An Essay on the Principle of Population
By Thomas Robert Malthus
There are two versions of Thomas Robert Malthus’s
Essay on the Principle of Population. The first, published anonymously in 1798, was so successful that Malthus soon elaborated on it under his real name.
* The rewrite, culminating in the sixth edition of 1826, was a scholarly expansion and generalization of the first.Following his success with his work on population, Malthus published often from his economics position on the faculty at the East India College at Haileybury. He was not only respected in his time by contemporaneous intellectuals for his clarity of thought and willingness to focus on the evidence at hand, but he was also an engaging writer capable of presenting logical and mathematical concepts succinctly and clearly. In addition to writing principles texts and articles on timely topics such as the corn laws, he wrote in many venues summarizing his initial works on population, including a summary essay in the
Encyclopædia Britannica on population.The first and sixth editions are presented on Econlib in full. Minor corrections of punctuation, obvious spelling errors, and some footnote clarifications are the only substantive changes.* Malthus’s “real name” may have been Thomas Robert Malthus, but a descendent, Nigel Malthus, reports that his family says he did not use the name Thomas and was known to friends and colleagues as Bob. See
The Malthus Homepage, a site maintained by Nigel Malthus, a descendent.For more information on Malthus’s life and works, see
New School Profiles: Thomas Robert Malthus and
The International Society of Malthus.Lauren Landsburg
Editor, Library of Economics and Liberty
First Pub. Date
London: John Murray
The text of this edition is in the public domain. Picture of Malthus courtesy of The Warren J. Samuels Portrait Collection at Duke University.
- Chapter I
- Chapter II
- Chapter III
- Chapter IV
- Chapter V
- Chapter VI
- Chapter VII
- Chapter VIII
- Chapter IX
- Chapter X
- Chapter XI
- Chapter XII
- Chapter XIII
- Chapter XIV
- Bk.II,Ch.XI, On the Fruitfulness of Marriages
- Appendix I
- Appendix II
Of the Checks to Population in England.
Book II, Chapter VIII
The most cursory view of society in this country must convince us, that throughout all ranks the preventive check to population prevails in a considerable degree. Those among the higher classes, who live principally in towns, often want the inclination to marry, from the facility with which they can indulge themselves in an illicit intercourse with the sex. And others are deterred from marrying by the idea of the expenses that they must retrench, and the pleasures of which they must deprive themselves, on the supposition of having a family. When the fortune is large, these considerations are certainly trivial; but a preventive foresight of this kind has objects of much greater weight for its contemplation as we go lower.
A man of liberal education, with an income only just sufficient to enable him to associate in the rank of gentlemen, must feel absolutely certain that, if he marry and have a family, he shall be obliged to give up all his former connexions. The woman, whom a man of education would naturally make the object of his choice, is one brought up in the same habits and sentiments with himself, and used to the familiar intercourse of a society totally different from that to which she must be reduced by marriage. Can a man easily consent to place the object of his affection in a situation so discordant, probably, to her habits and inclinations? Two or three steps of descent in society, particularly at this round of the ladder, where education ends and ignorance begins, will not be considered by the generality of people as a chimerical, but a real evil. If society be desirable, it surely must be free, equal and reciprocal society, where benefits are conferred as well as received, and not such as the dependent finds with his patron, or the poor with the rich.
These considerations certainly prevent many in this rank of life from following the bent of their inclinations in an early attachment. Others, influenced either by a stronger passion or a weaker judgment, disregard these considerations; and it would be hard, indeed, if the gratification of so delightful a passion as virtuous love did not sometimes more than counterbalance all its attendant evils. But I fear it must be acknowledged that the more general consequences of such marriages are rather calculated to justify than disappoint the forebodings of the prudent.
The sons of tradesmen and farmers are exhorted not to marry, and generally find it necessary to comply with this advice, till they are settled in some business or farm, which may enable them to support a family. These events may not perhaps occur till they are far advanced in life. The scarcity of farms is a very general complaint; and the competition in every kind of business is so great, that it is not possible that all should be successful. Among the clerks in counting-houses, and the competitors for all kinds of mercantile and professional employment, it is probable that the preventive check to population prevails more than in any other department of society.
