On the inaccuracies which probably exist in the census returns of ages

by Thomas A. Welton

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 per1000.
							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	Populationenumerated.			Deathsregistered.		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 [a/][23b]	1350819	. . .	546170	. . .	. . .	. . .	9287
1856–60	1751531 [a/][23b]	1354907	1220770	365536	180534	31088	. . .	. . .	46397
1851–55	1651656 [a/][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 [a/][23c]	1355707	. . .	473449	. . .	. . .	. . .	15075
1856–60	1681961 [a/][23c]	1345875	1203469	305511	172128	30575	. . .	. . .	29722
1851–55	1586949 [a/][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 [a/][24a]	1340794	. . .	473449	. . .	. . .	8709	. . .
1856–60	1690145 [a/][24a]	1379277	1203469	305511	172128	5357	. . .	3680	. . .
1851–65	1586949 [a/][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