DE. EAEE ON THE CONSTEHCTION OE LIFE-TABLES. 
839 
which, while they involve a minimum amount of arithmetical labour, will yield results 
as correct as can be obtained in the present state of our observations. 
1. GENEEAL DESCEIPTION OF A LIFE-TABLE. (See Table C, p. 870.) 
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 0 (birth), and proceeding to 100 or 110 years, the 
extreme Limit of observed life-time. 
If we could trace a given number of children, say 100,000, from the date of birth, 
and write the numbers down that die in the first year, living therefore less than one 
year, against 0 in the Table, and on succeeding lines the numbers that die in the second, 
third, and every subsequent year of age until the whole generation had passed away, 
these numbers would form a Table of Mortality, showing at what ages 100,000 lives 
become extinct. 
Again, if the 100,000 childi’en were followed, and the numbers living on the first, on 
the second, and on every subsequent birthday until none was left, the column of numbers 
would constitute a Table of Survivorship. So if of 100,000 children born at a given point 
of time, the numbers dying [d^) in each subsequent year were written in one column, 
and the numbers surviving [l^) at the end of each year in another column, the two 
primary columns of the Life-Table would be formed. 
It is e\ddent that if one of these columns is known the other may be immediately 
deduced from it; for if of 100,000 .children born 10,295 die in the first year of age, 
3005 in the second year of age, it follows that the numbers living at the end of one 
year must be 89,705, at the end of two years 86,700. Upon adding the column [df 
from the bottom up to the number against any age (w), the sum will represent the whole 
of the numbers dying after that age ; and consequently the numbers living at that age, as 
shown in the collateral column {l^). 
The 100,000 children born at the same moment, and counted annually to determine 
the numbers living at the end of every year, would by our Table completely pass away in 
less than 107 years. If another generation of 100,000, bom a year afterwards, were 
followed, the numbers dying in the various years of age would not be very difierent, 
the circumstances remaining the same ; and the numbers of those entering each year of 
age would vaiy inconsiderably from those of the first series. If 100,000 children again 
were bom at annual intervals, and were subject to an invariable law of mortality, they 
would form a community of which the numbers living at each age would be represented 
by the sucessive numbers {l^) in the Life-Table. The sum of these numbers, by the new 
Table of Healthy Districts, would be 4,951,908. The births are here assumed to take 
place simultaneously at annual intervals ; immediately before the births, therefore, in 
such a community its population would be 4,851,908, to which it would fall progressively 
from 4,951,908 by 100,000 successive deaths in the year. The average number con- 
stantly Ihdng would be some number between 4,951,908 and 4,851,908; and it would 
be very nearly the mean of these limiting numbers. 
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