Front Page Titles (by Subject) Chapter IX: Of the Checks to Population in England (continued). - An Essay on the Principle of Population, vol. 1 [1826, 6th ed.]
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Chapter IX: Of the Checks to Population in England (continued). - Thomas Robert Malthus, An Essay on the Principle of Population, vol. 1 [1826, 6th ed.] 
An Essay on the Principle of Population, or a View of its Past and Present Effects on Human Happiness; with an Inquiry into our Prospects respecting the Future Removal or Mitigation of the Evils which it Occasions (London: John Murray 1826). 6th ed.
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Book II, Chapter IX
Of the Checks to Population in England (continued).
The returns of the Population Act in 1811 undoubtedly presented extraordinary results. They shewed a greatly accelerated rate of progress, and a greatly improved healthiness of the people, notwithstanding the increase of the towns and the increased proportion of the population engaged in manufacturing employments. They thus furnished another striking instance of the readiness with which population starts forwards, under almost any weight, when the resources of a country are rapidly increasing.
The amount of the population in 1800, together with the proportions of births, deaths and marriages, given in the registers, had made it appear that the population had been for some time increasing at a rate rather exceeding what would result from a proportion of births to deaths as 4 to 3, with a mortality of 1 in 40.
These proportions would add to the population of a country every year 120th part; and if they were to continue, would, according to table ii., ch. xi. double the population in every successive period of 83½ years. This is a rate of progress which in a rich and well-peopled country might reasonably be expected to diminish rather than to increase. But instead of any such diminution, it appears that as far as 1810 it had been considerably accelerated.
In 1810, according to the returns from each parish, with the additions of 1/30 for the soldiers, sailors, 8c., the population of England and Wales was estimated at 10,488,000,1 which, compared with 9,168,000, the population of 1800, estimated in a similar manner, shews an increase in the ten years of 1,320,000.
The registered baptisms during ten years were 2,878,906, and the registered burials 1,950,189. The excess of the births is therefore 928,717, which falls very considerably short of the increase shewn by the two enumerations. This deficiency could only be occasioned either by the enumeration in 1800 being below the truth, or by the inaccuracy of the registers of births and burials, or by the operation of these two causes combined; as it is obvious that, if the population in 1800 were estimated correctly, and the registers contained all the births and burials, the difference must exceed rather than fall short of the real addition to the population; that is, it would exceed it exactly by the number of persons dying abroad in the army, navy, 8c.
There is reason to believe that both causes had a share in producing the effect observed, though the latter, that is, the inaccuracy of the registers, in much the greatest degree.
In estimating the population throughout the century,2 the births have been assumed to bear the same proportion at all times to the number of people. It has been seen that such an assumption might often lead to a very incorrect estimate of the population of a country at different and distant periods. As the population however is known to have increased with great rapidity from 1800 to 1810, it is probable that the proportion of births did not essentially diminish during that period. But if, taking the last enumeration as correct, we compare the births of 1810 with the births of 1800, the result will imply a larger population in 1800 than is given in the enumeration for that year.
Thus the average of the last five years' births to 1810 is 297,000, and the average of the five years' births to 1800 is 263,000. But 297,000 is to 263,000 as 10,488,000, the population of 1810, to 9,287,000, which must therefore have been the population in 1800, if the proportion of births be assumed to be the same, instead of 9,198,000, the result of the enumeration. It is further to be observed that the increase of population from 1795 to 1800 is according to the table unusually small, compared with most of the preceding periods of five years. And a slight inspection of the registers will shew that the proportion of births for five years from 1795, including the diminished numbers of 1796 and 1800, was more likely to be below than above the general average. For these reasons, together with the general impression on the subject, it is probable that the enumeration in 1800 was short of the truth, and perhaps the population at that time may be safely taken at as much as 9,287,000 at the least, or about 119,000 greater than the returns gave it.
But even upon this supposition, neither the excess of births above the deaths in the whole of the ten years, nor the proportion of births to deaths, as given in the registers, will account for an increase from 9,287,000, to 10,488,000. Yet it is not probable that the increase has been much less than is shewn by the proportion of the births at the two periods. Some allowance must therefore necessarily be made for omissions in the registers of births and deaths, which are known to be very far from correct, particularly the registers of births.