The labourer who earns eighteen pence or two shillings a day, and lives at his ease as a single man, will hesitate a little before he divides that pittance among four or five, which seems to be not more than sufficient for one. Harder fare and harder labour he would perhaps be willing to submit to for the sake of living with the woman he loves; but he must feel conscious, that, should he have a large family and any ill fortune whatever, no degree of frugality, no possible exertion of his manual strength, would preserve him from the heart-rending sensation of seeing his children starve, or of being obliged to the parish for their support. The love of independence is a sentiment that surely none would wish to see eradicated; though the poor-laws of England, it must be confessed, are a system of all others the most calculated gradually to weaken this sentiment, and in the end will probably destroy it completely.
The servants who live in the families of the rich have restraints yet stronger to break through in venturing upon marriage. They possess the necessaries, and even the comforts of life, almost in as great plenty as their masters. Their work is easy and their food luxurious, compared with the work and food of the class of labourers; and their sense of dependence is weakened by the conscious power of changing their masters if they feel themselves offended. Thus comfortably situated at present, what are their prospects if they marry? Without knowledge or capital, either for business or farming, and unused and therefore unable to earn a subsistence by daily labour, their only refuge seems to be a miserable alehouse, which certainly offers no very enchanting prospect of a happy evening to their lives. The greater number of them, therefore, deterred by this uninviting view of their future situation, content themselves with remaining single where they are.
If this sketch of the state of society in England be near the truth, it will be allowed that the preventive check to population operates with considerable force throughout all the classes of the community. And this observation is further confirmed by the abstracts from the registers returned in consequence of the Population Act
*62 passed in 1800.
The results of these abstracts shew, that the annual marriages in England and Wales are to the whole population as 1 to 123 1/5,
*63 a smaller proportion of marriages than is to be found in any of the countries which have been examined, except Norway and Switzerland.
In the earlier part of the last century, Dr. Short estimated this proportion at about 1 to 115.
*64 It is probable that this calculation was then correct; and the present diminution in the proportion of marriages, notwithstanding an increase of population more rapid than formerly, owing to the more rapid progress of commerce and agriculture, is partly a cause, and partly a consequence, of the diminished mortality observed of late years.
The returns of the marriages, pursuant to the late act, are supposed to be less liable to the suspicion of inaccuracy than any other parts of the registers.
Dr. Short, in his
New Observations on Town and Country Bills of Mortality, says, he will `”conclude with the observation of an eminent Judge of this nation, that the growth and increase of mankind is more stinted from the cautious difficulty people make to enter on marriage, from the prospect of the trouble and expenses in providing for a family, than from any thing in the nature of the species.” And, in conformity to this idea, Dr. Short proposes to lay heavy taxes and fines on those who live single, for the support of the married poor.
The observation of the eminent Judge is, with regard to the numbers which are prevented from being born, perfectly just; but the inference, that the unmarried ought to be punished, does not appear to be equally so. The prolific power of nature is very far indeed from being called fully into action in this country. And yet when we contemplate the insufficiency of the price of labour to maintain a large family, and the amount of mortality which arises directly and indirectly from poverty; and add to this the crowds of children, which are cut off prematurely in our great towns, our manufactories and our workhouses; we shall be compelled to acknowledge, that, if the number born annually were not greatly thinned by this premature mortality, the funds for the maintenance of labour must increase with much greater rapidity than they have ever done hitherto in this country, in order to find work and food for the additional numbers that would then grow up to manhood.
Those, therefore, who live single, or marry late, do not by such conduct contribute in any degree to diminish the actual population; but merely to diminish the proportion of premature mortality, which would otherwise be excessive; and consequently in this point of view do not seem to deserve any very severe reprobation or punishment.
The returns of the births and deaths are supposed, on good grounds, to be deficient; and it will therefore be difficult to estimate, with any degree of accuracy, the proportion which they bear to the whole population.
If we divide the existing population of England and Wales by the average of burials for the five years ending in 1800, it would appear, that the mortality was only 1 in 49;
*66 but this is a proportion so extraordinarily small, considering the number of our great towns and manufactories, that it cannot be considered as approaching to the truth.
