Various Tables of Annuities. 335 



is constant, the rate of increase of the population is necessarily 

 the same as that of the births. The rate of increase of the 

 births has been supposed to be constant ; a small inequality in 

 this rate, unless it be of long period, will not produce any 

 sensible difference in the results. But, although the total num- 

 ber of deaths which take place in a given population is not 

 much influenced by the rate of increase, the apparent table of 

 mortality is mvich altered. In order to shew the extent of the 

 error which is likely to arise from this circumstance, I have 

 given the apparent tables of mortality corresponding to each 

 rate of increase of the births. 



According to Mr. Rickman, in the Population Abstract 1821, 

 the latio of the deaths to the population in England at that 

 time was 1 to 57. This ratio is considerably less than would 

 be given by any table of mortality, and it is probable, therefore, 

 that the number of unentered burials is much greater than Mr. 

 Rickman has supposed. Since the ratio of the deaths to the 

 population is nearly constant when the law of mortality is given, 

 this rate would be an excellent criterion of the longevity of dif- 

 ferent countries, if it could be accurately ascertained ; to this, 

 however, many difficulties are opposed. 



In the Tables VIII. and IX. the rate of increase of the 

 births is arbitrary ; in order to .see how far the mortality in this 

 country coincides with that given by Table VII., I have formed 

 Table X., taking the values of p from that Table, and sup- 

 Ijosing the births in the century previous to 1821 to have been 

 the same as the christenings that are given in the Population 



Abstract before referred to; and since the ratio =rr^^^ 7-: in- 



volves only the ratios of the births, which must be nearly the 

 same as the ratios of the christenings, the error introduced by 

 this hypothesis is altogether insensible. 



