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



ences of the common logarithms of the same differential coeffi- 



,11 1 



cients are = —k x r x 1 = r~r 



k a + t a + t 



The value of the common logarithm of P may be most conve- 

 niently calculated in the two periods of childhood and manhood 

 from the formula 



a being the minimum rate of mortality in both periods at the 

 extreme distance, fifteen units, from the ideal zero of life, and 

 the value of « for the unit of 6 years in the period of manhood 

 being '0330, and for the unit of 9 months in the period of child- 

 hood being '004125. The age (t) measured from the limit of 

 minimum mortality is negative. 



From the above formula may be obtained the formula for 



AlogP 15 _ ( =log^=i 



15. k* 



(^•{('-i^r-i}. 



which, expressed in a series, becomes 



Alo g P 15 _ ( =-^(^{l + I |^ + ^ +& c.}. 



The coefficients B la B 2 , B 3 , &c. belong to the general formula, 

 and their value has already been given in a preceding page. 



The total population of every civilized nation is divisible into 

 three important parts, suffering different rates of mortality at the 

 same ages. The village population suffers a lower rate of mor- 

 tality than the town population, and the town population lower 

 than the city population. The proportional rates of mortality 

 for village, town, and city populations may be estimated as 5, 

 6, and 7\ respectively. 



The fact of the total population of a nation consisting of three 

 large classes suffering different rates of mortality at the same 

 ages, will exercise a disturbing effect on the manifestation of the 

 true law of mortality in adult life. At early ages, say from 20 

 to 45 years, the national Table for the total population will 

 represent the mean rate derived from due proportions of village, 

 town, and city populations. At middle age, say from 45 to 65 

 years, the national Table will represent the mean rate of a total 

 population consisting of more than a due proportion of village, 

 and less than a due proportion of city population, through the 



