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

Book Cover

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.

On the Fruitfulness of Marriages.

Book II, Chapter XI

It would be extremely desirable to be able to deduce from the registers of births, deaths and marriages in different countries, and the actual population with the rate of increase, the real prolifickness of marriages, and the true proportion of the born which lives to marry. Perhaps the problem may not be capable of an accurate solution; but we shall make some approximation towards it, and be able to account for some of the difficulties which appear in many registers, if we attend to the following considerations.

It should be premised, however, that in the registers of most countries there is reason to believe that the omissions in the births and deaths are greater than in the marriages; and consequently, that the proportion of marriages is almost always given too great. In the enumerations which have lately taken place in this country, while it is supposed with reason that the registry of marriages is nearly correct, it is known with certainty that there are very great omissions in the births and deaths; and it is probable that similar omissions, though not perhaps to the same extent, prevail in other countries.

If we suppose a country where the population is stationary, where there are no emigrations, immigrations, or illegitimate children, and where the registers of births deaths and marriages are accurate, and continue always in the same proportion to the population, then the proportion of the annual births to the annual marriages will express the number of children born to each marriage, including second and third marriages, and when corrected for second and third marriages, it will also express the proportion of the born which lives to marry, once or oftener; while the annual mortality will accurately express the expectation of life.

But if the population be either increasing or decreasing, and the births, deaths and marriages increasing or decreasing in the same ratio, such a movement will necessarily disturb all the proportions, because the events which are contemporary in the registers are not contemporary in the order of nature, and an increase or decrease must have been taking place in the interval.

In the first place, the births of any year cannot in the order of nature have come from the contemporary marriages, but must have been derived principally from the marriages of preceding years.

To form a judgment then of the prolifickness of marriages taken as they occur, including second and third marriages, let us cut off a certain period of the registers of any country (30 years for instance) and inquire what is the number of births which has been produced by all the marriages included in the period cut off. It is evident, that with the marriages at the beginning of the period will be arranged a number of births proceeding from marriages not included in the period; and at the end, a number of births produced by the marriages included in the period will be found arranged with the marriages of a succeeding period. Now, if we could subtract the former number, and add the latter, we should obtain exactly all the births produced by the marriages of the period, and of course the real prolifickness of those marriages. If the population be stationary, the number of births to be added would exactly equal the number to be subtracted, and the proportion of births to marriages, as found in the registers, would exactly represent the real prolifickness of marriages. But if the population be either increasing or decreasing, the number to be added would never be equal to the number to be subtracted, and the proportion of births to marriages in the registers would never truly represent the prolifickness of marriages. In an increasing population the number to be added would evidently be greater than the number to be subtracted, and of course the proportion of births to marriages as found in the registers would always be too small to represent the true prolifickness of marriages. And the contrary effect would take place in a decreasing population. The question therefore is, what we are to add, and what to subtract, when the births and deaths are not equal.

The average proportion of births to marriages in Europe is about 4 to 1. Let us suppose, for the sake of illustration, that each marriage yields four children, one every other year.
*42 In this case it is evident that, wherever we begin the period in the registers, the marriages of the preceding eight years will only have produced half of their births, and the other half will be arranged with the marriages included in the period, and ought to be subtracted from them. In the same spanner the marriages of the last eight years of the period will only have produced half of their births, and the other half ought to be added. But half of the births of any eight years may be considered as nearly equal to all the births of the succeeding 3¾ years. In instances of the most rapid increase it will rather exceed the births of the next 3½ years, and, in cases of slow increase, approach towards the births of the next 4 years. The mean therefore may be taken at 3¾ years.
*43 Consequently, if we subtract the births of the first 3¾ years of the period, and add the births of the 3¾ years subsequent to the period, we shall have a number of births nearly equal to the births produced by all the marriages included in the period, and of course the prolifickness of these marriages. But if the population of a country be increasing regularly, and the births, deaths and marriages continue always to bear the same proportion to each other, and to the whole population, it is evident that all the births of any period will bear the same proportion to all the births of any other period of the same extent, taken a certain number of years later, as the births of any single year, or an average of five years, to the births of a single year, or an average of five years, taken the same number of years later; and the same will be true with regard to the marriages. And consequently, to estimate the prolifickness of marriages, we have only to compare the marriages of the present year, or average of five years, with the births of a subsequent year, or average of five years, taken 3¾ years later.

