g40 DE. EAEE ON THE CONSTEECTION OF LIFE-TABLES. 
In the ordinary course of nature, the births in a community take place in remittent 
succession; and if it is assumed that the 100,000 births occur at equal interrals over 
every year, it is evident that at any given date a certain number will be found living at 
all the intermediate points of age betvreen 0 to 1 year, 1 to 2, 2 to 3, and all the remain- 
ing years of age. The population in the above instance would be found by enumera- 
tion to be nearly 4,899,665. 
The annual births would be 100,000 in such a community. The annual deaths would 
also be 100,000 ; and by taking out the deaths at each year of age, from the parish 
registers of a single year, the second column of the Life-Table would be found. 
adding this column of deaths up and entering the sum of the numbers year by jeai 
against every year of age {x), the third column {l^ of the Idfe-Table would be obtained , 
for it has been already shown that the numbers attaining any age x are equal to the 
numbers dying at that age, and all the subsequent ages. From the registers of the 
deaths, a Table of the numbers of ih.e population living in a parish so constituted could be 
immediately determined without any enumeration. Its deviations from the truth would 
be accidental ; and they would be set right by taldng the mean of many years. So also 
from a simultaneous enumeration of the numbers living in each year of age, the two 
columns d^. and 4 of the life could be constructed without reference to any registiy of 
the deaths at different ages. 
The mean age at death in such a community would express the mean lifetime, or the 
expectation of life at birth ; and the product of the number expressing the annual 
births multiplied into the mean age at death would give the numbers of the popula- 
tion. 
The facts which a Life-Table expresses in numbers may be represented by the lines 
of a figure; age [x) being indicated by the abscissas measured from 0, the numbers 
living (1) at each age by the ordinates of a curve line, and the numbers Ibiug between 
any two ages by the plane surface within the two ordinates, the curve line, and the 
corresponding portion of the abscissa. The relative numbers living at the ages 20 and 
21 are seen in the two lines of Plate XLII. fig. 1, over the ages 20 and 21 ; if the 
deaths in the intervening year all occurred immediately after the age 20 was attained, 
the numbers living would also be represented by the parallelogram having its tu'o sides 
equal to the ordinate over 21, and for its base the portion of the abscissa between 20 
and 21 ; but if all the deaths occurred only the instant before the age 21 was attained, 
the height of the parallelogram would be represented by the ordinate over the age of 20. 
The deaths occur at intervals between the two ages, so the numbers lining, and the 
lifetime which is passed between the two ages, are correctly represented by the curvi- 
linear area. 
The deaths in each year of age are called the decrements of life. They are repre- 
sented by the differences in the lengths of the successive ordinates. Thus by cutting off 
a small portion of the ordinate at the age 20, the ordinate at the age 21 is obtained; 
this small portion, shown in Plate XLII., represents the decrement of life in that 
year of age. It will be observed that the decrements vary at every year of age ; and 
