Éloge by Condorcet

The French Academy of Sciences published an Éloge of Patrick d'Arcy by Condorcet. Histoire de l'Académie royale des sciences, année 1779 (1782), 54–70. We giive a translation below.

EULOGY OF THE EARL OF ARCY.

PATRICK D'ARCY, Pensioner-Geometer of the Academy of Sciences, Marshal of the King's Camps and Armies, Knight of the Order of Saint Louis, and Commander of the Order of Saint Lazarus, was born in Galway, Ireland, on September 27, 1725, to John d'Arcy and Jane Lynch, daughter of Robert Lynch, Knight-Baronet.

The Earls of Holderness in England, whose name is d'Arcy, regard the d'Arcy family of Ireland as descended from the same stock as their own, and strengthened by a second marriage of John d'Arcy, Lord Justice of Ireland. Under Edward III, the House of Arcy, like other English houses whose name is French and whose origin is unknown, traces its roots back to one of the Norman knights who followed William the Conqueror to England. We will not dwell on these details, which are of little importance to a learned society where works are everything and titles are nothing; but the members of the Count of Arcy may well note with interest that France has some right to claim him over Ireland.

His parents, both Jacobites and Catholics, were oppressed, in the latter case, under cruel laws, unworthy of the wisdom and humanity of English law, but which a misguided policy had deemed necessary in the last century: they had preferred to renounce their rights rather than the loyalty they had vowed to their religion and to the Stuart family.

France is the natural refuge of Irish Catholics who demonstrate activity and talent, and whom the laws of their homeland condemn to uselessness and inaction. The young d'Arcy was sent to Paris in 1739 to stay with one of his uncles; by chance, he ended up in the house where Monsieur Clairaut the elder was staying; he became his pupil, and soon earned the right to be the disciple, or rather the study companion, of Monsieur Clairaut the younger: this was at the time when France was beginning to regain, in the mathematical sciences, the rank it had lost after the death of Descartes and Pascal, and which it has since maintained. Mr. d'Arcy made rapid progress: after three years of study, aged only seventeen, he gave a new solution to the problem of the curve of equal precision in a resistant medium. The early works of Mr. Clairaut had accustomed us to greater marvels; but it was a great deal then to know at seventeen the principles of Transcendent Mechanics and those of Integral Calculus, to set up an equation for a problem of Dynamics, and to construct a third-order differential equation, to which Mr. d'Arcy's method had led him: moreover, he attached to his solution remarks which announced a sagacity of which he gave more certain proofs. The following year, through the solution of a new problem, a solution which also won the approval of the Academy. It concerned determining the curve described in space by a heavy body that slides by its weight along a moving plane, while the pressure of this body simultaneously causes the plane on which it rests to move horizontally. In truth, this problem had been solved by Mr. Jean Bernoulli and Clairaut; but in the solution given by Mr. d'Arcy, using a method unique to him, one already perceives the mark of his talent, and even of that original character which is found in all his productions.

The war then came to take from Science M. le Chevalier d'Arcy (this is the name he took upon entering the Service, and which we will confer upon him in this Eulogy, because it is the one under which he published all his works) he made, as a Captain in the Condé regiment, two campaigns in Germany, and one in Flanders: in 1746 he was destined to join the aid that the King was sending to the Pretender, who had landed in Scotland; it was for his country, for his family, for the rights of the one he regarded as his Prince, that M. d'Arcy was going to fight; his hope was deceived, an English fleet took the convoy; it had been hoped that he would escape under cover of darkness, but he was discovered by Admiral Knowles, with the aid of a night-vision goggles, an instrument which was then beginning to be known in England. Born in Ireland, M. d'Arcy had been captured bearing arms against the Government of his homeland; the law condemned him, but humanity, justice, and politics compelled him to be treated as a French officer.

