But with regard to Balloons of different sizes and of the same shape,
the power required to produce the same rate of motion, would be as
the squares of their respective diameters: for the power is as the
resistance, the resistance as the surface, and the surface follows the
proportion just assigned. In order, therefore to propel a Balloon
of the same form and twice the diameter, at the same rate, it would
require a force of four times the amount.

Now to apply this to the consideration of a Balloon of superior
magnitude, let us assume one of 100 feet in length, and fifty feet in
height. The buoyant power of such a machine, or the weight it would
carry, supposing it inflated with gas of the same specific gravity,
compared with that of the model, would be as the cubes of their
respective diameters; or in, about, the ratio of 420 to one. Such a
Balloon, therefore, so inflated, would carry a weight of about 8700
pounds, or above three tons and three quarters. As, however, it would
be very expensive to inflate such a vessel with pure hydrogen gas, it
would be advisable to found our calculations upon the use of coal gas;
under which circumstances the weight it would carry would be limited
to about three tons. Deducting from this, one ton for the weight of
the Balloon itself and its necessary equipments, there would remain
two tons, or about 4500 pounds, to be devoted to the power, whatever
it might be, by which the machinery was to be moved, and the living
cargo it might have to carry. Nor let the reader be surprised at
the magnitude of the figures we are here employing, as if it were
something extraordinary or beyond the power of man to accomplish. The
dimensions and power we have here assumed is very little greater than
those of the great Vauxhall Balloon,[A] and considerably less than
some of _Montgolfieres_, or Fire-balloons, which were first
employed.

[Footnote A: The height of the Vauxhall Balloon is about eighty feet,
its breadth about fifty. It contains 85000 cubic feet of gas, and
supports a weight of upwards of two tons.]

Now the resistance which such a Balloon as I have here described would
experience in its passage through the air, and consequently the power
it would require to establish that resistance compared with those
of the model, we have said would be as the _squares_ of their
respective diameters, or in, about, the ratio of only fifty-six to
one; in other words, whatever force it would take to prop