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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]

Most recently updated: October 18, 2024

Language: English

Credits: Transcribed from the 1876 T. Brakell edition by David Price. Many thanks to the British Library for making their copy available

*** 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

in

1851.

Proportion of survivors out of 100 living 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.

as 100 to

Fem’l’s.

as 100 to

75 & under 80

373054

428741

74½ & under 79

369162

420783

99.0

98.1

80 „ „ 85

174287

213540

79 ,, ,, 84

207496

250662

119.1

117.4

85 „ „ 90

59641

79253

84 „ „ 89

76091

99340

127.6

125.3

90 ,, ,, 95

13652

20037

89 „ „ 94

19023

27331

139.3

136.4

95 „ „ 100

1887

3119

94 „ „ 99

2934

4728

155.5

151.6

100 & upwards.

145

279

99 and upwards

260

484

179.3

173.5

Ages.

Deaths.

Ages.

Deaths.

Proportion of the former to the latter.

Males.

Fem’l’s.

Males.

Fem’l’s.

Males.

as 100 to

Fem’ls.

as 100 to

75 & under 85

78695

84957

74½ & under 84

79184

84673

100.6

99.7

85 „ „ 95

19617

24868

84 „ „ 94

24024

29893

122.5

120.2

95 & upwards

932

1476

94 and upwards

1393

2152

149.5

145.8

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 years

Deaths of Females as in Table III.

As now Corrected.

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 of the year of migration)

1851–60.

1861–70.

Age (at the end of the decennium)

1851–60.

1861–70.

Immigrants. [8a]

Emigrants. [8b]

Immigrants. [8a]

Emi grants. [8b]

Net loss.

Net gain.

Net loss.

Net gain.

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

end of

Decennium.

1851–60.

1861–70.

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

as

aged

1851. [11a]

1861.

1871.

Really older.

Age correct.

Really y’nger.

Really older.

Age correct.

Really y’nger.

Really older.

Age correct.

Really 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 of the ten years.

Proportion of survivors (including emigrants) out of 100 Females who were living 10 years earlier.

The like proportion, according to the English Life Table, No. 3.

According to corrected figures, 1851 and 1861.

According to corrected figures, 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 of the year of migration.

1851–60.

1861–70.

Immigrants

from

Ireland, &c.

English

Emigrants.

Immigrants

from

Ireland, &c.

English Emigrants.

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

close of

decennium.

Net Loss.

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

as

aged

1851.

1861.

1871.

Really older.

Age correct.

Really y’nger.

Really older.

Age correct

Really y’nger.

Really older.

Age correct.

Really 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

end of the ten

years.

Proportion of survivors (including

emigrants) out of 100 males who were

living ten years earlier.

The like

proportion

according to the

English Life Table

No. 3.

According to

corrected figures,

1851 and 1861.

According to

corrected figures,

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

of

decennium.

Life Table.

Corrected

Population,

1851/60.

Corrected

Population,

1861/70.

Life Table.

Corrected

Population,

1851/60.

Corrected

Population,

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

1871.

Division VIII (North-Western).  Female Population in

Ratio of

Population in

1871

to that in

1861,

(per cent.)

National

ratio of

survivors

(including

allowance for

Emigrants.)

Difference.

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

Deaths,

1861–70.

Loss or

gain by

migrations.

Per cent. on

Population

in 1861.

The per centages in Table

VIII being consequently

made up thus—

Deaths

Loss or

Gain by

Migrations.

Loss or

gain

compared

with

average

death loss. [20]

Loss or

gain by

migrations.

Total.

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

1861–71, from

uncorrected

figures.

Mean population

1861–71, from

corrected

figures.

Deaths

1861–70.

Deaths per 1000.

From

uncorrected.

From

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

in

Population enumerated.

Deaths registered.

Difference—referable to errors

and migrations [23a]

MALES.

MALES.

1851–60.

1861–70.

1851.

1861.

1871.

1851–60.

1861–70.

