the usual estimation of the weight of air, is 131 grains. If the ratio of the bulk of the gunpowder to the bulk of this fluid is wanted, it will be determined by knowing that 17 drachms of powder fill 2 cubic inches; so that, proportioning the one to the other, it will be found that 472 cubic inches of elastic fluid are obtained from 2 cubic inches of powder.

But the amount of gas given off from a fixed quantity of powder is not always a test of its utility in throwing projectiles. Thus many explosive powders, such as fulminating silver and mercury, generate a much greater proportion of gas and far more rapidly than ordinary gunpowder; but the explosion being too sudden, they have not so good an effect upon the projectile in proportion to the power which they exert, and which, from its great suddenness, is apt to burst the tube in which it is contained. Up to the present time two substances only have been found which combine the exact properties required, and these are gunpowder and guncotton. In experimenting on different kinds of gunpowder, with a view to determine the relative powers of each, it is found that the density of the air has no effect whatever, but in proportion to its dryness will the elastic force of the powder be exerted. This is very important to know, for it very often happens that powder which has been used on a damp day with less effect than other powder tried in dry weather, loses credit, although, perhaps, really equal, or even superior to the antagonistic material. So also powder which is rendered damp by being poured down a foul barrel is weakened greatly in its effects; and here again is another element which must be taken into the account. In all trials of gunpowder, therefore, dry days should be selected.

ACTION OF THE POWDER ON THE PROJECTILE.

The action of the powder on the projectile ceases as soon as the latter escapes from the barrel. This fact is capable of demonstration mathematically; but as it is not disputed, I shall not go into the calculation. But there is another theory propounded by Robins on this subject which demands a little consideration, because it is contrary to the opinions of most other writers, and was subsequently modified by himself. He asserts, in his earlier writings, that all the powder in the

charge is fired and converted into an elastic fluid, before the bullet (or charge of shot) is sensibly moved from its place. This proposition he attempts to demonstrate as follows:"It might perhaps be sufficient for the proof of this position to observe the prodigious compression of the flame in the chamber of the piece. Those who will attend to this circumstance, and to the easy passage of the flame through the intervals of the grains, may soon satisfy themselves that no one grain contained in that chamber can continue for any time uninflamed when thus surrounded and violently pressed by so active a fire. However, not to rely on a mere speculation on a point of so much consequence, I considered that if part only of the powder is fired, and that successively, then by laying a greater weight before the charge (suppose two or three bullets instead of one), a greater quantity of powder would necessarily be fired, since a heavier weight would be a longer time in passing through the barrel. Whence it should follow that two or three bullets would be impelled by a much greater force than one only. But the contrary of this appears by experiment, for firing one, two, and three bullets laid contiguous to each other, with the same charge respectively, I have found (by a method to be mentioned hereafter) that their velocities were not much different from the reciprocal of the subduplicate of their quantities of matter; that is, if a given charge will communicate to one bullet a velocity of 1700 feet in 1", the same charge would communicate to two bullets a velocity from 1250 to 1300 feet in 1", and to three bullets a velocity from 1050 to 1100 feet in 1". From hence it appears that, whether the piece be loaded with a greater or less weight of bullet, the action of the powder is nearly the same, since all mathematicians know that, if bodies containing different quantities of matter are successively impelled through the same space by the same power, acting with a determined force at each point of that space, then the velocities given to those different bodies will be reciprocally on the subduplicate ratio of their quantities of matter. The excess of the velocities of the two and three bullets above what they should have been by this rule (namely, 1200 and 980 each in 1"), does doubtless arise from the flame, which, escaping by the side of the first bullet, acts on the surface of the second and

third. Now, this excess has in many experiments been imperceptible, and the velocities have been reciprocally on the subduplicate ratios of the number of bullets to sufficient exactness; and where this error has been the greater, it has never arisen to an eighth part of the whole; but if the common opinion was true, that a small part only of the powder fires at first, and other parts of it successively, as the bullet passes through the barrel, and that a considerable part of it is often blown out of the piece without firing at all; then the velocity which three bullets received from the explosion ought to have been much greater than we have ever found it to be, since the time of the passage of three bullets through the barrel being nearly double the time in which one passes, it should happen, according to this vulgar supposition, that in a double time a much greater quantity of the powder should be fired, and consequently a greater force should have been produced, than what acted on the single bullet only, contrary to all our experiments. But further, the truth of the second postulate will be more fully evinced when it shall appear, as it will hereafter, that the rules founded on this supposition ascertain the velocities of bullets impelled by powder to the same exactness when they are acted on through a barrel of four inches in length only, as when they are discharged from one of four feet."-Robins's New Principles of Gunnery, pp. 80-82.

