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On an application of the Theory of the Composition of Decremental Forces

Published online by Cambridge University Press:  18 August 2016

W. M. Makeham
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Extract

The determination of the probable effect, upon the increase of population, of the extinction of small pox, is a problem which has been discussed at some length by three of the great continental mathematicians of the last century, namely, D. Bernouilli, D'Alembert, and Laplace. I propose, first, to solve the problem by what may be termed the theory of the composition of decremental forces, and then to reproduce (by way of comparison) from Mr. Todhunter's History of the Theory of Probabilities, the solutions given by the three eminent mathematicians in question.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 18 , Issue 5 , October 1874 , pp. 317 - 322
Copyright
Copyright © Institute and Faculty of Actuaries 1875

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References

page 318 note * See Journal, vol. xiii, p. 350.

page 319 note * If F x denote the decremental force of any series Lx, the relation between them is universally represented by the equation ε-∫Fx dx=Lx.

page 321 note * S x is the function denoted by s in Laplace's investigation.