An Essay on the Principle of Population
By Thomas Robert Malthus
There are two versions of Thomas Robert Malthus’s
Essay on the Principle of Population. The first, published anonymously in 1798, was so successful that Malthus soon elaborated on it under his real name.
* The rewrite, culminating in the sixth edition of 1826, was a scholarly expansion and generalization of the first.Following his success with his work on population, Malthus published often from his economics position on the faculty at the East India College at Haileybury. He was not only respected in his time by contemporaneous intellectuals for his clarity of thought and willingness to focus on the evidence at hand, but he was also an engaging writer capable of presenting logical and mathematical concepts succinctly and clearly. In addition to writing principles texts and articles on timely topics such as the corn laws, he wrote in many venues summarizing his initial works on population, including a summary essay in the
Encyclopædia Britannica on population.The first and sixth editions are presented on Econlib in full. Minor corrections of punctuation, obvious spelling errors, and some footnote clarifications are the only substantive changes.* Malthus’s “real name” may have been Thomas Robert Malthus, but a descendent, Nigel Malthus, reports that his family says he did not use the name Thomas and was known to friends and colleagues as Bob. See
The Malthus Homepage, a site maintained by Nigel Malthus, a descendent.For more information on Malthus’s life and works, see
New School Profiles: Thomas Robert Malthus and
The International Society of Malthus.Lauren Landsburg
Editor, Library of Economics and Liberty
2000
First Pub. Date
1798
Publisher
London: John Murray
Pub. Date
1826
Comments
6th edition
Copyright
The text of this edition is in the public domain. Picture of Malthus courtesy of The Warren J. Samuels Portrait Collection at Duke University.
- Preface
- Chapter I
- Chapter II
- Chapter III
- Chapter IV
- Chapter V
- Chapter VI
- Chapter VII
- Chapter VIII
- Chapter IX
- Chapter X
- Chapter XI
- Chapter XII
- Chapter XIII
- Chapter XIV
- Bk.II,Ch.I
- Bk.II,Ch.II
- Bk.II,Ch.III
- Bk.II,Ch.IV
- Bk.II,Ch.V
- Bk.II,Ch.VI
- Bk.II,Ch.VII
- Bk.II,Ch.VIII
- Bk.II,Ch.IX
- Bk.II,Ch.X
- Bk.II,Ch.XI, On the Fruitfulness of Marriages
- Bk.II,Ch.XII
- Bk.II,Ch.XIII
- Bk.III,Ch.I
- Bk.III,Ch.II
- Bk.III,Ch.III
- Bk.III,Ch.IV
- Bk.III,Ch.V
- Bk.III,Ch.VI
- Bk.III,Ch.VII
- Bk.III,Ch.VIII
- Bk.III,Ch.IX
- Bk.III,Ch.X
- Bk.III,Ch.XI
- Bk.III,Ch.XII
- Bk.III,Ch.XIII
- Bk.III,Ch.XIV
- Bk.IV,Ch.I
- Bk.IV,Ch.II
- Bk.IV,Ch.III
- Bk.IV,Ch.IV
- Bk.IV,Ch.V
- Bk.IV,Ch.VI
- Bk.IV,Ch.VII
- Bk.IV,Ch.VIII
- Bk.IV,Ch.IX
- Bk.IV,Ch.X
- Bk.IV,Ch.XI
- Bk.IV,Ch.XII
- Bk.IV,Ch.XIII
- Bk.IV,Ch.XIV
- Appendix I
- Appendix II
General Deductions from the preceding View of Society.
Book II, Chapter XIII
That the checks which have been mentioned are the immediate causes of the slow increase of population, and that these checks result principally from an insufficiency of subsistence, will be evident from the comparatively rapid increase which has invariably taken place, whenever, by some sudden enlargement in the means of subsistence, these checks have in any considerable degree been removed.
It has been universally remarked that all new colonies settled in healthy countries, where room and food were abundant, have constantly made a rapid progress in population. Many of the colonies from ancient Greece, in the course of one or two centuries, appear to have rivalled, and even surpassed, their mother cities. Syracuse and Agrigentum in Sicily, Tarentum and Locri in Italy, Ephesus and Miletus in Lesser Asia, were, by all accounts, at least equal to any of the cities of ancient Greece. All these colonies had established themselves in countries inhabited by savage and barbarous nations, which easily gave place to the new settlers, who had of course plenty of good land. It is calculated that the Israelites, though they increased very slowly while they were wandering in the land of Canaan, on settling in a fertile district of Egypt, doubled their numbers every fifteen years during the whole period of their stay.