The Pretender's misfortunes could not alter his rights; not only did M. le Chevalier d'Arcy continue to regard him as the son and heir of his Sovereign, but he also retained the same attachment to the person of Prince Edward He defended the virtues or talents that he believed he saw in himself, with the same zeal with which he had defended his rights to the Crown of England: he had been ready to shed his blood to place him back on the Throne of his ancestors, he would have maintained, at the same risks, that he was worthy of ascending it. Finally, when France refused asylum to a descendant of Henry IV, when Rome abandoned the cause of a Prince whose ancestor had lost three crowns for his zeal for the Catholic religion, when public opinion judged with such severity an unfortunate Prince whose soul could not withstand such a long series of setbacks, M. d'Arcy was not shaken.

The House of Stuart seems to have been shown to the world only to teach kings a lesson in the misfortune and dangers attached to sovereign power; it alone, among so many dethroned families, has seen, in the space of sixty years, two crowned heads fall beneath the axe of the executioners, by artificers cloaked in the guise of Justice. But no family has ever preserved such zealous partisans for so long after its fall. It is impossible, however, to attribute this zeal either to attachment to the Catholic religion, which had been the pretext or the cause of the misfortunes of James II, since Protestants of all sects shared this sentiment; or to ambitious aims, since this zeal outlived all reasonable hope of the restoration of the Stuarts. The cause of such unwavering loyalty can only be found in the very excess of this House's misfortunes, in the terrible proscription pronounced against it by the family that replaced it on the Throne: so powerful is perfection in binding generous souls to those who make its victims!

It was only in 1749, after the peace, that Monsieur le Chevalier d'Arcy was able to enter the Academy; the war had not caused him to abandon the Sciences; but he had chosen in Geometry the type of work most compatible with the active and hectic life he was obliged to lead. In his first Memoir, he had employed Analysis; later he preferred Synthesis, a method that requires more meditation than calculation, and more effort than labor M. d'Arcy read two memoirs to the Academy, even during the war, one in 1746, before being captured by the English; the other in 1747, after his exchange. The first contained a general principle of mechanics, that of the conservation of rotary motion. This same principle had been given in 1745 by M. Daniel Bernoulli and Euler; but it is unlikely that their works would have sought out M. d'Arcy in the Flemish countryside. Moreover, it suffices to see how each of the inventors presented this same principle to feel that Mr. d'Arcy's method is truly his own, and that there is nothing in common between his way of treating mechanical questions and that of these two illustrious geometers. Finally, this principle applies immediately only to free motions, and to extend it to movements subject to certain conditions, M. d'Arcy employed a method that was at once original and simple, elegant and ingenious.

In 1750, he presented his principle in another form, he called it the principle of conservation of action, to strongly oppose it to the principle of least action, which M. de Maupertuis had managed to make very famous, and which M. d'Arcy had attacked in several memoirs. We know what disputes this principle produced, how useless they were to the progress of science, and distressing to those interested in its glory We will not enter into these discussions, which have ceased to interest mathematicians, and which we believe can be considered absolutely settled, since a philosophical geometer has fixed, with as much precision as impartiality, what should be thought of the metaphysics of this principle, in some of the articles with which he enriched the Encyclopedia.
Mr. d'Arcy employed his principle in the solution of several problems; among those to which he applied it, we note the problem of the precession of the equinoxes, perhaps the most difficult in physical astronomy, and the one whose solution contributed most to proving the truth of the general law discovered by Newton Mr. d'Alembert had first solved this problem several years earlier, by a direct method that encompasses the general theory of the motion of finite bodies, whatever their shape. Truth does not allow us to deny that geometers agree to find an error in the new solution given by Mr. d'Arcy; but one must consider that the first mathematicians of Europe had unsuccessfully attempted to solve this problem, that Newton himself had been no more successful than Mr. d'Arcy; and that, finally, since the flaw in his solution was noticed, learned geometers have published new ones, in which errors have also been observed. So, we will feel that the one that escaped Mr. d'Arcy in no way weakens the multiplied proofs that his other works have given of his sagacity and his talents.

