Part 388

Gallileo having discovered that bodies projected in vacuo, and in an oblique direction to the horizon, do always describe a parabola, he concluded that this doctrine was not sufficient to determine the real motion of a military projectile: for, since shells and shot move with a great velocity, the resistance of the air becomes so great with respect to the weight of the projectile, that its effect turns the body very considerably from the parabolic tract; so that all calculations, grounded on the nature of this curve, are of little use on these occasions. This is not to be wondered at, since Gallileo, in his enquiry, paid no regard to any other force acting on bodies, than the force of gravity only, without considering the resistance of the air.

Every body, moving in a fluid, suffers the action of two forces: the one is the force of gravity, or the weight of the body; and it is to be observed, that this weight is less than the natural weight of the body, that being diminished by an equal bulk of the fluid in which the body moves. The other force is that of the resistance, which is known to be proportional to the squares of the velocity of the body; and when the body is a globe, as is commonly supposed, the direction of this force is diametrically opposite to that of the motion of the body. This force changes continually, both in quantity and direction; but the first force remains constantly the same. Hence, the point in question is, to determine the curve which a body projected obliquely, must describe when acted upon by the two forces just now mentioned.

Although this question is easily reduced to a problem purely analytical, the great Newton, notwithstanding his ingenious endeavors, did not arrive at a complete solution of it. He was the first who attempted it, and having succeeded so well in the supposition, that the resistance is proportional to the velocity, it is almost inconceivable that he did not succeed, when the resistance is supposed proportional to the squares of the velocity, after solving a number of questions incomparably more difficult. The late Mr. John Bernoulli gave the first solution of this problem, from which he drew a construction of the curve, by means of the quadratures of some transcendent curves, whose description is not very difficult.

This great problem was, therefore, very well solved long ago; yet the solution, however good in theory, is such as has hitherto been of no use in practice, nor in correcting the false theory grounded on the parabola, to which the artillerist is still obliged to adhere, notwithstanding he knows it to be insufficient. It is certain, that that solution has been of no real advantage towards improving the art of gunnery: it has only served to convince the student in that art, of the error of his principles, drawn from the nature of the parabola, although he is still to abide by them. It is indeed something to know, that the common rules are erroneous; but unless we know how much they err in any case, the advantage is very little.

One may think it a work of infinite labor to establish rules for the flight of cannon shot, agreeable to the real curve which a body describes in the air: for although, according to the hypothesis of Gallileo, we want only the elevation of the piece, and the initial velocity, and it is therefore not difficult to calculate tables to show the greatest height of the projectile, and the point where it must fall in any proposed case; yet in order to calculate similar tables according to the true hypothesis, care must be taken, besides the two particulars already mentioned, to have respect as well to the diameter of the projectile as to its weight: therefore the practitioner will be reduced to the necessity of calculating tables, as well for the diameter of each projectile, as for its weight; and the execution of such a work would be almost impracticable. We therefore refer the curious to Mr. Euler’s True Principles of Gunnery, translated, with many necessary explanations and remarks, by the very learned and ingenious Hugh Brown.

PROJECTION, (Projection, Fr.) in mathematics, the action of giving a projectile its motion. It is also used to signify a scheme, plan, or delineation.

PROJECT, (Projet, Fr.) a term generally used among French engineers, to express what works are required to be made for the inward or outward defence of a fortified town or place. It likewise signifies, in diplomacy, a plan or statement of terms and conditions which one country makes to another for a final adjustment of differences.

Contre-PROJET, Fr. a receipt or answer to terms proposed, accompanied by a project from the other side.

PROLONGE, Fr. A long thick rope, which is used to drag artillery; but different from the bricole and drag rope; it is coiled round pins under the gun carriage travelling, it is loosed in action, and one end being attached to the limber, is of great use in moving the gun in action or in a retreat. See Am. Mil. Lib.

PROMOTION, (Promotion, Fr.) This word signifies, in military matters, the elevation of an individual to some appointment of greater rank and trust than the one he holds.

