From this period he seemed to decline in health, expressed a loathing for the place where he had once been so happy; change of air was prescribed, and he left the men whom he had deceived, chuckling at the success of his infamous scheme. It need not be repeated, that the poverty-stricken gentleman of the suburbs, the gambling captain of Queen Square, and the merchant of Liverpool, were identical. That so successful a series of frauds was practised appears wonderful at the present day; but that the woman either possessed that power of simulating death, of which we read occasional cases in the remarkable records of various times, or that the physicians were deceived or bribed, is certain. There is no other way of accounting for the success of a scheme which dipped so largely into the pockets of the underwriters. The next movement in the scientific annals of life assurance was made by Thomas Simpson, a natural and self-taught mathematician, whose life prior to throwing himself on the world of London for support had been somewhat of a vagrant one. He had cast rustic nativities, told fortunes, advanced courtships, and occasionally varied his vagabondism by undertaking to raise the devil, an attempt in which he was so successful, that he sent his pupil mad, and was obliged himself to leave the village. In 1740, he produced a volume “On the Nature and the Laws of Chance;” in 1742, this was followed by his “Doctrine of Annuities and Reversions,” deduced from general and evident principles, with tables showing the value of joint and single lives. In 1752, he made an additional contribution to the statistics of annuities, as he published in his “Select Exercises” a supplement, wherein he gave new tables of the values of annuities on two joint lives, and on the survivor of two lives, more copious than hitherto. He first attempted to compute the value of joint lives; but as these were still taken from the London Bills of Mortality, they were by no means fit for general acceptance. He treated his subject, however, more broadly and clearly than it had been previously treated, giving some of the best tables of the values of life annuities, which were published for many years. Though the manner in which they might be computed had been shown by Dr. Halley, it is to the self-taught Simpson we are indebted for their practical application. In 1760, M. Buffon published a further contribution to the statistics of assurance, in a table of the probabilities of life, estimated from the mortality bills of three parishes in Paris, and two country parishes in its neighbourhood. The following are some of his calculations:--“By this table,” says the author, “we may bet 1 to 1 that a new-born infant will live 8 years; that a child of one year old will live 33 years more, that a child of full two years old will live 33 years and 5 months more, that a man of thirty will live 28 years more; that a man of forty will live 22 years longer, and so through the other ages.”