We have supposed, in the present instance, that each marriage yields four births; but the average proportion of births to marriages in Europe is 4 to 1;
*44 and as the population of Europe is known to be increasing at present, the prolifickness of marriages must be greater than 4. If, allowing for this circumstance, we take the distance of 4 years instead of 3¾ years, we may not be far from the truth. And though undoubtedly the period will differ in different countries, yet it will not differ so much as we might at first imagine; because in countries where the marriages are more prolific, the births generally follow at shorter intervals, and where they are less prolific, at longer intervals; and with different degrees of prolifickness, the length of the period might still remain the same.
*45

It will follow from these observations, that the more rapid is the increase of population, the more will the real prolifickness of marriages exceed the proportion of births to marriages in the registers.

The rule which has been here laid down attempts to estimate the prolifickness of marriages taken as they occur; but this prolifickness should be carefully distinguished from the prolifickness of first marriages or of married women, and still more from the natural prolifickness of women in general taken at the most favourable age. It is probable, that the natural prolifickness of women is nearly the same in most parts of the world; but the prolifickness of marriages is liable to be affected by a variety of circumstances peculiar to each country, and particularly by the number of late marriages. In all countries the second and third marriages alone form a most important consideration, and materially influence the average proportions. According to Sussmilch, in all Pomerania, from 1748 to 1756 both included, the number of persons who married were 56,956, and of these 10,586 were widows and widowers.
*46 According to Busching, in Prussia and Silesia, for the year 1781, out of 29,308 persons who married, 4,841, were widows and widowers,
*47 and consequently the proportion of marriages will be given full one sixth too much. In estimating the prolifickness of married women, the number of illegitimate births
*48 would tend, though in a slight degree, to counterbalance the overplus of marriages; and as it is found that the number of widowers who marry again, is greater than the number of widows, the whole of the correction should not on this account be applied; but in estimating the proportion of the born which lives to marry from a comparison of the marriages with the births or deaths, which is what we are now about to proceed to, the whole of this correction is always necessary.

It is obvious, in the second place, that the marriages of any year can never be contemporary with the births from which they have resulted, but must always be at such a distance from them as is equal to the average age of marriage. If the population be increasing, the marriages of the present year have resulted from a smaller number of births than the births of the present year, and of course the marriages, compared with the contemporary births, will always be too few to represent the proportion of the born which lives to marry; and the contrary will take place if the population be decreasing; and, to find this proportion, we must compare the marriages of any year with the births of a previous year at the distance of the average age of marriage.

But on account of the distance of this period, it may be often more convenient, though it is not essentially so correct, to compare the marriages with the contemporary deaths. The average age of marriage will almost always be much nearer to the average age of death than marriage is to birth; and consequently the annual marriages compared with the contemporary annual deaths will much more nearly represent the true proportion of the born living to marry, than the marriages compared with the births.
*49 The marriages compared with the births, after a proper allowance has been made for second and third marriages, can never represent the true proportion of the born living to marry, unless when the population is absolutely stationary; but although the population be increasing or decreasing, the average age of marriage may still be equal to the average of death; and in this case the marriages in the registers compared with the contemporary deaths, (after the correction for second or third marriages, ) will nearly represent the true proportion of the born living to marry.
*50 Generally, however, when an increase of population is going forwards, the average age of marriage is less than the average of death, and then the proportion of marriages, compared with the contemporary deaths, will be too great to represent the true proportion of the born living to marry; and, to find this proportion, we must compare the marriages of any particular year with the deaths of a subsequent year at such a distance from it in the registers, as is equal to the difference between the average age of marriage and the average age of death.

There is no necessary connection between the average age of marriage and the average age of death. In a country, the resources of which will allow of a rapid increase of population, the expectation of life or the average age of death may be extremely high, and yet the age of marriage be very early; and the marriages then, compared with the contemporary deaths in the registers, would (even after the correction for second and third marriages) be very much too great to represent the true proportion of the born living to marry. In such a country we might suppose the average age of death to be 40, and the age of marriage only 20; and in this case, which however would be a rare one, the distance between marriage and death would be the same as between birth and marriage.