There is reason to believe that there are few or no omissions in the register of marriages; and if we suppose the omissions in the births to be one-6th, this will preserve a proportion of the births to the marriages as 4 to 1, a proportion which appears to be satisfactorily established upon other grounds;3 but if we are warranted in this supposition, it will be fair to take the omissions in the deaths at such a number as will make the excess of the births above the deaths in the ten years accord with the increase of population estimated by the increase of the births.
The registered births in the ten years, as was mentioned before, are 2,878,906, which increased by one-6th will be 3,358,723. The registered burials are 1,950,189, which increased by one-12th will be 2,112,704. The latter subtracted from the former will give 1,246,019 for the excess of births, and the increase of population in the ten years, which number added to 9,287,000, the corrected population of 1800, will give 10,533,019, forty-five thousand above the enumeration of 1810, leaving almost exactly the number which in the course of the ten years appears to have died abroad. This number has been calculated generally at about 4¼, per cent. on the male births; but in the present case there are the means of ascertaining more accurately the number of males dying abroad during the period in question. In the last population returns the male and female births and deaths are separated; and from the excess of the male births above the female births, compared with the male and female deaths, it appears that forty-five thousand males died abroad.4
The assumed omissions therefore in the births and burials seem to answer so far very well.
It remains to see whether the same suppositions will give such a proportion of births to deaths, with such a rate of mortality, as will also account for an increase of numbers in ten years from 9,287,000 to 10,488,000.
If we divide the population of 1810 by the average births of the preceding five years, with the addition of one-6th, it will appear that the proportion of births to the population is as 1 to 30. But it is obvious that if the population be increasing with some rapidity, the average of births for five years, compared with the population at the end of such period, must give the proportion of births too small. And further, there is always a probability that a proportion which is correct for five years may not be correct for ten years. In order to obtain the true proportion applicable to the progress of population during the period in question, we must compare the annual average of the births, for the whole term, with the average or mean population of the whole term.
The whole number of births, with the addition of 1/6, is, as before stated, 3,358,723, and the annual average during the ten years 335,872. The mean population, or the mean between 10,488,000 (the population of 1810) and 9,287,000 (the corrected population of 1800) is 9,887,000; and the latter number divided by the average of the births will give a proportion of births to the population as 1 to rather less than 29½, instead of 30, which will make a considerable difference.
In the same manner, if we divide the population of 1810 by the average of the burials for the preceding five years, with the addition of one-12th, the mortality will appear to be as 1 in nearly 50; but upon the same grounds as with regard to the births, an average of the burials for five years, compared with the population at the end of such term, must give the proportion of burials too small; and further, it is known, in the present case, that the proportion of burials to the population by no means continued the same during the whole time. In fact the registers clearly shew an improvement in the healthiness of the country, and a diminution of mortality progressively through the ten years; and while the average number of annual births increased from 263,000 to 287,000, or more than one-8th, the burials increased only from 192,000 to 196,000 or one-48th. It is obviously necessary then for the purpose in view to compare the average mortality with the average or mean population.
The whole number of burials in the ten years, with the addition of one-12th, is, as was before stated, 2,112,704, and the mean population 9,887,000. The latter, divided by the former, gives the annual average of burials compared with the population as 1 to rather less than 47. But a proportion of births as 1 to 29½, with a proportion of deaths as 1 to 47, will add yearly to the numbers of a country one-79th of the whole, and in ten years will increase the population from 9,287,000 to 10,531,000, leaving 43,000 for the deaths abroad, and agreeing very nearly with the calculation founded on the excess of births.5
We may presume therefore that the assumed omissions in the births and deaths from 1800 to 1810 are not far from the truth.