The principle of conservation of gyratory motion, like that of conservation of vis viva, like that of least action, finally, like all other principles of the same kind, can be subject to some exceptions, or rather to some modifications; calculation warns of this, it indicates, it corrects the errors into which one could fall by giving these principles too great an extension; thus, they can always be used as mathematical formulas. We note with what success Mr. Bernoulli made use of the principle of vis viva, and what fortunate use M.rs. Euler and de la Grange made of the principle of the least action, but (as these illustrious geometers themselves remarked) it would be a mistake to regard any of these principles as one of the invariable laws of Nature: it must also be noted that two of these principles, when they are not reduced to a single one presented in a different way, can solve all the problems of mechanics, but that in general it is necessary to employ two of them. The clear and simple principle, given by Mr. d'Alembert in 1742, is still valid. the only one that can suffice on its own to solve the problems, because it is direct, and is, so to speak, only the mathematical expression of the first and effective notions of action and motion; it is also the only one, and for the same reason, that can give the demonstration of all the others, and that makes us distinguish the sense in which each of them can be regarded as true.

When M. le Chevalier d'Arcy entered the Academy, Electricity occupied all Physicists. This kind of fashion, which successively fixes the public's gaze and the views of Scholars on the different branches of Science, serves their progress, although it is more often the consequence than the cause of the most brilliant discoveries: but brilliant discoveries almost always leave a gap between themselves and the truths that preceded them, a gap that must be filled. Inventors do not know all the consequences of their discoveries, do not develop all their uses, and that is to fill this void, to follow these conferences, to multiply these uses, the collaboration of several scholars becomes necessary.
Electricity acts on bodies with a force capable of being subjected to calculation, and to analyze electrical phenomena, it was interesting to measure this force; it was therefore necessary to find an electrometer. Electrified bodies attract those capable of receiving electricity from them; two bodies endowed with opposite electricity attract each other even more strongly; But the repulsive force exerted between bodies that have the same type of electricity, and that receive it from the same conductor, appears to be the one whose degrees of intensity are easiest to compare: it was employed in the construction of the electrometer proposed by M. d'Arcy and the King; for M. le Chevalier d'Arcy carried out these experiments in concert with M. le Roi, of this Academy, a student like himself of M. Clairaut. A shared taste for physics had strengthened this bond from their youth, which lasted until the death of M. d'Arcy. After a friendship of twenty years, both believed they had a right to the same position, and this rivalry, which might perhaps have irrevocably destroyed a common friendship, could not alter that between M. d'Arcy and the King, even during the discussion; neither, however, seemed inclined to propose sacrificing his claims, although his rival would not have wished to cede the advantage of compromising his rights to friendship.

M. d'Arcy could not wage war without reflecting on those aspects of that art to which the sciences he cultivated were most directly linked, and during the peace, he occupied himself with perfecting the theory of artillery.

War is a scourge, but it is war itself, and not the art of war, that is fatal. Even as the art is perfected, the evils it engenders become less cruel; for the more successes depend on science and talent, the less passion and fury multiply the massacres and devastation. Thus, just as progress in moral enlightenment will make wars less frequent and less bitter, progress in physics will make them less bloody and less destructive. It is therefore permissible, without harming humanity, to praise works whose object is the perfection of a destructive art. It is permissible to celebrate the genius that creates new means of defending the Fatherland and of forcing to peace those who have disturbed it; and one should only detest the murderous policy that makes these means of preservation and tranquility an instrument of injustice and destruction.

M. le Chevalier d'Arcy published his first Memoir on Artillery in 1750, continued his experiments for a long time, and compiled the results in *Effect on Artillery*, published in 1760. In his work, the author outlines a general theory of artillery, a plan he does not intend to fulfill entirely: he felt that this theory could only be supported by new experiments, and that these experiments required new methods.
One of the most important objectives was the understanding of gunpowder It was necessary to determine, through precise experiments, what proportion in the constituent parts, what quality of grain, and what handling methods gave the powder the most force. It was necessary to know if the force imparted to the projectiles depended on the promptness with which the powder ignited. But to carry out these experiments, a test tube was needed that would give precise results, and none existed. Mr. d'Arcy conceived the idea of suspending a small cannon from a pendulum and judging the force of the powder by the arc that the recoil would cause the cannon to describe. This instrument, which he himself later perfected, was adopted by the Powder Authority. It can make very small differences in the powder perceptible; no external circumstance alters the results. And to judge the superiority of one powder over another, one would hardly find a more sensitive or more reliable instrument.

