ON LIFE CONTINGENCIES. 179 



parties, though without any sufficient guarantee for the 

 accuracy of the information. The hypothesis upon which 

 alone registers of burials will give a correct law of mor- 

 tality, requires that one of two alternatives should exist : 

 either a permanent law of mortality, with a knowledge 

 of the population in every year, and of the number, of 

 emigrants and immigrants, with their ages ; or a 

 stationary population, with the same number of births 

 and of deaths in each year, and a permanent law of 

 mortality. This latter supposition is never exactly 

 true ; but, as many societies have made a near approach 

 to it, and as many tables have been constructed by its 

 means, it will be worth while to explain the conse- 

 quences of the supposition. 



If the Carlisle law of mortality remained in unin- 

 terupted operation for a century, and if 10,000 infants 

 were born alive in every year, the time would come 

 when the number of the living at any age in that table 

 would express the number alive at that age in the 

 society in question. Thus the number of persons aged 

 25 would be the 5879 survivors of those who were 

 born 25 years ago ; and the number of the living 

 at every age and upwards would be found by multi- 

 plying the number alive at that age by the mean 

 duration of life in the table in p. 166. If, then, the 

 law of mortality of such a society were required, it 

 would be found written in the burial registers of any 

 one year. For the numbers of births and deaths being 

 equal, there would be found for each year 10,000 

 burials ; which, if the law of mortality were permanent, 

 would be found distributed among the different ages 

 according to the table. Hence the number, out of 

 10,000 born, who attain a given age, would be found by 

 adding the number buried after that age* 



But let us now suppose a population uniformly 

 increasing from year to year, say at the rate of 2 per 

 cent, per annum ; such a population would double 

 itself in 35 years ; and the younger lives would always 

 exist in a greater proportion to the older ones than 

 N 2 



