Born: 27 September 1725 in Kiltullagh near Athenry, County Galway, Ireland
Died: 18 October 1779 in Paris, France
One of John d'Arcy's brothers was James d'Arcy (born about 1698) who lived in Nantes where he ran a successful winery with his wife Jane Martin. Patrick was smuggled aboard one of his uncle James's ships which sailed from Galway to Bordeaux. When the ship docked in Bordeaux, d'Arcy went to live with his uncle. This arrangement did not last too long for soon it was decided that he would do better in Paris where he could live with another of his uncles, Martin d'Arcy. When James II had been exiled to France in 1688 Martin d'Arcy had followed him and become a successful and wealthy property owner in Paris. D'Arcy was given lodgings in Paris in the home of Jean-Baptiste Clairaut. Jean-Baptiste Clairaut (1680-1766), the father of Alexis Clairaut, taught mathematics in Paris. He had taught his son Alexis mathematics to such a high standard that Alexis read his first paper to the Paris Academy of Sciences at the age of 13. By the time d'Arcy arrived in Jean-Baptiste Clairaut's apartment, Alexis Clairaut was 26 years old and had been a member of the Academy of Sciences for eight years. Jean-Baptiste Clairaut now began to tutor the young d'Arcy in mathematics using similar high powered techniques to those he had used with his own son.
D'Arcy's progress in mathematics was almost as remarkable as that of Alexis Clairaut. In 1742, when he was only seventeen years old, d'Arcy had a paper published by the Paris Academy of Sciences. This paper was Observation sur la courbe d'égale pression dans un milieu résistant . To mark this remarkable achievement, the Academy of Sciences arranged for the renowned artist Hubert Drouais (1699-1767) to paint his portrait. This portrait is displayed with this biography. In the following year he published Solution synthétique d'un Problême de Dynamique proposé par M Daniel Bernoulli . In this paper he solved the problem of determining the curve followed by a body moving under its own weight along a moveable plane which itself has a horizontal motion produced by the moving body.
This was a period with various wars involving many of the countries of Europe. We will not go into the causes of these wars in this article, these are too numerous and too complicated. The War of Austrian Succession began in 1740 and this was only one of several wars involving France through this decade. D'Arcy decided on a military career and joined the Condé Infanterie. He became a captain in this regiment and served under Maurice de Saxe (1696-1750) who led the French armies during the War of the Austrian Succession. D'Arcy was in the Condé regiment of the French army which captured the village of Augenheim on 23 August 1744 and also when they concluded the campaign, in November 1744, with the taking of Freiburg, under the walls of which alone they lost twelve thousand men. He fought with the Condé regiment in a second campaign when he was aide-de-camp to Marshal Maurice de Saxe at the battle of Fontenoy which was fought on 11 May 1745. This battle took place southeast of Tournai, which is in modern Belgium, when 52,000 French troops fought against 50,000 troops consisting of English, Hanoverian, Dutch, and Austrians commanded by William Augustus, Duke of Cumberland of England. The French army contained Irish units which took on the English units in the battle.
