^{page 69 note 1} See especially Wrigley, E. A. (ed.), An Introduction to English Historical Demography (1966)Google Scholar (hereafter referred to as Introduction), and P. Laslett, The World We Have Lost (1965).

^{page 69 note 2} This gives only a very broad outline of the method, for a more detailed description see Armstrong, W. A., “Social Structure from the Early Census Returns”, in: Introduction; and “The Interpretation of the Census Enumerators' Books for Victorian Towns”, in: The Study of Urban History, ed. H. J. Dyos (1968)Google Scholar (hereafter referred to as Interpretation).

^{page 69 note 3} Floud, R. C. and Schofield, R. S., “Social Structure from the Early Census Returns”, in: Econ. Hist. Rev., XXI (1968)Google Scholar, have argued that the sampling technique used by Armstrong is not random and so could be biased. Armstrong, in a rejoinder, maintains that whilst strictly speaking this criticism is justified, such a bias, in fact, is likely to be insignificant.

^{page 70 note 1} Based on Chapters 6 and 7 of my Ph.D. thesis, Social Structure of Nottingham and Adjacent Districts in the Mid-Nineteenth Century: An Essay in Quantitative Social History (presented to Nottingham University 1968) (hereafter referred to as Thesis).

^{page 70 note 2} Chambers, J. D., Modern Nottingham in the Making (1945)Google Scholar; Church, R. A., Economic and Social Change in a Midland Town: Victorian Nottingham 1815– 1900 (1966).Google Scholar

^{page 70 note 3} Females per 1,00 males, 1851: Nottingham, 1,158; Radford, 1,111; Bingham, 995; Bradford, 1,042; Leeds, 1,069; Sheffield, 991; Leicester, 1,004; Derby, 1,103; Liverpool, 1,032; England and Wales, 1,042.

^{page 70 note 4} See the evidence of Hawkesley, Thomas, “Ev. to R. C. on State of Large Towns and Populous Districts, 2nd Report”, in: Parl. Papers, XVIII, 1845;Google ScholarSeason, E., “A Report on the Sanitary Condition of Nottingham”, in: Nottingham Corporation Papers, 1873Google Scholar; Felkin, W., “Statistics of the Labouring Classes of Nottingham”, in: Journal of the Statistical Society, Vol. II (1839).Google Scholar

^{page 70 note 5} For a full analysis of the movement of population from Nottingham to Radford see Thesis, Chap. 3.

^{page 71 note 1} “Children's Employment, Appendix of Ev.”, in: Parl. Papers XIV, 1843, Ev. No 155Google Scholar; F., and White, J., History and Directory of Nottinghamshire (1853), p. 27Google Scholar; Lascells and Hegar, Commercial Directory of Nottingham (1848), pp. xxxvf.

^{page 71 note 2} Nottingham Review, 4/2/1842; 11/9/1846; 8/9/1848.

^{page 71 note 3} During the period 1849–'53 Nottingham had an average annual death rate of 29.0 per 1,00 population (standardised to the age structure of the population of England and Wales in 1851, thereby removing any age differential bias) compared with 24.5 for Radford. The statistics from which these figures were calculated came from the Annual Reports of Births, Marriages and Deaths, prepared by the Registrar General, together with the printed census volumes.

^{page 71 note 4} F. and J. White, op. cit. (1844 ed.), p. 40; Cossons, A., “The Villagers Remember”, in: Trans. of the Thoroton Soc, LXVI (1962), p. 79.Google Scholar

^{page 71 note 5} Howitt, W., Rural Life in England, Vol. I (1838), p. 142; General Board of Health Correspondence, Bingham Union Files, Public Record Office, MH 13/217 1863.Google Scholar

^{page 71 note 6} 1849–'53 death rates 17.2 per 1,00 standardised to the age structure of England and Wales 1851.

^{page 71 note 7} Between 1841 and 1851 there was a net emigration from Bingham of about 2,00 persons, or some 13% of the total 1841 population.

^{page 72 note 1} The enumerator' books are to be found at Public Record Office, HO 107 1851. This research was undertaken before Floud and Schofield, art. cit., wrote their criticism of the sampling technique. In the case of Nottingham the enumerators' books were worked through and every tenth household was selected; in the case of Radford, every fifth; in Bingham, every fourth. Chi-squared tests showed the samples to be good. See Thesis, Appendix E, Section 2. The raw tables from which Table 1 and subsequent tables have been calculated are in ibid., Appendix D.

