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



from 75 to 85 years. The appearances presented are not, how- 

 ever, inconsistent with the truth of the new formula. To recon- 

 cile the new formula with the facts, it will suffice to make the 

 reasonable supposition that the position of the ideal zero of life 

 in the period of manhood is variable in the different classes con- 

 stituting the total populations observed, say from the age 105 

 years for village population to the age 95 years for city population. 



In addition to the new formula, by which the law of human 

 mortality, according to age, may be expressed, there exists an 

 old formula by means of which the mortality at all ages may be 

 equally well expressed — with this difference only, that the new 

 formula fails for ages exceeding 85 years, whilst the old formula 

 fails for ages under 2 years. Both formulae may be said to ex- 

 press laws of mortality ; but the law contained in the old for- 

 mula is to be regarded as no more than an empirical law 

 secondary to, and dependent on, the true law exhibited by the 

 new formula. 



According to the empirical law contained in the old formula, 

 the rate of mortality at ages exceeding 55 years increases in a 

 constant ratio of 1*08 per cent, for every additional year of age. 

 From age 12 to age 55 the constant ratio of increase is 1*03 per 

 cent. From age 8 to age 12 the rate of mortality is constant 

 and at a minimum. From the time of birth to the age of 8 years 

 the annual ratio of decrease of mortality, according to the old 

 formula, is 67*6 per cent. From this empirical law is deducible 

 the differential equation 



d . log P,= — uptdt, 

 which on integration yields the equation following, 



comlogP,= ^(1-jp*), 



\p having three different values, —'17, + '0128, and + -0333 

 in the three periods of infancy, florescence, and senescence. 



The above formula for com log Y t was first published in the 

 year 1832. The formula with the three values of p above 

 given, was used for the construction of three theoretical Tables 

 distinguished as exhibiting village, mean, and city mortality re- 

 spectively. Accompanying these theoretical Tables was pub- 

 lished a full collection of derivative Tables, consisting chiefly of 

 values of annuities on single and joint lives at various ages and 

 various rates of interest*. The minimum rates of mortality 

 respectively adopted in the three Tables at the age of 10 years 

 were '005, *006, and '0075 per annum. 



The theoretical Table of " Village Mortality " indicates rates 

 of mortality which at all ages agree very closely with the rates 

 * Life Tables, by T. R. Edmonds, B.A. (1832). 



