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5
(c) Number at 2 years of age—
^ births in 1888 + total births in 1889-97 + 1 births in 1898.
Less deaths at age 0-1 in the decennium 1889-98.
„ „ 1-2 „ „ 1890-99.
(id) Number at 3 years of age—
½ births in 1887 + total births in 1888-96 + 5 births in 1897.
Less deaths at age 0-1 in the decennium 1888-97.
„ „ 1-2 „ „ 1889-98.
„ „ 2-3 „ „ 1890-99.
(e) Number at 4 years of age—
5 births in 1886 + total births in 1887-95 + ½ births in 1896.
Less deaths at age 0-1 in the decennium 1887-96.
„ „ 1-2 „ „ 1888-97.
„ „ 2-3 „ „ 1889-98.
„ 3-4 „ „ 1890-99.
The sum of these numbers (a), (b), (c), (d) and (e) in the case of males works out at 2,775,278.
The mean male population living at ages 0-5 has been shown to be 2,483,717, but this number
represents the number living at all ages between 0 and 1 year of age plus the number living at all
ages between 1 and 2 years of age etc., and in order to make it comparable with the number obtained
from the births and deaths, viz., 2,775,278, which is the sum of the numbers at birth, and at the exact
ages 1, 2, 3 and 4 it is necessary to add the deaths occurring in the decennium under 6 months of age,
and half the deaths at ages 1-2, 2-3, 3-4 and 4-5, the figures are as follows—
Mean population age 0-5 living in the 10 years 1891-1900 2,483,717
Deaths under 6 months of age 1891-1900 79,828
Half deaths aged 1-2 years, 1891-1900 17,169
„ „ 2-3 „ „ 6,782
„ „ 3-4 „ „ 4,292
„ „ 4-5 „ „ 2,889
Total 2,594,677
The number thus obtained, viz., 2,594,677 may be taken to be the sum of the number of males
at birth and at the exact ages 1, 2, 3 and 4, and the application of this number to the distribution at
each of these ages as obtained from the births and deaths gives the following numbers, which have
been adopted for the purposes of the life table—
Number at birth 632,698
age 1 522,777
„ „ 2 490,999
„ „ 3 478,440
„ „ 4 469,763
Total 2,594,677
From these numbers and the mortality figures for the five years of life in the decennium the
following probabilities of living one year at each age have been calculated—
Probability of living one year—Males.
At age 0 -81588 = p0
„ 1 -93432 = Pl
„ 2 -97237 = p2
„ 3 -98206 = p3
„ 4 -98770 = p4
Calculation of the probability of living one year at age 5 and upwards.
It has been shown (page 4) that the probability of living a year at age x (px) may be obtained
if the population living at all ages between x and x + 1 years of age and the number dying in this
interval be known. The chief difficulty in life table construction, however, lies in the fact that the
population and deaths at yearly intervals of age are unrecorded, and the facts can only be ascertained
for five year or ten year intervals. Under these circumstances it is necessary to adopt some method
of ascertaining the numbers of the population and deaths in each year of age from the recorded facts.
In the case of the Carlisle table of mortality it has been shown that a "graphic" process of construction
was adopted, and Dr. Newsholme's life table for Brighton, 1831-90, was also constructed by this
method, which consists in plotting out the population and deaths to scale as a series of rectangular
figures whose height is equal to the arithmetical mean of the populations and deaths, and whose breadth
is proportionate to the interval of time covered by the age period, A curve is then drawn, the mean
of whose ordinat.es at yearly intervals is equal to the height of the corresponding rectangular figure.
The principal objection to this method of construction is that accurate measurement of the ordinates
of the curve is extremely difficult unless the curve be drawn on a very large scale, and some allowance
must also be made for "personal equation" in drawing the curves, as it is obvious that many
curves may be drawn which satisfy the given conditions. As a matter of fact the series of px values
obtained by the graphic process is rarely so smooth and regular as the series obtained from the