It follows from Mr. d'Arcy's experiments that the faster the powder ignites, the more powerful it is; that the exact mixture of materials and the dryness of the powder contribute above all to making it better; that finally, small differences in handling produce much more noticeable effects than changes in the proportion of materials, which at first glance would appear much more important.
Mr. d'Arcy then examines what difference the length of pieces of the same caliber, fired with equal charges, produces in the velocity of the cannonball; and what the effects are of different quantities of powder used to load the same piece. To measure the force of the projectiles, he uses a pendulum against which these projectiles strike, and the magnitude of the arcs described by this pendulum gives the forces sought. This method, which Robins employed, is preferable to that in which one would judge forces by range, and Mr. d'Arcy has made the machine he copied from Robins more accurate.

These experiments prove that the greater the length of the pieces, the greater the force; or at least, that for very great lengths, the resulting increase far exceeds both the increase in friction and that of air resistance. On the contrary, the increase in force produced by a greater charge in a cannon of a given length has very narrow limits.

The law of resistance that air opposes to cannonballs was one of the most essential and at the same time the most difficult objects of these investigations. Robins had sensed that if the law which gives resistance proportional to the squares of the velocities holds true, even for elastic fluids at low velocities, it ceases to be accurate, or even approximate, when the velocities become very high. He had conducted a series of interesting experiments to determine the law that should replace this old law, but they were quite insufficient to resolve the question. This same object occupied M. d'Arcy, until the end of his life, with better instruments and a better-combined research plan, had more extensive mathematical resources than Robins, but he was still not satisfied with the results of his experiments and calculations; and this self-discipline, which deprived us of the fruit of his labour, is one more reason to regret his loss.

Attached as Colonel to the retinue of Fitz-James's regiment in 1752, M. d'Arcy served with this corps in the 1757 campaign and was present at the Battle of Rosbach. This regiment, too weakened by the loss it suffered that day, was forced to return to France; M. d'Arcy was then employed under M. le Comte d'Hérouville, to whom the preparations for a planned landing on the coasts of Great Britain had been entrusted. The examination that M. d'Arcy had made during the peace of the coasts of Ireland, an exact knowledge of the character of the inhabitants and their dispositions, the weight that he could have with the remnants of the Jacobite party and the Catholics, whom the injurious precautions taken against them had inflamed without making them any less to be feared; His intrepidity, his audacity, his natural eloquence, full of vehemence and action, his knowledge in all aspects of military art, and finally, his resources against unforeseen eventsresources one can only expect from those who combine practice with profound theoryall these advantages seemed to make M. d'Arcy not only useful, but even necessary, so to speak, for the success of an expedition to the coasts of Ireland. But this project was not carried out; the rank of Brigadier was the reward for M. d'Arcy's labors, and a feeble consolation for the futility of his zeal. Peace soon returned him to the Sciences and the Academy; In 1765 he published a Memoir on the duration of visual sensations, perhaps the work in which his talent for devising devices that lead to accurate and conclusive experiments, and the sagacity with which he was able to combine and vary the experiments to obtain certain and precise results.

A child, by waving a lit coal in a circular motion, produces the appearance of a wheel of fire; a rotating cogwheel presents only a continuous circle; a rapidly vibrating string appears as a lozenge: these effects have been known throughout history.

They prove that our sensations last longer than the action of their cause; the shock produced in the organ continues after the external body has ceased to act. This fact probably occurs for all our senses, and it is from this circumstance that, perhaps, the laws of musical composition can one day be deduced, if these laws have their basis in Nature; but it is especially for the sense of sight that this phenomenon is perceptible, because it is the sense for which we can most easily ascertain that the external action has ceased, and separate the duration of the cause from that of the effect.

No one had yet thought of subjecting these observations to calculation, of determining the speed necessary to produce these appearances, and consequently of measuring the duration of each instantaneous impression: this is the object that M. d'Arcy set for himself. He found that, during a dark night, the sensation produced by a lit coal lasted about eight thirds. If one rotates a circle with only an opening, and places a torch behind it, this torch remains visible when the circle takes only nine thirds to complete its revolution; The more brilliant and extensive the object, in short, the stronger its impression on the organ, the longer the sensation lasts, and the less rapid the movement needs to be.