If we apply these observations to registers in general, though we shall seldom be able to obtain the true proportion of the born living to marry on account of the proportions of births, deaths, and marriages not remaining the same, and of our not knowing the average age of marriage, yet we may draw many useful inferences from the information which they contain, and reconcile some apparent contradictions; and it will generally be found that, in those countries where the marriages bear a very large proportion to the deaths, we shall see reason to believe that the age of marriage is much earlier than the average age of death.

In the Russian table for the year 1799, produced by Mr. Tooke, and referred to,
p. 317, the proportion of marriages to deaths appeared to be as 100 to 210. When corrected for second and third marriages, by subtracting one sixth from the marriages, it will be as 100 to 252. From which it would seem to follow, that out of 252 births 200 of them had lived to marry; but we cannot conceive any country to be so healthy as that 200 out of 252 should live to marry. If however we suppose, what seems to be probable, that the age of marriage in Russia is 15 years earlier than the expectation of life or the average age of death, then, in order to find the proportion which lives to marry, we must compare the marriages of the present year with the deaths 15 years later. Supposing the births to deaths to be (as stated
p. 317) 183 to 100, and the mortality 1 in 50, the yearly increase will be about 1/60 of the population; and consequently in 15 years the deaths will have increased a little above .28; and the result will be, that the marriages, compared with the deaths 15 years later will be as 100 to 322. Out of 322 births it will appear that 200 live to marry, which, from the known healthiness of children in Russia, and the early age of marriage, is a possible proportion. The proportion of marriages to births, being as 100 to 385, the prolifickness of marriages, according to the rule laid down, will be as 100 to 411; or each marriage will on an average, including second and third marriages, produce 4.11 births.

The lists given in the earlier part of the chapter on Russia are probably not correct. It is suspected with reason, that there are considerable omissions both in the births and deaths, but particularly in the deaths; and consequently the proportion of marriages is given too great. There may also be a further reason for this large proportion of marriages in Russia. The Empress Catherine, in her instructions for a new code of laws, notices a custom prevalent among the peasants, of parents obliging their sons, while actually children, to marry full-grown women, in order to save the expense of buying female slaves. These women, it is said, generally become the mistresses of the father; and the custom is particularly reprobated by the Empress as prejudicial to population. This practice would naturally occasion a more than usual number of second and third marriages, and of course more than usually increase the proportion of marriages to births in the registers.

In the Transactions of the Society at Philadelphia (vol. iii. No. vii. p. 25,) there is a paper by Mr. Barton, entitled
Observations on the Probability of Life in the United States, in which it appears, that the proportion of marriages to births is as 1 to 4½. He mentions indeed 6½, but his numbers give only 4½. As however this proportion was taken principally from towns, it is probable that the births are given too low; and I think we may very safely take as many as five for the average of towns and country. According to the same authority the mortality is about 1 in 45; and if the population doubles every 25 years, the births would be about 1 in 20. The proportion of marriages to deaths would on these suppositions be as 1 to 2 2/9; and, corrected for second and third marriages, as 1 to 2.7 nearly. But we cannot suppose, that out of 27 births 20 should live to marry. If however the age of marriage be ten years earlier than the mean age of death, which is highly probable, we must compare the marriages of the present year with the deaths ten years later, in order to obtain the true proportion of the born which lives to marry. According to the progress of population here stated, the increase of the deaths in ten years would be a little above .3, and the result will be, that 200 out of 351, or about 20 out of 35, instead of twenty out of 27, will live to marry.
*51 The marriages compared with the births 4 years later, according to the rule laid down, will in this case give 5.58 for the prolifickness of marriages. The calculations of Mr. Barton respecting the age to which half of the born live, cannot possibly be applicable to America in general. The registers, on which they are founded, are taken from Philidelphia and one or two small towns and villages, which do not appear to be so healthy as the moderate towns of Europe, and therefore can form no criterion for the country in general.

In England the average proportion of marriages to births appears of late years to have been about 100 to 350. If we add 1/7 to the births instead of 1/6, which in the chapter on
the Checks to Population in England, I conjectured might be nearly the amount of the omissions in the births and deaths, this will allow for the circumstance of illegitimate births; and the marriages will then be to the births as 1 to 4, to the deaths as 1 to 3.
*52 Corrected for second and third marriages, the proportion of marriages to deaths will be as 1 to 3.6. Supposing the age of marriage in England about 7 years earlier than the mean age of death, the increase in these 7 years, according to the present progress of population of 1/120 yearly, would be .06, and the proportion living to marry would be 200 out of 381, or rather more than half.
*53 The marriages compared with the births four years later will give 4.136 for the prolifickness of marriages.