*68 But not to dwell on remote instances, the European settlements in America bear ample testimony to the truth of a remark, that has never I believe been doubted. Plenty of rich land to be had for little or nothing, is so powerful a cause of population, as generally to overcome all obstacles.
No settlements could easily have been worse managed than those of Spain, in Mexico, Peru, and Quito. The tyranny, superstition, and vices of the mother country were introduced in ample quantities among her children. Exorbitant taxes were exacted by the crown; the most arbitrary restrictions were imposed on their trade; and the governors were not behind hand in rapacity and extortion for themselves as well as their masters. Yet under all these difficulties, the colonies made a quick progress in population. The city of Quito, which was but a hamlet of Indians, is represented by Ulloa as containing fifty or sixty thousand inhabitants above fifty years ago.
*69 Lima, which was founded since the conquest, is mentioned by the same author as equally or more populous before the fatal earthquake in 1746. Mexico is said to contain a hundred thousand inhabitants; which, notwithstanding the exaggerations of the Spanish writers, is supposed to be five times greater than what it contained in the time of Montezuma.
*70
In the Portuguese colony of Brazil, governed with almost equal tyranny, there were supposed to be, above thirty years ago, six hundred thousand inhabitants of European extraction.
*71
The Dutch and French colonies, though under the government of exclusive companies of merchants, still persisted in thriving under every disadvantage.
*72
But the English North-American colonies, now the powerful people of the United States of America, far outstripped all the others in the progress of their population. To the quantity of rich land which they possessed in common with the Spanish and Portuguese colonies, they added a greater degree of liberty of liberty and equality. Though not without some restrictions on their foreign commerce, they were allowed the liberty of managing their own internal affairs. The political institutions which prevailed were favourable to the alienation and division of property. Lands which were not cultivated by the proprietor within a limited time, were declared grantable to any other person. In Pennsylvania there was no right of primogeniture; and in the provinces of New England, the eldest son had only a double share. There were no tithes in any of the States, and scarcely any taxes.
And on account of the extreme cheapness of good land, and a situation favourable to the exportation of grain, a capital could not be more advantageously employed than in agriculture; which, at the same time that it affords the greatest quantity of healthy work, supplies the most valuable produce to the society.
The consequence of these favourable circumstances united, was a rapidity of increase almost without parallel in history. Throughout all the northern provinces the population was found to double itself in 25 years. The original number of persons which had settled in the four provinces of New England in 1643, was 21,200. Afterwards it was calculated that more left them than went to them. In the year 1760 they were increased to half a million. They had, therefore, all along doubled their number in 25 years. In New Jersey the period of doubling appeared to be 22 years, and in Rhode Island still less. In the back settlements, where the inhabitants applied themselves solely to agriculture, and luxury was not known, they were supposed to double their number in fifteen years. Along the sea-coast, which would naturally be first inhabited, the period of doubling was about 35 years, and in some of the maritime towns the population was absolutely at a stand.
*73 From the late census made in America, it appears that, taking all the States together, they have still continued to double their numbers within 25 years;
*74 and as the whole population is now so great as not to be materially affected by the emigrations from Europe, and as it is known that, in some of the towns and districts near the sea-coast, the progress of population has been comparatively slow; it is evident, that in the interior of the country in general, the period of doubling from procreation only must have been considerably less than 25 years.
The population of the United States of America, according to the fourth census, in 1820, was 7,861,710. We have no reason to believe that Great Britain is less populous at present, for the emigration of the small parent stock which produced these numbers. On the contrary, a certain degree of emigration is known to be favourable to the population of the mother country. It has been particularly remarked that the two Spanish provinces, from which the greatest number of people emigrated to America, became in consequence more populous.
Whatever was the original number of British emigrants which increased so fast in North America, let us ask, Why does not an equal number produce an equal increase in the same time in Great Britain? The obvious reason to be assigned is the want of food; and that this want is the most efficient cause of the three immediate checks to population, which have been observed to prevail in all societies; is evident from the rapidity with which even old states recover the desolations of war, pestilence, famine, and the convulsions of nature. They are then for a short time placed a little in the situation of new colonies; and the effect is always answerable to what might be expected. If the industry of the inhabitants be not destroyed, subsistence will soon increase beyond the wants of the reduced numbers; and the invariable consequence will be, that population, which before perhaps was nearly stationary, will begin immediately to increase, and will continue its progress till the former population is recovered.
