The Online Library of Liberty

A project of Liberty Fund, Inc.

• Preface.
• Postscript.
• Book I.: Of the Population of Europe, Asia, Africa, and South America, In Ancient and Modern Times.
• Chapter I.: Introduction.
• Chapter II.: Survey of the Creation From Natural History.
• Chapter III.: General Views As to the Alleged Increase of Mankind.
• Chapter IV.: General View of the Arguments Against the Increase of Mankind.
• Chapter V.: Numbers of Mankind In Ancient and Modern Times.
• Chapter VI.: Illustrations From the History of China
• Chapter VII.: India.
• Chapter VIII.: South America.
• Chapter IX.: Paraguay.
• Chapter X.: Sparta.
• Chapter XI.: Rome.
• Chapter XII: Miscellaneous Observations.
• Chapter XIII.: Views of Man and Society Which Result From the Preceding Facts.
• Book II.: Of the Power of Increase In the Numbers of the Human Species, and the Limitations of That Power.
• Chapter I.: Proofs and Authorities For the Doctrine of the Essay of Population.
• Chapter II.: Animadversions On Mr. Malthus'ss, Authorities.
• Chapter III.: Principles Respecting the Increase Or Decrease of the Numbers of Mankind.
• Chapter IV.: Accounts Which Are Given of the Population of Sweden.
• Chapter V.: Inferences Suggestd By the Accounts of Sweden.
• Chapter VI.: Observations On the Swedish Tables Continued.
• Chapter VII.: Recapitulation of the Evidence of the Swedish Tables.
• Appendix to Chapters Iv, V, & VI.
• Chapter VIII.: Population of Other, Countries In Europe Considered
• Chapter IX.: Principles Respecting the Increase Or Decrease of the Numbers of Mankind Resumed.
• Chapter X.: Of the Population of England and Wales.
• Chapter XI.: Proofs of the Geometrical Ratio From the Phenomenon of a Pestilence.
• Dissertation On the Ratios of Increase In Population , and In the Means of Subsistence. By Mr. David Booth.
• Book III.: Of the Causes By Which the Amount of the Numbers of Mankind Is Reduced Or Restrained.
• Chapter I.: Futility of Mr. Malthus's Doctrine Respecting the Checks On Population.
• Chapter II.: Of Deaths and the Rate of Human Mortality.
• Chapter III.: Attempt Towards a Rational Theory of the Checks On Population.
• Chapter IV.: Attempt Towards a Rational Theory of the Checks On Population Continued.
• Chapter V.: Mr. Malthus's Eleven Heads of the Causes Which Keep Down Population Considered.
• Chapter VI.: Observations On the Countries In the Neighbourhood of the River Missouri.
• Book IV.: Of the Population of the United States of North America.
• Chapter I.: Introduction.
• Chapter II.: Of the Topography and Political Condition of the United States.
• Chapter III.: History of Emigration From Europe to North America In the Seventeenth Century.
• Chapter IV.: History of Emigration to North America From the Year 1700 to the Present Time .
• Chapter V.: Retrospect of the History of Population In the United States.
• Chapter VI.: Of the Amount of Births In the United States.
• Chapter VII.: Of the Period At Which Marriages Are Formed..
• Chapter VIII.: Diseases In the Territory of the United States.
• Chapter IX.: Reports of the Population of the United States Analysed and Examined.
• Book V.: Of the Means Which the Earth Affords For the Subsistence of Man.
• Chapter I.: Of the Present State of the Globe As It Relates to Human Subsistence.
• Chapter II.: Of the Number of Human Beings Which the Globe Is Capable of Maintaining On Our Present Systems of Husbandry and Cultivation.
• Chapter III.: Calculation of the Productive Powers of the Soil of England and Wales.
• Chapter IV.: Causes of the Scarcity of the Means of Human Subsistence.
• Chapter V.: Causes of the Scarcity of the Means of Human Subsistence Continued.
• Chapter VI.: Of the Improvements of Which the Productiveness of the Globe For the Purposes of Human Subsistence Is Capable
• Chapter VII.: Of the Principles of a Sound Policy On the Subject of Population.
• Book VI.: Of the Moral and Political Maxims Inculcated In the Essay On Population.
• Chapter I.: Character and Spirit of the Essay On Population Delineated.
• Chapter II.: Of the Positions Respecting the Nature of Man Upon Which the Essay On Population Is Constructed.
• Chapter III.: Of the Doctrines of the Essay On Population As They Affect the Principles of Morality.
• Chapter IV.: Of the Doctrines of the Essay On Population As They Affect the Condition of the Poor.
• Chapter V.: Of the Doctrines of the Essay On Population As They Affect the Condition of the Rich.
• Chapter VI.: Of Marriage, and the Persons Who May Justifiably Enter Into That State.
• Chapter VII.: A Few Contradictions In the Essay On Population Stated.
• Chapter VIII.: Of Wages.
• Chapter IX.: Conclusion.

DISSERTATION
on the
RATIOS OF INCREASE IN POPULATION,
and in
THE MEANS OF SUBSISTENCE.
BY MR. DAVID BOOTH.

SECTION I.

introductory observations.