These instances will be sufficient to shew the mode of applying the rules which have been given, in order to form a judgment, from registers, of the prolifickness of marriages, and the proportion of the born which lives to marry; but it must still be remembered that they are only approximations, and intended rather to explain apparent difficulties, than to obtain results which can be depended upon as correct.

It will be observed how very important the correction for second and third marriages is. Supposing each marriage to yield four births, and the births and deaths to be equal, it would at first appear necessary that, in order to produce this effect, exactly half of the born should live to marry; but if, on account of the second and third marriages, we subtract 1/6 from the marriages, and then compare them with the deaths, the proportion will be as 1 to 4 4/5; and it will appear that, instead of one half, it will only be necessary that 2 children out of 4 4/5 should live to marry. Upon the same principle, if the births were to the marriages as 4 to 1, and exactly half of the born live to marry, it might be supposed at first that the population would be stationary; but if we subtract 1/6 from the marriages; and then take the proportion of deaths to marriages as 4 to 1, we shall find that the deaths in the registers, compared with the marriages, would only be as 3 1/3 to 1; and the births would be to the deaths as 4 to 3 1/3, or 12 to 10, which is a tolerably fast rate of increase.

It should be further observed, that as a much greater number of widowers marry again than of widows, if we wish to know the proportion of males which lives to marry, we must subtract full 1/5 from the marriages instead of 1/6.
*54 According to this correction, if each marriage yielded 4 births, it would only be necessary that two male children out of 5 should live to marry in order to keep up the population; and if each marriage yielded 5 births, less than one third would be necessary for this purpose; and so for the other calculations. In estimating the proportion of males living to marry, some allowance ought also to be made for the greater proportion of male births.

Three causes appear to operate in producing an excess of the births above the deaths: 1. the prolifickness of marriages; 2. the proportion of the born which lives to marry; and 3. the earliness of these marriages compared with the expectation of life, or the shortness of a generation by marriage and birth, compared with the passing away of a generation by death. This latter cause Dr. Price seems to have omitted to consider. For though he very justly says that the rate of increase, supposing the prolific powers the same, depends upon the encouragement to marriage, and the expectation of a child just born; yet in explaining himself, he seems to consider an increase in the expectation of life, merely as it affects the increase of the number of persons who reach maturity and marry, and not as it affects, besides, the distance between the age of marriage and the age of death. But it is evident that, if there be any principle of increase, that is, if one marriage in the present generation yields more than one in the next, including second and third marriages, the quicker these generations are repeated, compared with the passing away of a generation by death, the more rapid will be the increase.

A favourable change in either of these three causes, the other two remaining the same, will clearly produce an effect upon population, and occasion a greater excess of the births above the deaths in the registers. With regard to the two first causes, though an increase in either of them will produce the same kind of effect on the proportion of births to deaths, yet their effects on the proportion of marriages to births will be in opposite directions. The greater is the prolifickness of marriages, the greater will be the proportion of births to marriages; and the greater is the number of the born which lives to be married, the less will be the proportion of births to marriages.
*55 Consequently, if within certain limits, the prolificness of marriages and the number of the born living to marry increase at the same time, the proportion of births to marriages in the registers may still remain unaltered. And this is the reason why the registers of different countries, with respect to births and marriages, are often found the same under very different rates of increase.

The proportion of births to marriages, indeed, forms no criterion whatever, by which to judge of the rate of increase. The population of a country may be stationary or declining with a proportion of 5 to 1, and may be increasing with some rapidity with a proportion of 4 to 1. But given the rate of increase, which may be obtained from other sources, it is clearly desirable to find in the registers a small rather than a large proportion of births to marriages; because the smaller this proportion is, the greater must be the proportion of the born which lives to marry, and of course the more healthy must be the country.

