To the same year which witnessed the proposition for the new companies we are indebted for the work entitled the “Doctrine of Chances,” written by Abraham de Moivre, who, owing to the revocation of the Edict of Nantes, was compelled to seek shelter in England, where he perfected the studies he had commenced in his own country. In his boyhood he had neglected classics for mathematics, to the great surprise of his master, who often asked “what the little rogue meant to do with those ciphers.” In 1718, he published the first edition of the above book; and a few extracts from this, which led him afterwards to his hypothetical application of those chances to the survivorship of life, may not be unacceptable; as, though the author deemed it wise to apologise in his dedication for publishing a work which “many people in the world might think had a tendency to promote play,” yet his volume will prove the best apology. The book is very entertaining in its character, and is an evidence of an inquiring and mathematical mind employing itself upon trifling questions rather than remain idle. Thus, Case 1. is “To find the probability of throwing an ace in two throws of one die.” And this kind of problem he varied to almost every possible form. There is “the probability of throwing an ace in three throws,” of “throwing an ace in four throws,” of “two aces in two throws,” of “two aces in three throws,” worked out in a most exact and elaborate manner. From dice he proceeded to lotteries, and showed how many tickets ought to be taken to secure the probability of a prize. The volume, a considerable quarto, was nothing more than an amusing book on gambling and its various chances. But it produced a better effect. A few years later, he published something more worthy of him, in his “Doctrine of Chances, applied to the Valuation of Annuities on Lives,” in which he says, with some appearance of surprise, “Two or three years after the publication of the first edition of my ‘Doctrine of Chances,’ I took the subject into consideration; and consulting Dr. Halley’s tables of observation, I found that the decrements of life, for considerable intervals of time, were in arithmetical progression; for instance, out of 646 persons of 12 years of age, there remain 640 after 1 year; 634 after 2 years; 628, 622, 616, 610, 604, 598, 592, and 586, after 3, 4, 5, 6, 7, 8, 9, and 10 years respectively, the common difference of those numbers being 6. Examining afterwards other cases, I found that the decrements of life for several years were still in arithmetical progression, which may be observed from the age of 54 to the age of 71, where the difference for 17 years is constantly 10.”