It is the object that most vividly strikes our eyes that we see and that hides the sight of others. Indeed, whether a more visible body passes before a less visible one, or a less visible body before a more visible one, it is always the less visible one that disappears. The object that produces a continuous sensation, although it has only struck the eyes for an instant, makes a weaker impression than if it acted on the organ for all that time; or rather, one has a mixed sensation which, when the difference in brightness is very great, appears only as a weakening of the greater light, but which, if the difference is less, is a true mixture of the two sensations.

Thus a body can pass before our eyes without being seen, and without marking its presence other than by the weakening of the brightness of the objects it covers.

Thus, when painted yellow and blue cards are rotated, only a continuous circle of green is seen. Similarly, the seven colors of the primer, when rotated rapidly, produce a dark white, and the less dark the faster the movement.

As this duration of sensation increases with the brightness of the object, it would have been interesting to know according to what laws the increase in duration follows that of the intensity of the light. Conversely, one could have investigated by how much the intensity of the light of an object that movement renders continuously visible is degraded; But such experiments presented an almost insurmountable difficulty, and M. d'Arcy had already experienced many of them in his first experiments. The state of his eyesight had forced him to rely on eyes other than his own, and these new investigations required an attention and immobility that he would have obtained with difficulty from an observer who would not have been sustained in this arduous work by the hope of glory, nor by the pleasure of following his own ideas.

The spirit that guided M. d'Arcy in this work also guided him in all his works on physics; he is always seen occupied with comparing the results of observations to mathematical theory. He sought in experience the elements upon which calculation should be exercised, and the foundations according to which Geometry can lead to the discovery of the laws of Nature. At the same time, he uses Mathematics to ask of experiments only what can be expected of them, and to force them to refuse nothing of all that they can give.

Such is in particular the object of a Memoir on hydraulic machines, printed in 1754; a Memoir in which M. d'Arcy shows how easy it is to go astray in seeking by experiment the laws of the possible effects of a maximum or a minimum, and indicates at the same time how one can form a system of experiments which, even in this case, leads to the discovery of these laws.

One also notices ingenious and philosophical views in all his works; The author always presents his research as experiments that he intends to expand and perfect, but he lacked the time to put the finishing touches on them. He had the ambition of his station, the only excusable ambition, the only one that could be useful. His zeal for the sciences had not been weakened by the distractions to which two wars had forced him; several of his works are even dated from the time of these wars. But these long distractions had caused him to lose the habit of working, and even more necessary, the habit of pursuing the same object and the same idea for a long time. Because he saw things on a grand scale, because he wanted to bring rigorous precision to his experiments, the lack of time and the limitations of his fortune too often allowed him to execute only a small part of what he had conceived.

Moreover, M. d'Arcy lived in society, and with a handsome face, an advantageous stature, an ardent character, and an active soul, it was difficult for him not to be drawn into a tedium whose constitution allowed him to forget the fatigue and feel only the pleasures; and the use of his talents for the Sciences must sometimes have suffered from the other advantages that Nature had given him.
In 1770, M. d'Arcy became Marshal-de-camp and President of the Academy; he then seemed to attach himself more particularly to this Company, he regarded it as his homeland, and as a Republic where he wished to be a respected citizen, but only a citizen. The rights, and above all the liberty of the Academy, appeared to be his primary interest; the appearance of the slightest infringement upon these objects, sacred to him, was enough to excite his indignation; he believed that liberty was worth even more than peacea republican opinion that it is dangerous to exaggerate. and which it might be easy to abuse, by applying it to the system of a Learned Society, where, unlike in political associations, the advantages of citizens are not achieved, but the progress of the Sciences, which should be the first goal of the society.

