to Age, and the " English Life Table." 25 



tion of new values of P between two or more values of P^ ex- 

 tracted from any Table of mortality not regulated by any definite 

 law of decrement of life according to age. 



In facilities afforded for the rapid construction of Tables of 

 mortality, the formula of 1832 has the advantage over the for- 

 mula of 1866, chiefly through yielding successive values of 

 log A log P; differing from one another by a constant quantity 

 which is the common logarithm of the annual ratio of increase 

 of the mortality according to age. The formula of 1832 yields 

 the equation following, 



log A log P< +1 - log A log P,= - hgp. 

 The formula of 1866 yields 



log A log P, + 1 - log A log P,= - — - nearly. 



In the former case the numbers in the column containing 

 log A log P are obtained with exactitude by successive additions 

 of a constant which is logjo. In the latter case the numbers in 

 the same column are obtained nearly by successive additions of 



the variable -. The smaller the intervals of age adopted, 



a + t L 



the nearer will be the approach to exactitude in the latter case. 

 For practical purposes, the results from both formulae, obtained 

 as above, will be equally valuable when the intervals of age are 

 yearly. Nevertheless the above short method of constructing 

 Tables according to the formula of 1866 is not likely to find 

 favour with calculators ; for they will generally prefer the 

 direct use of the formula yielding accurate results, to the indi- 

 rect and short course attended with errors however insignificant. 



The vital force relative to age is probably the same in all indi- 

 viduals, the rate of increase of such force during childhood and 

 the rate of decrease during manhood being the same for all. 

 But the absolute vital forces at the same ages may vary greatly 

 when individuals are compared with individuals and classes with 

 classes. One of the earliest fruits of the study of the law of 

 human mortality was the discovery of the fact that the rates of 

 mortality, at all ages, of the populations of large towns were 

 much greater than the rates, at the same ages, prevailing in the 

 populations of the small towns and villages of the same nation. 

 The general rule appeared to be, that the absolute rates of mor- 

 tality at every age increased according as the magnitude and 

 density of these town populations increased. The earlier writers 

 on human mortality considered large cities to perform the func- 

 tion of graves, in swallowing up all excess of births over deaths, 

 and thus preventing the populations of long settled countries 

 from increasing. 



In the year 1832 the present writer gave to the public three 