Whatever may be the exact proportion of the inhabitants of the towns to the inhabitants of the country, the southern part of this island certainly ranks in that class of states, where this proportion is greater than 1 to 3; indeed there is ample reason to believe, that it is greater than 1 to 2. According to the rule laid down by Crome, the mortality ought consequently to be above 1 in 30;
*67 according to Sussmilch, above 1 in 33.
*68 In the
Observations on the Results of the Population Act,*69 many probable causes of deficiency in the registry of the burials are pointed out; but no calculation is offered respecting the sum of these deficiencies, and I have no data whatever to supply such a calculation. I will only observe, therefore, that if we suppose them altogether to amount to such a number as will make the present annual mortality about 1 in 40, this must appear to be the lowest proportion of deaths that can well be supposed, considering the circumstances of the country; and, if true, would indicate a most astonishing superiority over the generality of other states, either in the habits of the people with respect to prudence and cleanliness, or in natural healthiness of situation.
*70 Indeed, it seems to be nearly ascertained that both these causes, which tend to diminish mortality, operate in this country to a considerable degree. The small proportion of annual marriages before mentioned indicates that habits of prudence, extremely favourable to happiness, prevail through a large part of the community in spite of the poor-laws; and it appears from the clearest evidence, that the generality of our country parishes are very healthy. Dr. Price quotes an account of Dr. Percival, collected from the ministers of different parishes and taken from positive enumerations, according to which, in some villages, only a 45th, a 50th, a 60th, a 66th, and even a 75th, part dies annually. In many of these parishes the births are to the deaths above 2 to 1, and 4n a single parish above 3 to 1.
*71 These however are particular instances, and cannot be applied to the agricultural part of the country in general. In some of the flat situations, and particularly those near marshes, the proportions are found very different, and in a few the deaths exceed the births. In the 54 country parishes, the registers of which Dr. Short collected, choosing them purposely in a great variety of situations, the average mortality was as high as 1 in 37.
*72 This is certainly much above the present mortality of our agricultural parishes in general. The period which Dr. Short took, included some considerable epidemics, which may possibly have been above the usual proportion. But sickly seasons should always be included, or we shall fall into great errors. In 1056 villages of Brandenburgh, which Sussmilch examined, the mortality for six good years was 1 in 43; for 10 mixed years about 1 in 38½.
*73 In the villages of England which Sir F. M. Eden mentions, the mortality seems to be about 1 in 47 or 48;
*74 and in the late returns pursuant to the Population Act, a still greater degree of healthiness appears. Combining these observations together, if we take 1 in 46 or 1 in 48, as the average mortality of the agricultural part of the country, including sickly seasons, this will be the lowest that can be supposed with any degree of probability. But this proportion will certainly be raised to 1 in 40, when we blend it with the mortality of the towns and the manufacturing part of the community, in order to obtain the average for the whole kingdom.
The mortality in London, which includes so considerable a part of the inhabitants of this country, was, according to Dr. Price, at the time he made his calculations, 1 in 20¾; in Norwich 1 in 24; in Northampton 1 in 26½; in Newbury 1 in 27½;
*75 in Manchester 1 in 28; in Liverpool 1 in 27½,
*76 &c. He observes that the number dying annually in towns is seldom so low as 1 in 28, except in consequence of a rapid increase produced by an influx of people at those periods of life when the fewest die, which is the case with Manchester and Liverpool,
*77 and other very flourishing manufacturing towns. In general he thinks that the mortality in great towns may be stated at from 1 in 19
*78 to 1 in 22 and 23; in moderate towns, from 1 in 24 to 1 in 28; and in the country villages, from 1 in 40 to 1 in 50.
The tendency of Dr. Price to exaggerate the unhealthiness of towns may perhaps be objected to these statements; but the objection seems to be only of weight with regard to London. The accounts from the other towns, which are given, are from documents which his particular opinions could not influence.
