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Title: On the inaccuracies which probably exist in the census returns of ages
Author: Thomas A. Welton
Release Date: December 29, 2021 [eBook #67037]
Language: English
***START OF THE PROJECT GUTENBERG EBOOK ON THE INACCURACIES WHICH PROBABLY
EXIST IN THE CENSUS RETURNS OF AGES***
Transcribed from the 1876 T. Brakell edition by David Price. Many thanks
to the British Library for making their copy available.
ON
THE INACCURACIES
WHICH PROBABLY EXIST IN THE
CENSUS RETURNS OF AGES.
* * * * *
BY
THOMAS A. WELTON, F.S.S.
* * * * *
* * * * *
* * * * *
LIVERPOOL:
T. BRAKELL, PRINTER, COOK STREET.
1876.
* * * * *
ON THE INACCURACIES WHICH PROBABLY EXIST IN THE CENSUS RETURNS OF AGES.
_By Thomas A. Welton_, _F.S.S._, &c.
SOME years ago, before the publication of the third volume of the Census
of England and Wales, 1871, I was anxious to calculate the approximate
death rates in particular parts of England, amongst females at certain
ages, during each of the years 1851–1870. I therefore applied myself to
the preliminary process of estimating the population in each year at the
ages in question.
I found that it was not safe to assume that, if population in a given
county or district had increased generally, at a certain rate, there had
been an increase at each particular age at something like the same rate.
On the contrary, there was a surprising irregularity in the respective
rates of increase or decrease observed amongst persons of the several
ages in the same population.
Table I shows the rates of increase in the numbers enumerated at each age
up to 80 amongst males and females respectively in the several
registration divisions, and in England and Wales. On inspecting this
table, it will be seen that, partly owing to the effect of emigration,
the ratios of increase at particular ages are very diversified. In the
Eastern Counties males aged 20–25 decreased by nearly one-tenth, but
males aged 65–70 increased by nearly a quarter. In the same division,
females aged 25–30 decreased by almost 5 per cent., whilst females aged
40–45 increased by more than 15 per cent.
Such being the state of the facts, I abandoned all thought of deducing
from the total numbers enumerated in 1871 any reliable estimates of the
numbers at particular ages, unless indeed some other mode of treatment of
the figures could be found leading to more regular results.
On comparing with the population enumerated in 1851 the numbers, ten
years older, found to be living in 1861, I obtained other sets of ratios,
which are shown in Table II.
The following is a comparison between the proportions for England and
Wales, shewn in Table II, and the numbers out of 100 living in 1851 who
would have survived in 1861 according to the English Life Table No. 3.
Ages Proportion of survivors out of 100 living in 1851.
in
1851.
By the Census. By the Life Table.
Males. Females. Males. Females.
0–5 {4} 90.1 89.2 86.4 86.7
5–10 91.2 93.5 94.2 94.0
10–15 89.2 102.1 93.7 93.4
15–20 84.1 94.4 92.0 91.6
20–25 83.2 83.2 90.9 90.4
25–30 84.4 82.3 89.9 89.6
30–35 89.2 88.6 88.6 88.6
35–40 85.1 85.9 86.8 87.4
40–45 82.3 83.8 84.3 85.9
45–50 76.1 77.6 80.5 83.2
50–55 76.7 80.2 75.3 78.2
55–60 68.9 74.1 67.7 70.7
60–65 56.5 60.2 56.9 60.3
65–70 47.3 50.5 43.5 47.2
The emigration of females of English birth has by no means been on an
insignificant scale, at any time since 1851; but owing to the immigration
of large numbers of women from Ireland, Scotland, and foreign parts, the
net loss has been only moderate. We should therefore be justified in
looking for a certain correspondence between the proportions of females
who might be expected to survive, according to the Life Table, and those
proportional figures which represent a comparison of the census figures
of 1861 with those of 1851. In point of fact, we discover that, at ages
10–20, the proportions who should survive the next ten years, according
to the Life Table, are far exceeded by those who apparently do survive;
and this state of things in the next ten years is reversed. So that the
figures suggest a faulty return of the ages of the female population,
exaggerating the numbers aged 20–30, and perhaps depressing those aged
30–40.
Again, we have reason to believe that some of the children under five
years old are returned as being fully of that age, whilst next to none
who have attained five years of age would be returned as being younger.
This would account for the dissimilarity of the ratios of survivors at
the earliest period of life.
By assuming, as experimental suppositions, that the proportionate errors
in the censuses of 1851 and 1861 at each age were equal, and that female
emigration and immigration neutralised each other, I obtained a set of
corrections of the census enumerations of females which indicated that
there was a tendency in the case of young persons under twenty to
exaggerate their ages, but that women aged 25–30, and at each successive
quinquennial period of life, at least up to 55–60, had a tendency to
understate their ages. There was likewise a certain disposition to
return ages in round numbers of years, though this was far less
remarkable than in the Irish census of 1851, from which the following
figures are taken.
Age returned. Males. Females.
35 and under 40 150,471 165,966
40 ,, 45 187,410 217,986
45 ,, 50 109,618 117,345
50 ,, 55 156,337 176,782
55 ,, 60 73,511 79,111
60 ,, 65 100,963 130,740
The understatement, at the ages mentioned, appeared to have been no
greater in this country than would have resulted from _every woman_, aged
25–60, calling herself one year younger than her true age.
It will be obvious how great the utility of censuses taken at intervals
of _five_ years would be, in enabling us to measure more accurately the
results of these tendencies to mis-state ages, and particularly the
effect of ages being returned in round numbers.
The corrections applicable to the returns of males could not be even
approximately determined without taking into account the effects of
emigration upon the numbers of that sex. And as the rates of mortality
are subject to considerable variation, year by year, I came to the
conclusion that more reliable results must be sought by the aid of—
(1) Estimates of the numbers of the _recorded_ deaths which happened
amongst persons _born_ in each quinquennial period. {6}
(2) A computed allowance for unregistered births in excess of the
unregistered deaths of infants.
(3) Estimates of the loss or gain of population through migrations at
each age.
Table III exhibits the results obtained by computing the first and second
of these elements, and showing the remaining difference between the two
sets of census figures, as the combined result of migrations and errors.
On examining this table, I thought it extremely probable that the numbers
of deaths at high ages were exaggerated, because I know of no reason for
supposing that the census numbers at such ages are less than the truth;
and if they are equal to or more than the real numbers of the living, we
are compelled to conclude either that there is a considerable immigration
of old people, or, what seems much more compatible with such knowledge as
we possess, a tendency exists to exaggerate the ages both of the living
and the dying amongst those who are over seventy years old.
By the aid of the “English Life Table No. 3” it was ascertained that in a
population resulting from births increasing at 1 per cent. per annum, the
following numbers would represent the proportions of persons living and
dying at high ages:—
Ages. Living. Ages. Living. Proportion of the
former to the latter.
Males. Fem’l’s. Males. Fem’l’s. Males. Fem’l’s.
as 100 to as 100 to
75 & 373054 428741 74½ & 369162 420783 99.0 98.1
under 80 under 79
80 „ „ 85 174287 213540 79 ,, ,, 207496 250662 119.1 117.4
84
85 „ „ 90 59641 79253 84 „ „ 89 76091 99340 127.6 125.3
90 ,, ,, 13652 20037 89 „ „ 94 19023 27331 139.3 136.4
95
95 „ „ 1887 3119 94 „ „ 99 2934 4728 155.5 151.6
100
100 & 145 279 99 and 260 484 179.3 173.5
upwards. upwards
Ages. Deaths. Ages. Deaths. Proportion of the
former to the latter.