Now all the facts here adduced may, and I believe are, correctly stated, and yet they do not prove the proposition with which this ingenious author sets out. Moreover, the difference which he explains by supposing that the flame escapes by the side of the first bullet, may far more readily be understood to be in consequence of the increased time which the powder is allowed for explosion. The counter argument may more readily be supported by extending the charge of powder, by loading a small tube several inches in length with it, when the grains in front are evidently blown out in an entire state, proving that there is a point beyond which instantaneous explosion does not go. All that Robins shows by this experiment is, that the charge of powder which he used burns entirely before the one ball leaves the muzzle; and, if that is the case, it can do no more if one or

even two other balls are added. It is now generally admitted, in accordance with the experiments made by a committee of the Royal Society in 1742, that Robins was wrong in his theory on this point; and not only is it shown that the combustion of all the grains in a charge of powder is not simultaneous, but it is pretty well ascertained that coarse-grained powder burns more slowly than fine, and for that reason it is preferred for mining charges. Indeed, so satisfied are practical miners of the importance of slow combustion, that they mix sawdust with their powder, for the purpose of producing it. In the old flint gun combustion was too slow, and for that reason very fine powder answered the best; but in detonators a coarser grain is preferred, and in needle-guns, or in those cartridges when the cap itself is introduced into the charge of powder, a coarser grain still is adopted. By the use of coarse powder, also, the projectile in front of it being more gradually moved, the recoil is diminished, and thereby a larger quantity can be used with comfort to the shooter and safety to his barrels.

MODE OF DETERMINING THE VELOCITY OF THE PROJECTILE.

Fig.7

In order to determine the velocity with which a ball moves at any distance from the piece, a simple plan, now commonly known as the ballistic pendulum, was invented by Robins, and has never yet been improved upon, though, from the difficulty of hitting its centre, it can only be used at short ranges. A square plate of iron faced with wood (Fig. 7, a) is suspended like a pendulum from a tripod; and to the lower part of two of the legs of this a cross bar (b) is attached. Then fixing a piece of tape to the lower edge of the pendulum, and letting it slide through a notch in a brass plate fixed upon the cross bar, the extent to which the pendulum, when struck by the ball, draws the tape, shows the force of the blow, and the velocity

with which the ball has travelled. As Robins remarks, "This instrument thus fitted, if the weight of the pendulum be known, and likewise the respective distances of its centre of gravity, and of its centre of oscillation from its axis of suspension, it will thence be known what motion will be communicated to this pendulum by the percussion of a body of a known weight, moving with a known degree of celerity, and striking it at a given point; that is, if the pendulum be supposed at rest before the percussion, it will be known what vibration it ought to make in consequence of such a determined blow; and, on the contrary, if the pendulum, being at rest, is struck by a body of a known weight, and the vibration which the pendulum makes after the blow is known, the velocity of the striking body may from thence be determined. . . . The computation by which the velocity of the ball is determined from the vibration of the pendulum after the stroke requires a more particular explication; and for this purpose we will exhibit, as an example, the pendulum made use of by us in some of our experiments. The weight of the whole pendulum was 56lbs. 3oz.; its centre of gravity was 52 inches distant from its axis of suspension, and 200 of its small swings were performed in the time of 253 seconds; whence its centre of oscillation is 623 inches distant from that axis. In the compound ratio of 66 to 623 and 66 to 52, take the quantity of matter of the pendulum to a fourth quantity, which will be 42lbs. oz. Now geometers will know that, if the blow be struck in the centre of the plate (a), the pendulum will resent the stroke, as if this last quantity of matter only (421bs. oz.) was concentrated in that point, and the rest of the pendulum was taken away; whence, supposing the weight of the bullet impinging on that point to be the twelfth of a pound, or the of this quantity of matter nearly, the velocity of 804 the point of oscillation after the stroke will, by the laws observed in the congress of such bodies as rebound not from each other, be the of the velocity the bullet moved with before the stroke; whence the velocity of this point of oscillation being ascertained, that, multiplied by 505, will give the velocity with which the ball impinged.

"But the velocity of the point of oscillation after the