THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



JANUARY 1866. 



I. On the Law of Human Mortality expressed by a New Formula, 

 By Thomas Rowe Edmonds, B.A. Cantab.* 



THE love of life being the strongest of human passions, the 

 most interesting of all laws ought to be the law which 

 regulates the rate of decrement of human life from the time of 

 birth until extreme old age. 



Tables of mortality, in great variety, have been constructed for 

 the purpose of exhibiting particular rates of decrement according 

 to age appropriate to particular populations at different times. 

 In nearly all these Tables there is exhibited a uniformly decreasing 

 rate of decrement from the time of birth until the age of about 

 10 years, and a uniformly increasing rate of decrement from the 

 age of about 15 years until the last age in the Tables. The ap- 

 pearances presented by all these Tables are such as to warrant 

 the supposition that the rates of decrement in the period of child- 

 hood, as well as in the period of manhood, are functions of the 

 age measured from birth or some other fixed time in the age of 

 man. It will presently be seen that such supposition is well 

 founded and in conformity with the facts given by observation. 

 The rate of decrement of life will be found to be a certain func- 

 tion of the age, which is remarkable for simplicity and novelty. 



If P, be taken to represent the number living or surviving at 

 the age t years, out of a given number born alive (P ), the 

 number dying in the (^H-l)thyearof age will be P* — V t+l = AP*. 

 The mean rate of decrement, or mean ratio of dying to living, 

 during this year of age will be represented by AP* divided by 

 the mean number living throughout the year. Such mean num- 

 ber is J(P*-f Pf +1 ), or P^ very nearly; so that the mean rate 



* Communicated by the Author. 

 Phil. Mag. S. 4. Vol. 31. No. 206. Jan. 1866. B 