The fertile province of Flanders, which has been so often the seat of the most destructive wars, after a respite of a few years has always appeared as rich and populous as ever. The undiminished population of France, which has before been noticed, is an instance very strongly in point. The tables of Sussmilch afford continual proofs of a very rapid increase after great mortalities; and the
table for Prussia and Lithuania, which I have inserted,
*75 is particularly striking in this respect. The effects of the dreadful plague in London, in 1666, were not perceptible 15 or 20 years afterwards. It may even be doubted whether Turkey and Egypt are upon an average much less populous for the plagues which periodically lay them waste. If the number of people which they contain be considerably less now than formerly, it is rather to be attributed to the tyranny and oppression of the governments under which they groan, and the consequent discouragements to agriculture, than to the losses which they sustain by the plague. The traces of the most destructive famines in China, Indostan, Egypt, and other countries, are by all accounts very soon obliterated; and the most tremendous convulsions of nature, such as volcanic eruptions and earthquakes, if they do not happen so frequently as to drive away the inhabitants or destroy their spirit of industry, have been found to produce but a trifling effect on the average population of any state.
It has appeared from the registers of different countries, which have already been produced, that the progress of their population is checked by the periodical, though irregular, returns of plagues and sickly seasons. Dr. Short, in his curious researches into bills of mortality, often uses the expression—”terrible correctives of the redundance of mankind;”
*76 and in a table of all the plagues, pestilences and famines, of which he could collect accounts, shews the constancy and universality of their operation.
The epidemical years in his table, or the years in which the plague or some great and wasting epidemic prevailed, (for smaller sickly seasons seem not to be included;) are 431,
*77 of which 32 were before the Christian æra.
*78 If we divide therefore the years of the present æra by 399, it will appear, that the periodical returns of such epidemics, to some countries that we are acquainted with, have been on an average only at the interval of about 4½ years.
Of the 254 great famines and dearths enumerated in the table, 15 were before the Christian æra,
*79 beginning with that which occurred in Palestine, in the time of Abraham. If, subtracting these 15, we divide the years of the present æra by the remainder, it will appear that the average interval between the visits of this dreadful scourge has been only about 7½ years.
How far these “terrible correctives to the redundance of mankind” have been occasioned by the too rapid increase of population, is a point which it would be very difficult to determine with any degree of precision. The causes of most of our diseases appear to us to be so mysterious, and probably are really so various, that it would be rashness to lay too much stress on any single one; but it will not perhaps be too much to say, that
among these causes we ought certainly to rank crowded houses and insufficient or unwholesome food, which are the natural consequences of an increase of population faster than the accommodations of a country with respect to habitations and food will allow.
Almost all the histories of epidemics, which we possess, tend to confirm this supposition, by describing them in general as making their principal ravages among the lower classes of people. In Dr. Short’s tables this circumstance is frequently mentioned;
*80 and it further appears that a very considerable proportion of the epidemic years either followed or were accompanied by seasons of dearth and bad food.
*81 In other places he also mentions great plagues as diminishing particularly the numbers of the lower or servile sort of people;
*82 and in speaking of different diseases he observes that those which are occasioned by bad and unwholesome food generally last the longest.
*83
We know from constant experience, that fevers are generated in our jails, our manufactories, our crowded workhouses and in the narrow and close streets of our large towns; all which situations appear to be similar in their effects to squalid poverty; and we cannot doubt that causes of this kind, aggravated in degree, contributed to the production and prevalence of those great and wasting plagues formerly so common in Europe, but which now, from the mitigation of these causes, are every where considerably abated, and in many places appear to be completely extirpated.
Of the other great scourge of mankind, famine, it may be observed that it is not in the nature of things, that the increase of population should absolutely produce one. This increase, though rapid, is necessarily gradual; and as the human frame cannot be supported, even for a very short time, without food, it is evident, that no more human beings can grow up than there is provision to maintain. But though the principle of population cannot absolutely produce a famine, it prepares the way for one; and by frequently obliging the lower classes of people to subsist nearly on the smallest quantity of food that will support life, turns even a slight deficiency from the failure of the seasons into a severe dearth; and may be fairly said, therefore, to be one of the principal causes of famine. Among the signs of an approaching dearth, Dr. Short mentions one or more years of luxuriant crops together;
*84 and this observation is probably just, as we know that the general effect of years of cheapness and abundance is to dispose a great number of persons to marry; and under such circumstances the return to a year merely of an average crop might produce a scarcity.
