ARCY D', PATRICK, one of the pensioners of the French academy, marshal of the armies of the king, and knight of the order of St Louis, was born of Roman Catholic parents, at Galway, in Ireland, on the 27th Sep tember, 1725. At the age of fourteen he was sent to Paris to one of his uncles, who accidentally placed him in the same house where M. Clairaut the elder happen ed to lodge. He immediately became his pupil, and was soon qualified to prosecute his studies along with M. Clairaut the younger. At the age of seventeen, he gave a new solution of the problem of the curve of equal pressure in a resisting medium ; and, in the following year, he determined the curve described by a heavy body, which moves by its own weight, along a moveable plane, at the same time that the pressure of this body gives a horizontal motion to the plane itself. had been resolved by John Bcrnouilli and Clairaut ; but the solution of the young D'Arcy exhibited great ingenuity and originality of thought.
As a captain in the regiment of Conde, he served two campaigns in Germany, and one in Flanders ; and, in the year 1746, he accompanied the expedition sent out by the French to convey succours to the pretender in Scot land. The fleet, however, was taken by the English, and the chevaliec,D'Arcy, though carrying arms against his native country, was humanely treated as a French officer, and was exchanged in 1747.
After the peace, in 1749, D'Arcy entered the aca demy. During the war he had read two memoirs, one in 1746, before his capture by the English, and another in 1747, after his exchange. The first of these memoirs contains an account of the general principle in Dyna mics, called the conservation of the momentum of rotato ry motion, which he discovered at the same time with Euler and Daniel Bernouilli. He has shewn that the sum of the products of the mass of each body, by the area which its radius vector describes round afixed point, is always proportional to the times. In the year 1750, he presented this principle under a new form, which he called the principle of the conservation of action, in opposition to the principle of least action, which Mau pertuis had discovered, and which the chevalier D'Arcy had attacked in several memoirs.
While D'Arcy was directing his attention to the ma thematical and physical sciences, he did not neglect those subjects which were more intimately connected with his profession. He published his first memoir on artil lery in 1750 ; and, after prosecuting his experiments on that subject for a long time, he published the results in his Essai sur l'Artillerie, which appeared in 1760.
He found that the force of gun-powder increases with the rapidity of its inflammation, and that it depends great ly on the exact proportion of the ingredients, on the dry ness of the powder, and on the mode of making it. From a number of experiments with an improved machine, similar to that which was used by our celebrated coun tryman, Mr Robins, the chevalier D'Arcy found that the force of the ball increases with the length of the gun ; and that, in very great lengths, the augumentation of force greatly exceeds the augmentation of friction, and that of the air's resistance. On the contrary, the increase of force obtained by a greater charge of powder in a can non of a given length, is confined within very narrow limits.
Being attached as colonel to the regiment of Fitz james in 1752, M. D'Arcy served along with it in the campaign of 1757, and was present at the battle of Ros bach. Weakened by the loss which it had sustained, this regiment returned to France, and M. D'Arcy was then employed under. the count Herouville, who was charged with the preparations for a descent upon the coast of Great Britain. The local information which he possessed, rendered him peculiarly qualified for assist ing in these preparations ; but the project was never executed, and M. D'Arcy was raised to the rank of bri gadier, as a reward for the zeal which lie had exhibted.