el the model
at any given rate, it would require just fifty-six times the power
to accomplish the same result with the large Balloon we have been
describing.

In order to ascertain precisely what this power would be in any given
instance, it only remains to find an expression for the spring power
with which we have been hitherto dealing, that shall be more generally
comprehensible.

This we shall do by a comparison with the power of steam, according to
the usual mode of estimating it; that is, reckoning a one-horse power
to be equal to the traction or draught of 32,000 lbs. through the
space of one foot in a minute. According to this scale, observing the
corresponding conditions of the spring--namely, the weight it balances
on the barrel, (answering to the force of traction) = 45 lbs., the
circumference of the barrel (answering to the space traversed) = one
foot, and the time of uncoiling for each turn, (answering to the rate
of the operation) say, three seconds and a half--we find the power of
the spring employed in the propulsion of the model, to be as nearly as
possible the forty-second part of the power of one horse; from whence
it is easy to deduce the conditions of flight assignable to the same,
and to different sized Balloons of the same shape, at any other degree
of speed. Assuming, for instance, a Balloon of 100 feet in length and
50 feet in height, and proposing a rate of motion equal to 20 miles an
hour, we have, in the first instance, the power required to propel
the model at that rate, compared with that already ascertained for a
velocity of six miles an hour, in the ratio of the _squares of the
two velocities_, as nearly ten to one; that is, ten forty-seconds,
or about one-fourth of a horse power. To apply this to the larger
Balloon, we must take the squares of their respective diameters; which
being nearly in the ratio of 56 to 1, gives an amount of 56 times
one-fourth or about 14 horses, as the sum of the power required.

From what particular source the power to be employed in the propulsion
of the Balloon should be deduced, is not indeed a question without
some difficulties and doubts in the determination. To all the moving
powers at present before the world some objections apply which
disparage their application, or altogether exclude them from our
consideration.

The power of the coiled spring is too limited to be employed upon
a larger scale. The use of the steam-engine is accompanied with a
gr