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 be lief 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 1066 1100 1200 1300 1400 1500 1600 1700 2,000,000 2,100,000 2,431,012 2,814,199 3,252,785 3,765,412 4,358,934 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 X 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 surplus 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 :- 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 cen tury by the following amounts : them,* 1710, 1720, 1730, more than the baptisms; and although the latter showed that at five of these times the births exceeded the deaths, yet their surplus was so small, that out of 1,351,616 baptisms, the deaths came so close that not quite 90,000 had been born beyond those who died.† It was not until 1740, in these periods, that the surplus of births began again to exceed the deaths in a small degree. This had increased in the next period of 1750, still more in 1760, and a little more in 1770. But, after this year, such a new impulse was, as it were, suddenly given to the reproducing causes, that in the twenty years between 1780 and 1800, the baptisms exceeded the deaths by above a million. The causes of increase were in this interval so unusually operative and effectual, and the abatement of declining appears so great, as to produce in these twenty years above thirteen times the surplus numbers which the seventy preceding years, according to these decennial calculations, had added to our population, But since 1800 the reproducing laws have acted with still larger efficacy, so as to make the augmentation of the last ten years amount to the addition of one tenth. The long continuity of such an increase as this has been very rare. Perhaps it can be found but very rarely anywhere else. In Rus †The excess of burials beyond baptisms in the above list in 1710, 1720, and 1730, was 21,318, The excess of baptisms above burials in the other five years was 111,252, leaving on these eight decennial years, out of the 1,351,616, which all these baptisms amount to, only 80,934; so that in these eight selected years the population increased no more than that number, or not quite one fifteenth part. The whole baptisms and burials, from 1780 to 1800, in England and Wales were Baptisms 5,084,494 Burials 3,904,162 Pop. Abst. sia, the productive results have varied. In the eleven years after 1811 her births exceeded her deaths by about one third.* In the next year her deaths were more than her births, but after that her nativities became more numerous than her burials. Yet her variations show the improbability of a country keeping up for twenty-five years successively that degree of superiority of births to deaths which a large, and quick, and lasting multiplication requires. Nothing of this sort is to be seen in the different enumerations of the Russian nation.‡ In * From 1812 to 1822 inclusive in these eleven years the amount was— 15,456,195 Births 10,085,395 5,370,800 Making this increase by her surplus births in these eleven years.Fer. Bull. Univ., 1827, p. 115. t In 1813, a year of war, the deaths of Russia exceeded her births by 2740.-Ib., 115. At St. Petersburg, from 1813 to 1822, there was also in these ten years an excess of deaths. The births were The deaths making 27,235 more dead than born.-Ib., 116. 80,265 107,500 Thus the whole amount of her male was less in 1816 than they had been five years before. Males in 1811 Males in 1816 17,952,424 Fer. Bull. Un., 1831, p. 184. In 1833 and 1834, the births and deaths stood in these proportions: 1833: Births Deaths Excess of births Males 942,836 |