“It has been said,” says Mr. Malthus, “that I have written a quarto volume to prove, that population increases in a geometrical, and food in an arithmetical ratio; but this is not quite true. The first of these propositions I considered as proved the moment the American increase was related, and the second proposition as soon as it was enunciated. The chief object of my work was to enquire, what effects those laws, which I considered as established in the first six pages, had produced, and were likely to produce, on society; a subject not very readily exhausted^a .” This, it must be acknowledged, is meeting his adversary fairly in the open field. His means of defence are displayed before us; and we shall see if Ins” first six pages” form an impenetrable shield.

The argument of Mr. Malthus is founded on the comparison of numerical progressions; and, as mathematical science has always been held as the only one that is demonstrably true, this comparison of numerical progressions has been hastily allowed as infallibly certain, and has obtained for its author all that implicit faith, which has been granted by his disciples to the corollaries which he has drawn.

It may be premised however, that the science of mathematics is a science of certainty, only in as far as it is a science of abstraction;—that when it ceases to be abstract, and becomes what is termed “mixed mathematics,” the numbers or quantities, assume definite designations; and the reasonings thence derived are true, or false, according to the accuracy, or inaccuracy, with which these numbers or quantities are designated.—Two times two, for instance, is four, because four is the term by which we have agreed to denominate the result of this multiplication; but when, in measuring surfaces, it is said that two feet multiplied by two feet will make four feet, there is an error in the syllogism; because the word “feet” in the product, has not the same meaning that it has in the factors:—in the latter it is lineal, and in the former superficial. In application then, mathematical reasoning partakes of all the uncertainty of the branches of knowledge with which it is combined; and hence the numerous paradoxes which, even in this science of demonstration, have puzzled the pupils, and have scarcely been explained by their masters. These observations are not foreign to our purpose, when we have to speak of the ratio of increase in human population.

Mr. Malthus, if he himself understood the subject, has taken it for granted that his comparison of ratios would escape the notice of mathematicians. He asserts that human population, if allowed to expand freely, would increase in a geometrical ratio, in the order of

1, 2, 4, 8, 16, 32, 64, 128, 256, &c.

Now it is obvious that this series can represent no connected chain of the expansion of human life. The quantity represented by 1 (the first term in the series) does not at any moment become 2 (the second term), but there are an indefinite number of terms of different magnitudes, to be interjected between these terms (and so between every two other successive ones) to fill up the links of the chain. This then supposes time: time therefore, the most metaphysical of all metaphysical beings, is an ingredient mixed up with the consideration of the abstract numbers of the progression. This time Mr. Malthus has specified to be 25 years. The series then which denotes the increase of human beings in America, is thus represented.

The philosophy of Mr. Malthus is not the method of induction. He perpetually appeals lo principles which have never been brought into action, and which are opposed to all experience. He speaks of tendencies to human increase, and of powers of population, which “in no state that we have yet known have been left to exert themselves with perfect freedom^b .” This is exactly in the style of those dreamers, who predict of the future something unlike and opposite to what has ever appeared in the past. They too talk of secret springs, that have never yet displayed their elasticity,—of latent energies which have never been exerted.

Latent signifies concealed, and consequently the latent power of increase in the human species is what we shall never know; but, even granting for a moment that the 3 or 4 censuses which have been taken in America do exhibit something like a duplication in 25 years;—granting too that this increase has arisen solely from propagation, independent of emigration, there certainly exist no data from which to infer the law of the series. We have only 4, or at most 5 terms given us,— some of them extracted at intervals of time by no means regular,—from a series perpetually flowing, and of the ebbs and floods of whose motion we know nothing; and from these the ordinary reader is presented with a picked set of numbers, in geometrical progression, with the ratio of two. From such an increasing series as the human race may be supposed to exhibit, any form of a progression may be taken:— why not that of 1, 4, 9, 16, 25, &c. which increase as the squares of the terms 1, 2, 3, 4, 5, &c.? For aught that Mr. Malthus has discovered this may be the latent law of increase. All that he has demonstrated, even granting his American censuses, as we for the moment have done, is that human beings are capable of increasing their numbers; or, rather that they have been found to do so for a specific time: but the series which would mark the Law of that Increase, he has either been unwilling or unable to develop.

“The rate,” says Mr. Malthus, “according to which the productions of the earth may be supposed to increase, it will not be easy to determine. Of this however we may be perfectly certain, that the ratio of their increase must be totally of a different nature from the ratio of the increase of population^c .” This passage is much more modest than that which we quoted at the beginning of this Dissertation, where he says, that food increases in an arithmetical ratio, and that he considered this proposition as proved the moment it was enunciated; but, as he proceeds, this modesty vanishes, and he comes to an undoubting conclusion that food can increase only in the series 1, 2, 3, 4, 5, 6, 7, 8, 9, &c. (an arithmetical progression whose ratio is one) and that the period between the terms, or time of increase, is also 25 years.

