Protestant Exiles from France/Volume 2 - Book Third - Chapter 9 - Section I
Chapter IX.
FELLOWS OF THE ROYAL SOCIETY:— DE MOIVRE, DURAND, DESAGULIERS, AND DESMAIZEAUX.
I. Abraham De Moivre, F.R.S.
The father of this able man was a surgeon at Vitry, in the province of Champagne. His surname was Moivre, according to Haag and the French authorities. Rut the young refugee styled himself De Moivre.
Abraham was born at Vitry, May 26th, 1667, and there his first school education was superintended by the Brethren of Christian Doctrine (les frères de la doctrine chrétienne). At the age of eleven he was sent to the University of Sedan, and was placed under the charge of the Greek Professor Du Rondel. His masters, struck with his precocious talents, aimed at making him an eminent classical scholar, and were disappointed by observing his strong bent for arithmetic. It was probably Du Rondel who was in the habit of asking “what the little rogue meant to do with those cyphers.” He dutifully pursued classical studies ; but he deserted his fellow-students in their hours of recreation, shutting himself up with a dumb companion, namely, Le Gendre’s Arithmetic. He had completed his “humanities” in 1681, when the College of Sedan was tyrannically suppressed. He took his course of philosophy at the University of Saumur. He then came to Paris for Physics. Here his father joined him, having retired from his medical practice at Vitry — probably a forced retirement, as Protestants were, by successive curtailments of the Edict of Nantes, excluded from the liberal professions. Abraham pursued his mathematical studies under a tutor of great reputation, Jacques Ozanam. But the Revocation of the Edict of .Nantes found the student firm in Protestant doctrine. The agents of government, accordingly, shut up the young heretic, now in his nineteenth year, in the Priory of St Martin, in order that he might discover it to be right or politic to go over to the Roman Catholic religion.
The obstinate boarder gave his ecclesiastical guardians no more satisfaction than the majority of the Huguenot boys and girls gave to the various teachers and masters under whom persecution drove them. There is nothing more interesting in Benoist’s History than his account of the steady resistance which mere children offered to ghostly proselytizers. This fortitude, associated with a mutual support of each other’s resolution, often resulted in their returning home better instructed in Protestant doctrines than other young persons carefully taught by their parents. Little girls, with nerves shaken by cruelty and false alarms, were unshaken in their faith. The boys wore out the patience of their teachers, or kept them so perseveringly on the defensive that categorical instruction could not be given for want of time. To questions out of the Roman Catholic catechism they replied with answers which they had formerly learned from the Protestant; and a devout audience, invited to hear the proficiency of a class of supposed proselytes, were startled with a loud repetition of such sentiments as that the Pope is Anti-Christ, that Romish worship is idolatrous, and that the so-called Catholic Church is the mystic Babylon, and is spiritually named Egypt. Sometimes the converters tried to humour them in their jocularity, and to insinuate their dogmas upon their memory by stratagem; but they succeeded only in making themselves and their tuition ludicrous. In the house the boys burnt devotional books, broke images, made an uproar at meal-times, and mixed lumps of lard with fast-day fare. In church they talked or sang where the rubric enjoined silence, moved about from seat to seat, turned their backs on the semi-pagan altar, and stood or sat cross-legged when the congregation knelt. Besides which, there were constant escapes, leaping over high walls, and jumping out of windows; and even when recaptured, the young lion-hearts were not conquered.
Whether Abraham De Moivre made as noisy resistance we are not informed; but the result was the same. Being quite resolute, he received his discharge on the 15th April 1687, and was allowed to retire to England. And so he came to London, accompanied by his brother Daniel.[1]
At the age of twenty he found himself in the city, where he had immediately to begin a defensive war against starvation. He turned his favourite studies to account in order to earn a livelihood. He became a teacher of mathematics. He also gave lectures on natural philosophy, which, however, he discontinued, having not acquired any great command of the English language, and being, like many scientific men, inexpert in performing experiments before an assemblage of spectators.
