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foregoing parabolic theory, and partly on the results of cer-
Again, in prop. 58, Statics, are delivered the theory and calculations of a beautiful military experiment, invented by Mr. Robins, for determining the true degree of velocity with which balls are projected from guns, with any charges of powder. The idea of this experiment, is simply, that the ball is discharged into a very large but moveable block of wood, whose small velocity, in consequence of that blow, can be easily observed and accurately measured. Then, from this small velocity, thus obtained, the great one of the ball is immediately derived by this simple proportion, viz. as the weight of the ball, is to the sum of the weights of the ball and the block, so is the observed velocity of the last, to a 4th proportional, which is the velocity of the ball sought. It is evident that this simple mode of experiment will be the source of numerous useful principles as results derived from the experiments thus made, with all lengths and sizes of guns, with all kinds and sizes of balls and other shot, and with all the various sorts and quantities of gunpowder; in short, the experiment will supply answers to all inquiries in projectiles, excepting the extent of their ranges; for it will even determine the resistance of the air, by causing the ball to strike the block of wood at different distances from the gun, thus showing the velocity lost by passing through those different spaces of air; all which circumstances are partly shown in my 4to. vol. of Tracts published in 1786, and which will be completed in my new volumes of miscellaneous tracts now printing.
Lastly, in prob. 17, Prac. Ex. on Forces, some results of the same kind of experiment are successfully applied to determine the curious circumstances of the first force or elasticity of the air resulting from fired gunpowder, and the velocity with which it expands itself. These are circumstances which have never before been determined with any precision. Mr. Robins, and other authors, it may be said, have only guessed at, rather than determined them. That ingenious philosopher, by a simple experiment, truly showed that by the firing of a parcel of gunpowder, a quantity of elastic air was disengaged, which when confined in the space only occupied by the powder before it was fired, was found to be near 250 times stronger than the weight or elasticity of the common atmospheric air. He then heated the same parcel of air to the degree of red hot iron, and found it in that temperature to be about 4 times as strong as before; whence he inferred, that the first strength of the inflamed fluid, must be nearly 1000 times the pressure of
the atmosphere. But this was merely guessing at the degree of heat in the inflamed fluid, and consequently of its first strength, both which in fact are found to be much greater. It is true that this assumed degree of strength accorded pretty well with that author's experiments; but this seeming agreement, it may easily be shown, could only be owing to the inaccuracy of his own further experiments; and, in fact, with far better opportunities than fell to the lot of Mr. Robins, we have shown that inflamed gunpowder is about double the strength that he has assigned to it, and that it expands itself with the velocity of about 5000 feet per second.
Fully sensible of the importance of experiments of this kind, first practised by Mr. Robins with musket balls only, my endeavours for many years were directed to the prosecution of the same on a larger scale, with cannon balls; and I having had the honour to be called on to give my assistance at several courses of such experiments, carried on at Woolwich by the ingenious officers of the Royal Artillery there, under the auspices of the Masters General of the Ordnance, I have assiduously attended them for many years. The first of these courses was performed in the year 1775, being 2 years after my establishment in the Royal Academy at that place and in the Philos. Trans. for the year 1778, 1 gave an account of these experiments, with deductions, in a memoir, which was honoured with the Royal Society's gold medal of that year. In conclusion, from the whole, the following important deductions were fairly drawn and stated, viz.
1st, It is made evident by these experiments, that gunpowder fires almost instantaneously. 2dly, The velocities communicated to shot of the same weight, with different charges of powder, are nearly as the square roots of those charges. 3dly, And when shot of different weights are fired with the same charge of powder, the velocities communicated to them, are nearly in the inverse ratio of the square roots of their weights. 4thly, So that, in general, shot which are of different weights, and impelled by the firing of different charges of powder, acquire velocities which are directly as the square roots of the charges of powder, and inversely as the square roots of the weights of the shot. 5thly, It would therefore be a great improvement in artillery, occasionally to make use of shot of a long shape, or of heavier matter, lead; for thus the momentum of a shot, when discharged with the same charge of powder, would be increased in the ratio of the square root of the weight of the shot; which would both augment proportionally the force of the blow with
which it would strike, and the extent of the range to which it would go. 6thly, it would also be an improvement, to diminish the windage; since by this means, one third or more of the quantity of powder might be saved. 7thly, When the improvements mentioned in the last two articles are considered as both taking place, it appears that about half the quantity of powder might be saved. But, important as the saving may be, it appears to be still exceeded by that of the guns: for thus a small gun may be made to have the effect and execution of another of two or three times its size in the present way, by discharging a long shot of 2 or 3 times the weight of its usual ball, or round shot; and thus a small ship might employ shot as heavy as those of the largest now in use.