Males. Fem’l’s. Males. Fem’l’s. Males. Fem’ls.
as 100 to as 100 to
75 & 78695 84957 74½ & 79184 84673 100.6 99.7
under 85 under 84
85 „ „ 95 19617 24868 84 „ „ 94 24024 29893 122.5 120.2
95 & 932 1476 94 and 1393 2152 149.5 145.8
upwards upwards
From the above table it may be deduced that, supposing persons aged 71–75
call themselves (or are described as being) on an average six months
older than their true age, and if after 75 the exaggeration averages an
entire year, a very great impression must be thereby made upon the
returns.
Having arrived thus far, I thought it would be convenient in the first
instance to try whether these suggestions, which I imagine will be deemed
moderate and probable, would suffice to explain the apparent influx of
aged persons, shown in Table III; and whether other suppositions, not
less reasonable, would serve to overcome the remaining difficulties which
appear on the face of that table.
The female population being least disturbed by migrations, the necessary
calculations were made in relation to it, before proceeding further.
First, the deaths shewn in Table III had to be modified, as follows:—
Born in the Deaths of Females as in As now Corrected.
years Table III.
1851–60. 1861–70. 1851–60 1861–70.
1801–05 65030 97481 65030 98802
1796–1800 72028 108636 72028 112636
1791–95 82975 114233 84226 118269
1786–90 93843 105704 97626 107225
1781–85 99612 78080 103438 76172
1776–80 94274 43589 95728 39172
1771–75 71487 17466 69678 14330
1766–70 40514 4849 36401 3732
1761–65 16604 894 13613 617
1756–60 4724 73 3631 50
1751–55 921 — 636 —
1746–50 76 — 53 —
Totals 642088 571005 642088 571005
Then it was necessary to make some assumptions as to the effect of
migrations of females into and from this country, and the following
estimates were provisionally adopted:—{8a}
ESTIMATED AVERAGE ANNUAL NET RESULT OF MIGRATIONS. CONSEQUENT ESTIMATE OF NET LOSS OR GAIN IN 10 YEARS. {8b}
Age (at end 1851–60. 1861–70. Age (at the 1851–60. 1861–70.
of the year end of the
of decennium)
migration)
Immigrants. Emigrants. Immigrants. Emi grants. Net loss. Net gain. Net loss. Net gain.
{8a} {8b} {8a} {8b}
0–5 2000 3250 1550 2675 0–5 3750 __ 3375 —
5–10 2000 3000 1530 2450 5–10 9250 — 8385 —
10–15 2800 2280 2170 1900 10–15 6000 — 6040 —
15–20 5300 3150 4200 2740 15–20 — 7000 — 3890
20–25 2400 3900 1860 3200 20–25 — 7300 — 3820
25–30 1050 2700 800 2190 25–30 8150 — 7950 —
30–35 630 1630 500 1340 30–35 14250 — 12150 —
35–40 400 1050 320 870 35–40 10250 — 8630 —
40–45 390 690 320 590 40–45 6150 — 5240 —
45–50 280 520 210 420 45–50 3500 — 3080 —
50–55 190 420 145 345 50–55 2500 — 2190 —
55–60 100 250 75 200 55–60 2000 — 1795 —
Totals 17540 22840 13680 18920 60–65 1200 — 1025 —
65–70 300 — 250 —
No great confidence can be placed in these last calculations as to the
effect of migrations at particular ages. The facts bearing on the
subject preserved in official records with which I am acquainted are but
scanty. The rough, general idea which may be gathered from the table
does, however, approximate more or less closely to the truth, and may be
usefully contrasted with the violent fluctuations indicated in Table III.
These shew, in the midst of their extravagance, a kind of regularity at
particular ages, thus—
Age at 1851–60. 1861–70.
end of
Decennium.
Loss. Gain. Loss. Gain.
0–5 30575 . . . 42643 . . .
5–10 . . . 3937 . . . 15075
10–15 . . . 24995 . . . 29722
15–20 7416 . . . 14314 . . .
20–25 . . . 85027 . . . 73654
25–30 . . . 27678 . . . 42046
30–35 69827 . . . 74590 . . .
35–40 63559 . . . 54880 . . .
40–45 4438 . . . 7513 . . .
45–50 11175 . . . 11472 . . .
50–55 16118 . . . 18811 . . .
55–60 26073 . . . 28220 . . .
60–65 . . . 35 1360 . . .
65–70 . . . 12614 . . . 18345
70–75 7310 . . . 7982 . . .
Finding it quite impossible to believe in the successive migrations which
must have taken place, if this extract from Table III represented the
truth, I pursued the enquiry as to what is the alternative of such a
belief.
Proceeding to calculate what corrections must be made in the census
returns of the numbers of females, if the amended estimates of losses by
death and the calculated results of migrations be adopted, I first
assumed that each of the three censuses of 1851, 1861, and 1871 might be
rendered erroneous by misstatements as to ages in _fixed proportions_ at
the several periods of life.
The endeavour to find such a fixed scale of proportions as would rectify
all the censuses was, however, unsuccessful; and it became evident that
the deviations from the truth were greatest in 1851 and least in 1871.
Three scales of proportions were then arrived at empirically, embodying
the idea of diminishing degrees of error. In the course of the
researches made for the sake of adjusting these scales, I found reason to
believe that the allowances for unregistered births in the years 1856–60
and 1861–65 should be increased by ½ per cent. That addition having been
made to the estimated numbers of births, it became requisite that equal
numbers should be added to the estimated losses by emigration; and by
finally amending the three scales of proportions in conformity with these
alterations, the results shewn in Table IV were at last arrived at.
These results require us to believe that, whilst our calculation of the
effect of migrations in 1851–60 was near the truth, the similar estimate
for 1861–70 was rather beside the mark. The numbers now required to be
substituted, however, appear to me to be acceptable, especially when we
have regard to our inability to form any opinion as to the ages of those
persons of English birth who returned in large numbers from the United
States about the time of the war of secession.
The next thing to do was to ascertain what transpositions of the census
figures are involved, in case we accept the numbers shewn in Table IV as
being approximately correct.
Table V exhibits these transpositions, and it will be seen that they lead
to the conclusions shewn in the following statement:—
STATEMENT A.—Shewing the proportions (per cent.) of female population
returned at each age, who were really older or younger than
represented.
Returned 1851. {11a} 1861. 1871.
as
aged
Really Age Really Really Age Really Really Age Really
older. correct. y’nger. older. correct. y’nger. older. correct. y’nger.
0–5 . . . 100.0 . . . . . . 100.0 . . . . . . 100.0 . . .
5–10 . . . 97.0 3.0 . . . 97.1 2.9 . . . 97.3 2.7
10–15 . . . 98.1 1.9 . . . 98.1 1.9 . . . 98.2 1.8
15–20 . . . 97.4 2.6 . . . 97.9 2.1 . . . 98.0 2.0
20–25 4.7 92.3 3.0 5.3 92.4 2.3 4.8 93.2 2.0
25–30 9.8 90.2 . . . 10.3 89.7 . . . 9.5 90.5 . . .
30–35 13.3 86.7 . . . 13.5 86.5 . . . 11.5 88.5 . . .
35–40 12.6 87.4 . . . 12.6 87.4 . . . 11.9 88.1 . . .
40–45 16.5 83.5 . . . 16.1 83.9 . . . 15.3 84.7 . . .
45–50 15.1 84.9 . . . 14.6 85.4 . . . 13.9 86.1 . . .
50–55 16.5 83.5 . . . 16.5 83.5 . . . 15.5 84.5 . . .
55–60 8.4 91.6 . . . 8.2 91.8 . . . 7.2 92.8 . . .
60–65 9.0 91.0 . . . 8.8 91.2 . . . 8.1 91.9 . . .
65–70 1.7 98.3 . . . 2.0 98.0 . . . 1.8 98.2 . . .
