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On the Method used by Milne in the Construction of the Carlisle Table of Mortality

Published online by Cambridge University Press:  18 August 2016

William Sutton
Registry of Friendly Societies Institute of Actuaries


Although the Carlisle Table of Mortality, constructed by the late Mr. Milne from certain tabulated facts given by Dr. Heysham, has for many years played an important part in life assurance calculations, I have not been able to find that anyone has taken the trouble to compare the original facts with the Carlisle Table as given to the world by Mr. Milne. This has probably arisen from the somewhat vague manner in which the methods employed are described in Milne's well-known treatise. For many matters, probably, this once-famous mortality table will in the future be supplanted by the Institute's tables published a few years ago; but it is still worthy of some attention, and I therefore make no further apology for bringing this short note before the readers of the Journal.

In Art. 705 (p. 410) of vol. ii of his Treatise, Milne says:— “ Table II ” [being the Carlisle Table, as known to actuaries], “ exhibiting the law of mortality at Carlisle, has been constructed “ from Tables A and C of the last article, by the methods laid “ down from Art. 174 to 183; except that, between the ages of “ 100 and 105 years, the decrements of life are greater than they “ should be, according to the formula of Art. 177. * * * * * “ The population of Carlisle is too small to afford a sufficient “ number of facts for determining the law of mortality with “ accuracy, after the age of 100. * * * * I have therefore “ assumed the annual decrements after the age of 100, as they “ appear in the table, somewhat arbitrarily, so as to fix the limit “ of life at 105 years.”

Research Article
Copyright © Institute and Faculty of Actuaries 1884

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page 114 note * It is evident that these ordinates may form any constant angle with the base; but a right one will be found the most convenient in practice.