to shew that, whether the new table be right or not, the old table must be wrong. Without any allowances being made for omissions in the registers, the excess of the births above the deaths, in the period from 1780 to 1785, shews an increase of 193,000, instead of 63,000. And, on the other hand, no allowances for omissions in the registers, that could with the slightest degree of probability be supposed, would make the excess of births above the deaths in the period from 1785 to 1790 equal to 659,000. Making no allowance for omissions, this excess only amounts to 317,406 ; and if we were to suppose the omissions in the births one 4th, instead of one 6th, and that there were no omissions in the registers of burials, and that no one died abroad, the excess would still fall short of the number stated by many thousands. The same results would follow, if we were to estimate the progress of population during these periods by the proportion of births to deaths, and the rate of mortality. In the first period the increase would turn out to be very much greater than VOL. II. H than the increase stated, and in the other very much less. Similar observations may be made with regard to some of the other periods in the old table, particularly that between 1795 and 1800, which has been already noticed. It will be found on the other hand that, if the proportion of births to deaths during each period be estimated with tolerable accuracy and compared with the mean population, the rate of the progress of the population determined by this criterion will, in every period, agree very nearly with the rate of progress determined by the excess of the births above the deaths, after applying the proposed corrections. And it is further worthy of remark that, if the corrections proposed should be in some degree inaccurate, as is probable, the errors arising from any such inaccuracies are likely to be very much less considerable than those which must necessarily arise from the assumption on which the old table is founded ; namely, that the births bear at all times the same proportion to the population. Of Of course I do not mean to reject any estimates of population formed in this way, when no better materials are to be found ; but, in the present case, the registers of the burials as well as baptisms are given every year, as far back as 1780, and these registers, with the firm ground of the last enumeration to stand upon, afford the means of giving a more correct table of the population from 1780 than was before furnished, and of shewing at the same time the uncertainty of estimates from the births alone, particularly with a view to the of population during particular periods. In estimating the whole population of a large country, two or three hundred thousand are not of much importance; but, in estimating the rate of increase during a period of five or ten years, an error to this amount is quite fatal. It will be allowed, I conceive, to make an essential difference in our conclusions respecting the rate of increase for any five years which we may fix upon, whether the addition made to the population during the term in question is 63,000 progress or 277,000, 115,000 or 456,000, 659,000 or 417,000. With regard to the period of the century previous to 1780, as the registers of the baptisms and burials are not returned for every year, it is not possible to apply the same corrections. And it will be obvious that, in the table calculated from the births previous to this period, when the registers are only given for insulated years at some distance from each other, very considerable errors may arise, not merely from the varying proportion of the births to the population, on averages of five years, but from the individual years produced not representing with tolerable correctness these averages *. A very slight glance at the valuable table of baptisms, burials and marriages, given in the Preliminary Observations, to the Population Abstracts), will shew 2 From the one or the other of these causes, I have little doubt, that the numbers in the table for 1760 and 1770, which imply so rapid an increase of population in that interval, do not bear the proper relation to each other. It is probable that the number given for 1770 is too great. b P. 20. how how very little dependence ought to be placed upon inferences respecting the population drawn from the number of births, deaths or marriages in individual years. If, for instance, we were estimating the population in the two years 1800 and 1801, compared with the two following years 1802 and 1803, from the proportion of marriages to the population, assuming this proportion to be always the same, it would appear that, if the population in the first two years were nine millions, in the second two years immediately succeeding it would be considerably above twelve millions, and thus it would seem to have increased above three millions, or more than one-third, in this short interval. Nor would the result of an estimate, formed from the births for the two years 1800 and 1801, compared with the two years 1803 and 1804, be materially different; at least such an estimate would indicate an increase of two millions six hundred thousand in three years. The reader can hardly be surprised at these results, if he recollects that the births, deaths and marriages bear but a small proportion |