the right or to the left, and thus commanding a sphere of locomotion
whose extent and facilities, compared with those afforded by the
water, are as the cube to the plane.

'Aërial navigation being thus, according to his theory, the highest
form of locomotion, M. Pétin considers himself as justified in
assuming, _a priori_, that this mode of transportation will offer
facilities superior to those of every other in point of safety, speed,
power, and cheapness; but on condition of its being carried into
effect upon a scale commensurate with the vastness of its field and
the importance of its results.

'To convince ourselves that such is really the intention of
Providence, and that balloons are destined to transport the heaviest
loads, we have only, continues M. Pétin, to examine the law which
presides over the development of spheric bodies; the surface of a
sphere being represented by the square of the radius, while its
_contenance_, or containing power, is represented by the cube of the
radius. In other words, if we increase the diameter of a sphere three
times, although we increase its surface only nine times, we increase
its containing power twenty-seven times. Therefore, by constructing
balloons on a very large scale, as the extent of surface, and
consequent resistance of the air, increases in an immensely smaller
proportion than the containing power, we may obtain an almost fabulous
amount of ascensional force. For instance: a balloon of one hundred
yards in diameter would suffice to raise only ten millions of pounds;
but ten such balloons ranged one behind the other, or, better still, a
cigar-shaped balloon, which would be equivalent to these ten balloons
united in one (an arrangement which, as the law of development is
similar for spheric and for cylindric bodies, would greatly diminish