But as an important epoch in the literature of the physical sciences, the date of his arrival in London was a happy one for him. In 1687 Isaac Newton had published the “Principia.” The fame of this great work soon reached the ears of De Moivre. Being written in Latin, it was no sealed book to him; and his classical and mathematical scholarship was such, that he thoroughly understood it, which few did. This led to his being admitted to the society of Newton and his learned friends. And although the renowned Englishman was his senior by a quarter of a century, he honoured the clever and accomplished refugee with his special regard. He thus obtained a gratifying position among English philosophers, which his own abilities enabled him to keep. It is said that in 1692 he had gained the friendship of Halley, and his intimacy with Newton began soon after that date.
The article in the “English Cyclopaedia of Biography” states that although De Moivre could appreciate such writings as Isaac Newton’s, there is scarcely a trace either of physical or geometrical investigations in his own writings, when his career of authorship began. His power lay in “pure mathematics of the kind now called analytical.” His first appearance in print was in the “Philosophical Transactions” for 1695; the subject of his paper was “The use and excellence of Newton’s Doctrine of Fluxions for the solution of geometric problems.” Another paper appeared in 1697 on the method for finding the root of an infinite equation. In this year, the thirtieth of his age, he was made a Fellow of the Royal Society.
Daniel De Moivre obtained a good position, but in w hat line we are not informed. In or before the year 1706 he was married to "Anne," and in the register of the French Church in West Street, on 16th January 1707, he appears as a father presenting his son, Daniel, for baptism; he is styled “Sieur Daniel De Moivre,”and the godfather is “Sieur Abraham De Moivre.” [A daughter, Anne, was baptized on 12th March 1708 (n.s.).]
Abraham De Moivre seems to have increased his reputation in a controversy with a Scottish author, Dr. George Cheyne, who settled in London in 1701. This medical gentleman having adopted a novel doctrine of fluxions, published a treatise in Latin against Newton and his admirers, including De Moivre. This was in 1703, and in the following year De Moivre published “Animadversiones in Geo. Chenoei Tractatum,” which was tolerably cutting. It drew out a still more cutting rejoinder from Cheyne, “Adversus Abr. De Moivre,” which being not mathematical, but personal, was left unanswered. The Frenchman had the best of it, which the Scotchman soon admitted with recovered temper, saying as to his own treatise that it was conceived in ambition and brought forth in vanity.
A contention arose between Newton and Leibnitz for the honour of the invention of the method of fluxions. The Royal Society appointed De Moivre to investigate and report upon the rival claims — a flattering tribute to “his abilities, acquirements, and impartiality.” The facts are now believed to be these, Newton invented the method in 1667; Leibnitz in 1677 sent his own method to Newton, with a complete system of notation, only in the latter particular excelling Newton, whose notation was then incomplete. But Leibnitz having published his method to the world in 1684, and Newton having delayed publication till 1687, the question as to originality very naturally arose.
De Moivre superintended and revised Clark’s translation of Newton’s Optics, and is said to have spared neither time nor trouble in the task. According to the style of life in those days, Newton met him every night at a coffee-house (probably Slaughters’) in St. Martin’s Lane. When they had finished their work, he took De Moivre home with him to spend the evening in philosophical conversation. It is said that when Sir Isaac was asked to explain statements occurring in his own works, he would often say, “Go to De Moivre, he knows better than I do.” Sir Isaac died on 28th March 1727 in his eighty-fifth year; he had often said to De Moivre (this anecdote was told by Dr. Maty) that, if he were not so old, he would like to have another pull at the moon.
De Moivre’s conversation, except in such a circle as Newton’s, was not abstruse or pedantic, but touched on every variety of interesting subjects. His style was forcible and solid, rather than lively and elegant, but it was singularly correct and distinct. A traveller named Jordan, who visited England in 1733, describes him as a man of talent, and very agreeable.