Crome
*56 observes that, when the marriages of a country yield less than 4 births, the population is in a very precarious state; and he estimates the prolifickness of marriages by the proportion of yearly births to marriages. If this observation were just, the population of many countries of Europe would be in a precarious state, as in many countries the proportion of births to marriages in the registers is rather below than above 4 to 1. It has been shown in what manner this proportion in the registers should be corrected, in order to make it a just representation of the prolifickness of marriages; and if a large part of the born live to marry, and the age of marriage be considerably earlier than the expectation of life, such a proportion in the registers is by no means inconsistent with a rapid increase. In Russia it has appeared that the proportion of births to marriages is less than 4 to 1; and yet its population increases faster than that of any other nation in Europe. In England the population increases more rapidly than in France; and yet in England the proportion of births to marriages, when allowance has been made for omissions, is about 4 to 1; in France 4 4/5 to 1. To occasion so rapid a progress as that which has taken place in America, it will indeed be necessary that all the causes of increase should be called into action; and if the prolifickness of marriages be very great, the proportion of births to marriages will certainly be above 4 to 1: but in all ordinary cases, where the whole power of procreation has not room to expand itself, it is surely better that the actual increase should arise from that degree of healthiness in the early stages of life which causes a great proportion of the born to live to maturity and to marry, than from a great degree of prolifickness accompanied by a great mortality. And consequently in all ordinary cases a proportion of births to marriages as 4, or less than 4, to 1 cannot be considered as an unfavourable sign.

It should be observed that it does not follow that the marriages of a country are early, or that the preventive check to population does not prevail, because the greater part of the born lives to marry. In such countries as Norway and Switzerland, where half of the born live to above 40, it is evident that, though rather more than half live to marry, a large portion of the people between the ages of 20 and 40 would be living in an unmarried state, and the preventive check would appear to prevail to a great degree. In England it is probable that half of the born live to above 35;
*57 and though rather more than half live to marry, the preventive check might prevail considerably (as we know it does), though not to the same extent as in Norway and Switzerland.

The preventive check is perhaps best measured by the smallness of the proportion of yearly births to the whole population. The proportion of yearly marriages to the population is only a just criterion in countries similarly circumstanced, but is incorrect where there is a difference in the prolifickness of marriages or in the proportion of the population under the age of puberty, and in the rate of increase. If all the marriages of a country, be they few or many, take place young, and be consequently prolific, it is evident that, to produce the same proportion of births, a smaller proportion of marriages will be necessary; or with the same proportion of marriages a greater proportion of births will be produced. This latter case seems to be applicable to France, where both the births and deaths are greater than in Sweden, though the proportion of marriages is nearly the same, or rather less. And when, in two countries compared, one of them has a much greater part of its population under the age of puberty than the other, it is evident that any general proportion of the yearly marriages to the whole population will not imply the same operation of the preventive check among those of a marriageable age.

It is, in part, the small proportion of the population under the age of puberty, as well as the influx of strangers, that occasions in towns a greater proportion of marriages than in the country, although there can be little doubt that the preventive check prevails most in towns. The converse of this will also be true; and consequently in such a country as America, where half of the population is under sixteen, the proportion of yearly marriages will not accurately express how little the preventive check really operates.

But on the supposition of nearly the same natural prolifickness in the women of most countries, the smallness of the proportion of births will generally indicate, with tolerable exactness, the degree in which the preventive check prevails, whether arising principally from late, and consequently unprolific, marriages, or from a large proportion of the population above the age of puberty dying unmarried.

That the reader may see at once the rate of increase, and the period of doubling, which would result from any observed proportion of births to deaths, and of these to the whole population, I subjoin two tables from Sussmilch, calculated by Euler, which I believe are very correct. The first is confined to the supposition of a mortality of 1 in 36, and therefore can only be applied to countries where such a mortality is known to take place. The other is general, depending solely upon the proportion which the excess of the births above the burials bears to the whole population, and therefore may be applied universally to all countries, whatever may be the degree of their mortality. I have now also (1825) added a third table as convenient on account of the custom of decennial enumerations in this and some other countries. It is calculated by the Rev. B. Bridge, of Peter House, Cambridge, and shows the rate of increase, or period of doubling, from the observed per-centage increase of any ten years, supposing such rate of increase to continue.

It will be observed that, when the proportion between the births and burials is given, the period of doubling will be shorter, the greater the mortality; because the births as well as deaths are increased by this supposition, and they both bear a greater proportion to the whole population than if the mortality were smaller, and there were a greater number of people in advanced life.

