The velocity which a balloon would gain from unobstructed acceleration must, from the theory of dynamics, be to that which a falling body acquires in the same time as the efficient buoyancy is to the aggregate weight of the apparatus and of the contained fluid. Thus, if a balloon were to rise with a force equal to the eighth part of its compound weight, the celerity resulting from a constant acceleration would be expressed by multiplying four feet into the number of seconds elapsed since it was launched into the air. Its advance, however, being opposed, the balloon though still affected with partial oscillations, the final velocity is effected in perhaps little more than double the time required without such obstruction.
This final velocity, or the velocity at which the ascent becomes uniform, the resistance from the air being then equal to the efficient buoyancy of the balloon, is easily calculated.
The resistance a circle encounters in moving through any fluid in the direction perpendicular to its plane, is measured by the weight of a column of that fluid, having the circle for its base, and an altitude equal to the height from which a heavy body in falling would acquire the given celerity.
Near the level of the sea, and at the mean temperature, a column of atmospheric air seventeen feet high, and incumbent on a circle of one foot in diameter, weighs a pound avoirdupois, which is, therefore, the resistance that a circle would suffer if carried forwards with the celerity of thirty-three feet each second.
According to the same theory, however, which we owe to the sagacity of Newton, the resistance of a sphere is just the half of that of its generating circle, and consequently a velocity of forty-six and two-fifths feet in a second through the air would in ordinary cases create a resistance of one pound to a ball of one foot in diameter.
In other circumstances, the quantity of resistance must be proportional to the square of velocities, and of the diameters. Whence, if the buoyant power were always the same, the velocity of the ascent of a balloon would be inversely as its diameter.
I introduce these few observations, which are by a much higher authority than my own, because it occurred to me that my own remarks might be considered too homely for some of those who may read these lines, but as I have merely aimed at affording amusement with a moderate portion of instruction, and do not write for scientific men, but for general readers, I shall hope to gradually progress in this treatment in a subsequent volume.
A JUMP OUT OF THE CAR IN AMERICA.
Among the numerous newspaper reports which are on my table, are several relative to what, in plain unvarnished English, we should describe as a parachute descent. But the one I allude to was not like Cocking’s, Garnerin’s, Le Turr’s, or Hampton’s, it had a size and peculiarity worth notice.
This American parachute had a very small and possibly inferior covering; it was hardly equal to the man who is sketched with herculean proportions, and required, one would say, a more efficient support, especially as he indulged in no car or wicker protection, but hung earthwards with his hands grasping the hoop.