (746 R)

Q:H::F:E-F

The water analogy was again called into play in the shape of a model
for the better demonstration of the problem. The defects in existing