The mortality of Russia, according to Mr. Tooke, is 1 in 58, and the proportion of births 1 in 26. Allowing for the omissions in the burials, if we assume the mortality to be 1 in 52, then the births will be to the deaths as 2 to 1, and the proportion which the excess of births bears to the whole population will be 1/52.
*58 According to
Table II. the period of doubling will, in this case, be about 36 years. But if we were to keep the proportion of births to deaths as 2 to 1, and suppose a mortality of 1 in 36, as in
Table I., the excess of births above the burials would be 1/36 of the whole population, and the period of doubling would be only 25 years.

Book II, Chapter XI, Table I.

When in any country there are 103,000 persons living, and the mortality is 1 in 36.

If the proportion of deaths to births be as		Then the excess of the births will be	The proportion of the excess of the births, to the whole population, will be	And therefore the period of doubling will be
	11	277	1/360	250	years.
	12	555	1/180	125
	13	833	1/120	83	½
	14	1110	1/90	62	¾
	15	1388	1/72	50	¼
	16	1666	1/60	42
10:	17	1943	1/51	35	¾
	18	2221	1/45	31	2/3
	19	2499	1/40	28
	20	2777	1/36	25	3/10
	22	3332	1/30	21	1/6
	25	4165	1/24	17
	30	5554	1/18	12	4/5

Book II, Chapter XI, Table II.

The proportion of the excess of births above the deaths to the whole of the living.		Periods of doubling in years and ten thousandth parts.	The proportion of the excess of births above the deaths to the whole of the living.		Periods of doubling in years and ten thousandth parts.
	10	7.2722		110	76.5923
	11	7.9659		120	83.5230
	12	8.6595		130	90.4554
	13	9.3530		140	97.3868
1:	14	10.0465	1:	150	104.3183
	15	10.7400		160	111.2598
	16	111.2598		170	118.1813
	17	12.1266		180	125.1128
	18	12.8200		190	138.9757
	19	13.5133		200	138.9757

	21	14.9000		210	145.9072
	22	15.5932		220	152.8387
	23	16.2864		230	159.7702
	24	16.9797		240	166.7017
1:	25	17.6729	1:	250	173.6332
	26	18.3662		260	180.5647
	27	19.0594		270	187.4961
	28	19.7527		280	194.4275
	29	20.4458		290	201.3590
	30	21.1391		300	208.2905

	32	22.5255		310	215.2220
	34	23.9119		320	222.1535
	36	25.2983		330	229.0850
	38	26.6847		340	236.0164
1:	40	28.0711	1:	350	242.9479
	42	29.4574		360	249.8794
	44	30.8438		370	256.8109
	46	32.2302		380	263.7425
	48	43.6161		390	270.6740
	50	35.0029		400	277.6055

	55	38.4687		410	284.5370
	60	41.9345		420	291.4685
	65	45.4003		430	298.4000
	70	48.8661		440	305.3314
1:	75	52.3318	1:	450	312.2629
	80	55.7977		460	319.1943
	85	59.2634		470	326.1258
	90	62.7292		480	333.0573
	95	66.1950		490	339.9888
	100	69.6607		500	346.9202

			1:	1000	693.49.

Book II, Chapter XI, Table III.

I. Per centage increase in ten years.	II. Period of doubling.	I. Per centage increase in ten years.	II. Period of doubling.	I. Per centage increase in ten years.	II. Period of doubling.
1	696.60	16	46.70	30.5	26.03
1.5	465.55	16.5	45.38	31	25.67
2	350.02	17	44.14	31.5	25.31
2.5	280.70	17.5	42.98	32	24.96
3	234.49	18	41.87	32.5	24.63
3.5	201.48	18.5	40.83	33	24.30
4	176.73	19	39.84	33.5	23.99
4.5	157.47	19.5	38.91	34	23.68
5	142.06	20	38.01	34.5	23.38
5.5	129.46			35	23.09
6	118.95	20.5	37.17	35.5	22.81
6.5	110.06	21	36.36	36	22.54
7	102.44	21.5	35.59	36.5	22.27
7.5	95.84	22	34.85	37	22.01
8	90.06	22.5	34.15	37.5	21.76
8.5	84.96	23	33.48	38	21.52
9	80.43	23.5	32.83	38.5	21.28
9.5	76.37	24	32.22	39	21.04
10	72.72	24.5	31.63	39.5	20.82
		25	31.06	40	20.61
10.5	69.42	25.5	30.51
11	66.41	26	29.99	41	20.17
11.5	63.67	26.5	29.48	42	19.76
12	61.12	27	28.99	43	19.37
12.5	58.06	27.5	28.53	44	19.00
13	56.71	28	28.07	45	18.65
13.5	54.73	28.5	27.65	46	18.31
14	52.90	29	27.22	47	17.99
14.5	51.19	29.5	26.81	48	17.68
15	49.59	30	26.41	49	17.38
15.5	48.10			50	17.06

