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Russia; but, as I have before observed, she has been so frequently augmenting her territories, and therefore her popula tson, by the addition of new provinces and tribes to her em pare, and also inviting and receiving new settlers from other countries, that it is not safe to rest any calculation of the natural law upon her augmentations. All these instances, from so many countries in Europe, under circumstances very dissimilar to each other, but all existing in the most prosperous age that our world has known, and when population has been receiving impulses highly favourable to it from the general intelligence, improvement, activity, and increasing property and employment of all kinds, concur to indicate that the supposed law of the geometrical increase is not that general system under which our Creator has willed and causes his human race to multiply. It has been one of those mistaken deductions which captivate from their novelty, and claim attention by their plausibility, and are well meant by their sup porters; but which, being too hastily made, from insufficient twelve years.-Bull. Univ., 1830, p. 435; and would not double the amount for nearly seventy years.

In Guelderland the numbers in 1815 were 259,784, and in 1825 were 25.573-Bull. Univ., 1827, p. 102. This ratio would require a century for its duplication.

Corsica, in the five years from 1822 to 1827, increased 4,731, or 180.348. This rate would not double till nearly 190 years.-Bull. Univ., 1828, p. 21, 95.

Denmark in nine years, from 1816 to 1825, advanced from 931,600 to 1,143,193.-Bull. Univ., 1829, p. 134. This rate would be above fifty years in doubling if it continued.

The kingdom of Naples in 1813 contained 5,822,303, and in 1834 only enlarged to 5,883,373. This augmetation would require ninety-five years for doubling.

in Palermo the population, according to Dr. Calcagni, was 156,876 in 1816, and in 1825 had become 167,505.-Bull. Univ., 1827, p. 121. This increase in nine years would not double the numbers in 140 years. In Saxony the population in July, 1832, was 1,558,153, and in December, 1634, was 1,595,668, being an increase of one per cent. per annum. Seventy years would be requisite for its doubling at this ratio of increase. -Mr. Preston to Statistical Society.

At Frankfort the population had increased, in twelve years preceding 1829, during which 13,754 had been born, only 316, which was but a forty-third part-Bull. Univ., 1831, p. 50. At this rate this city would not double its numbers in less than 300 or 400 years.

⚫ See before, p. 57.

Mr. Malthus thus mentions those foreign colonizers. He says of the Empress Catharine, “Her immense importation of German settlers not only contributed to people her state with free citizens instead of slaves, but to set an example of industry, and of modes of directing that industry, totally unknown to the Russian peasants."-Malthus on Pop., vol. i., p. 370. VOL. III-G

materials, depart from the mind as soon as fuller and more correct information, and the just reasoning on that, advance in society. We drop, then, our errors as naturally and as creditably as we at first had conceived them.*

LETTER X.

A Rule suggested by which the Malthusian Ratio may be always tried. -Its Conditions have not occurred anywhere.-The more probable Rate shown in the late Increases of our own Population.-In Russia a similar Gradation.-Also in Prussia and Lithuania.

MY DEAR SON,

As very important political systems and legislative measures have been recommended on the principle and the belief that the Malthusian ratio is the true law of population, I have endeavoured to find out some simple element by which, I will not say its possibility, because that is not a statesman's inquiry, but its probability, according to all known experience, could be put to an arithmetical and applicable test. If I do not deceive myself, one has at last occurred to me, which I will now mention. This is the rule, that no population anywhere can double in twenty-five years, unless the births are, for all that time, 65 in every 1000 of the people, and the deaths all that while only 26. There must be a continuing

The English population in the year 1710 was, according to Mr. Finlaison, 5,134.516. Now supposing it to have been 2,000,000 at the Norman Conquest, a steady increase, at one twentieth in every generation, at three twentieths in a century, would bring it very nearly to the ascertained amount; thus

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5,045,998

We here see that it was above 450 years before it doubled; yet the country was continually increasing in its national improvements and prosperity, notwithstanding its civil and foreign wars.

surplus of the births above the deaths of every year of 39 in every 1000 for the whole period of twenty-five years, or the numbers will not double in that time. To express this rule in other words, we may say that the births must be, every year, for the twenty-five years, one in 15 5-13 of the whole population, or nearly one fifteenth, and the deaths all that time only one in 39, or nearly a thirty-ninth part of the population, making invariably the difference of two births and a half to one death, or 65 births in 1000 to 26 deaths. Whenever these conditions steadily occur for twenty-five years together, that population will be doubled in that time, but not under any other proportions. Now, if this be so, I would beg leave to ask those who may be inclined to support the geometrical ratio whether they have ever met with any authenticated document of such a proportion of births to the population, and of deaths to those births, as is above mentioned, for a continuity of twenty-five years, in any age or country of the world. I have found none myself. I do not believe it to be possible to adduce any. The births, nearly a fifteenth part of the population in every year, and always twice and a half the number of the annual deaths, for twenty-five years, will make a doubling in that time.* The principle may be expressed in another form, thus: to double any population in twenty-five years, there must, in each of these years, be born and live a one twenty-fifth portion of its whole numbers above those who shall annually die; a little less than one fifteenth part born, and than one thirty-ninth dying, every year, would be the nearest proportions to fulfil this rule. The fractional subtractions from these numbers would make the result exact. The practical laws of daily nature do not accomplish these conditions, as far as my inquiries have extended.

Our own population, for the last thirty years, is an instance of as steady a national increase as any that can be quoted. I

*We may try this rule by any number: suppose a population of 100,000; for these to double in 25 years, the rule would require 6500 to be born every year for 25 years successively, and 2600 only to die annually for that time; 6500 x 25= 162,500 births; deduct for deaths 2600 X 2565,000, the surplus from the births would be 97,500, or a surplus of 39 births on 1000 in every year; 3900 × 25 would also give 97,500.

So, if the births be calculated as one in 15 5-13 of the population, and the deaths as nearly one in 39 for 25 years, the result would be the addition of nearly 100,000 at the end of the 25 years.

am not aware that any has surpassed this augmentation for a greater continuity. This has caused a multiplication of about one tenth in every ten years. Now, to do this, the regular result must be, that the births shall, on the average, during all that time, be on the whole one half more than the deaths. One and a half births to one death will produce an increase of numbers like our own, and double the population in about seventy-four years, if the relative progress never lessens or ceases. But if either of these events takes place, if it for any time diminishes or pauses, the people cannot be doubled even in that length of time.*

But because England has in the last thirty years increased by one tenth, we are not therefore to infer that she has always had such a rate of increase, or that this is the general standard of nature in all times and in all ages; for this was not the case before. Instead of the births being always above 100,000 beyond the deaths, as, with two exceptions, there were in each of the twenty-seven years after 1803, their sur plus was not one third of that number in 1801, but began to increase in the two following years.

If we look at our population before 1800, in the seventy years between 1700 and 1770, we find that, taking eight decennial periods of this interval, the burials were, at three of

* That a steady increase of one tenth in every 10 years for 70 years would in that time double the population, the following figures show: taking the population at 1000, this would be :-

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But an increase of one tenth in ten years would be an average augmentation of one hundredth every year. Calculate this in the same way, and you will find that it will be doubled about the seventy-third year. But if the annual increase became diminished in any part of this long series, the time of doubling would be correspondently protracted. † Our baptisms exceeded the burials in the first six years of this century by the following amounts :

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