VOL. XLVII.] PHILOSOPHICAL TRANSACTIONS. 225 



Lonclon and Breslaw can possibly be ; and consequently so must the times of 

 their dissolution. All which has been, with a great deal of clearness, evinced 

 by the gentleman above quoted ; 3dly, because those persons who suppose that 

 Mr. De Moivre's hypothesis has its foundation peculiarly in the Breslaw obser- 

 vations, are greatly mistaken : for Mr. D. having lately been endeavouring to 

 discover some further helps to the speedy valuation of lives, he found that, on 

 the contrary, if tlie London observations had been then in Mr. De Moivre's 

 hands, he might as justly have derived his hypothesis from them. 



For the same thing, which Mr. De Moivre mentions, concerning the equal 

 annual decrease in a certain number of persons, happens in the table of the Lon- 

 don observations ; and the like happens in other instances, to be met with in the 

 London observations, as published by different authors. Add to this, that 

 having calculated the value of an annuity on a life of 10 years of age, by both 

 tables, and also by the hypothesis, Mr. D. finds it to turn out thus : 



By the Breslaw tables of observations 17-7237 years purchase. 



By supposing the decrements of life equal. . . , 16.8814 



By the London tables of observations , 16.3907 



From which there seems to be some reason to conclude, that the hypothesis 

 (as it gives an answer less than the Breslaw, and greater than the London obser- 

 vations) may be the best method of the three. And it is further remarkable, 

 that the result by the hypothesis, is nearer to that by the London, than to that 

 by the Breslaw observations. However, if the argument for using the London 

 observations has any force at all, the computation of the value of each person's 

 life must be made from observations drawn from the bills of mortality, kept at 

 the place of his or her residence : and therefore it is, that Mr. D. contributes as 

 much as he can, to preserve a sufficient number of good bills of mortality. 

 There seeins to be an objection, both to the hypothesis, and to the observations ; 

 for it is well known that females, especially at two periods of their life, are ob- 

 noxious to fatal disorders not incident to the other sex, nor distinguished in the 

 present bills of mortality ; and consequently neither the tables of observations 

 nor the hypothesis (which is derived from them) will render the calculations of 

 the values of lives sufficiently certain ; unless there be a periodical distinction of 

 sexes in those bills : as it would probably appear, if such a distinction had been 

 introduced, that there is a wide difTerence between the values of a male and fe- 

 male life of the same age. 



But there will be a great inconvenience, in rejecting the hypothesis, which 

 none of these gentlemen have remedied ; viz. the prolix and laborious compu- 

 tation hitherto directed for finding the values of lives from tables of observations; 

 whereas, by the hypothesis, as its author justly observes, more can be con- 



VOL. X. G G 