70–75 . . . 100.0 . . . .3 99.7 . . . .5 99.5 . . .
75–80 . . . 99.9 .1 . . . 100.0 . . . . . . 100.0 . . .
80–85 . . . 91.6 8.4 . . . 92.6 7.4 . . . 93.2 6.8
85–90 . . . 90.5 9.5 . . . 92.1 7.9 . . . 93.1 6.9
90–95 . . . 84.2 15.8 . . . 85.6 14.4 . . . 88.7 11.3
95–100 . . . 62.2 37.8 . . . 62.5 37.5 . . . 68.1 31.9
100 & up. . . . 38.0 62.0 . . . 38.4 61.6 . . . 50.4 49.6
The ratios in the above statement signify that at no time of life does
the apparent _under statement_ of age average so much as an entire year;
{11b} and the exaggeration even at high ages also appears to average less
than a year, so that there is, I think, no such unlikelihood about the
figures as should lessen their credibility. When the irregular results
of Table III for females are compared with the much more probable results
shewn in Table IV, and the assumptions by which the latter were arrived
at, and through the adoption of which the registered births and deaths,
the returns at successive censuses of the numbers of the female
population at several ages, and the computed losses by migration have
been brought into close agreement, are considered, I think it will be
seen that it is very much safer to adopt my corrections than to rely on
the actual returns.
As the operation by which the age-returns are to be corrected is
essentially one of transposition, I suppress the ratios upon the footing
of which I constructed Table IV, and would employ the proportions shewn
in Statement A, in applying similar corrections to the population returns
in detail. In the absence of any means of judging what variations there
may be in different parts of the country in the extent of the
misrepresentations as to ages, I should be inclined to make use of these
proportions in every case, though not without apprehending that
inaccuracies of some consequence may thus be fallen into.
One more test may be applied before we finally adopt the figures
exhibited in Table IV as representing (very nearly) the true female
population. The ratios borne by the population there shewn to exist in
1861 and 1871 respectively, _plus_ emigrants, to the numbers ten years
earlier, may be computed and compared with those already shewn, which
were derived from the English Life Table No. 3, thus:—
Age at the end Proportion of survivors The like
of the ten (including emigrants) out of 100 proportion,
years. Females who were living 10 years according to
earlier. the English
Life Table, No.
3.
According to According to
corrected corrected
figures, 1851 figures, 1861
and 1861. and 1871.
10–15 87.4 87.5 86.7
15–20 94.2 94.7 94.0
20–25 93.2 93.7 93.4
25–30 91.4 91.9 91.6
30–35 90.5 91.0 90.4
35–40 90.0 90.1 89.6
40–45 89.0 89.1 88.6
45–50 88.3 88.2 87.4
50–55 86.8 86.8 85.9
55–60 84.7 84.6 83.2
60–65 80.2 79.5 78.2
65–70 72.7 72.4 70.7
70–75 61.6 61.3 60.3
75–80 47.1 46.9 47.2
On examining the ratios thus obtained, it will be seen that they
harmonise well with the probability shewn by the Life Table. Each set of
ratios is symmetrically graduated, whilst the proportions obtained by the
use of the uncorrected Census Tables were, as has already been observed,
by turns exaggerated and depressed.
Having thus arrived at a sufficiently near approximation to the truth in
the case of females, it remains for us to endeavour to do the same in
that of males. The effect of emigration must be first computed, which
may be done thus:—
Age at end 1851–60. 1861–70.
of the year
of
migration.
Immigrants English Immigrants English
from Emigrants. from Emigrants.
Ireland, Ireland,
&c. &c.
0–5 2000 3500 1500 2200
5–10 2000 3500 1500 2200
10–15 3000 3000 2200 2000
15–20 6000 6500 4200 4000
20–25 2500 9000 1750 6000
25–30 1000 8000 750 5000
30–35 500 5000 400 3400
35–40 500 3000 350 2100
40–45 400 1850 260 1200
45–50 300 1300 200 800
50–55 200 1000 150 600
55–60 100 700 100 440
Totals 18500 46350 13360 29940
The above figures are based on an augmented estimate of unregistered male
births, to correspond with the increased estimate of unregistered female
births used in compiling Table IV.
The total loss or gain of male inhabitants at each age, resulting from
the above migrations, might possibly have been as under, assuming the
course of events to have been quite unvarying year by year:—
Age at Net Loss.
close of
decennium.
1851–60. 1861–70.
0–5 4500 2100
5–10 12000 5600
10–15 10500 4300
15–20 4500 200 {14}
20–25 22000 11350
25–30 54500 33600
30–35 61500 38750
35–40 44000 28750
40–45 25850 17570
45–50 15250 10000
50–55 10300 6230
55–60 7800 4470
60–65 4600 2600
65–70 1200 680
Totals 278500 165800
As, however, those who departed in the earlier years of the decennium
1861–70 for the United States, may, to a great extent, have returned
home, as well as many of those who had previously left the country, it
seems natural to suppose that the emigrants of 1861–70 were, on the
whole, much younger than the above Table would shew.
The result of a careful study of the various figures has been to convince
me that the ages of male children, as well as those of female children,
are overstated. At the age 15 and under 20 males do not appear to
exaggerate their ages so often as females do. From 25 to 70 there seems
to be a general but slight tendency to understate age, to the extent, on
an average, of a quarter or at most nearly half a year. After 70, the
same tendency to exaggerate age, which was noticed in the case of
females, seems to prevail.
In Tables VI and VII are contained the same approximate facts respecting
males, as are furnished by Tables IV and V for our female population.
The figures of all these statements have been arrived at empirically, but
so as to involve the most moderate and regular corrections which will
meet the difficulties of the case.
The resulting proportions of supposed accurate and inaccurate returns at
each age may be thus shewn:—
STATEMENT B.
Shewing the proportions (per cent.) of male population returned at each
age, who were really older or younger than represented.
Returned 1851. 1861. 1871.
as
aged
Really Age Really Really Age Really Really Age Really
older. correct. y’nger. older. correct y’nger. older. correct. y’nger.
0–5 . . . 1000 . . . . . . 100.0 . . . . . . 100.0 . . .
5–10 . . . 97.0 3.0 . . . 97.1 2.9 . . . 97.3 2.7
10–15 . . . 98.8 1.2 . . . 98.3 1.7 . . . 98.3 1.7
15–20 . . . 99.1 .9 . . . 98.3 1.7 . . . 98.2 1.8
20–25 1.0 98.7 .3 .9 98.4 .7 .5 98.6 .9
25–30 1.6 98.4 . . . 1.0 99.0 . . . .6 99.4 . . .
30–35 .7 99.3 . . . .1 99.9 . . . . . . 100.0 . . .
35–40 .2 99.8 . . . . . . 100.0 . . . . . . 100.0 . . .
40–45 3.5 96.5 . . . 1.6 97.8 .6 1.0 98.3 .7
45–50 5.0 95.0 . . . 1.9 98.1 . . . 1.2 98.8 . . .
50–55 9.0 91.0 . . . 4.2 95.8 . . . 3.1 96.9 . . .
55–60 4.7 95.3 . . . 1.2 98.8 . . . .6 99.4 . . .
60–65 7.2 92.8 . . . 4.9 95.1 . . . 4.1 95.9 . . .
65–70 . . . 100.0 . . . . . . 100.0 . . . . . . 100.0 . . .
70–75 . . . 100.0 . . . . . . 100.0 . . . . . . 100.0 . . .