De Moivre is regarded as the father of tables of rates according to which a life is assured, or annuities for the remainder of life are negotiated. His calculations at first seemed trifling, even to himself, as they appeared in a quarto volume which he published in 1718, and dedicated to Newton, entitled “The Doctrine of Chances, or the method of calculating the probability of events at play.” In his preface, he pleasingly acknowledged the friendship of Monsieur de Monmort (author of the “Analyse des jeux de hazard”), also of the Hon. Francis Robartes, on account of whose desire and encouragement he had about seven years before given “a specimen in the Philosophical Transactions of what I now more largely treat of in this book.” The following is the dedication:—
“To Sir Isaac Newton, Knight, President of the Royal Society. — Sir, — The greatest help I have received in writing upon this subject having been from your incomparable works, especially your method of series, I think it my duty publicly to acknowledge that the improvements I have made, in the matter here treated of, are principally derived from yourself. The great benefit, which has accrued to me in this respect, requires my share in the general tribute of thanks due to you from the learned world. But one advantage, which is more particularly my own, is the honour I have frequently had of being admitted to your private conversation, wherein the doubts I have had upon any subject relating to mathematics have been resolved by you with the greatest humanity and condescension. Those marks of your favour are the more valuable to me, because I had no other pretence to them, but the earnest desire of understanding your sublime and universally useful speculations. I should think myself very happy if, having given my readers a method of calculating the effects of chance as they are the result of play, and having thereby fixed certain rules for estimating how far some sort of events may rather be owing to design than chance, I could by this small essay excite in others a desire of prosecuting these studies, and of learning from your philosophy how to collect, by a just calculation, the evidences of exquisite wisdom and design which appear in the phenomena of nature throughout the universe. — I am, with the utmost respect, Sir, your most humble and obedient servant,
He was consulted on more substantial matters than games of chance. On Mr Peter Le Neve’s death in 1729, his estates at Wychingham and other towns of Norfolk, were claimed by John Norris, Esq., whose grandfather had purchased the reversion upon the failure of the male line for £30. The litigation was ended by an appeal to the House of Lords, who sustained Mr Norris’s claim. On the other side it had been contended that £30 was no valuable consideration for estates which were yielding £ 1500 a year; but on the evidence of De Moivre and others well versed in calculations, it was judged to have been a full price for the chance at the time of the purchase, when many remainders to heirs-male were in force.[2]
His miscellaneous investigation ripened into a useful theorem, by which the values of annuities on single lives might be determined. “By the most simple and elegant formulae,” says Francis Baily. “he pointed out the method of solving all the most common questions relative to the value of annuities on single and joint lives, reversions, and survivorships.”[3] This eulogium refers to De Moivre’s work on “Annuities and Lives,” published in 1724. In 1742 Professor Simpson of Woolwich took up this subject, and his book called up De Moivre in a second edition, criticising this apparent intruder on his own field with some harshness. In a third edition published in 1750, “he omitted the offensive reflections of his former preface.” It has been erroneously stated that Simpson had done justice to his predecessor in his Treatise on Life Annuities. Wishing to quote “the well-deserved compliments to De Moivre,” I searched Simpson’s pages, and found that he recognised no contributions to the study since the publication of Halley’s Papers, although the greatest scientific men acknowledge that De Moivre had ably and largely supplemented Halley’s speculations and calculations. De Moivre was not mentioned, unless he was alluded to in the statement that “some writers” were neither precise nor consistent (Simpson’s exact words I forget). That the venerable mathematician felt indignant with the juvenile author was scarcely to be wondered at.
The Fourth Edition, published in 1752, has the following dedication:—
“To the Right Honourable, George, Earl of Macclesfield, My Lord, I have had the honour of dedicating three editions of this work, the first to your noble father, the other two to your Lordship, who, in a continual endeavour to promote arts and sciences, especially those called mathematical, — in a constant benevolence to all mankind, particularly to those who study the good of society, — and in a regular discharge of all the important duties of life, are truly his successor. I can have no pretence to seek elsewhere for a patron to this fourth edition, which the demand I have met with for the copies, and some typographical errors (heretofore overlooked), have rendered necessary. And therefore I again trespass on your Lordship’s indulgence in this address, well knowing that your usual candour and goodness will excuse any imperfections that may still remain in the performance of, My Lord, Your Lordship’s most obedient and most humble servant,
His various Papers in the Philosophical Transactions are, says the English Cyclopedia, “of sterling value on the subjects of which they treat.” Their dates range from 1695 to 1744. The same authority states, that his mathematical “writings on analysis abound with consummate contrivance and skill; and one at least of his investigations had the effect of completely changing the whole character of trigonometrical science in its higher department.” It was in 1730 that he published his “Miscellanea Analytica de Seriebus et Quadraturis,” a work which, we are informed, “contains several very elegant improvements in the known methods of termination of series, as well as some new methods.” The author had not the gratification of presenting it to Newton, for the veteran philosopher had died three years before, but on a copy being sent to Berlin, Monsieur Naudé proposed the election of De Moivre as a member of the Academy of Berlin, and he was elected by acclamation.
