Vanous Tables of Annuities. 333 



same time it was only 1.016. In order to shew directly the effect 

 which an increase in the population produces in the Table of 

 mortality, I have calculated three Tables from the Chester Tables 

 of mortality, supposing the deaths at the time of the observation 

 to be equal to the deaths 40 years jireviously (which was nearly 

 the case in this country in the last century), and the births to 

 increase annually in a geometrical progression of which the 

 common ratio is given. 



The column A supposes the ratio of increase to be 1.005, 



B 1.010, 



C 1.015. 



The column D is calculated in the same way for females, 

 and supposes the ratio of increase to be 1.005. The ratio 1.005 

 is very nearly what obtained in England during the last century 

 according to the Parliamentary Reports. The births in all Eng- 

 land in the year 1700 were 138.979, and in 1780, 201.310, making 

 the mean annual rate of increase 1.0046: in the county of 

 Chester taken by itself in 1700 they were 2690, and in 1780 

 4592, making the mean annual rate of increase 1.0061 ; therefore 

 the columns A and D, which T have given at lenglh in Table VIT. 

 must approach very nearly to exactitude, and considering atten- 

 tively the limits of the errors of which observations of this kind 

 are susceptible, I think that it is improbable that the longevity 

 in this country generally, when the Chester Table was formed, 

 was quite so great as that indicated by Mr. Finlaison's Tables 

 and the experience of the Equitable Society. It may have im- 

 proved since. 



When the law of mortality in any country, and the number 

 of births in each year during the century previous to any given 

 epoch, are known, it is easy to assign the total number of 