Loss.

Gain.

Loss.

Gain.

1866–70

. . .

2011024 [23b]

1536464

. . .

427200

. . .

. . .

47360

. . .

1861–65

. . .

1887702 [23b]

1350819

. . .

546170

. . .

. . .

. . .

9287

1856–60

1751531  [23b]

1354907

1220770

365536

180534

31088

. . .

. . .

46397

1851–55

1651656 [23b]

1172960

1084713

482227

60259

. . .

3531

27988

. . .

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 stated

. . .

. . .

. . .

908

. . .

. . .

908

. . .

. . .

Totals

12184412

13674985

11058934

2138536

2459489

342279

72662

256733

100171

FEMALES.

FEMALES.

1866–70

. . .

1936784 [23c]

1534812

. . .

359329

. . .

. . .

42643

. . .

1861–65

. . .

1814081 [23c]

1355707

. . .

473449

. . .

. . .

. . .

15075

1856–60

1681961 [23c]

1345875

1203469

305511

172128

30575

. . .

. . .

29722

1851–55

1586949 [23c]

1171106

1095699

419780

61093

. . .

3937

14314

. . .

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 stated

. . .

. . .

. . .

502

. . .

. . .

502

. . .

. . .

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. [24b]

1861–70.

Loss.

Gain.

Lose.

Gain.

1866–70

. . .

1936784 [24a]

1571448

. . .

359329

. . .

. . .

6007

. . .

1861–65

. . .

1822952 [24a]

1340794

. . .

473449

. . .

. . .

8709

. . .

1856–60

1690145 [24a]

1379277

1203469

305511

172128

5357

. . .

3680

. . .

1851–65

1586949 [24a]

1157052

1094603

419780

61093

10117

. . .

1350

. . .

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 next lower age.

Returned correctly.

Returned at next higher age.

Returned at next lower age.

Returned correctly.

Returned at next higher age.

Returned at next lower age.

Returned correctly.

Returned at next higher 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.)

Males.

Deaths Registered.

Males.

Loss or gain by migrations.

1851–60.

1861–70.

1851.

1861.

1871.

1851–60. [25b]

1861–70.

Loss.

Gain.

Loss.

Gain.

1866–70

. . .

2006083 [25a]

1572464

. . .

427200

. . .

. . .

6419

. . .

1861–65

. . .

1892329 [25a]

1335819

. . .

546170

. . .

. . .

10340

. . .

1866–60

1758383 [25a]

1388307

1218770

365536

180534

4540

. . .

. . .

10997

1851–55

1651656 [25a]

1157960

1674713

482227

60259

11469

. . .

22988

. . .

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

Age.

1851.

1861.

1871.

Returned at next lower age.

Returned

correctly.

Returned

at next

higher age.

Returned

at next

lower age.

Returned

correctly.

Returned

at next

higher age.

Returned

at next

lower age.

Returned

correctly.

Returned

at next

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 1871

I.

London.

II.

South Eastern.

III.

South Midland.

IV.

Eastern.

V.

South Western.

VI.

West Midland.

VII.

North Midland.

VIII.

North Western.

IX.

Yorkshire.

X.

Northern.

XI.

Welsh.

England

and

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 Death.

Born 1851–55.

Born 1816–20.

Born 1811–15.

Age

5–10.

Age

10–15.

Age

15–20.

Totals.

Age

35–45.

Age

45–55.

Totals.

Age

45–55.

Age

55–65.

Totals.

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

1841–45.

Population in 1871

born 1841–45.

Proportion

as 100 to—

I.  London

316037

289951

91.7

V.  South-western

266860

126219

47.3

VIII.  North-western

392151

279606

71.3

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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Table of Contents

ON THE INACCURACIES WHICH PROBABLY EXIST IN THE CENSUS RETURNS OF AGES.

ON THE INACCURACIES WHICH PROBABLY EXIST IN THE CENSUS RETURNS OF AGES.

FOOTNOTES.

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