^{page 72 note 2} , where σ is the standard deviation of the sample mean, n the number of cases and x the sample mean.

^{page 72 note 3} For a more detailed explanation see Armstrong, Introduction, pp. 223 and 272f., and his Interpretation, pp. 78f.

^{page 73 note 1} The ranges of error of a proportion are obtained from the formula: , where p is the sample proportion and n the number of cases.

^{page 75 note 1} These three general findings are based upon a more detailed analysis of Tables 1, 2 and 3, i.e.: i. Nottingham had a smaller mean sized sibling group than Radford; Radford had a larger group than Bingham (see Table 1); Bingham had a larger proportion of families with four or more children than Nottingham (see Table 3).

ii. Differences in the mean size of sibling groups of the two classes in each district are apparent only (see Table 2), i.e. their ranges of error overlap. However, the upper classes of Bingham had a lower proportion of their families with one or more children than the families of the working classes there (Table 3 (c)).

iii. Working classes of Nottingham had a smaller mean sized sibling group than the working classes of Radford; Bingham's working classes had a smaller mean sized sibling group than the working classes of Nottingham (Table 2); differences between the working classes of Bingham and Radford are apparent only.

^{page 76 note 1} 21.2 (± 8.0)% of farmer heads were bachelors compared with 15.1 (± 5.3)% of the upper classes of Bingham as a whole.

^{page 76 note 2} In Ireland in the nineteenth century it has been shown that on the whole a farmer would marry upon inheriting his farm (Connell, K. H., “Peasant Marriage in Ireland: Its Structure and Development Since the Famine”, in: Econ. Hist. Rev., XIV (1962)).Google Scholar This clearly did not happen in Nottinghamshire.

^{page 76 note 3} % Widows who were Household Heads: Nottingham Radford Bingham Upper classes 11.0 8.0 7.0 Working classes 11.7 7.5 5.7

^{page 76 note 4} In times of prosperity a woman could earn 9/-d and more per week in the lace industry; rents for a small house could be as low as a shilling a week.

^{page 77 note 1} Infant Death Rates, 1839–'43 (excluding those in Workhouse and Hospital): St Mary St Ann Byron Sherwood % upper class heads. 6.0 7.3 9.0 20.1 Infant deaths per 1,00 births 213 239 244 193 Exchange Castle Park % upper class heads. 18.3 23.6 31.9 Infant deaths per 1,00 births 134 193 175

^{page 77 note 2} The ages of wives are not given for registration districts in the printed volumes of the 1851 census. However, the samples from the enumerators' books enable the percentage of wives under 45 in the sample to be calculated. This percentage applied to the known number of all married women in each community enables the number of wives aged under 45 to be estimated.

^{page 78 note 1} i.e. a high death rate amongst the under five year olds in a community or class would tend to lower estimates of fertility based on this method, and vice versa.

^{page 78 note 2} By taking into account inter class and district child mortality (see Table 5), these views would be strengthened.

^{page 78 note 3} See Eversley, D. E. C., Social Theories of Fertility and the Malthusian Debate (1959), p. 43.Google Scholar

^{page 79 note 1} Evidence of the Nottingham Coroner in “Ev. to R. C. Children's Employment, 2nd Report”, in: Parl. Papers, LXXX, 1864, p. 242.Google Scholar The Nottingham Coroner believed that women did not want children because this interfered with their earning capacity. This attitude may have reflected their poverty.

^{page 79 note 2} “Child. Emp.”, 1843, Ev. No 175. The working conditions of women in the town are described in Pinchbeck, I., Women Workers and the Industrial Revolution, 1750–1850 (1930), p. 236.Google Scholar

^{page 79 note 3} Howitt, op. cit., pp. 156f.

^{page 81 note 1} Chambers, J. D. and Mingay, G., The Agricultural Revolution, 1750–1880 (1966), pp. 192f.Google Scholar

^{page 81 note 2} Op. cit., p. 155.

^{page 81 note 3} In Bingham 69.8 (± 5.9) % were aged under 25 and 83.4 (± 4.2)% were male.

^{page 82 note 1} In Nottingham 56.4 (± 5.8)% of the lodgers were aged over 24 and 57.4 (± 4.2)% were female.

^{page 82 note 2} Because the ranges of error overlap, to demonstrate a significant difference in this respect between Nottingham and Bingham, pooled tests are required, (for a description of these see Allen, R. G. D., Statistics for Economists (1949), pp. 172ff.)Google Scholar

^{page 82 note 3} Nottingham Review, 3/10/1851.