The inheritance of an uncle whom M. d'Arcy had in France, and who had served as his father, military rewards and interests in the mines, where he had provided both funds and useful insights, had increased his fortune; he felt he should share it with a niece raised in Paris under his supervision, and whose mind, character and nascent virtues he had long observed with interest; He married her in 1777, and then took the name of Count d'Arcy: he was at the age when society at large scarcely offers diversions, when it costs more than it gives, and when all men who are dominated neither by ambition nor by a passion for study feel the need for an intimate and domestic society. By marrying his niece, M. d'Arcy hoped to secure their mutual happiness; marriage had strengthened ties already dear to both; the habit of seeing and loving each other had made disappear the distance that the difference in their ages might have placed between them; the authority of a husband... losing what she... The imposing power in the hands of a stranger, and the gentleness of a father's authority, should no longer appear as a yoke, but as a support; finally, from the very first moments of their union, they could flatter themselves that they would experience the happiness of this deep personal trust, of that pure and unalterable friendship which, in ordinary unions, can only be the fruit of a constant tenderness, and which is its sweetest reward. This union, which should have been so happy, lasted little; M. d'Arcy died of cholera morbus on October 18, 1779, having lived with his wife only long enough for her to learn to feel the full extent of the loss she had suffered.

Mr. d'Arcy had friends everywhere, among the Military, in the Academy; if he had had a sociable and easy character, one would only conclude that he was amiable, and not that he was worthy of being loved; but with a firm, independent character and easy to irritate, he could only have friends because he felt the value of friendship, knew its duties, and knew how to deserve it.

The Irish who came to France seeking a friend found in M. d'Arcy a protector, or rather a friend. He shared his fortune with them, looked after their interests, followed their affairs with fervor, and used for them the influence his reputation and the influence of his friends gave him. He consoled or exalted misfortune, defended or supported talent, and protected neither greed nor intrigue, the misfortune into which so often fall those who do good, less out of benevolence than out of vanity or weakness.
A fondness for the English was noticeable in him, which seemed to contrast with the ardor he had shown against England; this is because the difference in governments does not constitute the difference in nations. A single language, similar customs and political opinions, the same tastes, the same love of liberty, make the Irish and the English one people. In pitying his nation oppressed by England, in detesting English domination, M. d'Arcy loved the English nation, was proud of its successes in all fields, even its military successes, although he witnessed them with sorrow. The great men and scholars of England were his compatriots; the English constitution, the one under which he would have preferred to live, only the Prince was a stranger to him. Thus, M. d'Arcy, like many of his compatriots, combined two passions that appear contradictory, but which are merely two variations of the same sentiment: love for his country and its laws, coupled with hatred for its government.

During a trip he made to Ireland in 1767, one of his uncles offered him a considerable fortune if he would settle there; He refused, not wanting to live in a country that appeared free but which England held under its yoke through tyrannical formalities, a country where one would have had to live deprived of the rights of citizenship, or buy them through perjury. He passed through London on the same journey: the English treated him as a man who did honor to the British Nation, and who, by his very refusal to remain under their rule, had acquired a new title in their esteem: his name, however, was not inscribed on the list of the Royal Society, the Law had proscribed him; but the public esteem and generosity of the English Nation protected his person against the attacks of the Law. Ainti, among this people so proud of their liberty and their legislation, there also exist laws which reason and honour forbid to be obeyed.

Death struck Mr. d'Arcy precisely at the moment when the Irish Nation was about to regain, through its courage, a liberty which its divisions and fanaticism had caused it to lose: he would have seen the Ministers of England forced to recognize rights which belong to the Irish, as men rather than as citizens, and which justice does not allow a Nation to deprive of a people over whom it believes it has the right to rule: he would have seen the firm and moderate conduct of his compatriots force the English Nation to understand well enough the interests of its power and its happiness, to prefer having brothers to slaves; And a sovereign people, instructed by its misfortunes, to give, perhaps too reluctantly, an example of justice towards a subject people, a unique example in history, which England must regret not having provided a few years earlier. This revolution would have been for M. d'Arcy the happiest day of his life, but the strong envied him this consolation, and his last gaze did not see the liberty of his country.

The position of Pensioner-Geometer, which M. d'Arcy occupied, has been filled by M. l'abbé Bossut, already an Associate in the same Class.

Last Updated August 2026