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



or the other of the two ways just mentioned. The direct method, 

 by observing the number of survivors at particular ages out of a 

 given number living at birth-time, or out of a given number 

 living at any other age, is applicable chiefly to selected classes 

 distinct from the general population of a nation or district, 

 such as classes of persons on whose lives annuities or assu- 

 rances have been granted for money by trading companies or by 

 governments. 



The most common method of observation, by observing the 

 rate of decrement at every age, is indirect, and is the only method 

 used for determining the law of mortality, according to age, of 

 the total population of a nation, or of the constituent parts of 

 such population distinguished as village, town, or city population. 

 Observations according to this method are made by periodical 

 enumerations of the numbers living and the numbers who have 

 died in annual, quinquennial, or decennial intervals of age. 

 The ratios of the numbers dying to the numbers living (which 

 are the rates of decrement of life) are thus obtained for every 

 age. These rates being known, the consequent Table of morta- 

 lity representing survivors at every year of age may be deduced 

 by calculation. 



The law of human mortality may be most simply expressed by 

 means of the rates of decrement and the relation between these 

 rates at different ages. If at two known ages the rates of decre- 

 ment are a and a t3 then, if the rate of decrement at one age is 

 known, the rate of decrement at the other age may be found from 

 the proportion 



— = ( a 1 

 a \a + 1) 



wherein t is the difference of age, a is a constant representing 

 distance (in time or age) from a fixed point, which is the ideal 



zero of life or vital force, and j is the hyperbolic logarithm of 



10, and equal to 2*302585. There are two ideal zeros of human 

 life — one belonging to the period of childhood, and the other to 

 the period of manhood. The curve which indicates the law of 

 decrease of human life consists of two branches — one on each side 

 of the period of puberty. There apparently exists a short inter- 

 mediate branch at or near the junction of the two others. The 

 existence of such short branch may be due to the differences of 

 age at which puberty is attained by different individuals. 



The complete expression for the law of human mortality is 

 contained in two similar formulas, — one for the period of increase 

 of vital force, extending from birth to the age of about 9 years ; 

 the other for the period of decrease of vital force, extending from 