*80 It should be remarked; however, that there is good reason to believe, that not only London, but the other towns in England, and probably also country villages, were at the time of these calculations less healthy than at present. Dr. William Heberden observes, that the registers of the ten years from 1759 to 1768,
*81, from which Dr. Price calculated the probabilities of life in London, indicate a much greater degree of unhealthiness than the registers of late years. And the returns pursuant to the Population Act, even after allowing for great omissions in the burials, exhibit in all our provincial towns, and in the country, a degree of healthiness much greater than had before been calculated. At the same time I cannot but think that 1 in 31, the proportion of mortality for London mentioned in the
Observations on the Results of the Population Act,*82 is smaller than the truth. Five thousand are not probably enough to allow for the omissions in the burials; and the absentees in the employments of war and commerce are not sufficiently adverted to. In estimating the proportional mortality the resident population alone should be considered.
There certainly seems to be something in great towns, and even in moderate towns, peculiarly unfavourable to the very early stages of life; and the part of the community, on which the mortality principally falls, seems to indicate that it arises more from the closeness and foulness of the air, which may be supposed to be unfavourable to the tender lungs of children, and the greater confinement which they almost necessarily experience, than from the superior degree of luxury and debauchery usually and justly attributed to towns. A married pair with the best constitutions, who lead the most regular and quiet life, seldom find that their children enjoy the same health in towns as in the country.
In London, according to former calculations, one half of the born died under three years of age; in Vienna and Stockholm under two; in Manchester under five; in Norwich under five: in Northampton under ten.
*83 In country villages, on the contrary, half of the born live till thirty, thirty-five, forty, forty-six, and above. In the parish of Ackworth, in Yorkshire, it appears, from a very exact account kept by Dr. Lee of the ages at which all died there for 20 years, that half of the inhabitants live to the age of 46;
*84 and there is little doubt, that, if the same kind of account had been kept in some of those parishes before mentioned, in which the mortality is so small as 1 in 60, 1 in 66, and even 1 in 75, half of the born would be found to have lived to 50 or 55.
As the calculations respecting the ages to which half of the born live in towns depend more upon the births and deaths which appear in the registers, than upon any estimates of the number of people, they are on this account less liable to uncertainty, than the calculations respecting the proportion of the inhabitants of any place which dies annually.
To fill up the void occasioned by this mortality in towns, and to answer all further demands for population, it is evident that a constant supply of recruits from the country is necessary; and this supply appears in fact to be always flowing in from the redundant births of the country. Even in those towns where the births exceed the deaths, this effect is produced by the marriages of persons not born in the place. At a time when our provincial towns were increasing much less rapidly than at present, Dr. Short calculated that 9/19 of the married were strangers.
*85 Of 1618 married men, and 1618 married women, examined at the Westminster infirmary, only 329 of the men and 495 of the women had been born in London.
Dr. Price supposes that London with its neighbouring parishes, where the deaths exceed the births, requires a supply of 10,000 persons annually. Graunt, in his time, estimated the supply for London alone at 6,000;
*87 and he further observes, that, let the mortality of the city be what it will, arising from plague, or any other great cause of destruction, it always fully repairs its loss in two years.
As all these demands, therefore, are supplied from the country, it is evident that we should fall into a very great error, if we were to estimate the proportion of births to deaths for the whole kingdom, by the proportion observed in country parishes, from which there must be such numerous emigrations.
We need not, however, accompany Dr. Price in his apprehensions that the country will be depopulated by these emigrations, at least as long as the funds for the maintenance of agricultural labour remain unimpaired. The proportion of births, as well as the proportion of marriages, clearly proves, that, in spite of our increasing towns and manufactories, the demand on the country for people is by no means very pressing.
If we divide the present population of England and Wales by the average number of baptisms for the last five years,
*89 it will appear, that the baptisms are to the population as 1 to very nearly 36;
*90 but it is supposed, with reason, that there are great omissions in the baptisms.
Dr. Short estimated the proportion of births to the population of England as one to 28.
*91 In the agricultural report of Suffolk, the proportion of births to the population was calculated at 1 to 30. For the whole of Suffolk, according to the late returns, this proportion is not much less than 1 to 33.
*92 According to a correct account of thirteen villages from actual enumerations, produced by Sir F. M. Eden, the proportion of births to the population was as 1 to 33; and according to another account on the same authority; taken from towns and manufacturing parishes, as 1 to 27¾.
