'Aerial navigation being thus, according to his theory, the highest form of locomotion, M. Petin 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. Petin, 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 the resistance of the air, without occasioning any loss of containing power), would suffice to raise one hundred millions of pounds; and allowing some four or five millions of pounds for the weight of the vessel and its machinery, which, for a ship of this size--supposing it were possible to make its various parts hold together--should be, M. Petin computes, of twelve hundred horse-power, we should still have at command a surplus ascensional force of upwards of ninety millions of pounds; a force sufficient to sustain a body of fifty thousand men! 'In the construction of these enormous balloons, M. Petin proposes to substitute, in place of the silken bag hitherto used to contain the gas, a rigid envelope of a cylindro-conical form, composed of a series of metallic tubes, laid one above the other, and supplied with gas--obtainable to any amount and almost instantaneously--from the decomposition of water by a powerful electric battery; and with these resources at command, M. Petin conceives that balloons might be constructed on a scale even larger than that just given!