75–80 . . . 97.3 2.7 . . . 97.9 2.1 . . . 98.8 1.2
80–85 . . . 88.9 11.1 . . . 91.2 8.8 . . . 94.8 5.2
85–90 . . . 87.3 12.7 . . . 89.4 10.6 . . . 94.9 5.1
90–95 . . . 86.3 13.7 . . . 88.6 11.4 . . . 93.7 6.3
95–100 . . . 57.0 43.0 . . . 59.9 40.1 . . . 74.4 25.6
100 & up. . . . 25.6 74.4 . . . 36.4 63.6 . . . 41.5 58.5
The emigration {15} at several ages shewn in Table VI, though graduated
with much regularity, is very different in amount at particular ages from
that which has been computed on page 14 (_ante_), and each person must
form his own opinion as to which set of figures is likely to be nearest
the truth.
Applying the final test previously used, by calculating the ratios of
survivors indicated by the corrected figures, we have:—
Age at the Proportion of survivors The like
end of the ten (including proportion
years. emigrants) out of 100 males who according to
were the
living ten years earlier. English Life
Table
No. 3.
According to According to
corrected corrected
figures, figures,
1851 and 1861. 1861 and 1871.
10–15 87.1 87.0 86.4
15–20 94.3 94.8 94.2
20–25 93.7 94.1 93.7
25–30 92.0 92.0 92.0
30–35 91.4 91.1 90.9
35–40 90.6 89.8 89.9
40–45 89.3 88.3 88.6
45–50 87.4 86.4 86.8
50–55 84.9 84.3 84.3
55–60 81.0 80.2 80.5
60–65 76.6 75.1 75.3
65–70 68.8 66.5 67.7
70–75 57.7 56.3 56.9
75–80 42.9 40.8 43.5
These ratios, like those obtained from the corrected female population,
shew a great deal of regularity, and resemble those derived from the
English Life Table very closely, whilst they deviate widely from those
based upon the uncorrected census figures.
It may perhaps be supposed that such resemblance is artificial, and is
really the result of the adoption of the Life Table as a guide in the
apportionment of the recorded deaths under the years of birth. I am,
however, sure that such a use of the Life Table cannot have controlled
the result to any very important extent. Any apportionment of deaths
occurring amongst a gradually increasing population like that of England,
effected on a consistent and reasonable plan, would necessarily come
within a very few thousands of the figures shewn in Tables IV and VI, at
least for that period of life extending over fifty years or thereabouts,
which lies between childhood and old age. {16}
There is this further remark to be made, viz., that the series of ratios,
though they resemble those derived from the Life Table, deviate from them
at particular ages to a very appreciable extent thus:—
MALES—Loss by death. FEMALES—Loss by death.
Age at end Life Table. Corrected Corrected Life Table. Corrected Corrected
of Population, Population, Population, Population,
decennium. 1851/60. 1861/70. 1851/60. 1861/70.
25–30 8.0 8.0 8.0 8.4 8.6 8.1
30–35 9.1 8.6 8.9 9.6 9.5 9.0
35–40 10.1 9.4 10.2 10.4 10.0 9.9
40–45 11.4 10.7 11.7 11.4 11.0 10.9
45–50 13.2 12.6 13.6 12.6 11.7 11.8
50–55 15.7 15.1 15.7 14.1 13.2 13.2
55–60 19.5 19.0 19.8 16.8 15.3 15.4
60–65 24.7 23.4 24.9 21.8 19.8 20.5
The actual mortality seems in general to be lower than that shewn in the
Life Table, sometimes to the extent of five or six or even nine per cent.
If, therefore, we were to compute the numbers of deaths on the basis of
the Life Table, the result would be found to exceed the recorded deaths
by many thousands. I naturally prefer to accept the teachings of the
recorded facts, although they may not have been transposed quite
correctly, rather than rely upon the Life Table,—which I feel sure has
been graduated by some mathematical process at least as empirical as any
estimate of mine. At the same time, I think I am bound to point out that
so near a correspondence between the general character of my results and
that of those obtained by mathematical graduation is a most important
fact, tending to convince us more strongly than ever that great
regularity would be found to exist in the age-distribution of deaths
occurring amongst a large population, and during a moderately long period
of time, if only a truthful record of ages could be secured.
APPLICATION OF THE SUGGESTED CORRECTIONS.
On applying to the census figures of 1861 and 1871 for each of the eleven
divisions, the proportional corrections shewn in Statements A and B,
certain results were obtained, of which the following is an example:—
Age in Division VIII Ratio of National Difference.
1871. (North-Western). Population in ratio of
Female Population in 1871 survivors
to that in (including
1861, allowance for
(per cent.) Emigrants.)
1861. 1871.
10–15 205692 179947 87.5 87.5 . . .
15–20 167248 171382 102.5 94.7 +7.8
20–25 151238 155554 102.9 93.7 +9.2
25–30 149921 145825 97.3 91.9 +5.4
30–35 144649 131174 90.7 91.0 -.3
The final result of the above calculation is a column of differences
which, if the rate of mortality in Lancashire and Cheshire exactly
equalled that of the nation, would represent the gain or loss at each age
on a balance of migrations. The whole of the differences thus
ascertained for the eleven divisions respectively are shewn in Table
VIII.
The last column in that table, shewing the differences for England and
Wales, of course represents simply the effect of migrations. I think
that the differences in the other columns, at ages up to 35, are almost
wholly consequent upon migrations. {19a} The mortality in London and in
Lancashire being greater than the average, the figures at those ages are
perhaps less striking (because partially neutralised by such excessive
mortality) than if the results of migrations stood out by themselves. It
seems clear, in fact, that whilst the South-western counties _lose_ more
than 26.8 per cent. of their young men in the ten years beginning with
age 10 to 15 and ending with age 20 to 25, London _gains_ rather more
than 14.5 per cent. at the same time of life.
The ratios last mentioned, and many others which are shewn in Table VIII,
are of great importance, as indicating the movements of large numbers of
persons, {19b} and therefore, by way of rendering our impressions about
their meaning more definite, I have taken the pains to apportion the
deaths recorded in Divisions I, V, and VIII at certain ages, with the
following results:—
Born in. 1861. 1871. Apportioned Loss or Per cent. on The per centages in Table
Deaths, gain by Population VIII being consequently
1861–70. migrations. in 1861. made up thus—
Deaths Loss or Loss or Loss or Total.
Gain by gain gain by
Migrations. compared migrations.
with
average
death loss.
{20}
Male Population (corrected.)
DIV. I. LONDON.
1851–55 147228 141937 7849 +2558 5.3 +1.7 -.1 +1.7 +1.6
1846–50 130615 141809 8042 +19236 6.1 +14.7 -.2 +14.7 +14.5
1841–45 118767 134948 11004 +27185 9.3 +22.9 -1.3 +22.9 +21.6
1836–40 120587 118776 12405 +10594 10.3 +8.8 -1.4 +8.8 +7.4
DIV. V. SO.-WEST.
1851–55 106614 91014 4601 -10999 4.3 -10.3 +.9 -10.3 -9.4
1846–50 100897 67943 4838 -28116 4.8 -27.9 +1.1 -27.9 -26.8
1841–45 96505 57468 5637 -27400 6.2 -30.3 +1.8 -30.3 -28.5
1836–40 69223 50745 5430 -13048 7.8 -18.9 +1.1 -18.9 -17.8
DIV. VIII. LANC. AND CHESH.
1851–55 166782 160706 10641 +4565 6.4 +2.7 -1.2 +2.7 +1.6
1846–50 150583 145788 10945 +6150 7.3 +4.1 -1.4 +4.1 +2.7
1841–45 138424 133781 13247 +8604 9.6 +6.2 -1.6 +6.2 +4.6
1836–40 132498 119061 13348 -89 10.1 -.1 -1.2 -.1 -1.2
Female Population (corrected.)
DIV. I. LONDON.
