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 theyears | 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 ofMigrations. | Consequent Estimate of net Loss or Gain in10 Years. [8b] | ||||||||
Age (at end of theyear of migration) | 1851–60. | 1861–70. | Age (at the end ofthe decennium) | 1851–60. | 1861–70. | ||||
Immigrants. [a/][8a] | Emigrants. [a/][8b] | Immigrants. [a/][8a] | Emi grants. [a/][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 | 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.