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. It is sufficiently known that the coffee-houses of the eighteenth century were the resort of all who sought intelligence or loved the company of the wits and fine men about town. To one of these, in St. Martin’s Lane, De Moivre went, where it was customary to apply to him for the solution of many questions connected with annuities, and for answers to queries concerning games of hazard, which were propounded to him by those who hoped to turn the chance of loss into a certainty of gain. The payment of these questions was his chief mode of subsistence; and there is something unpleasant in the memory of this man, compelled, in his old age, to be at the bidding of gamesters, and to consort with men who lived on the town by their wits.