PROMOUVOIR, Fr. to promote.

PROMU, Fr. promoted.

PROOF, in arithmetic, an operation whereby the truth and justness of a calculation are examined and ascertained.

PROOF of artillery and small arms, is a trial whether they will stand the quantity of powder allotted for that purpose.

The British government allow 11 bullets of lead in the pound for the proof of musquets, and 29 in two pounds, for service; 17 in the pound for the proof of carabines, and 20 for service; 28 in the pound for the proof of pistols, and 34 for service.

When guns of a new metal, or of lighter construction, are proved, then besides the common proof, they are fired 2 or 300 times, as quick as they can be, loaded with the common charge given in actual service. British light 6 pounders were fired 300 times in three hours, 27 minutes, loaded with 1lb. 4oz. without receiving any damage.

PROOF of ordnance. All natures of ordnance undergo several kinds of proof before they are received into the British service; viz. 1st, they are guaged as to their several dimensions, internal and external, as to the justness of the position of the bore, the chamber, the vent, the trunnions, &c.

2d, They are fired with a regulated charge of powder and shot, and afterwards searched to discover irregularities or holes produced by the firing.

3d, By means of engines an endeavor is made to force water through them; and,

4th, They are examined internally, by means of light reflected from a mirror.

Iron guns. The guns are first examined as to their proper dimensions, in which, in no case more than ³⁄₁₀ of an inch variation is allowed; and in the diameter of the bore only ¹⁄₃₀ from 42 to 18 pounders, and ¹⁄₄₀ from 12 to 4 pounders; but in the position of the bore ¹⁄₂ an inch out of the axis of a piece from a 42 to an 18 pounder, and ¹⁄₃ of an inch from a 12 to a 4 pounder is allowed. They are then fired twice with the charge in the following table, with one shot and two high junk wads; and examined with a searcher after each round. In this examination they must not have any hole or cavity in the bore of ²⁄₁₀ of an inch in depth, behind the first reinforce ring, or ¹⁄₄ of an inch in depth before this ring.

-------+-------- Nature.| Proof |charge. -------+-------- Prs. |lbs. oz. 42 | 25 -- 32 | 21 8 24 | 18 -- 18 | 15 -- 12 | 12 -- 9 | 9 -- 6 | 6 -- 4 | 4 -- 3 | 3 -- 2 | 2 -- 1¹⁄₂| 1 8 1 | 1 --

Iron guns are scaled with ¹⁄₁₂ the weight of the shot.

Brass guns. From 1 pounders to 12 pounders the diameter of the bore must not vary more than ¹⁄₄₀ of an inch, and in no dimensions more than ²⁄₁₀. The following are the established charges for their proof. The heavy and medium guns with a charge equal to the weight of the shot, except the medium 12 pounder, which is proved with only 9lbs. The light guns with half the weight of the shot. The brass ordnance have not however been proved of late with such heavy charges, but with the following:

3 Prs. light, 3 times, with 1 lb. each round. 6 Prs. light, 3 times, with 2 lbs. each. 12 Prs. light, 2 times, with 4 lbs. each. 12 Prs. med., 2 times, with 5 lbs. each.

Any hole ·15 of an inch deep upwards or sideways in the bore, or ·1 in the bottom, between the breach and first reinforce; or ·2 of an inch upwards or sideways, or ·15 in the bottom of the bore, before the first reinforce ring, will be sufficient to condemn them.

Brass Mortars and Howitzers. The exterior dimensions are in no respect to deviate more than ¹⁄₁₀ of an inch in an 8 inch howitzer, and ¹⁄₂₀ in the Cohorn mortars and howitzers. Their bores and chambers not to deviate from their true diameters or positions more than ¹⁄₄₀ of an inch.

The brass mortars and howitzers are fired twice with their chambers full of powder, and an iron shell. The mortars on their own beds, at about 75 degrees elevation; and the howitzers on their carriages, at about 12 degrees. Iron mortars are proved on their iron beds, with a charge equal to the full chamber, and an iron shot equal in diameter to the shell.