Academic Career
In January 1810 he obtained an engagement at Mr. Rainhall's school as teacher of arithmetic, at a salary of 20l., and there commenced calculating the times of the eclipses and exhibiting their mode of occurrence by diagrams. He opened a school of his own in the summer of 1811 in James Street, Old Street; in the following year moved into a better house in Lizard Street, Bartholomew Square, St. Luke's, and joined the Mathematical Society in Crispin Street, Spitalfields, where the extensive library was of much use to him. Meanwhile he corrected the press of a Welsh magazine then published, and wrote his ‘Key to Bonnycastle's Trigonometry’ (1814), which established his character as a mathematician.
After this he received private pupils, and among them a person connected with an assurance office desirous of studying the theory of life assurance. Davies had no knowledge of the subject, but soon mastered it. Sir John Franklin came to Davies after many years of service at sea to increase his knowledge of some of the higher branches of the science of navigation. Davies now gave instruction to several gentlemen connected with insurance associations, and was employed to do work for some of the offices. William Morgan, the actuary of the Equitable, furnished him with a certificate of actuarial competency. In 1820 he received the large silver medal of the Society of Arts for a most ingenious sundial constructed by him. The Directors of the Guardian Assurance Company applied to him for advice and assistance when drawing up their constitution, and he was engaged to construct the necessary tables. About the close of 1823 he was appointed the regular and permanent actuary of that company, an appointment which he held for nearly a third of a century. In the same year (1823) the Reversionary Interest Society was established, and for this company he constructed many elaborate and useful tables. In the first of his reports to the founders of that institution he announced that he had ‘ascertained upon indubitable evidence that a diminution had taken place in the mortality of Great Britain during the last hundred years.’ In 1825 he published ‘Tables of Life Contingencies, containing the rates of mortality among the members of the Equitable Society, and the value of life annuities, reversions, &c. computed therefrom; together with a more extensive scale of premiums for life assurance, deduced from the Northampton rate of mortality, than any hitherto published, and the progressive values of life policies.’ Davies was the remodeller of George Barrett's columnar plan of constructing mortality tables, and so arranged his tables that they may almost be said to be a new discovery (WALFORD, Cyclopædia, i. 618–23). Davies's fame as an actuary became widely known.
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