The complete title of his “Miscellanea Analytica” is as follows:— “Miscellanea Analytica de Seriebus et Quadraturis — accessere variae considerationes de methodis comparationum, combinationum et differentiarum, solutiones difficiliorum aliquot problematum ad sortem spectantium, itemque constructiones faciles orbium planetarum, unà cum determinatione maximarum et minimarum mutationum quae in motibus corporum coelestium occurrunt. Londini, Excudebant J. Tonson et J. Watts, 1750.” The dedication, which is “spectatissimo viro Martino Folkes armigero,” mentions that the principal contents of the book had been submitted to, and approved by Newton (14th January 1723), Professor D. Sanderson and Rev. D. Colson; and that the theorem concerning the section of an angle had been read to the Royal Society, 15th November 1722.
The honour which he most dearly prized was reserved for the last year of his life. The Academy of Sciences at Paris, overcoming all prejudices against a branded refugee, elected him as one of its Foreign Associates on the 27th of June 1754 On receiving the news of his death, which took place on the 27th November following,[4] an Eloge on the far-famed exile was drawn up by Grandjean de Fouchy, and inserted in the “Recueil de l’Academie des Sciences.”
De Moivre received honours, but no emoluments. He earned a precarious support by working out calculations on probabilities at play and on contingencies of various kinds, and he took fees from his employers. He was one of the attractions for an evening’s lounge in the coffee-house; and without doubt many of the eminent frequenters of this place of literary resort commiserated his straitened circumstances, and were glad to furnish him with work suited to his talents and tastes. At the age of eighty-seven he was left almost alone in the world, and was dependent on the fees above-mentioned. He continued in the possession of his faculties almost to the last. During the last month of his life he lost his sight and hearing, and during a visitation of lethargy, he slept his last sleep; thus he passed away in his eighty-eighth year.
The best monument to Abraham De Moivre is the honourable mention made of him by Sir John Leslie, in his dissertation prefixed to the Encyclopaedia Britannica. The pre-eminent Scottish mathematician testifies that “De Moivre, a French refugee,” was “a man of learning and profound science;” “his analytical discoveries extended his fame, and his good conduct earned him respect.”[5]
- ↑ I have ventured to say “1687” in spite of Haag’s “1688,” because our King James’ warrant “to our Attorney or Sollicitor-Generall” for the Naturalisation of Abraham and Daniel De Moivre was dated Whitehall, 16th December 1687, and the naturalization was granted at Westminster 5th January 1688 (new style).
- ↑ Nichols’ “Literary Anecdotes.”
- ↑ In an Essay by De Parcieux (1746), I find materials for a brief description of De Moivre’s investigations on the probabilities as to life and death among individuals in the population. De Moivre followed Halley in adopting the death-registers of Breslau as his basis, its population being more stationary than that of London. His calculations of the value of annuities extend from the age of one year up to eighty-four, while Simpson’s calculations extend from six to seventy-five, Simpson’s basis being an annuity of £10, and De Moivre’s an annuity of £100, both at 5 per cent.
- ↑ “Died 27th Nov. 1754, Mr. Abraham De Moivre, well known for his mathematical writings, F.R.S., and of the Royal Academy of Sciences at Paris.” — Gentleman’s Magazine.
- ↑ There is no known link of the De Moivre family with this century except one in the Gomm Pedigree. Daniel De Moivre, junr., son of the refugee Daniel, married Marianne Jaquin, and left a daughter, Anne De Moivre, who died in 1814. [Marianne, having become a widow, re-married in 1737 with William Gomm, ancestor of Field-Marshal Sir William Maynard Gomm.]