If the quantity of the food of man be increased, it is obvious that the increase will not be by starts every 25 years; but that it will be increased through many intervening times; and, consequently, even granting that such quantities as 1, 2, 3, 4, &c. were extracted from the flow of increase, at certain periods, the arithmetical progression thus exhibited would be a picked set of numbers, (as we stated respecting population) and might have been any other series rather than that which Mr. Malthus has chosen, for aught that experience has told him on the subject. The successive terms of all increasing series whatever present nothing but additions. The mathematician forms series at his own pleasure, where the additions are regulated by certain laws. It is not so with those of Nature. Whether her series alternately progress and retrograde;—whether they circulate, or decrease, or flow in straight and eternal lines, is beyond the ken of the philosopher. He snatches at intervals, a few links in the immeasurable and ever moving chain of the universe; and dividing these links into such portions as are perceived by the glance of a moment, he cries out in extacy, “I have found it!” This remark however is general. It refers to the boundaries of human knowledge, and is applicable to a Newton as well as to a Malthus:—Our business is with the latter.

Taking the series 1, 2, 3, 4, &c. as that of the increase of human subsistence, or of any thing else, we may, by picking the terms, extract from it any progression we chuse: for instance, in — 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16, &c. the 1st, 2d, 4th, 8th, and 16th terms, form the precise geometrical progression, which Mr. Malthus has chosen to represent the increase of human beings. The progressions themselves then would have signified nothing, had not Mr. Malthus assumed the principle, that an equal period of time, 25 years, was to elapse between the production of every subsequent term of either progression. Thus arranged:

he believes that he has demonstrated that in 8 periods of time of 25 years each, the population if unchecked, would increase to 256 times its present number, while the food would only be 9 times what it now is. Let us endeavour to view the grounds on which these different progressions have been raised.

SECTION II.

of the ratio of increase in the means of subsistence.

The phrase, “means of subsistence,” as applied to human beings is in the utmost degree loose and indefinite. In a general sense almost every thing that grows, walks, swims, or flies, is capable of being converted into the food of man, and hence every vegetable and every animal must cease to exist, before it can be said that his means of subsistence are exhausted; and, till then, the grown up man would always find sufficient to feed his young. In a particular view however, it may be, and often is otherwise. Man in society is a being of habits and prejudices He is moreover a slave. His food must be of a certain kind, dressed in a certain manner, and provided, not by the whole, but by a small portion of the species. In this situation a famine may occur while the world teems with animal and vegetable life^d . He may starve in a workshop, as well as within the walls of a dungeon; because, in neither case, has he any food except what is brought by his keepers. It is food so prepared and so distributed, which constitutes the means of subsistence among the nations of Europe, where the labourer

• “Starves, in the midst of Nature's bounty curst,
• And in the loaden vineyard, dies for thirst.”

As it is in America that Mr. Malthus has discovered his ratio of propagation, it is there also we should look for the ratio of increased subsistence; and in doing so we shall find reason to be astonished at his choice of an arithmetical one. As far as animals constitute the food of man, its increase must be in the same sort of series as that of human beings: and, if a geometrical ratio exist any where, it is surely in the vegetable produce of the soil. Animals and vegetables multiply as rapidly at least as man, if submitted to his care and protection: and, as the love of his offspring is implanted in his nature, he would, if free, always exert himself to rear the food, which his children might require. The limits of this production of food would not be discovered, as long as any land lay waste. Until the whole were cultivated in the highest degree,—until the sea were drained of its inhabitants, and no wild beast or fowl were found upon the earth, the food of man would always increase in an equal ratio with the human race^e . If America have doubled its inhabitants every 25 years, the prepared food must have increased in equal proportion: for all the inhabitants have plenty, and are able to export grain to foreign countries. In the only country then, where Mr. Malthus has discovered any ratio of increase of human population, the same, if not a greater ratio has been observed in the increase of the means of subsistence. As before observed, natural subsistence is indefinite, and prepared subsistence, which is a manufacture from what nature has in store, must always increase in quantity in proportion to the number of manufacturers employed, until the raw material can no longer be furnished; and so long at least the ratios of human increase and of the means of subsistence must necessarily be the same. What will happen when the prolific power of man shall enable him to outstrip the fertility of the globe which he inhabits: when the head of the serpent shall bite off its tail, and no longer remain an emblem of the universe, we leave to the conjectures of those whose imaginations are able to people the universe with human beings^f . Meantime, whether vice, misery, or (what Mr. Malthus never chooses to mention) the less extent of prolific power, and the shortness of time appointed for man upon the earth,—shall interfere with tins peopling of the stars, we may rest assured that, until men can exist without food, the ratio of increase of population will never exceed that of the means of subsistence. Food may be reared beyond the wants of a people, and such a case has produced slavery and misery to the cultivators of Botany Bayg ; but it is impossible that any term in the progression of subsistence can be less than its corresponding term in that of population, else that corresponding term would cease to be. Experience then never did nor ever can shew different progressions in population and in food, in favour of the former; and, as to the difference of inherent power (if a power which can never be exerted have a meaning), the power of increase in plants and animals is obviously equal to that of man.

Section III

Ofthe ratio of increase in human population.

We have already observed that the progressions of nature are not formed like those of the mathematician. They do not start from one term to another, but proceed insensibly, so as to fill up all the interstices between the terms of the series; and it is only by catching at different points in the order of time, that progressions are extracted, to form (or oftener to suit) the theories of philosophers. It is known for instance that bodies fall to the earth with an accelerated motion. That acceleration has been assumed to be such, that the spaces described by the falling body shall always be in proportion to the squares of the times. Experiments were made on a petty scale to prove the truth of this theory, some of which appeared to coincide in a remarkable degree, while others presented very different results. It was then assumed that the ratio could exist only in a vacuum, on account of the resistance of the atmospherical air,—and as we have no means of making the experiment in vacuo, the principle still remains a mere gratisdictum. It is nevertheless considered as unquestionable; and is even made to guide the planets in their orbits.

