Life tables founded upon the discovery of a numerical law, regulating the existence of every human being : illustrated by a new theory of the causes producing health and longevity / by T.R. Edmonds.

  • Edmonds, T. R. (Thomas Rowe), 1803-1889.
Date:
1832
Catalogue details

Licence: Public Domain Mark

Credit: Life tables founded upon the discovery of a numerical law, regulating the existence of every human being : illustrated by a new theory of the causes producing health and longevity / by T.R. Edmonds. Source: Wellcome Collection.

Provider: This material has been provided by The University of Glasgow Library. The original may be consulted at The University of Glasgow Library.

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    xvu that age and any other in the same period for the sake of simplicity, the o-iven ase may be assumed to coincide with that at which the period commences. Let, now, {y) represent the number Living or Surviving at any time {x). The force of mortality at that time = up' = decrement in unit of time on unit of hfe; the finite decrement of (?/) at that time = 1/ x ecp; and the true decre- ment, or the decrement in an infinitely small given time, = yxp'^dx ; that is, — dy ■= yxp'^dx. Using (l) to signify hyperbolic logarithm, and (e) to denote the base of a. 9 T^'°' that system, we obtain by integration I- = j^p' and ~ = ^ a If it be assumed that y = 1 when x = 0, then g = e^P and the equation becomes y = e^P x e or y = e^P And calling the modulus of the common system (k), and using (a) to signify common logarithm, the equation will finally become,— Fa y =:\0^P The above is the equation to the curve of Vitality, or rather is the form of the equation to each of the three segments of that curve. In each segment, the quantity (p) has its appropriate value. The first segment terminates near the age of nine years; the second near the age of fifty-five. There may exist a very small fourth segment near the age of ten, in which p=\. The above formula will not serve to dis- cover directly the number of survivors from birth at any age above nine years. Before it can be so applied, two constants must previously be deduced from it: first, the value of (y) at the end of the first seeraent and then the value of (?/) at the end of the second segment. These constants, being used as multipliers, will give the values of (1/) at any age, corresponding to a given number born. These values of (1/) at annual intervals constitute a Table of Mortality. From the general formula may easily be deduced an expression for the probability of living one year, at any age; by means of which, Tables of Mortality may be constructed with great rapidity and security from error. The honour of first discovering that some connexion existed between Tables of Mortality and the algebraic expression {a!^) belongs to Mr. Gompertz: but, to arrive at this single common point, his course of investigation differs so widely from mine, that appearances will be found