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 (includingemigrants) out of 100 Females who were living 10 yearsearlier.

The like proportion, according to theEnglish 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:—