1851–55 149084 164132 7810 +22858 5.2 +15.3 +.1 +15.3 +15.4
1846–50 133936 165675 7908 +39647 5.9 +29.6 +.4 +29.6 +30.0
1841–45 139844 155003 10469 +25628 7.5 +18.3 +.6 +18.3 +18.9
1836–40 143074 136729 11944 +5599 8.3 +3.9 +7 +3.9 +4.6
DIV. V. SO.-WEST.
1851–55 106074 90500 4892 -10682 4.6 -10.1 +.7 -10.1 -9.4
1846–50 97784 77303 5375 -15106 5.5 -15.4 +.8 -15.4 -14.6
1841–45 91581 68751 6249 -16581 6.8 -18.1 +1.3 -18.1 -16.8
1836–40 77717 61231 5950 -10536 7.7 -13.5 +1.3 -13.5 -12.2
DIV. VIII. LANC. AND CHESH.
1851–55 167248 171382 10115 +14249 6.0 +8.5 -.7 +8.5 +7.8
1846–50 151238 155554 11094 +15410 7.3 +10.2 -1.0 +10.2 +9.2
1841–45 149921 145825 14024 +9928 9.3 +6.6 -1.2 +6.6 +5.4
1836–40 144649 131174 14900 +1425 10.3 +1.0 -1.3 +1.0 -.3
Similar tables might be constructed for every age, and not only for each
registration division, but for every registration district in the
kingdom.
It will be observed that the apparent gain of the metropolitan division
through migrations is less striking than might have been expected,
although it is very large. But what is really shewn is the _balance_
resulting, after deducting from the _gain_ of strangers, the _loss_
arising from the removal of families over the border of the division into
extra metropolitan Middlesex, Surrey and Kent, or even into the nearer
parts of Essex and Hertfordshire. If the London boundary were largely
extended, it would be found that the _gain_ by immigration from a
distance is larger, and the _loss_ by emigration is less, than now
appears; and, in short, the statements whether of urban gain or of rural
loss at ages up to 35 would be more striking than those exhibited in
Table VIII.
After 35, both sexes in London and in the north-western counties exhibit
a steady loss at each age, no doubt attributable in the main to the heavy
mortality experienced in those divisions. The rural divisions numbered V
and XI shew a loss until past the age of 50, due to emigration. These
and several other agricultural divisions (those numbered II, III, and
IV), shew considerable gains at the higher ages, partly due to their
mortality being low, and partly resulting from other causes.
It is evident that those who emigrate beyond sea (from Division V for
example) are older persons than those who leave their native division to
seek employment at a short distance, as do the majority of those who
migrate from the eastern counties (Division IV). Two-thirds of these
latter are perhaps between the ages of 14 and 20 years when they depart,
and very few of them can be more than 25 years old.
The apparent relative mortality of the sexes at certain ages must be
influenced by the dissimilar degrees of inaccuracy in the population
returns for males and females respectively, as the following short
statement will shew:—
Mean population Mean population Deaths Deaths per 1000.
1861–71, from 1861–71, from 1861–70.
uncorrected corrected
figures. figures.
From From
uncorrected. corrected.
Males. Fem’l’s. Males. Fem’l’s. Males. Fem’l’s. M. F. M. F.
15–20 1021321 1035205 1011321 1035632 62921 68553 6.2 6.6 6.2 6.6
20–25 906063 1011063 892063 938433 76591 80463 8.5 8.0 8.6 8.6
25–30 788782 886088 788782 849341 147734 160329 9.9 9.7 9.9 10.0
30–35 704005 769381 710005 761546
The facts I have stated, and the experiments I have made, are perhaps
sufficient to suggest by what methods of estimation an idea can be gained
of the distribution of population as to ages, when once the total
increase or decrease is known. {22} But they also tend to shew the
difficulties which surround the subject, and the need which exists that
enquirers should summon up sufficient courage to treat with a certain
degree of freedom the returns of the census and registration offices.
* * * * *
TABLE I.—Showing the Rate of Increase of Population (per cent.) of each
sex and _at each age_ in the several Registration Divisions of England
and Wales during the ten years, 1851–61.
TABLE II.—Shewing the Proportion (per cent.) of Population enumerated in
1861 to that enumerated _at corresponding ages ten years earlier_, in the
several Registration Divisions, and in England and Wales.
[These two Tables having been calculated simply with the object of
shewing that the proportional results obtainable by a comparison of the
numbers enumerated at successive censuses, at particular ages, do not
display sufficient regularity to justify the belief that such proportions
would be approximately maintained decennium after decennium,—it is
considered unnecessary to print them. The remaining Tables are printed
in full, as without reference to, and careful consideration of, the facts
they display, the paper would almost lose its significance.]
TABLE III.—Shewing the enumerated population in 1851, 1861, and 1871, at
each quinquennial period of life, the estimated births in 1851–70, the
registered deaths apportioned according to date of birth, and the numbers
of inhabitants lost or gained, on the hypothesis of the correctness of
the preceding figures.
Born Population enumerated. Deaths registered. Difference—referable to errors
in and migrations {23a}
MALES. MALES. 1851–60. 1861–70.
1851. 1861. 1871. 1851–60. 1861–70. Loss. Gain. Loss. Gain.
1866–70 . . . 2011024 1536464 . . . 427200 . . . . . . 47360 . . .
{23b}
1861–65 . . . 1887702 1350819 . . . 546170 . . . . . . . . . 9287
{23b}
1856–60 1751531 1354907 1220770 365536 180534 31088 . . . . . . 46397
{23b}
1851–55 1651656 1172960 1084713 482227 60259 . . . 3531 27988 . . .
{23b}
1846–50 1176753 1059889 951917 156291 62499 . . . 39427 45473 . . .
1841–45 1050228 957930 843278 58497 75494 33801 . . . 39158 . . .
1836–40 963995 860210 746320 60004 75606 43781 . . . 38284 . . .
1831–35 873236 734287 640819 69604 74657 69345 . . . 18811 . . .
1826–30 795455 661690 590097 67451 77910 66314 . . . . . . 6317
1821–25 699345 590280 506947 65694 81085 43371 . . . 2248 . . .
1816–20 617889 551058 455788 66739 84309 92 . . . 10901 . . .
1811–15 532680 453310 345907 67483 89886 11887 . . . 17517 . . .
1806–10 474211 392196 294675 69394 95736 12621 . . . 1785 . . .
1801–05 392882 299000 205370 73888 103431 19994 . . . . . . 9801
1796–1800 346104 265536 149887 78530 108473 2038 . . . 7176 . . .
1791–95 254892 175538 82091 84399 108450 . . . 5045 . . . 15003
1786–90 227240 128428 38573 90915 94795 7897 . . . . . . 4940
1781–85 151640 71780 11685 92953 64919 . . . 13093 . . . 4824
1776–80 114730 34256 2383 83815 33036 . . . 3341 . . . 1163
1771–75 65016 10359 390 58972 11790 . . . 4315 . . . 1821
1766–70 31690 2191 41 30694 2768 . . . 1195 . . . 618
1761–65 10423 399 . . . 11270 397 . . . 1246 2 . . .
1756–60 2282 55 . . . 2781 25 . . . 554 30 . . .
1751–55 456 . . . . . . 463 . . . . . . 7 . . . . . .
1746–50 78 . . . . . . 28 . . . 50 . . . . . . . . .
Age not . . . . . . . . . 908 . . . . . . 908 . . . . . .
stated
Totals 12184412 13674985 11058934 2138536 2459489 342279 72662 256733 100171
FEMALES. FEMALES.
1866–70 . . . 1936784 1534812 . . . 359329 . . . . . . 42643 . . .