*93 If, combining all these circumstances, and adverting at the same time to the acknowledged deficiency in the registry of births, and the known increase of our population of late years, we suppose the true proportion of the births to the population to be as 1 to 30; then assuming the present mortality to be 1 in 40, as before suggested, we shall nearly keep the proportion of baptisms to burials which appears in the late returns. The births will be to the deaths as 4 to 3 or 13 1/3 to 10, a proportion more than sufficient to account for the increase of population which has taken place since the American war, after allowing for those who may be supposed to have died abroad.
Observations on the Results of the Population Act it is remarked that the average duration of life in England appears to have increased in the proportion of 117 to 100,
*94 since the year 1780. So great a change, in so short a time, if true, would be a most striking phenomenon. But I am inclined to suspect that the whole of this proportional diminution of burials does not arise from increased healthiness, but is occasioned, in part, by the greater number of deaths which must necessarily have taken place abroad, owing to the very rapid increase of our foreign commerce since this period; and to the great number of persons absent on naval and military employments, and the constant supply of fresh recruits necessary to maintain undiminished so great a force. A perpetual drain of this kind would certainly have a tendency to produce the effect observed in the returns, and might keep the burials stationary, while the births and marriages were increasing with some rapidity. At the same time, as the increase of population since 1780 is incontrovertible, and the present mortality extraordinarily small, I should still be disposed to believe, that much the greater part of the effect is to be attributed to increased healthiness.
A mortality of 1 in 36 is perhaps too small a proportion of deaths for the average of the whole century; but a proportion of births to deaths as 12 to 10, calculated on a mortality of 1 in 36, would double the population of a country in 125 years, and is therefore as great a proportion of births to deaths, as can be true for the average of the whole century. None of the late calculations imply a more rapid increase than this.
We must not suppose, however, that this proportion of births to deaths, or any assumed proportion of births and deaths to the whole population, has continued nearly uniform throughout the century. It appears from the registers of every country which have been kept for any length of time, that considerable variations occur at different periods. Dr. Short, about the middle of the century, estimated the proportion of births to deaths as 11 to 10;
*95 and if the births were at the same time a twenty-eighth part of the population, the mortality was then as high as 1 in 30 4/5. We now suppose that the proportion of births to deaths is above 13 to 10; but if we were to assume this proportion as a criterion by which to estimate the increase of population for the next hundred years, we should probably fall into a very gross error. We cannot reasonably suppose that the resources of this country should increase for any long continuance with such rapidity as to allow of a permanent proportion of births to deaths as 13 to 10, unless indeed this proportion were principally caused by great foreign drains.
From all the data that could be collected, the proportion of births to the whole population of England and Wales, has been assumed to be as 1 to 30; but this is a smaller proportion of births than has appeared in the course of this review to take place in any other country except Norway and Switzerland; and it has been hitherto usual with political calculators, to consider a great proportion of births as the surest sign of a vigorous and flourishing state. It is to be hoped, however, that this prejudice will not last long. In countries circumstanced like America or Russia, or in other countries after any great mortality, a large proportion of births is a favourable symptom; but in the average state of a well-peopled territory there cannot well be a worse sign than a large proportion of births, nor can there well be a better sign than a small proportion.
Sir Francis d’Ivernois very justly observes, that, “if the various states of Europe kept and published annually an exact account of their population, noting carefully in a second column the exact age at which the children die, this second column would shew the relative merit of the governments, and the comparative happiness of their subjects. A simple arithmetical statement would then perhaps be more conclusive than all the arguments that could be adduced.”
*96 In the importance of the inferences to be drawn from such tables, I fully agree with him; and to make these inferences, it is evident, that we should attend less to the column expressing the number of children born, than to the column expressing the number which survived the age of infancy and reached manhood; and this number will almost invariably be the greatest, where the proportion of the births to the whole population is the least. In this point, we rank next after Norway and Switzerland, which, considering the number of our great towns and manufactories, is certainly a very extraordinary fact. As nothing can be more clear, than that all our demands for population are fully supplied, if this be done with a small proportion of births, it is a decided proof of a very small mortality, a distinction on which we may justly pride ourselves. Should it appear from future investigations that I have made too great an allowance for omissions both in the births and in the burials, I shall be extremely happy to find that this distinction, which, other circumstances being the same, I consider as the surest test of happiness and good government, is even greater than I have supposed it to be. In despotic, miserable, or naturally unhealthy countries, the proportion of births to the whole population will generally be found very great.