The small-pox, which may be considered as the most prevalent and fatal epidemic in Europe, is of all others, perhaps, the most difficult to account for, though the periods of its returns are in many places regular.
*85 Dr. Short observes, that from the histories of this disorder it seems to have very little dependence upon the past or present constitution of the weather or seasons, and that it appears epidemically at all times and in all states of the air, though not so frequently in a hard frost. We know of no instances, I believe, of its being clearly generated under any circumstances of situation. I do not mean therefore to insinuate that poverty and crowded houses ever absolutely produced it; but I may be allowed to remark, that in those places where its returns are regular, and its ravages among children, particularly among those of the lower class, are considerable, it necessarily follows that these circumstances, in a greater degree than usual, must always precede and accompany its appearance; that is, from the time of its last visit, the average number of children will be increasing, the people will, in consequence, be growing poorer, and the houses will be more crowded till another visit removes this superabundant population.
In all these cases, how little soever force we maybe disposed to attribute to the effects of the principle of population in the actual production of disorders, we cannot avoid allowing their force as predisposing causes to the reception of contagion, and as giving very great additional force to the extensiveness and fatality of its ravages.
It is observed by Dr. Short that a severe mortal epidemic is generally succeeded by an uncommon healthiness, from the late distemper having carried off most of the declining and worn out constitutions.
*86 It is probable, also, that another cause of it may be the greater plenty of room and food, and the consequently meliorated condition of the lower classes of the people. Sometimes, according to Dr. Short, a very fruitful year is followed by a very mortal and sickly one, and mortal ones often succeeded by very fruitful, as if Nature sought either to prevent or quickly repair the loss by death. In general the next year after sickly and mortal ones is prolific in proportion to the breeders left.
*87
This last effect we have seen most strikingly exemplified in the
table for Prussia and Lithuania.*88 And from this and other tables of Sussmilch, it also appears that, when the increasing produce of a country and the increasing demand for labour, so far meliorate the condition of the labourer as greatly to encourage marriage, the custom of early marriages is generally continued, till the population has gone beyond the increased produce, and sickly seasons appear to be the natural and necessary consequence. The continental registers exhibit many instances of rapid increase, interrupted in this manner by mortal diseases; and the inference seems to be, that those countries where subsistence is increasing sufficiently to encourage population, but not to answer all its demands, will be more subject to periodical epidemics, than those where the increase of population is more nearly accommodated to the average produce.
The converse of this will of course be true. In those countries which are subject to periodical sicknesses, the increase of population, or the excess of births above the deaths, will be greater in the intervals of these periods than is usual in countries not so much subject to these diseases. If Turkey and Egypt have been nearly stationary in their average population for the last century, in the intervals of their periodical plagues, the births must have exceeded the deaths in a much greater proportion than in such countries as France and England.
It is for these reasons that no estimates of future population or depopulation, formed from any existing rate of increase or decrease, can be depended upon. Sir William Petty calculated that in the year 1800 the city of London would contain 5,359,000
*89 inhabitants, instead of which it does not now contain a fifth part of that number. Mr. Eaton has lately prophesied the extinction of the population of the Turkish empire in another century,
*90 an event which will certainly fail of taking place. If America were to continue increasing at the same rate as at present for the next 150 years, her population would exceed the population of China; but though prophecies are dangerous, I will venture to say that such an increase will not take place in that time, though it may perhaps in five or six hundred years.
Europe was without doubt formerly more subject to plagues and wasting epidemics than at present; and this will account, in a great measure, for the greater proportion of births to deaths in former times, mentioned by many authors; as it has always been a common practice to estimate these proportions from too short periods, and generally to reject the years of plague as accidental.
The average proportion of births to deaths in England during the last century may be considered as about 12 to 10, or 120 to 100. The proportion in France for ten years, ending in 1780, was about 115 to 100.