In a similar manner, though with humbler claims to confidence, Mr. Malthus has adopted the principle, assumed by his predecessors, of a tendency to a continued geometrical ratio in the increase of human population; and has built upon this hypothesis, his theory of accounting for the vice and misery which exist among mankind. We have now to consider from what data this principle of increase has been inferred; but we may previously remark, that it is the tendency to this ratio of increase, and not the increase itself, which Mr. Malthus exhibits as the evil genius of the human race. This embryo of future famine—this being that is yet to be—is perpetually at war with the good genius of subsistence. The hand of industry is palsied, and the fruits of nature are shrivelled, by the touch of the demon. He hangs the ruin over our heads, and we are crushed by its weight before it falls.

Granting the power of increase to the human species, the methods of investigating the law of the series will vary according to our view of the origin of mankind. On this subject, however much men may differ in minute particulars, there are only two general and acknowledged systems of belief. The one is the peopling of the earth as recorded in the scriptures: the other is the aspect of human society as it appears to every succeeding generation, modified by the degree of confidence that such generation entertains in the traditions and uninspired written records of its ancestors. We will consider the case from each of these points of view.

On the first hypothesis the whole of the present race of men have descended from a single pair. In consequence, there is no question ot the existence of a power of increase among the early inhabitants of the earth; and the only point of controversy is, whether that power be not now diminished. But, however that may be, the investigator of ratios proceeds upon the same principle, and uniformly constructs his tables from a single pair. It is nevertheless evident that every table so constructed must proceed upon data furnished by the imagination We have no complete genealogy of the first peopling of the globe; and, as brothers do rot marry their sisters in our times, the descendants of a single pair cannot now be kept separate from the population of a district. Such imaginary tables have notwithstanding been constructed; and we give the following from Suss-milch, which was calculated by Euler. He takes a married pair of 20 years old, as the founders of his race. This pair have six children at three births (each birth producing twins—a male and a female) and these births are in the 22d, 24th, and 26th years of the age of the parents, who live till 40 years old, and then die. Every successive pair marry at 20, and have 6 children at 3 births, in their 22d, 24th, and 26th years, and live till the age of 40, as their parents did before them. The same succession of births, marriages, and deaths, continues from generation to generation, and the results are given for every 2d year, during a period of 3 centuries. These data are sufficiently extravagant. The Table presents, as might be expected, an abundant increase; and surely here, if any where, the geometrical ratio should be found.

In this Table the first column contains the years to which the numbers in the other columns respectively refer. The 2d column gives the number of the born in each particular year. The 3d column gives the number of the born altogether; which, if there were no deaths, would be the number of the living; but as all die in the 41st year of their age, the number of the dead is placed in the 4th column, which, subtracted from the whole number born as expressed in the 3d column, forms the 5th and last column, or the number of the living.

The mathematician, who is acquainted with the data on which this Table is constructed, knows that it presents a recurring series, the law of which might be expressed by an algebraic formula; while the ordinary reader will be astonished at its ebbs and flows, and will labour in vain, if he attempt to pick out an increasing geometrical ratio from its numbers. There is only one law in a geometrical progression, which is, that every succeeding term shall have a certain fixed proportion to the preceding; and hence, if, in a series of increasing numbers, every set of equidistant terms (such as every 20th or 25th, &c.) presents a geometrical ratio, then all the terms in the series are also in geometrical progression. Thus if in the numbers 1, 2, 4, 8,16, 32, 64, 128, 256, 512, 1024, we take every third term, beginning with 1, we shall have 1, 8, 64 512, a geometrical progression, where every succeeding term is 8 times that which went before it. If we chuse every second term we have, 1, 4,16,64, 256,1024, a progression where the ratio is 4, and universally, pick as we will, if we do so at equal distances, we shall always have a geometrical progression: because the numbers from which we have to chuse are all arranged in that sort of series. Before then a geometrical progression can be picked, at regular intervals, from any succession of numbers, every 3 or more terms, that follow one another in that succession, must themselves be in geometrical proportion. It is in vain therefore to look for a doubling of mankind in certain periods, if there be not an equable progression from year to year. But, under any form of increase from a single pair, this is impossible; for the terms are only numerically, not substantially the same. The number of the living in the Table before us is doubled in the second year, tripled in the 4th, and quadrupled in the 6th year, but these 4, 6, and 8 persons, are not similar to the first two. The two are a man and a woman, while the increase are children, who have to live a certain number of years before they can add to the race. The geometrical ratio therefore can never exist under such circumstances. In this Table, though every contingency that could arise from constitution, climate, or other causes, is studiously rejected in the calculation, the “regular confusion” is apparent, particularly in the 2d column, through a period of three hundred years; and though the numbers would not be so obviously irregular to common observers, they would never run into a geometrical ratio, though extended to as many centuries.