But if these omissions of one-6th for the births, and one-12th for the burials, may be considered as nearly right for the period between 1800 and 1810, it is probable that they may be applied without much danger of error to the period between 1780 and 1800, and may serve to correct some of the conclusions founded on the births alone. Next to an accurate enumeration, a calculation from the excess of births above the deaths is the most to be depended upon. Indeed when the registers contain all the births and deaths, and there are the means of setting out from a known population, it is obviously the same as an actual enumeration; and where a nearly correct allowance can be made for the omissions in the registers, and for the deaths abroad, a much nearer approximation to it may be obtained in this way than from the proportion of births to the whole population, which is known to be liable to such frequent variations.
The whole number of births returned in the twenty years, from 1780 to 1800, is 5,014,899, and of the burials 3,840,455. If we add one-6th to the former, and one-12th to the latter, the two numbers will be 5,850,715, and 4,160,492; and subtracting the latter from the former, the excess of the births above the deaths will be 1,690,223. Adding this excess to the population of 1780, as calculated in Mr. Rickman's tables, from the births, which is 7,953,000, the result will be 9,643,000, a number which, after making a proper allowance for the deaths abroad, is very much above the population of 1800, as before corrected, and still more above the number which is given in the table as of the enumeration.
But if we proceed upon the safer ground just suggested, and, taking the corrected population of 1800 as established, subtract from it the excess of the births during the twenty years, diminished by the probable number of deaths abroad, which in this case will be about 124,000, we shall have the number 7,721,000 for the population of 1780, instead of 7,953,000; and there is good reason to believe that this is nearer the truth;6 and that not only in 1780, but in many of the intermediate periods, the estimate from the births has represented the population as greater, and increasing more irregularly, than would be found to be true, if recourse could be had to enumerations. This has arisen from the proportion of births to the population being variable, and, on the whole, greater in 1780, and at other periods during the course of the twenty years, than it was in 1800.
In 1795, for instance, the population is represented to be 9,055,000, and in 1800, 9,168,000;7 but if we suppose the first number to be correct, and add the excess of the births above the deaths in the five intervening years, even without making any allowance for omissions in the registers, we shall find that the population in 1800 ought to have been 9,398,000, instead of 9,168,000; or if we take the number returned for 1800 as correct, it will appear, by subtracting from it the excess of births during the five preceding years, that the population in 1795 ought to have been 8,825,000, instead of 9,055,000. Hence it follows, that the estimate from the births in 1795 cannot be correct.
To obtain the population at that period, the safest way is to apply the before-mentioned corrections to the registers, and, having made the allowance of 4¼ per cent. on the male births for the deaths abroad, subtract the remaining excess of the births from the corrected returns of 1800. The result in this case will be 8,831,086 for the population of 1795, implying an increase in the five years of 455,914, instead of only 1,13,000, as shewn by the table calculated from the births.
If we proceed in the same manner with the period from 1790 to 1795, we shall find that the excess of births above the deaths (after the foregoing corrections have been applied, and an allowance has been made of 4¼ per cent. upon the male births for the deaths abroad), will be 415,669, which, subtracted from 8,831,086, the population of 1795, as above estimated, leaves 8,415,417 for the population of 1790.
Upon the same principle, the excess of the births above the deaths in the interval between 1785 and 1790 will turn out to be 416,776. The population in 1785 will therefore be 7,998,641. And in like manner the excess of the births above the deaths in the interval between 1780 and 1785 will be 277,544, and the population in 1780 7,721,097.
The two tables therefore, of the population, from 1780 to 1810, will stand thus:
In the first table, or table calculated from the births alone, the additions made to the population in each period of five years are as follow;—
In the second table, or table calculated from the excess of the births above the deaths, after the proposed corrections have been applied, the additions made to the population in each period of five years will stand thus:—
The progress of the population, according to this latter table, appears much more natural and probable than according to the former.
It is in no respect likely that, in the interval between 1780 and 1785, the increase of the population should only have been 63,000, and in the next period 659,000; or that, in the interval between 1795 and 1800, it should have been only 113,000, and in the next period 660,000. But it is not necessary to dwell on probabilities; the most distinct proofs may be brought 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 317,306; 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 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 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 progress 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 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.8 A very slight glance at the valuable table of baptisms, burials and marriages, given in the Preliminary Observations to the Population Abstracts,9 will shew 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 to the whole population; and that consequently variations in either of these, which may take place from temporary causes, cannot possibly be accompanied by similar variations in, the whole mass of the population. An increase in the births of one-third, which might occur in a single year, instead of increasing the population one-third, would only perhaps increase it one-eightieth or ninetieth.
