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diff --git a/old/67037-0.txt b/old/67037-0.txt deleted file mode 100644 index 957ea8d..0000000 --- a/old/67037-0.txt +++ /dev/null @@ -1,1582 +0,0 @@ -The Project Gutenberg eBook, On the inaccuracies which probably exist in -the census returns of ages, by Thomas A. Welton - - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - - - - -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 - -Character set encoding: UTF-8 - - -***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. - - - - -***END OF THE PROJECT GUTENBERG EBOOK ON THE INACCURACIES WHICH PROBABLY -EXIST IN THE CENSUS RETURNS OF AGES*** - - -******* This file should be named 67037-0.txt or 67037-0.zip ******* - - -This and all associated files of various formats will be found in: -http://www.gutenberg.org/dirs/6/7/0/3/67037 - - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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