8 Mr. T. R. Edmonds on the Law of Human Mortality 



tion of persons whose period of immaturity is prolonged beyond 

 the average period is considerably greater in the population of 

 Sweden than in the population of England. There is, however, 

 some reason to doubt the correctness of the English observations 

 at the age mentioned. Eor errors (in excess of the true rate of 

 mortality) are admitted to exist at the quinquennial intervals of 

 age ending at 30, 40, 50, &c. years ; whilst the rates given by 

 observation for the quinquennial interval of age ending at 20 

 years are assumed to be correct. A correction in diminution of 

 the apparent rate of mortality has been applied in the former 

 case ; and no reason has been assigned for not applying a similar 

 correction to the apparent rate for the quinquennial interval 

 of age ending with 20 years. 



The short intermediate branch of the curve of human life at 

 which the rate of mortality is stationary, or apparently stationary, 

 will be represented by a logarithmic curve of which the equa- 

 tion is Pj=e _(X *, or log e P^=— at. This equation may be 

 deduced from the general formula, which is 



■*'.--?{•- (»+;r) 



,/- n+l t n + l.n + 2 t* \ 



= -"* I 1 " ~2~ a + 2.3 ?- &C 'J 



= -*/■(" 1-M51292- + 1-267414^ -1-363290-^ +&c.T. 

 L a a z a 3 J 



On making a infinite all the terms vanish except the first, 

 leaving log e P,= — ctt, or V t =e" a K If *=1 and a = '0055, 

 then 



P 1=e - fl = e - ,0055 =10-' 0055xA: = -9945150=l-r=l--0054850. 



That is, the constant ratio of decrease in one year of the living 

 between the ages of 9 and 12 years is the number whose hyper- 

 bolic logarithm is — *0055. 



The distinguishing and very useful property of the new for- 

 mula consists in the simple relation which connects together 

 the ratios of the finite differences A log P. If the unit interval 

 of age is small and does not exceed 6 years in the period of 

 manhood, it will be found (using common logarithms) that 



A log A log P, +1 - A log A log T f = 



a + t 



very nearly, a + t representing distance of the ideal zero of 

 life from the middle point common to the two intervals com- 