Finally, as these experiments prove the regulations with respect to the weight of powder and shot, when discharged from the same piece of ordnance; so, by making similar experiments with a gun varied in its length by cutting off from it a certain part, before each set of trials, the effects and general rules for the different lengths of guns, may be with certainty determined by them. In short the principles on which these experiments were made, are so fruitful in consequences, that, in conjunction with the effects of the resistance of the medium, they appear to be sufficient for answering all the inquiries of the speculative philosopher, as well as those of the practical artillerist.
Such then was the summary conclusion from the first set of experiments with cannon balls, in the year 1775, and such were the probable advantages to be derived from them. I am not aware however that any alterations were adopted from them by authority in the public service: unless we are to except the instance of carronades, a species of ordnance that was afterwards invented, and in some degree adopted in the public service; for, in this instance, the proprietors of those pieces by availing themselves of the circumstances of large balls, and very small windage, have, with small charges of powder, and at little expense, been enabled to produce very considerable and useful effects with those light pieces.
The 2d set of these experiments extended through most part of the summer seasons of the years 1783, 1784, 1785, and some in 1786. The objects of this course were numerous and various but the principal articles as follow: 1. The velocities, with which balls are projected by equal charges of powder, from pieces of equal weight and calibre, but of dif ferent lengths. 2. The velocities with different charges of powder, the weight and length of the guns being equal. 3. The greatest velocities due to the different lengths of guns,
to be ascertained by successively increasing the charge, till the bore should be filled, or till the velocity should decrease again. 4. The effect of varying the weight of the piece; every thing else being the same. 5. The penetrations of balls into blocks of wood. 6. The ranges and times of flight of balls; to compare them with their first velocities, for ascertaining the resistance of the medium. 7. The effect of wads; of different degrees of ramming, or compressing the charge; of different degrees of windage; of different positions of the vent; of chambers and trunnions, and every other circumstance necessary to be known for the improvement of artillery.
An ample account is given of these experiments, and the results deduced from them in my volume of Tracts published in 1786; some few circumstances only of which can be noted here. In this course, 4 brass guns were employed, very nicely bored and cast on purpose, of different lengths, but equal in all other respects, viz. in weight and bore, &c. The lengths of the bores of the guns were,
the gun no 1, was 15 calibres, length of bore 28.5 inc.
the calibre of each being 2 inches, and the medium weight of the balls 16 oz. 13 drams.
The mediums of all the experimented velocities of the balls with which they struck the pendulous block of wood, placed at the distance of 32 feet from the muzzle of the gun, for several charges of powder, were as in the following table,
placed in the 1st column, for all the four guns, the num bers denoting so many feet per second. Whence in general
it appears how the velocities increase with the charges of powder, for each gun, and also how they increase as the guns are longer, with the same charge, in every instance.
By increasing the quantity of the charges continually, for each gun, it was found that the velocities continued to increase till they arrived at a certain degree, different in each gun; after which, they constantly decreased again, till the bore was quite filled with the charge. The charges of powder when the velocities arrived at their maximum or greatest state, were various, as might be expected, according to the lengths of the guns; and the weight of powder, with the length it extended in the bore, and the fractional part of the bore it occupied, are shown in the following table, of the charges for the greatest effect.
Some few experiments in this course were made to obtain the ranges and times of flight, the mediums of which are exhibited in the following table.
n°3. 8 15 8 1.96 15
In this table are contained the following concomitant data, determined with a tolerable degree of precision; viz. the weight of the powder, the weight and diameter of the ball, the initial or projectile velocity, the angle of elevation of the VOL. II.