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.