718 



The Table may be read thus: of 100,000 children born, 10,295 

 die in the first year, 89,705 survive. 



It will be observed that, upon the hypothesis that the annual 

 births equal the annual deaths in number, and that the law of mortal- 

 ity remains invariable, the series of the living (4) can be constructed 

 from the series of numbers (<4) representing the dying, or from the 

 numbers dying at different ages, as returned in the parish registers. 

 That course was adopted by Halley, and afterwards by Dr. Price, in 

 constructing the Northampton Table. But the hypothesis of an 

 invariable annual number of births equalling the deaths has never 

 been verified by observation, and consequently tables on the plan of 

 Halley' s are often exceedingly erroneous. In the healthiest districts 

 of England the births were 29,715, the deaths 17,469 annually : a 

 Table constructed upon that plan, like Dr. Price's, makes the mean 

 lifetime or as it is sometimes called, the expectation of life for 

 Northampton, 25 years, while the mean lifetime by a correct 

 Northampton Table is 38 years. 



It is shown by a diagram that if age (x) is represented by the 

 abscissas, the numbers living (#) will be represented by the ordinates 

 of a curve. De Moivre constructed this curve by assuming that 

 the series l x is from the age 12 to 86, in arithmetical progression; 

 decreasing thus, 74, 73, 72 ... 3, 2, 1, 0. By another hypothesis, 

 the rate of mortality is assumed to decrease or to increase in geome- 

 trical progression at different rates in different periods of life ; and 

 it is found that this hypothesis represents the results deduced from 

 the observed facts approximative^. 



As v y the velocity, expresses a ratio, so m, the rate of mortality, 

 is the ratio of the number dying to the number living in a unit of 