If the descendants of a single pair can never increase in a geometrical proportion, neither can those of a modern colony, for such a colony is only a certain number of grown up pairs; and besides, as they are real beings, they are liable to many accidents, defying all calculation, from which the preceding Table is by supposition free. A colony of grown up men and women insulated from the rest of the world, would resemble in a great, degree the first parents of the human race. Society, as it exists in Europe, presents us with numbers of all ages from the cradle to the grave; and in gradations which could not exist in a colony, such as we have mentioned, for centuries. Mr. Malthus finds his geometrical ratio in America: but the least reflection might convince him that this ratio cannot possibly take place among the descendants of grown up propagators; and that, though it were supposed to exist, the continued influx of emigrants from Europe would so overwhelm it with stranger numbers, as to make it impossible to shew the progression. We are not, in this place, denying the assertion, that there has been an increase in America “from procreation only.” We only deny, and we do it peremptorily, that the increase is in any species of geometrical progression.

We have hitherto considered the laws of the increase of human population, as originating from one or more pairs of grown up persons. We have now to contemplate mankind as they are found existing upon the earth;—as if they were beings but recently discovered by the philosopher. In this view, the origin of nations is lost in the mist of antiquity; and, we presume, it will be granted us, resting, as we must do, on the authority of profane history, that we have no conclusive evidence, whether the number of the inhabitants of the globe is greater, or less now, than it was 2000 years ago. Of the whole population we observe only a small portion, and that for a very limited period of time.

Could we take an exact census of a populous nation, we should find it materially different in its construction from the enumeration of an infant colony, or the tabular genealogy from primitive progenitors. The multitude of human beings, whose origin is lost in history and who seem as it were indigenous to the soil, is composed of persons of every age from the moment of birth to the point of dissolution, including, in general, a period of about 100 years, that being the term which may ordinarily be considered as the extreme limit of human life. How many of these were born at every particular minute, hour, or day of the century immediately preceding the census, it is practically impossible to determine. The only Tables of any value on this subject are the population-lists of Sweden; for there has never been a census in any other country on which there could be placed the least dependence, or from which any useful consequence could be drawn.

The population of Sweden, of which there have been frequent enumerations during the last 60 years, appears to be increasing, but certainly in no ratio approaching to geometrical. The irregularity of the increase is extreme, and occasionally we find a considerable diminution. How much of the increase may be attributed to a greater accuracy in taking the censuses, and how much of the irregularity may arise from the variations in its political boundaries, we must leave to the determination of the statesmen of that country. It is sufficient to say that they continually complain of the want of population. Our present business however is not with the increase itself, but with the law of that increase.

The following table is formed from the censuses for 9 years from 1755 to 1763 inclusive. Though it exhibits an increase, the population about that period may be considered as having been nearly stationaryh ; and certainly not increasing, if we keep in view the necessity of a fund to supply the waste occasioned by those unexpected convulsions of society, and calamities of nature, which history records as having so often retarded and diminished the population of kingdoms.

These Tables are formed from the comparison of 9 years; but, did they represent the average of centuries, they would then give us a fair view of the progress and waste of human life, in the state and climate of Sweden. We will suppose that they do so.

It appears then that 370 annual births are just sufficient to keep up a population of 10,000 persons. These 370 (or 1850 in 5 years) constitute a population of 1408, under 5 years of age, who are renewed by the births as they grow older or die. These 1408 are reduced by deaths to 1076 between the ages of 5 and 10, who are again reduced to 1015, being the number living between 10 and 15. In the same manner, from the continual supply by births and reductions by deaths, the different numbers of every age, making up the whole population, are regularly kept up throughout the century, which here appears to be the limit of the age of man. In actual existence these numbers will vary above or below the numbers of the Table, which are here given as an average proportion of a society of little or no increase.

The supply of this society is by children in nonage. The 370 annually born are expanded so as to keep up all the ranks of the different ages of which the 10,000 population consists; and for that purpose it matters not whether they be produced by the whole, or by a part of the tribe,—or whether they drop from the clouds. In fact however these children are brought into the world by the child-bearing females. The period, during which women are capable of child-bearing is, in few cases, above 20 years,— rarely more than 25. Early marriages seem to produce no difference in this respect; because, the sooner they begin, the sooner they cease to be prolific. The whole range in Europe is between 15 and 45; and, in taking the numbers from the table, it matters little whether we count them between 15 and 40, or between 20 and 45: the amount is not materially different. Polygamy is not allowed in Sweden; and therefore these 370 children may be considered as produced by not more than the number of the population between 20 and 45; that is, by 3534 married persons. It will signify nothing that the husbands are occasionally of other ages, for the number (3534) would not thereby be increased: the females of these ages only being capable of child-bearing. Of these 3534, a proportion of women (diseased from birth or by after accidents) are never fitted for marriage; and it will therefore be no extravagant assertion to say that the married persons in this society will never exceed 3000, if ever they amount to that number. These 3000 persons then are the ever-during source from which this society flows. Their children fill up the vacancies of death, and recruit the ranks of propagators as they are invalided by age; but all the females, and a number equal to all the males, above 45 years old, cease to be useful in the continuation of the race. There are 2108 persons above the age of 45; and if we add to these the number who are too diseased for marrying (of which we supposed 534 between 20 and 45) and the number of children, who, though counted with the others, are doomed never to swell the list of real propagators, we speak within bounds when we assert, that of these 10,000 persons, there are 3000 who are useless in the work of procreation. These 3000 —more or less, according to healthy or unhealthy seasons,—form the fluctuating balance of what would otherwise be a permanent population. The 370 children annually born, contain among their number the proportion necessary to keep up these 3000 useless adjuncts to the hive: and, though all the 3000 were to perish in a morning, so as to reduce the society to 7000, the effective propagators would remain, the births would continue the same, and the 3000 would gradually be renewed like the severed limbs of the polypus. As an example, we will suppose that the 2108 persons above 45 years of age are all destroyed by accident or design. Their gradual renewal will be apparent from the following Table:

