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.
BY THOMAS A. WELTON, F.S.S.
LIVERPOOL: T. BRAKELL, PRINTER, COOK STREET.
1876.
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.