provided with four times the power. Thus as the spring power employed
in the model is equal to a weight of 45 pounds, upon a barrel of four
inches in diameter, it would require one competent to raise 180 pounds
on the same sized barrel, to enable it to propel the same Balloon at
double the present rate.

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