From the foregoing table we find that, although we destroyed more than a fifth of the population, the whole are created anew in the course of 50 years. The 10,000 inhabitants are again brought forward, and the society ceases to have any further increase. If, in addition to the 2108 persons here cut off, all the diseased and inefficient had been likewise exterminated, the society would have been reduced to less than 7000. The apparent number of propagators would have thus been lessened, but the births would not therefore have been fewer; and in a certain number of years, as in the present case, every chasm would have been filled, and the original number of 10,000 human beings would have been brought again, and in the same order, to our view. There may therefore happen to be very extensive variations in the census of a society, in the germ of which there is no principle of permanent increase. They are precisely those adventitious beings who increase with favourable years, and who, when unfavourable seasons arrive, swell by clusters the bills of mortality. A series of seasons unfavourable to the vegetable productions of the earth, is also unfavourable to human life, particularly to that of the infirm and the aged. These die of disease, not of famine: for, except in the nauseous and hidden dens, of a crowded and selfish metropolis, where man lies unseen and unpitied, there are comparatively few in Europe who perish of hunger. Of the 3000 who are old or diseased, two or three un-genial seasons may sweep two thirds from the earth. These two thirds are a fifth of the whole population, and would leave a mighty blank in the census of a nation. We see however that this blank would be rapidly filled up, and a return of genial years might make them even more numerous than they had previously been.

If, in the society which we have taken for our example, we were to suppose that all those who reached the age of 45 were to exist a thousand years, while the law of population remained otherwise the same, the elders of the society would continue to increase during these ten centuries, when, after having risen to a number which we will not now stay to calculate, the increase would again come to a stand, and the census of the nation would afterwards remain stationary.

Again: keeping in View our table of 10,000, let us suppose a colony of 3837 persons, male and female, between the ages of 15 and 40 (which we will take for the marriageable ages in a new country), and in such proportions as they are found in Europe. Let them be from Sweden, and be possessed of only the Swedish powers of propagation. These persons then, being the exact numbers in our table of 10,000, will form the nidus of a race, in the same manner as the persons at the outset of the immediately preceding Table; except that, until their children arrive at the age of 15, the propagators not being supplied by their growing successors, would diminish in numbers for a certain time. To remedy this, Jet there be an immigration, for the first 15 years, of 172 annually, or about a twenty-second part of the original colonists, which 172 will exactly keep up the number of our first column (those between 15 and 20) as they waste by age and death. The following table will shew the progress of the colony for the first 15 years:

At the end of these 15 years, the number of the propagators will be continued the same, by means of the grown up children, without further importation. The society now exhibits an extraordinary increase. The original settlers were 3837, and the annual immigrants amount altogether to 2580. The latter however, as far as propagation is concerned, may be reckoned at only half that number, because on an average they have lived only 7[w1] years in the colony. About 5000 propagators then have, in 15 years, increased their number by nearly 3000 additional human beings, independent of those that have been lost by death. It may be remarked too, that we took our colonists from the general mass between 15 and 40, which included the blind and the maimed, the diseased and the dying. But such persons do not emigrate: and this increased population might have sprung from a colony much less numerous than what we have here stated. In taking a census therefore of an infant colony, we need not wonder that it should double its numbers in a very short period. The emigrants, who arrive in small numbers afterwards, are less observed than the primitive founders; and it is extremely probable that many such establishments may double their numbers, apparently from propagation alone, in less than 20 years. The principle however on which this duplication rests, escapes the eye of the common observer. The colony is not a society in the sense which we understand of a nation. It is the first expansion of a set of picked propagators, without parents and without children, which two classes, together with the diseased and ineffective, constitute nearly three-fourths of the population of modern Europe. It is the body of the polypus without its limbs, which its inherent energies are able to renew. Till these are completed, the increase will continue. If our colony have no further accession of immigrants, it will increase until it muster its number of 10,000, after which it will continue permanent. Mr. Malthus catches the polypus in the middle of its growth;—he measures the length of limbs already attained, and, comparing these with time, he forms a ratio of increase, in which, he asserts, they will expand for ever!

A careful census of our 15 years' colony will give ample evidence that it increases solely because it is a society that is incomplete. In an indigenous society there are nearly a fourth of its numbers above 45 years of age. Here there are only 878 out of 8770, or about a tenth of the population. The higher ages,—the extremities of the polypus,—are not yet formed; neither, if immigration were continued, would they ever be. Of this the American censuses give sufficient proof. In none of the United States is the number of persons above 45 more than from 16 to 17 per cent, of the population, while in many of the newly settled districts they do not exceed 7 or 8, as will appear more particularly in the following table.