On an average of the five years ending in 1800, the proportion of births to marriages is 347 to 100. In 1760, it was 362 to 100, from which an inference is drawn, that the registers of births, however deficient, were certainly not more deficient formerly than at present.
*97 But a change of this nature, in the appearance of the registers, might arise from causes totally unconnected with deficiencies. If from the acknowledged greater healthiness of the latter part of the century, compared with the middle of it, a greater number of children survived the age of infancy, a greater proportion of the born would of course live to marry, and this circumstance would produce a greater present proportion of marriages compared with the births. On the other hand, if the marriages were rather more prolific formerly than at present, owing to their being contracted at an earlier age, the effect would be a greater proportion of births compared with the marriages. The operation of either or both of these causes would produce exactly the effect observed in the registers: and consequently from the existence of such an effect no inference can justly be drawn against the supposed increasing accuracy of the registers. The influence of the two causes just mentioned on the proportions of annual births to marriages will be explained in a subsequent chapter.
With regard to the general question, whether we have just grounds for supposing that the registry of births and deaths was more deficient in the former part of the century than in the latter part; I should say, that the late returns tend to confirm the suspicion of former inaccuracy, and to shew that the registers of the earlier part of the century, in every point of view, afford very uncertain data on which to ground any estimates of past population. In the years 1710, 1720, and 1730, it appears from the returns that the deaths exceeded the births; and taking the six periods ending in 1750,
*98 including the first half of the century, if we compare the sum of the births with the sum of the deaths, the excess of the births is so small, as to be perfectly inadequate to account for the increase of a million, which, upon a calculation from the births alone, is supposed to have taken place in that time.
*99 Consequently, either the registers are very inaccurate, and the deficiencies in the births greater than in the deaths; or these periods, each at the distance of ten years, do not express the just average. These particular years may have been more unfavourable with respect to the proportion of births to deaths than the rest; indeed one of them, 1710, is known to have been a year of great scarcity and distress. But if this suspicion, which is very probable, be admitted, so as to affect the six first periods, we may justly suspect the contrary accident to have happened with regard to the three following periods ending with 1780; in which thirty years it would seem, by the same mode of calculation, that an increase of a million and a half had taken place.
*100 At any rate it must be allowed, that the three separate years, taken in this manner, can by no means be considered as sufficient to establish a just average; and what rather encourages the suspicion, that these particular years might be more than usually favourable with regard to births is, that the increase of births from 1780 to 1785 is unusually small,
*101 which would naturally be the case without supposing a slower progress than before, if the births in 1780 had been accidentally above the average.
On the whole, therefore, considering the probable inaccuracy of the earlier registers, and the very great danger of fallacy in drawing general inferences from a few detached years, I do not think that we can depend upon any estimates of past population, founded on a calculation from the births, till after the year 1780, when every following year is given; and a just average of the births may be obtained. As a further confirmation of this remark I will just observe, that in the final summary of the abstracts from the registers of England and Wales it appears, that in the year 1790, the total number of births was 248,774, in the year 1795, 247,218, and in 1800, 247,147.
*102 Consequently if we had been estimating the population from the births, taken at three separate periods of five years, it would have appeared, that the population during the last ten years had been regularly decreasing, though we have very good reason to believe, that it has increased considerably.
Observations on the Results of the Population Act,*103 a table is given of the population of England and Wales throughout the last century, calculated from the births; but for the reasons given above, little reliance can be placed upon it; and for the population at the revolution, I should be inclined to place more dependence on the old calculations from the number of houses.