42.

In the statistical account of Scotland it is said, that the average distance between the children of the same family has been calculated to be about two years.

43.

According to the rate of increase which has lately been taking place in England (1802,) the period by calculation would be about 3¾ years.

44.

The true proportion will be greater, if, as before stated, there is reason to believe that in all registers the omissions in the births and deaths are more numerous than in the marriages.

45.

In places where there are many migrations of people, the calculations will of course be disturbed. In towns, particularly, where there is a frequent change of inhabitants, and where it often happens that the marriages of the people in the neighbouring country are celebrated, the inferences from the proportion of births to marriages are not to be depended on.

46.

Göttliche Ordnung, vol. i. tables, p. 98.

47.

Sussmilch, vol. iii. tables, p. 95.

48.

In France, before the revolution, the proportion of illegitimate births was 1/47 of the whole number. Probably it is less in this country.

49.

Dr. Price very justly says (Observ. on Revers. Pay. vol. i. p. 269. 4th. edit.) “that the general effect of an increase while it is going on in a country is to render the proportion of persons marrying annually, to the annual deaths
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.

50.

The reader will be aware that, as all the born must die, deaths, may in some cases be taken as synonymous with births. If we had the deaths registered of all the births which had taken place in a country during a certain period, distinguishing the married from the unmarried, it is evident that the number of those who died married, compared with the whole number of deaths, would accurately express the proportion of the births which had lived to marry.

51.

If the proportions mentioned by Mr. Barton be just, the expectation of life in America is considerably less than in Russia, which is the reason that I have taken only ten years for the difference between the age of marriage and the age of death, instead of fifteen years, as in Russia. According to the mode adopted by Dr. Price, (vol. i. p. 272,) of estimating the expectation of life in countries the population of which is increasing, this expectation in Russia would be about 38, (births 1/26, deaths 1/50, mean 1/38), and supposing the age of marriage to be 23, the difference would be 15.

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.

52.

This applies to the state of population before 1800.

53.

Births 1/30, deaths 1/40, mean 1/35; and on the supposition that the age of marriage is 28, the difference would be 7.

54.

Of 28,473 marriages in Pomerania, 5,964 of the men were widowers. Sussmilch, vol. i. tables, p. 98. And according to Busching, of 14,759 marriages in Prussia and Silesia, 3,071 of the men were widowers. Sussmilcb, vol iii. tables, p. 95. Muret calculates that 100 men generally marry 110 women. Mémoires par la Société Economique de Berne. Année 1766, premiere partie, page 30.

55.

Dr. Price himself has insisted strongly upon this, (vol. i. p. 270. 4th edit.) and yet he says (p. 275) that healthfulness and prolifickness are probably causes of increase seldom separated, and refers to registers of births and weddings as a proof of it. But though these causes may undoubtedly exist together, yet if Dr. Price’s reasoning be just, such co-existence cannot possibly be inferred from the lists of births and weddings. Indeed the two countries, Sweden and France, to the registers of which he refers as showing the prolifickness of their marriages, are known to be by no means remarkably healthy; and the registers of towns to which be alludes, though they may show, as be intends, a want of prolifickness, yet, according, to his previous reasoning, show at the same time great healthiness, and therefore ought not to be produced as a proof of the absence of both. The general fact that Dr. Price wishes to establish may still remain true, that country situations are both more healthy and more prolific than towns: but this fact certainly cannot be inferred merely from lists of births and marriages. With regard to the different countries of Europe, it will generally be found, that those are the most healthy which are the least prolific, and those the most prolific which are the least healthy. The earlier age of marriage in unhealthy countries is the obvious reason of this fact.

