C 336 ] 
Thirdly, becaufe thofe perfons, who fuppofe, that 
Mr. De Moivre’s hypothecs has its foundation, pecu- 
liarly, in the Breflaw obfervations, are greatly mif- 
taken : for, having lately been endeavouring to dif- 
cover fome farther helps to the fpeedv valuation of 
lives, I have found, that, on the contrary, if the 
London obfervations had been then in Mr. De 
Moivre’s hands, he might, as juftly, have derived 
his hypothefis therefrom; which will appear from 
his own words, in the preface to his treadle of An- 
nuities on Lives , compared with the London ob- 
fervations. 
£c Two or three years after the publication of the 
u firfi: edition of my Doftrine of Chances (fays that 
u excellent mathematician) I took the fubjed into 
“ confideration ; and confulting Dr. Halley’s table of 
tc obfervations, I found, that the decrements of life, 
“ for confiderable intervals of time, were in arithmetic 
<c progrefiion : for infiance, out of 6\,6 perfons of 12 
u years of age, there remain 640, after one year : 
“ 634, after two years ; 628, 622, 6 16, 610, 604, 
“ f5>8, 592, y8 6, after 3, 4, 5, 6, 7, 8, 9, 10 
£ ‘ years refpedively ; the common difference of thofe 
“ numbers being 6. Examining afterwards other 
tc cafes, I found, that the decrements of life, for 
a feveral years, were ftill in arithmetic progrefiion, 
tc which may be obferved from the age of 5-4 to the 
u age of 71, where the difference, for 17 years to- 
tc gether, is conftantly 10. After having tho- 
• £ roughly examined the tables of obfervations, and 
“ difcover’d that property of the decrements of life, 
tc I was inclined to compofe a table of the values of 
“ annuities on lives, by keeping clofe to the tables 
u of obfervation; which would have been done 
with 