After these campaigns, d'Arcy took part in an expedition which attempted to go to Scotland to support Prince Charles Edward Stuart, known as "Bonnie Prince Charlie" or the "Young Pretender". Prince Charles Edward was the grandson of James II, the Roman Catholic king of England who had been deposed in 1688. Prince Charles Edward claimed the British throne and landed in Scotland in July 1745. After military successes he marched south with an army but lack of support persuaded him to return to Scotland. William Augustus, duke of Cumberland, marched north with an army to confront Prince Charles Edward. D'Arcy set out with Count Fitzjames and several hundred men on the ships Bourbon and Charité attempting to sail to Scotland to give support to Prince Charles Edward. The February 1746 London Gazette reported:-
The Bourbon and Charité, two French transports, from Ostend for Scotland, taken 21 February off Ostend by Commander Knowles. They had on board the Bourbon, the Count de Fitzjames [and] M D'Arcy, Captain of Condé's regiment of horse, Aid de camp to Count Fitzjames ... a total of 199 men. On board the Charité ... about 160 men. There was on board likewise all their saddles, arms and horse-furniture, some ammunition, and the military chest containing about 5000 l.The report may be inaccurate as it seems more likely the ships sailed from Dunkirk but were taken off Ostend. D'Arcy was taken prisoner and held for a while in the Tower of London. He was released and was able to return to France in 1747 when the French and English arranged a prisoner exchange. He continued his mathematical studies and published Problème de Dynamique in 1747 and four memoirs in 1749 namely (i) Principe général de Dynamique , (ii) Réflexions sur le principe de moindre action de M de Maupertuis , (iii) Réflexions sur la théorie de la lune, donnée par Clairaut, and (iv) Mémoire sur l'électricité contenant la description d'un électromètre, ou d'un instrument servant à mesurer la force électrique . The memoirs on dynamics studied the 'conservation of momentum of rotatory motion' and the 'principle of conservation of action'. We discuss briefly the memoir on electricity below. He also published Suite d'un Mémoire de Dynamique (1750) and De la courbe d'égale pression lorsque le milieu résiste comme le quarré des vitesses (1750). He was elected to the Paris Academy of Sciences in 1749.
Soon d'Arcy was back in the military. He was made a colonel in Count Fitzjames' Regiment in 1752. However, he continued to publish scientific papers several of which were related to military applications of mathematics. For example he published Mémoire sur la théorie de l'artillerie, ou sur les effets de la poudre, & sur les conséquences qui en résultent par rapport aux armes à feu (1751), Observations et expériences sur la théorie et la pratique de l'artillerie, auxquelles on a joint réponses qu'a faites M de Saint-Auban (1751), Réplique à un mémoire de M de Maupertuis, sur le principe de la moindre action, inséré dans les mémoires de l'Académie royale des Sciences de Berlin, de l'année 1752 (1752), Nouvelle construction de canons légers (1753), and Réflexions sur les machines hydrauliques (1754).
In 1756 the Seven Years War began which was effectively a war between Britain and France but it involved most of the nations of Europe as well as several outside Europe. In 1757 d'Arcy was with the French troops as they took on the Prussians under Frederick the Great near the town of Rosburg. The French with their Austrian allies outnumbered the Prussians two to one, but clever tactics by Frederick the Great saw the Prussians victorious. Many in Fitzjames' Regiment were killed and the remainder, including d'Arcy, returned to France. D'Arcy now worked for Antoine Ricouart d'Herouville (1713-1782) who was planning a French attack on England. D'Arcy had considerable expertise concerning the waters round Ireland and he joined with d'Herouville in the project and carried out some surveys. The plan came to nothing for it was never carried through but for the enthusiastic way that d'Arcy had undertaken the work he was promoted to brigadier.
Let us return to d'Arcy's mathematical and other scientific studies which he carried out after the military campaigns we described above. He published Théorèmes de dynamique (1758), Mémoire sur les degrés de l'ellipticité des sphéroïdes par rapport à l'intensité de l'attraction (1758), Manière de décrire les ovales de Descartes par un mouvement continu (1758), Mémoire sur la précession des équinoxes (1759), and Essai d'une théorie d'artillerie (1760). The last of these memoirs was published by the Paris Academy of Sciences and had a note regarding the refereeing process attached to it:-
Messieurs Clairaut and de Montigny, who had been appointed to examine a work by M Chevalier d'Arcy, entitled "Essai d'une Théorie d'Artillerie" , having made their report, the Academy has deemed this work worthy of printing, in witness whereof I have signed this certificate. Grandjean de Fouchy. Paris, 1 December 1760.We note that 'Clairaut' is Alexis Clairaut, 'de Montigny' is Jean Charles Philibert Trudaine de Montigny (1733-1777), a chemist and member of the Academy of Sciences, and 'Grandjean de Fouchy' is Jean-Paul Grandjean de Fouchy (1707-1788), an astronomer and the Perpetual Secretary of the Academy of Sciences.
