That they took warning from this caution may be deduced from the circumstance already stated, that when they petitioned to be released from the payment of so much of the 300,000l. as was not paid[9], the Chancellor of the Exchequer signified his consent, and a clause was inserted to that effect in a bill then passing through the House.
It must not be supposed that any more scientific system than that adopted by the Amicable Society guided these companies. On the contrary, whether an applicant were 12 or whether he were 45, one premium was asked. The policy was granted for a single year, and renewed without reference to age or to health. The earliest document possessed by either of these companies is dated 25th November, 1721. It was granted by the London Assurance to Mr. Thomas Baldwin, on the life of Nicholas Bourne, for 100l., five guineas being the premium for twelve months; and this was the annual per centage paid for many years. With such a system, it is not to be wondered that the success of the company was slow.
CHAP. VI.
SKETCH OF DE MOIVRE.—HIS DOCTRINE OF CHANCES.—KERSSEBOOM.—DE PARCIEUX.—HODGSON.—DODSON.—FIRST FRAUD IN LIFE ASSURANCE—ITS ROMANTIC CHARACTER.—THOMAS SIMPSON.—CALCULATIONS OF DE BUFFON.
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.”
The greatest difficulty which occurred to him was to invent practical rules that might readily be applied to the valuation of several lives, “which was, however, happily overcome, the rules being so easy that, by the help of them, more can be performed in a quarter of an hour, than by any method before extant in a quarter of a year.”
It was first published in 1725; and finding thus from Halley that, for several years together the decrement of life was uniform, it being only in youth and old age any considerable deviation took place, he founded an hypothesis that it was uniform from birth to extreme old age; in other words, that out of a given number of persons living at any age, “an equal number die every year until they are all extinct.” On this he gave a general theorem, by which the values of annuities on single lives might be easily determined. This was of great use at the time, no table of the real value of annuities having then been published, except a very contracted one founded on Halley’s paper; and if subsequent investigations proved that De Moivre was utterly wrong, his conclusions formed the basis of many a future calculation.
Although the ability of De Moivre was recognised by the Royal Society when it appointed him arbitrator in the contest betwixt Newton and Leibnitz, and although Newton, when applied to for an explanation of his own works, would often say “Go to De Moivre, he knows better than I do,” yet it is to be feared that golden opinions were won by him more freely than guineas.