*91 Though these proportions undoubtedly varied at different periods during the century, yet we have reason to think that they did not vary in any very considerable degree; and it will appear therefore, that the population of France and England had accommodated itself more nearly to the average produce of each country than many other states. The operation of the preventive check—wars—the silent though certain destruction of life in large towns and manufactories—and the close habitations and insufficient food of many of the poor—prevent population from outrunning the means of subsistence; and, if I may use an expression which certainly at first appears strange, supersede the necessity of great and ravaging epidemics to destroy what is redundant. If a wasting plague were to sweep off two millions in England, and six millions in France, it cannot be doubted that, after the inhabitants had recovered from the dreadful shock, the proportion of births to deaths would rise much above the usual average in either country during the last century.
In New Jersey the proportion of births to deaths, on an average of 7 years, ending with 1743, was 300 to 100. In France and England the average proportion cannot be reckoned at more than 120 to 100. Great and astonishing as this difference is, we ought not to be so wonder-struck at it, as to attribute it to the miraculous interposition of Heaven. The causes of it are not remote, latent and mysterious, but near us, round about us, and open to the investigation of every inquiring mind. It accords with the most liberal spirit of philosophy to believe that no stone can fall, or plant rise, without the immediate agency of divine power. But we know from experience, that these operations of what we call nature have been conducted almost invariably according to fixed laws. And since the world began, the causes of population and depopulation have been probably as constant as any of the laws of nature with which we are acquainted.
The passion between the sexes has appeared in every age to be so nearly the same, that it may always be considered, in algebraic language, as a given quantity. The great law of necessity, which prevents population from increasing in any country beyond the food which it can either produce or acquire, is a law so open to our view, so obvious and evident to our understandings, that we cannot for a moment doubt it. The different modes which nature takes to repress a redundant population, do not indeed appear to us so certain and regular; but though we cannot always predict the mode, we may with certainty predict the fact. If the proportion of the births to the deaths for a few years indicates an increase of numbers much beyond the proportional increased or acquired food of the country, we may be perfectly certain that, unless an emigration take place, the deaths will shortly exceed the births, and that the increase which had been observed for a few years cannot be the real average increase of the population of the country. If there were no other depopulating causes, and if the preventive check did not operate very strongly, every country would without doubt be subject to periodical plagues and famines.
The only true criterion of a real and permanent increase in the population of any country, is the increase of the means of subsistence. But even this criterion is subject to some slight variations, which however are completely open to our observation. In some countries population seems to have been forced; that is, the people have been habituated by degrees to live almost upon the smallest possible quantity of food. There must have been periods in such countries, when population increased permanently without an increase in the means of subsistence. China, India and the countries possessed by the Bedoween Arabs, as we have seen in the former part of this work, appear to answer to this description. The average produce of these countries seems to be but barely sufficient to support the lives of the inhabitants, and of course any deficiency from the badness of the seasons must be fatal. Nations in this state must necessarily be subject to famines.
In America, where the reward of labour is at present so liberal, the lower classes might retrench very considerably in a year of scarcity, without materially distressing themselves. A famine therefore seems to be almost impossible. It may be expected, that in the progress of the population of America, the labourers will in time be much less liberally rewarded. The numbers will in this case permanently increase, without a proportional increase in the means of subsistence.
In the different countries of Europe there must be some variations in the proportion of the number of inhabitants, and the quantity of food consumed, arising from the different habits of living which prevail in each state. The labourers in the south of England are so accustomed to eat fine wheaten bread, that they will suffer themselves to be half starved before they will submit to live like the Scotch peasants.
They might perhaps, in time, by the constant operation of the hard law of necessity, be reduced to live even like the lower classes of the Chinese, and the country would then with the same quantity of food support a greater population. But to effect this must always be a difficult, and every friend to humanity will hope, an abortive attempt.
I have mentioned some cases where population may permanently increase without a proportional increase in the means of subsistence. But it is evident that the variation in different states between the food and the numbers supported by it is restricted to a limit beyond which it cannot pass. In every country, the population of which is not absolutely decreasing, the food must be necessarily sufficient to support and continue the race of labourers.
Other circumstances being the same, it may be affirmed that countries are populous according to the quantity of human food which they produce or can acquire; and happy, according to the liberality with which this food is divided, or the quantity which a day’s labour will purchase. Corn countries are more populous than pasture countries, and rice countries more populous than corn countries. But their happiness does not depend either upon their being thinly or fully inhabited, upon their poverty or their riches, their youth or their age; but on the proportion which the population and the food bear to each other.
