[Footnote A: The condition of a Balloon propelled by machinery is very
analogous to that of a boat in the water driven by oars or paddles.
Suppose such a boat to be rowing or paddling up a river against the
stream, if a piece of cork be thrown overboard it appears to be
carried away with the current. But this is delusive; it is the boat
_alone_ which really moves away from the cork. For if the boat be
left to its own course, both it and the cork will float down together;
and if the use of the oars or paddles be resumed, the distance
between the boat and the cork will proceed to develope itself exactly
according to the rate of the _boat_, without any regard to that
of the _stream_. If the stream be excessively rapid, the boatsmen
will appear to be exercising very great force to enable them to stem
the torrent and avoid being carried backward. Now the resistance which
they experience and all its attendant effects are only those which
they create for themselves, and which they would experience in exactly
the same degree were they to endeavour to move _at the same rate_
in calm water or with the current in their favour. If the current be
at the rate of ten miles an hour and they are just able to maintain
their place, they are proceeding at the rate of ten miles an hour, and
they experience the opposition due to that rate of motion; precisely
the same as they would experience if they sought to accomplish the
same rate of motion under any other circumstances. And if the current
were 100 miles an hour, they would suffer no more from endeavouring to
go against it, with the force just ascribed to them, than if they
were to exercise the same force in any other direction, or in a water
perfectly tranquil. Apply this reasoning to the case of a Balloon
propelled by machinery, and much of the obscurity in which it is
involved will disappear.]

With these conditions established, it will now be seen that we have