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 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.” 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, 