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 , 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. 