It follows therefore, as I stated in the last chapter, that the table of the population for the century previous to 1780, calculated from the returns of the births alone, at the distance of ten years each, can only be considered as a very rough approximation towards the truth, in the absence of better materials, and can scarcely in any degree be depended upon for the comparative rate of increase at particular periods.
The population in 1810, compared with that of 1800, corrected as proposed in this chapter, implies a less rapid increase than the difference between the two enumerations; and it has further appeared that the assumed proportion of births to deaths as 47 to 29½ is rather below than above the truth. Yet this proportion is quite extraordinary for a rich and well-peopled territory. It would add to the population of a country one-79th every year, and, were it to continue, would, according to table ii. ch. xi. of this book, double the number of inhabitants in less than fifty-five years.
This is a rate of increase, which in the nature of things cannot be permanent. It has been occasioned by the stimulus of a greatly-increased demand for labour, combined with a greatly-increased power of production, both in agriculture and manufactures. These are the two elements which form the most effective encouragement to a rapid increase of population. What has taken place is a striking illustration of the principle of population, and a proof that in spite of great towns, manufacturing occupations, and the gradually-acquired habits of an opulent anti luxuriant people, if the resources of a country will admit of a rapid increase, anal if these resources are so advantageously distributed as to occasion a constantly-increasing demand for labour, the population will not fail to keep pace with them.
Since the publication of the last edition of this work in 1817, a third census of the population has taken place, and the results are highly worthy of our attention.
According to the enumeration in 1821, and the corrected returns of 1811, and 1801, as given in the preliminary observations to the published account by Mr. Rickman, the population of Great Britain was, in 1801, 10,942,646; in 1811, 12,596,803, and in 1821, 14,391,631.
These numbers taken as first stated, and including the very large numbers of males added in 1811 for the army and navy, give an increase of 15 per cent. in the ten years, from 1800 to 1811, and only 14¼ per cent. from 1810 to 1821.10 But it is calculated that out of the 640,500 males added for the army, navy, and merchant service, above one-third must have been Irish and foreigners. Adding therefore only 1/30 to the resident population in 1801 and 1811, and on account of the peace allowing only 1/50 for the absent males in 1821, the population of England and Wales at the three different periods, without reference to any supposed deficiency in the first enumeration, will stand thus: in 1801, 9,168,000; in 1811, 10,502,500; and in 1821, 12,218,500, giving an increase in the interval between 1800 and 1811 of 14¼ per cent. and in the interval between 1810 and 1821, of 16 1/3 percent. The first of these two rates of increase would double the population in 51 and the other in 46 years. As, however, there must always be some uncertainty respecting the proportion of the persons employed in the army, navy and merchant service, properly belonging to the resident population, and as the male population is on other accounts more frequently on the move than the female, it has been judiciously proposed to estimate the rate of increase by the female population alone. The number of females in Great Britain was in 1801, 5,492,354; in 1811, 6,262,716; and in 1821, 7,253,728, giving an increase in the first period of 14.02 per cent. and in the second of 15.82.11
The increase of Scotland taken by itself was in the first period 13 per cent. and in the second 14½. The increase of England and Wales exclusive of Scotland appears to be almost exactly the same; particularly in the second period, whether we estimate it from the females alone, or from the whole population, with the proposed allowances for the army and navy, 8c. a proof that these allowances are not far from the truth. At the same time, it should perhaps be remarked, that if, on account of the war, during the greater part of the period from 1800 to 1821, there must have been a greater portion of the male population destroyed than usual, the increase of the whole population ought not to be so great in proportion as the increase of the females; and that if such an increase appears, it is probably owing to too great a number of males having been added to the resident population for the army and navy, or to an influx from Scotland and Ireland.