This proportion is generally the most favourable in new colonies, where the knowledge and industry of an old state operate on the fertile unappropriated land of a new one. In other cases the youth or the age of a state is not, in this respect, of great importance. It is probable that the food of Great Britain is divided in more liberal shares to her inhabitants at the present period, than it was two thousand, three thousand, or four thousand years ago. And it has appeared that the poor and thinly-inhabited tracts of the Scotch Highlands are more distressed by a redundant population than the most populous parts of Europe.
If a country were never to be overrun by a people more advanced in arts, but left to its own natural progress in civilization; from the time that its produce might be considered as an unit, to the time that it might be considered as a million, during the lapse of many thousand years, there might not be a single period when the mass of the people could be said to be free from distress, either directly or indirectly, for want of food. In every state in Europe, since we have first had accounts of it, millions and millions of human existences have been repressed from this simple cause, though perhaps in some of these states an absolute famine may never have been known.
Must it not then be acknowledged by an attentive examiner of the histories of mankind, that, in every age and in every state in which man has existed or does now exist,
The increase of population is necessarily limited by the means of subsistence:
Population invariably increases when the means of subsistence increase,
*92 unless prevented by powerful and obvious checks:
These checks, and the checks which keep the population down to the level of the means of subsistence, are moral restraint, vice, and misery?
In comparing the state of society which has been considered in this second book with that which formed the subject of the first, I think it appears that in modern Europe the positive checks to population prevail less, and the preventive checks more than in past times, and in the more uncivilized parts of the world.
War, the predominant check to the population of savage nations, has certainly abated, even including the late unhappy revolutionary contests; and since the prevalence of a greater degree of personal cleanliness, of better modes of clearing and building towns, and of a more equable distribution of the products of the soil from improving knowledge in political economy, plagues, violent diseases and famines have been certainly mitigated, and have become less frequent.
With regard to the preventive check to population, though it must be acknowledged that that branch of it which comes under the head of moral restraint,
*93 does not at present prevail much among the male part of society; yet I am strongly disposed to believe that it prevails more than in those states which were first considered; and it can scarcely be doubted that in modern Europe a much larger proportion of women pass a considerable part of their lives in the exercise of this virtue, than in past times and among uncivilized nations. But however this may be, if we consider only the general term which implies principally a delay of the marriage union from prudential considerations, without reference to consequences, it may be considered in this light as the most powerful of the checks, which in modern Europe keep down the population to the level of the means of subsistence.
greater and to the annual births
less than the true proportion marrying out of any given number born. This proportion generally lies between the other two proportions, but always nearest the first.” In these observations I entirely agree with him, but in a note to this passage he appears to me to fall into an error. He says, that if the prolifickness of marriages be increased (the
probabilities of life and
the encouragement to marriage remaining the same) both the annual births and burials would increase in proportion to the annual weddings. That the proportion of annual births would increase is certainly true; and I here acknowledge my error in differing from Dr. Price on this point in my last edition; but I still think that the proportion of burials to weddings would not necessarily increase under the circumstances here supposed.
The reason why the proportion of births to weddings increases is, that the births occurring in the order of nature considerably prior to the marriages which result from them, their increase will affect the register of births much more than the contemporary register of marriages. But the same reason by no means holds with regard to the deaths, the average age of which is generally later than the age of marriage. And in this case, after the first interval between birth and marriage, the permanent effect would be, that the register of marriages would be more affected by the increase of births than the contemporary register of deaths; and consequently the proportion of the burials to the weddings would be rather decreased than increased. From not attending to the circumstance that the average age of marriage may often be considerably earlier than the mean age of death, the general conclusion also which Dr. Price draws in this note does not appear to be strictly correct.
In America the expectation of life would, upon the same principles, be only 32½, (births, 1/20, deaths, 1/45, mean 1/32 ½); and supposing the age of marriage 22½, the difference would be 10.
Since this was written, I have seen reason to believe, from some calculations of Mr. Milne, actuary to the Sun Life Assurance Society, that Dr. Price’s mode of estimating the expectation of life in countries that are increasing is by no means correct, and that the true expectation of life in such countries lies very much nearer the proportion of the annual mortality, than a mean between the annual mortality and the proportion of annual births; but I retain the mean proportion in the calculations of this chapter, because I find that this mean expresses more nearly the period when the deaths will equal the present births, or accord with the present marriages, than the distance of the expectation of life. In a progressive country, where the annual births considerably exceed the annual deaths, the period at which the annual deaths will equal the present annual births is less distant than the expectation of life.
vol. ii. b. iv. ch. viii. p. 363.