468 



Royal Society:—^ 



and to illustrate this by a new Table representing the vitality of the 

 healthiest part of the population of England. 



The Life-Table is an instrument of investigation ; it may be called 

 a biotneter, for it gives the exact measure of the duration of life under 

 given circumstances. Such a Table has to be constructed for each 

 district and for each profession, to determine their degrees of salu- 

 brity. To multiply these constructions, then, it is necessary to lay 

 down rules, which, while they involve a minimum amount of arith- 

 metical labour, will yield results as correct as can be obtamed in the 

 present state of our observations. 



A Life-Table represents a generation of men passing through time ; 

 and time under this aspect, dating from birth, is called age. In the 

 first column of a Life-Table age is expressed in years, commencing 

 at (birth), and proceeding to 100 or to 110 years, the extreme 

 limit of observed lifetime. Annexed is an outline of the two primary 

 series of the Life-Table, representing the surviving at each year of 

 age (Jx), and the first differences representing the dying {d^), in annual 

 intervals of age. 



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

 die in the first year, 89,70.5 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 ((/,r) representing the dying, or from the 

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

 That course was adopted by Ilalley, 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 1 7,4 C9 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 (a?) is represented by the 

 abscissas, the numbers living (6.r) will be represented by the ordinates 

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

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