{23c}
1861–65 . . . 1814081 1355707 . . . 473449 . . . . . . . . . 15075
{23c}
1856–60 1681961 1345875 1203469 305511 172128 30575 . . . . . . 29722
{23c}
1851–55 1586949 1171106 1095699 419780 61093 . . . 3937 14314 . . .
{23c}
1846–50 1171354 1045287 1052843 151062 66098 . . . 24995 . . . 73654
1841–45 1042131 974712 937299 60003 79459 7416 . . . . . . 42016
1836–40 949362 969283 813675 65106 81018 . . . 85027 74590 . . .
1831–35 883953 834877 700534 76754 79463 . . . 27678 54880 . . .
1826–30 871152 725088 639705 76237 77870 69827 . . . 7513 . . .
1821–25 771130 634262 546094 73309 76696 63559 . . . 11472 . . .
1816–20 658237 583069 488901 70730 75357 4438 . . . 18811 . . .
1811–15 555879 477530 372261 67174 77049 11175 . . . 28220 . . .
1806–10 494408 414367 328010 63923 84997 16118 . . . 1360 . . .
1801–05 406107 315004 235868 65030 97481 26073 . . . . . . 18345
1796–1800 362697 290704 174086 72028 108636 . . . 35 7982 . . .
1791–95 271395 201034 99896 82975 114233 . . . 12614 . . . 13095
1786–90 254070 152917 51265 93843 105704 7310 . . . . . . 4052
1781–85 175879 88860 17896 99612 78080 . . . 12593 . . . 7116
1776–80 135432 45403 4338 94274 43589 . . . 4245 . . . 2524
1771–75 81086 15608 855 71487 17466 . . . 6009 . . . 2713
1766–70 42150 3994 119 40514 4849 . . . 2358 . . . 974
1761–65 14982 839 . . . 16604 894 . . . 2461 . . . 55
1756–60 3969 146 . . . 4724 73 . . . 901 73 . . .
1751–55 874 . . . . . . 921 . . . . . . 47 . . . . . .
1746–50 137 . . . . . . 76 . . . 61 . . . . . . . . .
Age not . . . . . . . . . 502 . . . . . . 502 . . . . . .
stated
Totals 12415294 14040830 11653332 2072179 2386011 236552 183402 261858 209371
TABLE IV.—Shewing the Female population in 1851, 1861, and 1871, as
corrected upon certain hypotheses, the estimated births in 1851–70, the
registered deaths, apportioned according to date of birth, after
adjustment, and the loss or gain of inhabitants upon a balance of
migrations.
Born in Population (corrected). Deaths registered. Loss or gain by migrations.
FEMALES. FEMALES. 1851–60. 1861–70.
1851. 1861. 1871. 1851–60. 1861–70. Loss. Gain. Lose. Gain.
{24b}
1866–70 . . . 1936784 1571448 . . . 359329 . . . . . . 6007 . . .
{24a}
1861–65 . . . 1822952 1340794 . . . 473449 . . . . . . 8709 . . .
{24a}
1856–60 1690145 1379277 1203469 305511 172128 5357 . . . 3680 . . .
{24a}
1851–65 1586949 1157052 1094603 419780 61093 10117 . . . 1350 . . .
{24a}
1846–50 1203052 1046332 981249 151062 66098 5658 . . . . . . 1015
1841–45 1028583 976661 898871 60003 79459 . . . 8081 . . . 1669
1836–40 954109 895618 809607 65106 81018 . . . 6015 4993 . . .
1831–35 887489 799812 711042 76754 79463 10923 . . . 9307 . . .
1826–30 804073 713486 624991 76237 77870 14350 . . . 10625 . . .
1821–25 736430 652021 567938 73309 76696 11100 . . . 7387 . . .
1816–20 645730 569658 488901 70730 75357 5342 . . . 5400 . . .
1811–15 573667 501406 421400 67174 77019 5087 . . . 2957 . . .
1806–10 483036 415610 328010 63923 84997 3503 . . . 2603 . . .
1801–05 426412 357844 258275 65030 98802 3538 . . . 767 . . .
1796–1800 364148 290704 177568 72028 112636 1416 . . . 500 . . .
1791–95 308305 222745 104192 84226 118269 1334 . . . 284 . . .
1786–90 254070 156434 49008 97626 107225 10 . . . 201 . . .
1781–85 195578 92680 17144 103438 70172 . . . 540 . . . 636
1776–80 138547 43269 4121 95728 39172 . . . 450 . . . 24
1771–75 84572 14952 641 69678 14330 . . . 58 . . . 19
1766–70 40043 3734 60 36401 3732 . . . 92 . . . 58
1761–65 14188 614 . . . 13613 617 . . . 39 . . . 3
1756–60 3671 56 . . . 3631 50 . . . 16 6 . . .
1751–55 629 . . . . . . 636 . . . . . . 7 . . . . . .
1746–50 52 . . . . . . 53 . . . . . . 1 . . . . . .
Totals 12423478 14049701 11653332 2071677 2335011 77735 15899 64782 3424
TABLE V.—Shewing the degree of incorrectness of the returns of the ages
of the female population, according to the hypotheses upon which Table IV
is based.
1851. 1861. 1871.
True Age. Returned at Returned Returned at Returned at Returned Returned at Returned at Returned Returned at
next lower correctly. next higher next lower correctly. next higher next lower correctly. next higher
age. age. age. age. age. age.
0–5 . . . 1171354 31698 . . . 1345875 33402 . . . 1534812 36636
5–10 . . . 1010433 18150 . . . 1137704 19348 . . . 1319071 21723
10–15 . . . 931212 22897 . . . 1025939 20393 . . . 1181746 21723
15–20 . . . 861056 26433 . . . 954319 22342 . . . 1073976 20627
20–25 . . . 804073 . . . . . . 895618 . . . . . . 981249 . . .
25–30 40646 695784 . . . 51323 748489 . . . 50967 847904 . . .
30–35 75346 570384 . . . 86388 627098 . . . 89395 720212 . . .
35–40 87853 485814 . . . 97990 554031 . . . 93463 617579 . . .
40–45 70065 412971 . . . 80231 489427 . . . 82955 542036 . . .
45–50 81437 344975 . . . 93642 407764 . . . 97669 470269 . . .
50–55 61132 303016 . . . 69766 345844 . . . 75825 413076 . . .
55–60 59681 248624 . . . 68523 289321 . . . 75325 345575 . . .
60–65 22771 231299 . . . 25683 265021 . . . 26686 301324 . . .
65–70 22771 172807 . . . 25683 197062 . . . 26686 231589 . . .
70–75 3072 135432 43 3972 152462 . . . 4279 173289 . . .
75–80 . . . 81043 3529 455 88860 3365 797 99896 3499
80–85 . . . 38621 1422 . . . 42038 1231 . . . 47766 1242
85–90 . . . 13560 628 . . . 14377 575 . . . 16654 490
90–95 . . . 3341 330 . . . 3419 315 . . . 3848 273
95–100 . . . 544 85 . . . 524 90 . . . 582 59
100– . . . 52 . . . . . . 56 . . . . . . 60 . . .
TABLE VI.—Shewing the Male population in 1851, 1861 and 1871, as
corrected upon certain hypotheses; the estimated births in 1851–70; the
registered deaths apportioned according to date of birth, after
adjustment; and the loss or gain of inhabitants upon a balance of
migrations.
Born in Population (Corrected.) Deaths Registered. Loss or gain by migrations.
Males. Males.
1851–60. 1861–70.
1851. 1861. 1871. 1851–60. 1861–70. Loss. Gain. Loss. Gain.
{25b}
1866–70 . . . 2006083 1572464 . . . 427200 . . . . . . 6419 . . .
{25a}
1861–65 . . . 1892329 1335819 . . . 546170 . . . . . . 10340 . . .