The numbers above-mentioned, and the rates of increase, have been stated as given by Mr. Rickman in the Preliminary Observations to the Population Abstracts. But in the former part of this chapter, I assumed on what appeared to me to be sufficient grounds that the first enumeration was not so correct as that of 1811, and it is probable that the enumeration of 1811 is not quite so correct as that of 1821. In this case the rates of increase in the two periods will not be so great as above stated, but still they will appear to be very extraordinary.
According to the assumed estimate the population, as given in the enumeration of 1801, was about 119,000 short of the truth; and if on this ground we take the female population of the census in 1801 as deficient 60,000, and suppose that in 1811 it was deficient 30,000, the numbers of females in England and Wales at the different periods will stand thus: In 1801, 4,687,867; in 1811, 5,313,219; and in 1821, 6,144,709; giving an increase of 13.3 per cent. in the period from 1800 to 1811, and of 15.6 per cent. in the period from 1800 to 1821; making the rate of increase in the former period such as, if continued, would double the population in about 55 years, and in the latter, such as would double it in 48 years. Taking the whole 20 years together, the rate of increase would be such as, if continued, would double the population in about 51 years.
This is no doubt a most extraordinary rate of increase, considering the actual population of the country compared with its territory, and the number of its great towns and manufactories. It is less however than that which is stated in the Preliminary Observations to the Population Abstracts. Yet even according to this slower rate of increase it is necessary to suppose that the omissions in the parish registers, particularly in regard to the births, have latterly rather increased than diminished; and this is rendered probable by a statement of Mr. Rickman in the Preliminary Observations. He says, "the question respecting unentered baptisms and burials showed a difference of nearly four to one in the degree of deficiency in the year 1811, the annual average number of unentered baptisms (as stated at the end of the several counties) having been 14,860; of burials, (setting aside London) 3,899; at present the proportion is five to one in the degree of deficiency; the annual average number of unentered baptisms (as stated at the end of the several counties) being 23,066; of burials, (setting aside London) 4,657." And he goes on to say, "Nor does this represent the full amount or proportion of unentered baptisms, the clergy of the most populous places, especially where many of the inhabitants are dissenters, usually declining to hazard an estimate." A burial ground, on the contrary, is a visible object, and among the persons connected with it, the clergyman can usually procure an account (more or less accurate) of the number of interments.
On these grounds it would appear probable that, owing to the increasing number of dissenters, or other causes, the omissions in the registers of births had been lately increasing, rather than diminishing. Yet it has been thought that since the Act of 1812 the registers of births have been more carefully kept; and it is certain that, in the 10 years ending with 1820, the proportion of births to marriages is greater, though the proportions of births and marriages to the whole population are both less than they were either in 1800, or in the ten years ending with 1810. Under these circumstances, it may be advisable to wait for further documents before any fresh conclusion is drawn respecting the probable amount of omissions in the births and burials. What may be considered as certain is, that, whereas the supposed admissions of one sixth in the births and one twelfth in the burials, with a proper allowance for the deaths abroad, are more than sufficient to account for the increase of population during the twenty years from 1781 to 1801, according to the numbers stated by Mr. Rickman, they are not sufficient to account for the increase of population in the 20 years from 1801 to 1821, according to the enumerations.
I have heard it surmised that the enumerations, particularly the two last, may by possibility exceed rather than fall short of the truth, owing to persons being reckoned more than once, from their having different places of residence. It must be allowed, that this supposition would account for the fact of the diminished proportions of births and marriages to the whole population, notwithstanding the apparent increase of that population with extraordinary rapidity. But the same diminished proportions would take place owing to a diminished mortality; and as a diminished mortality has been satisfactorily established on other grounds, it will fairly account for much of what appears. And if anything can justly be attributed to over enumerations, it must be of trifling amount.
That there are great omissions both in the births and burials, and greater in the former than in the latter, it is quite impossible to doubt. The testimony of all the clergy concerned in making the returns was, according to Mr. Rickman, uniform in this respect. And if we suppose only the same proportion of omissions from 1801 to 1821 as we supposed from 1781 to 1801, and commence with the census of 1801, on the presumption that the number of double entries in that enumeration would be balanced probably by the number of deficiencies, it will appear that the excess of the births alone, excluding the deaths abroad, would bring the population to within 184,404 of the enumeration of 1821, and including the allowance for deaths abroad, (which, in this case, from a comparison of the excess of male births with the male and female deaths, appears to be 128,651,) to within 313,055.