It is possible, indeed, though not probable, that these estimates of the population at the different periods of the century may not be very far from the truth, because opposite errors may have corrected each other; but the assumption of the uniform proportion of births on which they are founded is false on the face of the calculations themselves. According to these calculations, the increase of population was more rapid in the period from 1760 to 1780, than from 1780 to 1800; yet it appears, that the proportion of deaths about the year 1780 was greater than in 1800 in the ratio of 117 to 100. Consequently the proportion of births before 1780 must have been much greater than in 1800, or the population in that period could not possibly have increased faster. This overthrows at once the supposition of any thing like uniformity in the proportion of births.
I should indeed have supposed from the analogy of other countries, and the calculations of Mr. King and Dr. Short, that the proportion of births at the beginning and in the middle of the century was greater than at the end. But this supposition would, in a calculation from the births, give a smaller population in the early part of the century than is given in the
Results of the Population Act, though there are strong reasons for supposing that the population there given is too small. According to Davenant, the number of houses in 1690 was 1,319,215, and there is no reason to think that this calculation erred on the side of excess. Allowing only five to a house instead of 5 3/5, which is supposed to be the proportion at present, this would give a population of above six millions and a half, and it is perfectly incredible, that from this time to the year 1710, the population should have diminished nearly a million and a half. It is far more probable that the omissions in the births should have been much greater than at present, and greater than in the deaths; and this is further confirmed by the observation before alluded to, that in the first half of the century the increase of population, as calculated from the births, is much greater than is warranted by the proportion of births to deaths. In every point of view, therefore, the calculations from the births are little to be depended on.
It must indeed have appeared to the reader, in the course of this work, that registers of births or deaths, excluding any suspicion of deficiencies, must at all times afford very uncertain data for an estimate of population. On account of the varying circumstances of every country, they are both precarious guides. From the greater apparent regularity of the births, political calculators have generally adopted them as the ground of their estimates in preference to the deaths. Necker, in estimating the population of France, observes, that an epidemic disease, or an emigration, may occasion temporary differences in the deaths, and that therefore the number of births is the most certain criterion.
*104 But the very circumstance of the apparent regularity of the births in the registers will now and then lead into great errors. If in any country we can obtain registers of burials for two or three years together, a plague or mortal epidemic will always shew itself, from the very sudden increase of the deaths during its operation, and the still greater diminution of them afterwards. From these appearances, we should of course be directed, not to include the whole of a great mortality in any very short term of years. But there would be nothing of this kind to guide us in the registers of births; and after a country had lost an eighth part of its population by a plague, an average of the five or six subsequent years might shew an increase in the number of births, and our calculations would give the population the highest at the very time that it was the lowest. This appears very strikingly in many of Sussmilch’s tables, and most particularly in a table for Prussia and Lithuania, which I shall insert in a subsequent chapter; where, in the year following to the loss of one third of the population, the births were considerably increased, and in an average of five years but very little diminished; and this at a time when, of course, the country could have made but a very small progress towards recovering its former population.
We do not know indeed of any extraordinary mortality which has occurred in England since 1700; and there are reasons for supposing that the proportions of the births and deaths to the population during the last century have not experienced such great variations as in many countries on the continent; at the same time it is certain that the sickly seasons which are known to have occurred, would, in proportion to the degree of their fatality, produce similar effects; and the change which has been observed in the mortality of late years, should dispose us to believe, that similar changes might formerly have taken place respecting the births, and should instruct us to be extremely cautious in applying the proportions, which are observed to be true at present, to past or future periods.
It is certainly very extraordinary that a smaller proportion of males than usual should appear to have died abroad from 1800 to 1810; but as the registers for this period seem to prove it, I have made my calculations accordingly.
|Log. A = log. P + n
� log. 1 +
|m – b|
A representing the required population at the end of any number of years; n the number of years; P the actual population at the given period; 1/m the proportion of yearly deaths to the population; or ratio of mortality; 1/b the proportion of yearly births to the population, or ratio of births.
In the present case, P = 9,287,000; n = 10; m = 47; b = 29½.
|m – b||1||m – b||80|
||and 1 +||
|The log. of 80/79 = 00546;
� log. 1 +
|m – b|
= 05460. Log. P. = 6.96787, which added to 05460 = 7.02247 the log of A, the number answering to which is 10,531,000.