{25a}
1866–60 1758383 1388307 1218770 365536 180534 4540 . . . . . . 10997
{25a}
1851–55 1651656 1157960 1674713 482227 60259 11469 . . . 22988 . . .
{25a}
1846–60 1208453 1057889 937917 156291 62499 . . . 5727 57473 . . .
1841–45 1030228 947930 843278 58497 75494 23801 . . . 29158 . . .
1836–40 960000 846210 751320 60004 75606 53786 . . . 19284 . . .
1831–35 868231 734287 644819 69604 74657 64340 . . . 14811 . . .
1826–30 784455 668690 580097 67451 77910 48314 . . . 10683 . . .
1821–25 696345 594280 506947 65694 81085 36371 . . . 6248 . . .
1816–20 624889 539058 447788 66739 84369 19092 . . . 6901 . . .
1811–15 535680 453310 357907 67483 89886 14887 . . . 5517 . . .
1806–10 458711 384196 284675 69394 95736 5121 . . . 3785 . . .
1801–05 389882 312000 217370 73888 104635 3994 . . . . . . 10005
1796–1800 334904 256136 150887 78530 111999 238 . . . . . . 6750
1791–95 273892 188538 83091 85504 111681 . . . 150 . . . 6234
1786–90 222840 129928 37173 94206 95445 . . . 1294 . . . 2690
1781–85 168040 73280 11235 96016 62880 . . . 1256 . . . 835
1776–80 116466 32356 2333 84496 29493 . . . 386 530 {25c} . . .
1771–75 66800 9509 314 57119 9550 172 . . . . . . 355 {25c}
1766–70 29493 2101 17 27390 2118 2 . . . . . . 34
1761–65 9412 274 . . . 9116 266 22 . . . 8 . . .
1756–60 2166 20 . . . 2114 17 32 . . . 3 . . .
1751–55 318 . . . . . . 310 . . . 8 . . . . . . . . .
1746–50 20 . . . . . . 19 . . . 1 . . . . . . . . .
Totals 12191264 13674671 11058934 2137628 2459489 286190 8813 194148 37900
TABLE VII.—Shewing the degree of incorrectness of the returns of the ages
of the Male population, according to the hypotheses upon which Table VI
is based.
True 1851. 1861. 1871.
Age.
Returned at Returned Returned Returned Returned Returned Returned Returned Returned
next lower correctly. at next at next correctly. at next at next correctly. at next
age. higher age. lower age. higher age. lower age. higher age.
0–5 . . . 1176753 31700 . . . 1354907 33400 . . . 1536464 36000
5–10 . . . 1018528 11700 . . . 1139560 18400 . . . 1314819 21000
10–15 . . . 952295 7705 . . . 1041489 16400 . . . 1199770 19000
15–20 . . . 865531 2700 . . . 941530 6400 . . . 1065713 9000
20–25 . . . 784455 . . . . . . 846210 . . . . . . 937917 . . .
25–30 8300 688045 . . . 7600 726687 . . . 5000 838278 . . .
30–35 11300 613589 . . . 7600 661090 . . . 5000 746320 . . .
35–40 4300 531380 . . . 600 590280 3400 . . . 640819 4000
40–45 1300 457411 . . . . . . 539058 . . . . . . 580097 . . .
45–50 16800 373082 . . . 8600 444710 . . . 6000 500947 . . .
50–55 19800 315104 . . . 8600 375596 . . . 6000 441788 . . .
55–60 31000 242892 . . . 16600 295400 . . . 14000 343907 . . .
60–65 12000 210840 . . . 3600 252536 . . . 2000 282675 . . .
65–70 16400 151640 . . . 13000 175538 . . . 12000 205370 . . .
70–75 . . . 114730 1736 . . . 128428 1500 . . . 149887 1000
75–80 . . . 63280 3520 . . . 70280 3000 . . . 81091 2000
80–85 . . . 28170 1323 . . . 31256 1100 . . . 36573 600
85–90 . . . 9100 312 . . . 9259 250 . . . 11085 150
90–95 . . . 1970 196 . . . 1941 160 . . . 2233 100
95–100 . . . 260 58 . . . 239 35 . . . 290 24
100– . . . 20 . . . . . . 20 . . . . . . 17 . . .
TABLE VIII.—Shewing the differences between (1) The National percentage
of persons surviving at each age in 1871, (including estimated loss by
emigration in 1861–71) calculated on the numbers ten years younger
enumerated in 1861; and (2) the ratios of inhabitants enumerated in each
Division in 1871, compared with the respective populations ten years
younger enumerated in 1861. The populations employed have first been
corrected according to Statements A and B.
Age in I. II. III. IV. V. VI. VII. VIII. IX. X. XI. England
1871 London. South South Eastern. South West North North Yorkshire. Northern. Welsh. and
Eastern. Midland. Western. Midland. Midland. Western. Wales.
MALES. Excess or deficiency of the ratio of survivors, compared with National ratio.
10–15 -4.3 +7.6 +6.1 +1.9 -1.3 -.3 -.6 -.7 +2.8 +4.2 -.7 +0.8
15–20 +1.6 +1.2 -8.8 -11.2 -9.4 -3.6 -6.0 +1.6 +3.6 +4.8 -3.6 -2.0
20–25 +14.5 -4.0 -20.9 -25.3 -26.8 -10.0 +14.2 +2.7 +4.4 +12.8 -9.9 -6.4
25–30 +21.6 -3.2 -14.1 -21.2 -28 5 -8.4 +13.0 +4.6 +6.0 +14.6 -13.1 -3 0
30–35 +7.4 -2.8 -4.2 -6.6 -17.8 -5.9 -6.0 -1.2 +4.5 +5.5 -9 5 -2.3
35–40 -1.6 +.1 +1.0 -.3 -8.8 +4.4 -2.3 -3.4 +3.8 +2.0 -7.0 -2.0
40–45 -3.6 +.2 +1.8 +.5 -4.9 -3.4 +1.0 -2.3 +3.7 +3.3 -7.2 -1.5
45–50 -5.9 +1.7 +2.4 +1.9 +1.1 +1.8 +.6 -3.5 +1.8 +2.9 -3.0 -1.1
50–55 -7.2 +2.1 +2.1 +2.4 -.8 -2.1 +1.8 -4.9 +2.5 +2.0 -.6 -1.2
55–60 -10.6 +5.5 +2.6 +2.7 +1.3 -1.8 +2.9 -6.7 +1.4 +.9 +.9 -1.3
60–65 -8.5 +4.2 +4.8 +5.7 +1.3 -1.2 +2.5 -7.3 -1.7 +.7 +.6 -1.0
65–70 -4.2 +10.5 +8.3 +10.5 +7.2 +3.6 +6.0 -3.9 +.9 +1.8 +2.3 +3.2
70–75 -5.4 +9.0 +7.8 +10.0 +7.7 +2.5 +6.5 -6.3 -.3 +2.2 +2.1 +2.6
75–80 -4.8 +8.0 +6.5 +9.4 +7.1 +4.3 +5.5 -4.5 -1.3 +1.7 +6.6 +3.3
80–85 -3.1 +4.4 +2.6 +6.1 +4.9 +2.8 +3.0 -3.4 -2.1 +.5 +8.0 +2.1
85–90 -.4 +2.8 +.1 +3.5 +1.6 +1.4 +.6 -2.2 -1.5 +2.3 +4.7 +1.1
FEMALES. Excess or deficiency of the ratio of survivors, compared with the National ratio.
