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

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.
Age at the end of the ten years.	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.
Age in 1871.	1861.	1871.	Ratio of Population in 1871 to that in 1861, (per cent.)		Difference.
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—
Born in.	1861.	1871.	Apportioned Deaths, 1861–70.	Loss or gain by migrations.	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.
	Mean population 1861–71, from uncorrected figures.		Mean population 1861–71, from corrected figures.		Deaths 1861–70.		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	147734	160329	9.9	9.7	9.9	10.0

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]
Born in	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