a. To determine the greatest velocity due to different lengths, by making the charge as great as the gun will bear.
4. To determine the effect of varying the weight of the gun, every thing else remaining the same.
5. To determine the penetration of balls into blocks of wood.
6. To determine the ranges and times of flight, and the velocities of balls, by striking the ballistic pendulum at various distances, and to compare them with their initial velocities, in order to ascertain the air's resistance.
7. To determine the effect of wads ; of different degrees of ramming; of different degrees of windage, and of dif ferent positions of the vent ; of chambers and trunnions, and every other circumstance necessary to he known for the improvement of artillery.
These experiments were carried on with great success, excepting in the subject of ranges, which were less regu lar and uniform than could have been wished. The ballis tic pendulum was from 600 to 800 pounds weight. The balk were generally one pound weight, and the powder was in creased from one ounce till the bore was quite full.
The following are the general results, as given by Dr. Mutton utton : 1. 'That the velocity is directly as the square root of the weight of powder, as far as to about the charge of eight ounces; and so it would continue for all charges, were the guns of an indefinite length. But as the length of the charge is increased, and bears a more considerable propot lion to the length of the bore, the velocity falls the more shot t of that proportion.
2. That the velocity of the ball increases with the charge to a certain point, which is peculiar to each gun where it is greatest ; and that, by further increasing the charge, the velocity gradually diminishes till the bore is quite full of powder. That this charge, for the greatest velocity, is greater as the gun is longer, but not greater, however, in so high a proportion as the length of the gun is ; so that the part of the bore filled with powder bears a less pro portion to the whole in the long guns than it does in the short ones ; the part of the whole which is filled being in deed nearly in the reciprocal subduplicate ratio of the length of the empty part. And the other circumstan ces are as in thisTable.
3. It appears that the velocity continually increases as the gun is longer, though the increase in velocity is but very small in respect of the increase in length, the veloci ties being in a ratio somewhat less than that of the square roots of the length of the bore, but somewhat greater than that of the cube roots of the length, and is indeed nearly in the middle ratio between the two.
4. The range increases in a much less ratio than the velocity, and indeed is nearly as the square root of the ve locity, the gun and elevation being the same. And when this is compared with the property of the velocity and length of gun in the foregoing paragraph, we perceive that very little is gained in the range by a great increase in the length of the gun, the charge being the same.
And, indeed, the range is nearly as the 5th root of the length of the bore, which is so small an increase as to amount only to about one•seventh part more range for a double length of gun.
5. It appears also that the time of the ball's flight is nearly as the range ; the gun and the elevation being the same.
6. It appears that there is no sensible difference caused in the velocity or range, by varying the weight of the gun, nor by the use of wads, nor by different degrees of ram ming, nor by firing the charge of powder in different parts of it.
7. But a great difference in the velocity arises from a small degree of windage. Indeed, with the usual established windage only, namely, about I-20th of the calibre, no less than between I-3d and 1.4th of the powder escapes and is lost. And as the balls are often smaller than that size, it frequently happens that half the powder is lost by unneces sary windage.
8. It appears that the resisting force of wood to balls fired into it is not constant. And that the depths penetrat ed by different velocities or charges are nearly as the log arithms of the charges, instead of being as the charges themselves, or, which is the same thing, as the square of the velocity, 9. These, and most other experiments, slim, that balls are greatly deflected from the direction they are projected in, and that so much as 300 or 400 yards in a range of a mile, or almost 1-4th of the range, which is nearly a de flection of an angle ,of 10. Finally, these experiments furnish us with the follow ing data to a tolerable degree of accuracy, viz. the dimen sions and elevation of the gun, the weight and dimensions of the powder and shot, with the range and time of flight, and the first velocity of the ball.