Chapter 3

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 the magnitude of the figures we are here employing, as if it were something extraordinary or beyond the power of man to accomplish. The dimensions and power we have here assumed is very little greater than those of the great Vauxhall Balloon,[A] and considerably less than some of _Montgolfières_, or Fire-balloons, which were first employed.

[Footnote A: The height of the Vauxhall Balloon is about eighty feet, its breadth about fifty. It contains 85000 cubic feet of gas, and supports a weight of upwards of two tons.]

Now the resistance which such a Balloon as I have here described would experience in its passage through the air, and consequently the power it would require to establish that resistance compared with those of the model, we have said would be as the _squares_ of their respective diameters, or in, about, the ratio of only fifty-six to one; in other words, whatever force it would take to propel 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 gradual consumption of the resources of the Balloon in ballast, and consequently in gas, the one being exactly answerable to the other, and is therefore not calculated for voyages of long duration. Human strength appears to be too feeble for great results, and moreover, requires repose; which reduces the amount assignable to each man to a fraction of its nominal value. Of electro-magnetism as yet we know too little to enable us to pronounce upon it with certainty. Of the remaining powers known only one is worth mentioning in connexion with this subject, namely, the elastic force of air; and this I only mention because it has been taken up by one whose authority in these matters is deservedly entitled to much weight, and who entertains great hopes of making it ultimately subservient to the purpose in view.

But although none of these powers, in their present state, be so perfectly adapted to the propulsion of the Balloon as to leave nothing further to desire, yet are some of them so far applicable as, undoubtedly, to enable us to accomplish, by their means, a very large amount of success. A steam engine of the power required, namely, equal to fourteen horses, could be easily constructed, far within the limits of weight which we have at our disposal upon that account in the Balloon under consideration, or even in one much smaller; and recent improvements have so far reduced the amount of coal required for its maintenance, that perhaps as long a voyage could be made by means of it now, as would be expected or required. Even human strength, by a certain mode of applying it, might be made effectual to the accomplishment of a very sufficient rate of motion, say fourteen or fifteen miles an hour, for, continuously, as long a period as the natural strength of man, moderately taxed, could endure, and which we may reckon at twelve hours.

It is true that neither the velocity here quoted, nor that before assumed is so great as to enable the aeronaut to compete with some of the modes of transit employed on the surface of the earth; as, for instance, the railroads, where 25 miles an hour is not an unusual speed. Yet is not the aerial machine which could command such a rate of motion to be despised, or set aside as inferior in actual accomplishments to what is already at our disposal; for it must not be lost sight of, that railroads, or terrestrial roads of every description, must ever be limited in their extent and direction, and travelling on them, however perfectly contrived, subject to deviations and interruptions, particularly in passing from one country to another beyond the seas, which if taken into account, would reduce the apparent estimate of their rates, considerably under the lowest of those assigned to the Balloon in the previous calculation; and at all events, by sea, much less, under the most favourable circumstances is the ordinary rate of ships.

But, it may be observed, we are here counting upon a rate of motion as established, which is only effectual to that extent in the absence of contrary currents of wind. This is true; nevertheless it is no bar to the use which might be made of the aerial conveyance so furnished, nor any disparagement to the advantages which might be drawn from it; for not only does the aeronaut possess the means of choosing, within certain limits, the currents to which he may please to commit himself, and of which, abundance of every variety is sure to be met with at some elevation or other in the atmosphere, but, as in all general arguments, where the conditions are equally applicable to both sides of the question, they may be fairly left out as neutralising each other, so, here it must not be forgotten, that the currents in question, being altogether indeterminate, and equally to be expected from all quarters, an equal chance exists of advantages to be derived, as of disadvantages to be encountered from their occurrence; and that, even without the means of making a selection, the admitted laws of reasoning would justify us in considering the chances of the latter to be fully counterbalanced by those of the former. It is enough, for moderate success at least, if, possessing the power of avoiding the bad, and of availing himself of the good, the aeronaut be furnished with the means of making a sufficient progress for himself when the atmosphere is such as neither to favour nor to obstruct him; and in this condition I humbly conceive he would be placed, with even a less rate of motion than that which we have before assigned, and confidently reckon upon being able to accomplish.

FINIS.