56.

Ueber die Bevölkerung der Europais. Staat. p. 91.

57.

At present (1825), and for the last ten, or even twenty years, there is reason to believe that half of the born live to 45 years.

58.

The proportions here mentioned are different from those which have been taken from the additional table in Mr. Tooke’s second edition; but they are assumed here as more easily and clearly illustrating the subject. .

59.

Sussmilch, Göttliche Ordnung, vol. i. table xxi. p. 83 of the tables.

60.

The number of people before the plague, according to Sussmilch’s calculations, (vol. i. ch. ix. sect. 173,) was 570,000, from which if we subtract 247,733, the number dying in the plague, the remainder, 322,267, will be the population after the plague; which, divided by the number of marriages and the number of births for the year 1711, makes the marriages about one twenty-sixth part of the population, and the births about one tenth part. Such extraordinary proportions could only occur in any country in an individual year. If they were to continue, they would double the population in less than ten years. It is possible that there may be a mistake in the table, and that the births and marriages of the plague years are included in the year 1711; though as the deaths are carefully separated, it seems very strange that it should be so. It is however a matter of no great importance. The other years are sufficient to illustrate the general principle.

61.

Sussmilch, Göttliche Ordnung, vol. i. c. v. s. lxxxvi. p. 175.

62.

History of Air, Seasons, &c. vol. ii. p. 344.

63.

Sussmilch’s Göttliche Ordnung, vol. i. tables, p. 88.

64.

Sussmilch, vol. i, tables, p. 91.

65.

Id. p. 99.

66.

Sussmilch, vol. i. tables, p. 103.

67.

Sussmilch, vol. i. tables, p. 108. .

68.

Short’s New Observ. on Bills of Mortality, p. 259, 8vo. 1750.

69.

Voy. d’Ulloa, tom. i. liv. v. ch. v. p. 229, 4to. 1752.

70.

Smith’s Wealth of Nations,
vol. ii. b. iv. ch. viii. p. 363.

71.

Id. p. 365.

72.

Id. p. 368, 369.

73.

Price’ s Observ. on Revers. Paym. vol. i. p. 282, 283, and vol. ii. p. 260. I have lately had an opportunity of seeing some extracts from the sermon of Dr. Styles, from which Dr. Price has taken these facts. Speaking of Rhode Island, Dr. Styles says that, though the period of doubling for the whole colony is 25 years, yet that it is different in different parts, and within land is 20 and 15 years. The population of the five towns of Gloucester, Situate, Coventry, West Greenwich and Exeter, was 5033, A. D. 1798, and 6986, A. D. 1755; which implies a period of doubling of 15 years only. He mentions afterwards, that the county of Kent doubles in 20 years, and the county of Providence in 18 years.

74.

See an article in the Supplement to the Encyclopædia Britannica on Population, p. 308; and a curious table, p. 310, calculated by Mr. Milne, Actuary to the Sun Life Assurance Office, which strikingly confirms and illustrates the computed rate of increase in the United States, and shews that it cannot be essentially affected by immigrations.

75.

See p. 500.

76.

New Observ. on Bills of Mortality, p. 96.

77.

Hist. of Air, Seasons, &c. vol. ii. p. 366.

78.

Id. vol. ii. p. 202.

79.

Hist. of Air, Seasons, &c, vol. ii. p. 206.

80.

Hist. of Air; Seasons, &c. vol. ii. p. 206. et seq.

81.

Id. vol. ii. p. 206. et seq. and 336.

82.

New Observ. p. 125.

83.

New Observ. p. 108.

84.

Hist. of Air, Seasons, &c: vol. ii. p. 367.

85.

Id. vol. ii. p. 411.

86.

Hist. of Air, Seasons, &c. vol. ii. p. 344.

87.

New Observ. p. 191.

88.

Id. p. 500.

89.

Political Arithmetic, p. 17.

90.

Survey of the Turkish Empire, c. vii. p. 281.

91.

Necker de l’Administration des Finances, tom. i. c. ix. p. 255.

92.

By an increase in the means of subsistence, as the expression is used here, is always meant such an increase as the mass of the population can command; otherwise it can be of no avail in encouraging an increase of people.

93.

The reader will recollect the confined sense in which I use this term.

Categories: Thomas Robert Malthus