different Tables of Mortality. 345 



each a maximum about the middle of the whole range of life. The 

 abridged formula, which I suggested in my former letter to you, was 

 368 + 10a; for the decrement of life, which is a combination of 

 the arithmetical and quadratic hypotheses in equal proportions at 

 the age of about 37, and expresses, as it was intended to do, a 

 mean mortality between the old and the new observations ; but it is 

 more convenient to keep them separate in computation. 



9. I shall now proceed to compare, with the different tables of 

 Morgan, Milne, and others, the results of the arithmetical hypothesis, 



X OCX 



as expressed by 5 = 1 — — ; and those of the formula s rr 1 — — , 

 c cc 



which is the quadratic hypothesis ; s being the comparative number 

 of survivors at the age ar, and c a constant quantity, which may be 

 varied at pleasure from 80 to 100. 



10. The first point of comparison is the annual mortality of the 

 arithmetical hypothesis with that of the tables of Northampton, 

 and the bills of mortality of London. 



A. ^7i7maZ mortality approaching to — = .0115. 



c 



11. With the decrements of the quadratic hypothesis, we may 

 compare those of the tables of Deparcieux and of Carlisle, and 

 those which I have lately computed from the supposed experience 

 of the Equitable Office. 



