Godwin, William. Of Population. London: Longman, Hurst, Rees, Orme and Brown, Paternoster Row, 1820.

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DISSERTATION

ON THE

RATIOS OF INCREASE IN POPULATION,

AND IN

THE MEANS OF SUBSISTENCE.

BY MR. DAVID BOOTH

.

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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 inquire, 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 acknow-

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ledged, is meeting his adversary fairly in the open field. His means of defense are displayed before us; and we shall see if his " 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.

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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 terra), 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

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which denotes the increase of human beings in America, is thus represented.

First term, or original propagators,    1 
2d,             in 25 years,            2
3d,             50 —              4 
4th,            75 —              8
5th,            100 —            16
6th,            125 —            32
&c.         &c. —        &c.

The philosophy of Mr. Malthus thus is not the method of induction. He perpetually appeals to 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

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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

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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 thai; 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.

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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 Ase, we may, by picking the terms, extract from it any progression we chuse: for instance, in — 1,2,3, 4,5, 6, 7, 8,9,10,11,12,13,14,15,10, &c. the 1st, 2nd, 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:

Population, 1, 2, 4, 8, 16, 32, 64, 128, 256
Food, 1, 2, 3, 4, 5, 6, 7, 8, 9

he believes that he has demonstrated that in 8 periods of time of 25 years each, the population

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if unchecked, would increase to 256 times its present number, while the food would only be 9 times what it now is. Let us endeavor to view the grounds on which these different progressions have been raised.

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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

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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 laborer

"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,

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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

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of the universe, we leave to the conjectures of those whose imaginations are able to people the universe with human beings.^f Meantime, whether vise, 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 this 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 Bay;^g 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 favor 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.

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SECTION III.

OF THE 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 gratis dictum. It is nevertheless considered as unquestionable; and is even made to guide the planets in their orbits.

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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 vise 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 shriveled, 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

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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.

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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 childbearing. 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

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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:

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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 favorable years, and who, when unfavorable seasons arrive, swell by clusters the bills of mortality. A series of seasons unfavorable to the] vegetable productions of the earth, is also unfavorable 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 bidden 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

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8000 who are old or diseased, two or three ungenial 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 are of 15, the propagators

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not being supplied by their growing successors, would diminish in numbers for a certain time. To remedy this, let 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 show the progress of the colony for the first 15 years:

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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 1/2 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, m 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

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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 m many of the newly settled districts they do not exceed 7 or 8, as will appear more particularly in the following table.

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Proportion of white inhabitants, above and below the age of 45, (to a propulation of 10,000) in the different districts and territories of the United States of America in 1810, compared with the kingdom of Sweden from 1755 to 1763.

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Resting, as Mr. Malthas has done, the whole0 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.

White inhabitants in Kentucky, Tennessee, Mississippi and Indiana in 1800 and in 1810.

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

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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 favorable 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.

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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 3,845,389, 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 inhabitants 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 population.^h 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

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successively fills up the ranks of the rare, as they are 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

285

10,000 every century, being an increase in the ratio of 1, 2, 3, 4, &c. But at the end of 20 years (taking an average period) as many as remain alive of the 370 additional children that were bora 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.

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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

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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. Malthus, 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 he 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 vise 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

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no longer ranges over the globe, though for a time he must have lived with extensive power. What vise, 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.

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^aEssay on Population, Vol. III, p. 343, 344, Note.

^bVol. I. p. 5, 6.

^cVol. I. p. 9.

^dWitness the horrible famine i India in 1771.

^eIf want alone or the desire of the laboring clasies 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 established &c &c." Vide Malthus on Political Economy p. 348.

^fSee Malthus on Political Economy, as quoted in page 484.

^gSee Wentworth's Account of that Colony.

^h Vide page 268.