“Very well. Let us advance a step. Your addition to the speed of the
engine is trivial, and the space in which you can exercise it, limited.
Now, suppose two stations, A and B, two miles distant by the track.
Imagine a train of platform cars, the last car resting at station A.
The train is a mile long, say. The engine is therefore within a mile
of station B. Say the train can move a mile in ten minutes. The last
car, having two miles to go, would reach B in twenty minutes, but the
engine, a mile ahead, would get there in ten. You jump on the last car
at A in a prodigious hurry to reach Abscissa, who is at B. If you stay
on the last car, it will be twenty long minutes before you see her. But
the engine reaches B and the fair lady in ten. You will be a stupid
reasoner and an indifferent lover if you don’t put for the engine over
those platform cars as fast as your legs will carry you. You can run
a mile, the length of the train, in ten minutes. Therefore you reach
Abscissa when the engine does, or in ten minutes--ten minutes sooner
than if you had lazily sat down upon the rear car and talked politics
with the brakeman. You have diminished the time by one half. You have
added your speed to that of the locomotive to some purpose. _Nicht
wahr?_”
I saw it perfectly; much plainer, perhaps, for his putting in the
clause about Abscissa.
He continued:
“This illustration, though a slow one, leads up to a principle which
may be carried to any extent. Our first anxiety will be to spare
your legs and wind. Let us suppose that the two miles of track are
perfectly straight, and make our train one platform car, a mile long,
with parallel rails laid upon its top. Put a little dummy engine on
these rails, and let it run to and fro along the platform car, while
the platform car is pulled along the ground track. Catch the idea? The
dummy takes your place. But it can run its mile much faster. Fancy that
our locomotive is strong enough to pull the platform car over the two
miles in two minutes. The dummy can attain the same speed. When the
engine reaches B in one minute, the dummy, having gone a mile atop the
platform car, reaches B also. We have so combined the speeds of those
two engines as to accomplish two miles in one minute. Is this all we
can do? Prepare to exercise your imagination.”