‎"GOMPERTZ, BENJAMIN. - PIONEER-WORKS ON LIFE CONTINGENCIES - ""GOMPERTZ'S LAW OF MORTALITY""‎
‎A Sketch of an Analysis and Notation applicable to the estimation of the value of Life Contingencies. Read June 29, 1820. (+) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of Life Co...‎

‎London, W. Bulmer and W. Nicol, 1820, 1825 a. 1862. 4to. No wrappers as extracted from ""Philosophical Transactions"" 1820 - Part II. Pp. 214-294. With titlepage to Part II. + 1825 - Part II. With titlepage to Part II. Pp. 513-585. + Vol. 152 - Part I. Pp. 511-559. All three papers clean and fine.‎

Reference : 46095

‎First appearance of these pioneer-works on life contingencies and insurance mathematics, named by Gompertz himself as ""the science connected with Human Mortality"". He here described how he applied the method of fluxions (first paper) and the mathematical tables for life expectancy (second paper). His model is a refinement of a demographic model of Robert Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz-Makeham law of mortality.""In 1820, in a paper to the Royal Society (the first paper offered), he applied the method of fluxions to the investigation of various life contingencies. In 1824 he was appointed actuary and head clerk of the newly founded Alliance Assurance Company. A year later he published (the second paper offered) what is now called Gompertz’s law of mortality, which states "".... the average exhaustion of man’s power to avoid death to be such that at the end of equal infinitely small intervals of time he lost equal portions of his remaining power to oppose destruction which he had at the commencement of these intervals"". His rigid adherence to Newton’s fluxional notation prevented wide recognition of this accomplishment, but he must be rated as a pioneer in actuarial science and one of the great amateur scholars of his day. Augustus De Morgan called Gompertz ""the link between the old and new"" when he mourned ""the passing of the last of the learned Newtonians."" (DSB).‎