Resting, as Mr. Malthus has done, the whole of the proof of his geometrical ratio on the censuses of the United States, it must be acknowledged that he has by no means stretched his evidence beyond what it would bear. The increase in the population of the new colonies between 1800 and 1810 is such as almost to stagger belief. The following Table is extracted from the censuses, but arranged so as best to elucidate our observations.

Here we have a population of 281,341 persons, which more than doubles its numbers in 10 years, while one division of this population is increased, within that period, to more than 5 times its original amount. These are ratios of which Mr. Malthus might boast, but of which he has not boasted.

When enumerations are taken every 10 years, it is obvious, exclusive of immigration, that in any particular census the persons living above 10 years of age must have all existed in the census immediately preceding. In that of 1810 for instance, all above 10 years formed part of the population of 1800; and are in reality the same, except inasmuch as they are diminished by death. Those under 10 have all been born in the interval between the censuses.

The whole population of 1800 in the preceding Table was 281,341. These in 10 years would be diminished to 200,000, under the most favourable laws that have hitherto been observed of human mortality:—but the number of persons above 10 years of age in 1810 were found to be 357,102; and therefore it is clear to a demonstration that this society must have been recruited by more than 160,000 immigrants: for, of these immigrants themselves many must have died, and besides, some of those under 10 years of age, may have been born in other countries

It may be said, and perhaps with truth, that many of these immigrants may have been from other parts of the United States, and not from Europe: but, comparing in the same manner the whole of the American census we shall find an astonishing extent of immigration: The white population of 1800 was 4,305,971. These in 10 years would be diminished by a fourth. It is very improbable that more than 3,200,000 would have been alive in 1810, for whatever proportion the births of that country may bear to the whole population, the proportion of deaths is certainly greater than in Europe. These 3,200,000 then should have constituted the number of those' above 10 years of age in the census of 1810, had there been no importation from other countries. But the actual census above 10 years of age was 8,845,389, giving a surplus of 645,389, which can be accounted for in no other way than by immigration The census of 1810 contains also 2,016,704 children under 10 years. Part of these too, as well as the deaths of immigrants since their arrival, should be added to the 645,389 above stated; and therefore of the 1,556,122 persons, which the census of 1810 exhibits;beyond that of 1800, it is as clear as sunshine that nearly one half was added by direct immigration. Of the effects on the increase of population by the introduction of grown-up persons we have already spoken; and, adverting to these effects along with the statements now given the additional population is completely accounted for, without supposing a power of procreation beyond what is found to prevail among European nations.

But it is needless to dwell longer on this part of the subject, for he, who will attentively examine the statistical tables of the United States, will discover, in every line a marked distinction between them and those of Europe. At every step they announce a race, who, as has been supposed of their country, have but lately emerged from the waves. America has more resemblance to a camp than to a nation. Its in habitants are a band of adventurers, continually recruited by men like themselves, who seek for conquests in a new world, and have left their parents to perish on a distant shore. It is in vain therefore to look to that country for a geometrical or any other regulated increase of population. Immigration must cease for centuries, before such a law could be there developed, even allowing it to belong to human nature.

But it may be asked, if a colony were constituted of persons of all ages, such as they exist in Europe, and were the proportion of births raised in a great degree by the removal of the present checks to population, might not the inhabitants increase in a geometrical ratio, and double their numbers in 25 years? This is the only question that remains to be considered, and its discussion will close the present Dissertation. In order to have a clear view of this proposition, we shall again refer to our Table of 10,000 which we proportioned from the Swedish populationa . We must also remind our readers that this Table was formed from a society of little or no increase. We have already considered this society as stationary; but, whether so or not, it is equally effective for the sake of illustration.

We have before observed that the waste of these 10,000 is replaced by the 370 annual births; and that this perpetual flow of children successively fills up the ranks of the race, as they ate thinned by the hand of death. Where man is indigenous, these are the gradations of society; and, before it could be doubled, we must have two for one of every age from the cradle to the tomb. Now, by what means are these additional human beings to be brought upon the stage of life in 10, 15, or even in 25 years? Imagination may add birth to birth at pleasure, but how shall our old men and old women be so rapidly created, unless we can close the gates of death, and hasten the flight of time? Were we indeed to attend to numbers only, without regard to age, we might easily conceive an abundant increase; but it does not therefore follow that this imaginary increase must proceed in a geometrical progression.

Supposing that from some extraordinary fortuitous circumstances,—from an increase in the genial powers of nature, or from a particular interposition of Providence,—the females of our little society were all at once to become doubly prolific; and that thereby the annual births were to be double what they now are, or 740 in place of 370. It is plain that these additional 370 annual children would, independent of their own progeny, form a new race, the exact counterpart of the old; and that the whole of the society would be thereby doubled in about 100 years. Were the original stock alone to be propagators, we should thus have an addition of 10,000 every century, being an increase in the ratio of 1, 2, 3, 4, &e. But at the end of 20 years (taking an average period) as many as remain alive of the 370 additional children that were born in the first year, will arrive at the marriageable age. The next, and every succeeding year, a like number will be added to the list of propagators, and will become the parents of a new race. The children of these last will become parents in their turn, thus engrafting a succession of scions, one upon the other, and all originally springing from a parent tree. Instead then of a geometrical ratio the period of duplication would be continually lessening, as the several scions were added to the stock. Supposing the new propagators to have the same prolific power that we have given to their progenitors, it would require 40 years for the first doubling, and about 30 for each of the two succeeding ones; and this period would become less and less, through a series of a very complicated form, though it would never be under 25 years. Besides, these duplications would be numerical only; for the numbers of the early ages would go on in an increasing ratio, but there would not be the same proportion of increase among those of riper years. We have calculated the progress of that series, but the Tables are too extended to be conveniently inserted in this place.