10–15 -3.0 +5.5 +1.6 -.5 -2 9 -1.4 -1.9 . . . +1.2 +26 -2.3 -.3
15–20 +15.4 -1.0 -7.1 -15.0 -9.4 +3.1 -6.9 +7.8 +3.9 +1.2 -7.8 -.l
20–25 +30.0 +1.5 -11.7 -20.3 -14.6 -4.9 -11.1 +9.2 +3.6 +8 -12.9 +.1
25–30 +18.9 +8.0 -6.0 -12.5 -16.8 -5.3 -10.3 +5.4 +3.5 +4.6 -11.9 +.1
30–35 +4.6 +7.9 -1.0 +5.5 -12.2 -4.8 -5.9 -.3 +3.7 +5.6 +5.8 -.7
35–40 +3.1 +5.3 +1.3 -2.5 -7.2 +2.2 -3.3 -2.9 +3.7 +4.4 -4.4 -1.3
40–45 -5.0 +4.2 +1.3 -.3 -4.3 -1.8 -1.8 -2.1 +2.5 +1.5 -5.8 -1.4
45–50 -6.4 +3.7 +2.1 +.3 -1.1 -.9 -1.1 -2.4 +1.8 +1.4 -2.8 -1.1
50–55 -5.8 +4.1 +1.7 +.3 +.7 -1.3 +.3 -4.1 +1.5 +2.3 -.2 -.9
55–60 -6.9 +5.7 +3.6 +1.2 +.1 -.8 +1.2 -5.0 +2.1 +2.2 -.3 -.6
60–65 -4.7 +4.3 +3.7 +2.2 +1.1 -.6 +.5 -4.9 -1.1 -.1 +2.1 -.5
65–70 -3.9 +3.7 +4.0 +5.5 +3.2 +.5 -.1 -6.9 -2.3 -.5 +1.2 -.3
70–75 -4.0 +6.0 +4.1 +6.1 +3.5 +.3 +1.0 -8.4 +3.0 -.8 +.8 -.2
75–80 -3.2 +3.5 +.7 +5.7 +3.0 +.3 +.6 -7.1 -4.6 -.4 +4.3 -.1
80–85 -2.4 +2.1 -.1 +4.3 +.4 +.5 -1.2 -5.7 +3.8 -2.0 +8.1 -.2
85–90 +.1 +1.6 +.2 +3.8 +1.5 +.8 -.7 -2.6 -1.4 -.1 +4.7 +.7
Memo.—If the mortality in each Division was exactly the same, these
ratios would truly represent loss by emigration or gain by immigration;
however, there is a good reason to think that at the higher ages the
losses are (in Divisions I and VIII especially) caused by excessive
mortality, and the gains in other Divisions are largely occasioned by the
mortality therein being below the average.
FOOTNOTES.
{4} This should be read “0 and under 5.”
{6} These estimates have been made upon the basis of an apportionment
derived from a consideration of the “English Life Table No. 3;” but I
refrain from going into a detailed account of the process, for fear of
rendering this paper more prolix and uninteresting than its character
necessitates.
{8a} Net gain of incoming Irish, foreigners, &c., in excess of those
departing. Net loss of English-born Emigrants, in excess of English
returning home.
{8b} This is framed on the assumption that the migrations in each year
were exactly alike in number.
{11a} It will be noticed that some of the ratios of inaccuracy
attributed to the census figures of 1851 are lower than those for later
censuses. These exceptions to the rule of decreasing inaccuracy might be
removed without any very violent disturbance of the estimates shewn in
Table IV, but it is thought scarcely requisite to do so.
{11b} The percentage would be 20.0 (more or less), except at high ages,
for each year of error.
{14} Net Gain.
{15} A further slight modification in the estimates of unregistered male
births will be noticed. It affects the estimated emigration in 1861–70
to the extent of about 10,000 persons,—making it 156,248 instead of
165,800.
{16} The following specimen calculation, shewing the ingredients which
constitute the computed deaths in 1861–1870 amongst females born in
1851–1855, in 1816–1820, and in 1811–1815 respectively, will illustrate
what I mean:—
Year of Born 1851–55. Born 1816–20. Born 1811–15.
Death.
Age Age Age Totals. Age Age Totals. Age Age Totals.
5–10. 10–15. 15–20. 35–45. 45–55. 45–55. 55–65.
1861 6730 518 . . . 7248 6234 645 6879 6514 . . . 6514
1862 5259 1603 . . . 6862 4999 1994 6993 6669 . . . 6669
1863 4630 2915 . . . 7575 3688 3392 7080 6813 . . . 6813
1864 2452 3989 . . . 6441 2350 5366 7716 7686 . . . 7686
1865 678 4626 . . . 5304 785 6993 7778 7873 . . . 7873
1866 . . . 4499 620 5119 . . . 8048 8048 7413 844 8257
1867 . . . 2949 1786 4735 . . . 7547 7547 5443 2410 7853
1868 . . . 2274 3045 5319 . . . 7359 7359 3813 3983 7796
1860 . . . 1437 4351 5788 . . . 7859 7859 2466 5985 8451
1870 . . . 510 6192 6702 . . . 8098 8098 873 8264 9137
19749 25350 15994 61093 18056 57301 75357 55563 21486 77049
{19a} The first line of Table VIII shews the effect of the removal of
families from the first division to the semi-suburban districts in
divisions II and III. Such families take with them a good many children;
hence the loss to the metropolitan division, and the gain to the two
divisions mentioned of both boys and girls.
{19b} The following statement may make this fact clearer:—
Division. Births recorded Population in Proportion
1841–45. 1871 as 100 to—
born 1841–45.
I. London 316037 289951 91.7
V. 266860 126219 47.3
South-western
VIII. 392151 279606 71.3
North-western
The survivors, according to the English Life Table No. 3, should be about
62.2 per cent. The low rate of mortality in the South-western counties
renders it certain that, but for migrations, the ratio of enumerated
population to the corresponding births would be higher than 62.2 in that
division; in the other divisions it would be lower.
{20} I am of opinion that the gain in this column, so far as regards
London death-rates, is due to the departure of many women when in bad
health, some of whom die in the country. But for the effect of such
departures, the recorded deaths and the apparent net gain by migrations
would reach higher numbers.
{22} The procedure for instance in 1881 might be:—Take the English
population at each age in 1871 as already corrected, and introduce the
numbers of births returned in 1876–80 and 1871–75 as the first two terms
of the series, adding a reasonable allowance for non-registration.
Deduct the deaths in 1871–80, duly apportioned under periods of birth.
The gross number of either sex enumerated in 1881 being known, the net
loss or gain by migrations can then be ascertained. Apportion this in
somewhat similar proportions to those observed in 1851–60. The final
results will exhibit approximately the distribution of population by ages
in 1881.
{23a} It will be noticed that I have paid no regard to the interval of
time between the census day and the January preceding, treating the exact
decennium as being a near enough equivalent of the interval between
census and census.
{23b} These numbers represent the births in the periods mentioned,
_plus_ an allowance for omissions, viz. 1¾ per cent. on births in
1866–70, and 2, 2¼, and 3½ per cent. on births in the earlier periods
respectively.
{23c} The correction adopted in the case of female births is rather
larger than in that of male births. These figures are those returned,
_plus_ 2 per cent. on the births in 1866–70, and 2¼, 2¾, and 4 per cent.
respectively on the births in the earlier periods.
{24a} Births, plus allowance for those unregistered, say 2 per cent. on
births in 1866–70, and 2¾, 3¼, and 4 per cent. respectively on births in
the earlier periods.
{24b} The few deaths “age not stated” are disregarded.
{25a} Births, _plus_ allowance for those unregistered, say 1½ per cent.
on births in 1866–70, and 2¼, 2.65 and 3.5 per cent. respectively on
births in the earlier periods.
{25b} The few deaths “are not stated” are disregarded.
{25c} These figures are, I think, improbable; I suppose the
apportionment of deaths may be chiefly in fault.
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