3. That with the same gun and elevation, the time of the ball's flight is nearly as the range.
4. That no sensible difference is produced in the range or velocity, by varying the weight of the gun, by the use of wads, by different degrees of ramming, or by firing the charge of powder in different parts of it.
5. That a great difference, however, in the velocity, is occasioned by a small variation in the windage; so much so, indeed, that with the usual windage of one-twentieth of the caliber, no less than between one-third and one-fourth of the whole charge of the powder escapes and is entirely lost; and that as the windage is often greater, one-half the powder is unnecessarily lost.
6. That the resisting force of wood to balls fired into it, is not constant, and that the depths penetrated by different velocities, or charges, are not as the charges themselves, or, which comes to the same thing, as the squares of the velocities.
7. That balls are greatly deflected from the direction they are projected in, sometimes, indeed, so much as 300 or 400 yards in a range of a mile, or almost a fourth part of the whole range, which is nearly a deflection of an angle of 15 degrees.
The observations of Glenie, (History of Gunnery, 1776,) show the theory of projectiles in vacuo by plain geometry, or by means of the square and rhombus; with a method of reducing projections on inclined planes, whether elevated or depressed below the horizontal plane, to those which are made on the horizon.
This author, in his treatise, after stating in page 48, the two following positions of Mr. Robins, namely, "that till the velocity of the projectile surpasses that of 118 feet in a second; the resistance of the air may be estimated to be in the duplicate of the velocity;" that "if the velocity be greater than that of 11 or 1200 feet in a second, the absolute quantity of the resistance will be nearly three times as great as it should be by a comparison with the smaller velocities;" says, that he is certain from some experiments, which he and two other gentlemen tried with a rifle piece properly fitted for experimental purposes, that the resistance of the air to a velocity somewhat less than that mentioned in the first of these proportions, is considerably greater than in the duplicate ratio of the velocity; and that to a celerity somewhat greater than that stated in the second, the resistance is less than that which is treble the resistance of the same ratio. He observes, also, that some of Mr. Robins's own experiments come to this conclusion; since to a velocity no quicker than 200 feet in a second, he found the resistance to be somewhat greater than in that ratio, and remarks, therefore, that "after ascertaining the velocities of the bullets with as much accuracy as possible, I instituted a calculus from principles which had been laying by me for some time before, and found the resistance to approach nearer to that, which exceeds the resistance in the duplicate ratio of the velocity, by that which is the ratio of the velocity, than to that, which is only in the duplicate ratio."
The experiments of Mr. Dalton, confirm the premises of Mr. Robins, that the elasticity of the gases produced from a given quantity of powder, is equally increased by heat and diminished by cold as that of atmospheric air. Hence, as we before remarked, and from direct experiments, he concludes that the elastic fluid produced by the firing of gunpowder, is nearly three-tenths of the weight of the powder itself, which, expanded to the rarity of common air, is about 244 greater than the elasticity of common air, or in other words, than the pressure of the atmosphere. To this, however, must be superadded the increase of expansive power produced by the heat generated, which is very intense. The mere conversion of confined powder into elastic vapour, would exert against the sides of the containing vessel, an expansive force 244 times greater than the elasticity of common air, or, in other words, than the pressure of the atmosphere. If the heat, for the expansion of the gases, should be equal to that of red-hot iron, this would increase the expansion of common air, (and also of all gases) about four times, which in the present instance would be as we stated in the preceding pages, 244 to nearly 1000; so that in a general way it may be assumed, that the expansive force of closely confined powder at the instant of firing, is 1000 times greater than the pressure of common air; and as this latter is known to press with the weight of 143/4 pounds on every square inch, the force of explosion of gunpowder is 1000 times this, or 14750 lbs. or about six tons and a half upon every square inch. This enormous force diminishes in proportion as the elastic fluid dilates, being only half the strength when it occupies a double space, one-third of the strength when in a triple space, and so on.
There is one more fact worthy of notice, that Mr. Robins found the strength of powder to be the same in all variations of the density of the atmosphere, but not so in every state of moisture, being much impaired by a damp air, or with powder damped by careless keeping, or any other cause; so that the same powder which will discharge a bullet at the rate of 1700 feet in a second in dry air, will only propel it about 1200 feet when the air is fully moist, and a similar difference was observed between dry and moist powder. The sum of these remarks, with the necessary illustrations, may be found in the extract we have given from Gregory's Mechanics.
Before we mention the different modes of proving powder, we will offer some remarks respecting the use of sulphur in gunpowder. The conclusions on this head are drawn from the experiments made at Essonne, near Paris.