On the supposition of such an amount of double entries unbalanced by deficiencies in the two last returns, the enumerations would still shew a very extraordinary increase of population. The rate of increase in the period from 1801 to 1811 would be nearly 13 per cent. (12.88) which would double the population in about 57 years; and in the period from 1811 to 1821, it would be very nearly 15 per cent. (14.95), which would double the population in 50 years.
Under the uncertainty in which we must remain at present as to whether the enumerations partially err in defect or in excess, I have not thought it advisable to alter the amended table of the population from 1781 to 1811, given in the former part of this chapter. It is founded on a principle so very much safer than an estimate for the births alone, that it must at any rate shew the progress of the population more correctly than that given in the Preliminary Observations.
The more indeed the population returns are considered, the more uncertain will appear all estimates of the past population founded on the assumptions that the proportion of the births will always be nearly the same. If the population since the year 1801 were to be estimated in the same way as Mr. Rickman has estimated it before that year, it would appear that the population in 1821, instead of being, according to the enumeration, 12,218,500, would only be 11,625,334, that is, 593,166 or nearly 600,000 short of the enumeration of 1821. And the reason is, that the proportion of births to the population, which, estimated in the way suggested by Mr. Rickman, and without allowing for omissions, was, in 1821, only as 1 to 36.58, was, in 1801, as much as 1 to 34.8.
Supposing the enumerations to be correct, the varying proportions of the births (without allowance for omissions, and comparing the population at the end of each term with the average births for the five preceding years,) would be for 1801 as 1 to 34.8, for 1811 as 1 to 35.3, and for 1821 as 1 to 36.58.
Similar and even greater variations will be found to take place in regard to the proportions of the marriages to the population.
In 1801, the proportion was 1 to 122.2, in 1811, 1 to 126.6, in 1821, 1 to 131.1; and if, assuming that, for the 20 years ending with 1820, the marriages, in which it is supposed that there are very few omissions, would remain in the same proportion to the population as in 1801, we had estimated the population by the marriages, the numbers in 1821, instead of being 12,218,500, would only have been 11,377,548, that is, 840,952 short of the enumeration of 1821.
It appears, then, that if we can put any trust in our enumerations,12 no reliance can be placed on an estimate of past population founded on the proportions of the births, deaths, or marriages: The same causes which have operated to alter so essentially these proportions during the 20 years for which we have enumerations may have operated in an equal degree before; and it will be generally found true, that the increasing healthiness of a country will not only diminish the proportions of deaths, but the proportions of births and marriages.
[1.]See the Population Abstracts published in 1811, and the valuable Preliminary Observations by Mr. Rickman.
[2.]See a table of the population throughout the century, in page xxv. of the Preliminary Observations to the Population Abstracts, printed in 1811.
[3.]See the Preliminary Observations on the Population Abstracts, p. xxvi.
[4.]See Population Abstracts, 1811, page 196 of the Parish Register Abstract.
[5.]A general formula for estimating the population of a country at any distance from a certain period, under given circumstances of births and mortality, may be found in Bridge's Elements of Algebra, p. 225.
In the present case, P = 9,287,000; n = 10; m = 47; b = 29½.
= 05460. Log. P. = 6.96787, which added to 05460 = 7.02247 the log of A, the number answering to which is 10,531,000.
[6.]The very small difference between the population of 1780 and 1785, as given in the table, seems strongly to imply that one of the two estimates is erroneous.
[7.]Population Abstracts, 1811. Preliminary View, p. xxv.
[8.]From the one or other of these causes, I have little doubt, that the numbers in the table, for 1760 and 1780, 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.
[10.]Preliminary Observations, p. viii.
[12.]The migrations into England from Ireland and Scotland may account for some portion of the excess of the enumerations above what is warranted by the excess of the births above the deaths.