162 



ESSAY ON PROBABILITIES. 



number of years enjoyed by individuals of every age. 

 This, in another variety of the Carlisle tables, opposite 

 to 50 and 60, we find 21*11 and 14*34 ; meaning that, 

 according to these tables, persons aged fifty live, one 

 with another, 21*11 years more, and persons aged 60, 

 14*34 years more. 



Until observations of human mortality become more 

 extensive and correct, I prefer the tables of mean 

 duration to all others. The events of single years are 

 subject to considerable error, and generally present 

 such varieties of fluctuation, that it has become usual to 

 take some arbitrary and purely hypothetical mode of 

 introducing regularity. This practice cannot be too 

 strongly condemned, since the tables thereby lose some 

 of their value as representations of physical facts, 

 without any advantage ultimately gained. For if by 

 using the raw result of experiments, tables of annuities 

 were rendered unequal and irregular, it would be as 

 easy, and much more safe, to apply the arbitrary method 

 of correction to the money results themselves, than to 

 introduce it at a previous stage of the process. It is 

 not, however, a matter of much consequence as to the 

 annuities, &c., deduced from the tables : and as yet, the 

 rudeness of the original observations renders the effect 

 of any such alteration not so great as the probable 

 errors of the observations themselves. 



The mean duration of life is approximately calculated 

 as follows. Suppose (taking an instance from the Car- 

 lisle tables) that 75 persons are alive at the age of 92, 

 of whom are left at the successive birthdays, 54, 40, 

 30, 23, 18, 14, 11, 9, 7, 5, 3, 1, 0. Consequently, in 

 their 93d year, 54 persons enjoy a complete year of life, 

 and 21 die, whom we may suppose, one with another, 

 to live through half the year, and 54 years and 21 half 

 years make 64^ years, which is the total life of 75 per- 

 sons for that year. Proceeding in this way, we find 

 that there are, 



in the 93d year 54 + i of 21 years. 

 94th 40 + ^ of 14 



