51C> PHILOSOPHICAL TRANSACTlOKSr [aNNO ]6Q3. 



Some further Considerations on the Breslaiv Bills of Mortality * By Mr. Halley, 

 . ' N° 198, p. 654. 



Were the calculus from the bills of mortality founded on the experience 

 of a very great number of years, it would be worth while to think of methods 

 for facilitating the computation of the value of two, three, or more lives, which 

 is perhaps a work of too much difficulty for the ordinary arithmetician to under- 

 take. 1 have endeavoured to find a theorem that might be more concise than 

 the rules before laid down, but in vain ; for all that can be done to expedite it 

 is, by tables of logarithms ready computed, to exhibit the ratios of N to Y in 

 each single life, for every third, fourth, or fifth year of age, as occasion shall 

 require ; and these logarithms being added to the logarithms of the present 

 value of money, payable after so many years, will give a series of numbers, the 

 sum of which will show the value of the annuity sought. However, for each 

 number of this series, two logarithms for a single life, three for two lives, and 

 four for three lives, must necessarily be added together. 



Besides the uses mentioned in my former, it may not perhaps be unacceptable 

 to infer from the same tables, how unjustly we repine at the shortness of our 

 lives, and think ourselves wronged if we attain not to old age, whereas it hereby 

 appears, that the half of those that are born are dead in 17 years time, 1238 

 being in that time reduced to 616. So that, instead of murmuring at what we 

 call an untimely death, we ought with patience and unconcern to submit to 

 that dissolution which is the necessary condition of our perishable materials, and 

 of our nice and frail structure and composition ; and to account it as a blessing 

 that we have survived, perhaps by many years, that period of life, at which the 

 half of the whole race of mankind does not arrive. 



A second observation is, that the growth and increase of mankind is not so 

 much stinted by any thing in the nature of the species, as it is from the cautious 

 difficulty most people make to adventure on the state of marriage, from the 

 prospect of the trouble and charge of providing for a family. Nor are the 

 poorer sort of people herein to be blamed, since their difficulty of subsisting is 

 occasioned by the unequal distribution of possessions, all being necessarily fed 

 from the earth, of which yet so few are masters. So that besides themselves 

 and families, they are also to work for those who own the ground that feeds 

 them ; and of such does by far the greater part of makind consist ; otherwise 

 it is plain, that there might well be 4 times as many births as we now find. For 



• 8«e N" 156, p. 483, of this volume. 