It is in vain to look for a geometrical ratio in the increase of any society, unless the society were originally constituted in that progression. Assuming the females between 20 and 45 years of age to be the only source from which the continuance of the race can be derived, the series which would denote the varying numbers of those females, in the order of time, would also denote the law of increase in the censuses of the tribe or nation. All the females now existing between 20 and 45 will be gradually erased from the list, by superannuation or by death, in the space of 25 years. Their place will be filled by others; and if the number of the new mothers be not then double what they now are, we may rest assured that the society does not exhibit a permanent principle of increase, in the ratio and in the time prescribed by Mr. Malthus. Had it been the order of Nature that the human race should have originally been arranged in a geometrical progression; had the law been such that every year the births should have increased in a fixed proportion to the preceding;—had the number of the living at every succeeding age been increased in the same manner and in the same proportion: and, had the whole frame of society been so constituted that the child-bearing females should, by this regular succession of the inferior ages, have doubled their numbers at equal periods, such as every 25 years;—then, and then only, could a geometrical ratio of the increase of population have existed. But mankind have never been found so arranged, and the laws that regulate the succession of human beings do not seem to be of that feeble texture, which would warrant us in predicting that what has never been will ever be. On the whole it is obvious that the assertion, that human population has a tendency to increase in a geometrical ratio, is, in the utmost degree, arbitrary. It is the mere dictum of Mr. Mal-thus, and when he finds, as he always does, that this ratio of increase has not hitherto acted, instead of doubting, as he ought, the truth of his hypothesis, he looks around for concomitant circumstances which, he says, have retarded or destroyed its operation: that is, for circumstances which have retarded or destroyed the operation of a principle, of which lie has brought no evidence that it ever existed. But he even gives these retarding circumstances themselves as evidence. He calls them checks upon population, before he has proved that population required such checks. “There exist vice and misery in the world; therefore these prevent mankind from doubling their number every 25 years!” Such is the reasoning.—The point in dispute is always taken for granted.

Were we to draw our inferences from a survey of the world and its history, we should come to no such conclusion as the principle of an unlimited increase. Man is individually a transient visitor of the earth. A few revolutions of the sun, and this proud being is thrust from the scene. Is the race then permanent? Many species of animals have disappeared, and fill our cabinets with their fossil remains. The mammuth no longer ranges over the globe, though for a time he must have lived with extensive power. What vice, misery or moral restraint has prevented the unlimited increase of the eagles in the air, or of the sharks in the ocean, where they reign paramount lords and masters? May not the law of increase—may not the duration of life itself diminish as it radiates from the primeval stock? Something of this kind is observed in vegetables, whose qualities deteriorate, and whose seeds more and more degenerate as they are distant from the parent tree. So far from having to frighten ourselves with the idea of an overwhelming population, have we not rather to fear that we are sinking by degrees into a degenerate race, which in the lapse of time may be swept from the globe? The earth itself is probably not immortal, and why should its puny inhabitants? All these, to be sure, are questions of mere possibilities, but they are as probable and as demonstrable, as the possibilities of Mr. Malthus. If the terms of the proposition do not involve a contradiction, there is no assertion, with regard to future contingencies, that can be proved to be untrue. But possibilities are inhabitants of the land of dreams. They may amuse in the closet, but they are useless in the conduct of life; and ought to be far beneath the notice of the legislators of nations.

TABLES of theAMERICAN CENSUS.

That the reader may be fully possessed of all the documents which should enable him to form correct notions on the subject, I have thought proper to insert here the Three Tables of the American Census, as they appear in Pitkin's Statistical View of the United States.I should have been glad to have printed from the Tables published by the authority of the American government; but I have been able to procure only those for 1810.

ENQUIRY
concerning POPULATION.

BOOK III.

of the causes by which the amount of the numbers of mankind is reduced or restrained.

[a]Essay on Population, Vol. III, p. 343, 344, Note.

[b]Vol. I. p. 5, 6.

[c]Vol I. p. 9.

[d]Witness the horrible famine in India in 1771.

[e]“If want alone, or the desire of the labouring classes to possess the necessaries and conveniences of life, were a sufficient stimulus to production, there is no state in Europe or in the world that would have found any other practical limit to its wealth than its power to produce; and the earth would probably before this period have contained, at the very least, ten times as many inhabitants as are supported on its surface at present. But........where the right of private property is tablished, &c. &c. &c.”Vide Malthus on Political Economy, p. 348.

[f]See Malthus on Political Economy, as quoted in page 484.

[g]See Wentworth's Account of that Colony.

[h]See the remarks of Dr. Price in Appendix to Chapters IV, V, VI. p, 192, 193.

[a]Vide page 268.