D'Arcy also published Précis de l'essai sur la théorie de l'artillerie (1760), Mémoire sur la durée de la sensation de la vue (1765), and Recueil de pièces sur un nouveau fusil (1767).
His 1765 paper on the persistence of vision describes an experiment that he had carried out. It is described in :-
The setting for d'Arcy's investigation was a darkened building in which he constructed a revolving cross, the speed of which he could measure. To one arm of the cross he attached a burning coal and set it spinning. As it gathered speed he noted the point at which the coal appeared to draw a continuous line in the dark. He spun it back and forth, sometimes noting the critical minimum speed for the illusion to take effect as the cross lost momentum. He changed the position of the coal on the cross; viewed it through a telescope, squinted at it through a pinhole; and changed the distance from which he viewed the spinning coal. The results all seemed to be the same, which suggested that the retention of an image lasts 130 milliseconds.In 1767 d'Arcy made a visit to Kiltullagh in Ireland, the place of his birth. One of his uncles offered him a substantial sum of money if he would agree to remain in Ireland but the Penal Laws, which severely discriminated against Roman Catholics, meant that he felt he could not live under such conditions. He returned to France via London where he was well treated by members of the Royal Society who were impressed by his scientific publications and would have liked to have made him a fellow of the Society but his political stance made this impossible. When Martin d'Arcy, the uncle who had looked after d'Arcy when he arrived in Paris as a young man, died he left d'Arcy a considerable fortune. He then married his niece, Jane d'Arcy, in 1777. She had previously moved to Paris to receive an education there and d'Arcy had become very fond of her. He had to obtain permission to marry his niece but this was granted. The marriage took place in the church of Saint Philippe du Roule in the 8th arrondissement, which at that time was near the outskirts of Paris where d'Arcy owned property. The church, designed by Jean-François-Thérèse Chalgrin (1739-1811), was built only a few years before d'Arcy was married there, building having only started in 1774. D'Arcy carried on with his scientific work, collaborating with Jean Baptiste Le Roy (1720-1800) on electricity, and their work was of interest to Benjamin Franklin who was a close friend of Le Roy. Le Roy and d'Arcy had jointly worked on measuring electricity in 1748 and had invented a floating repulsion electrometer to measure electrostatic repulsion. We know that d'Arcy was in London in 1770 since he delivered a letter, a book and pump machine from Le Roy to Franklin's London home. However, the two missed each other and did not meet at that time as Franklin explained in a letter to Le Roy written from London on 2 October 1770.
Only two years after his marriage, d'Arcy died having contracted cholera. He was buried in the church of Saint Philippe du Roule that he had married in. Countess d'Arcy :-
... was an extremely charming woman and she became lady-in-waiting to Marie Antoinette.She returned to Ireland a few years before the French revolution and so avoided the problems that someone of her status would have had in Paris. She remarried in 1783 and died in 1826.
We quote from  regarding d'Arcy's appearance and character:-
The count d'Arcy was of middle stature, and was distinguished by his fine commanding figure. His temper was ardent, his mind penetrating and active, and his soul ambitiously devoted to the pursuit of science. The gaiety of his life, however, the professional interruptions which he experienced, and his limited fortune, prevented him from executing the various experiments which he had conceived. His experiments are all marked by fertility of invention, and his writings are distinguished by profound and ingenious views. His name will be associated with those of Euler, Bernouilli, D'Alembert, and Clairaut, and will long adorn the history of science.Sadly, although the names of Euler, Bernouilli, D'Alembert, and Clairaut still "adorn the history of science", the name of Patrick d'Arcy has been almost totally forgotten. Let us hope that this biography goes just a little way towards remembering d'Arcy in the 21st century.
Article by: J J O'Connor and E F Robertson
MacTutor History of Mathematics