Ch. ix. in England (continued). 431 



of deaths as 1 to 47, will add yearly to the num- 

 bers of a country one-79th of the whole, and in 

 ten years will increase the population from 

 9,287,000 to 10,531,000, leaving 43,000 for the 

 deaths abroad, and agreeing very nearly with the 

 calculation founded on the excess of births.* 



We may presume therefore that the assumed 

 omissions in the births and deaths from 1800 to 

 1810 are not far from the truth. 



But if these omissions of one-6th for the births, 

 and one- 12th for the burials, may be considered as 

 nearly right for the period between 1800 and 

 1810, it is probable that they may be applied 

 without much danger of error to the period be- 

 tween 1780 and 1800, and may serve to correct 



* A general formula for estimating the population of a country 

 at any distance from a certain period, under given circumstances 

 of births and mortality, may be found in Bridge's Elements of 

 Algebra, p. 225. 



Log. A = log. P + n x log. 1 + m — b 



m b 

 A representing the required population at the end of any number of 

 years ; n the number of years ; P the actual population at the given 

 period ; £ the proportion of yearly deaths to the population, or 

 ratio of mortality ; \ the proportion of yearly births to the popu- 

 lation, or ratio of births. 



In the present case, P = 9,287,000 ; n = 1 ; m = 47 

 b = 29£. 



. = ?V and l + m — b _ in 



m b ' : tit 



in b 



The log. of %$ = 0054 6 ; .', n x log. 1 + m — b 



m b 

 = 05460. Log. P. = 6.96787, which added to 05460 = 7.02247 

 the log of A, the number answering to which is 10,531,000. 



