Miscellaneous Writings and Speeches - Volume 2 by Thomas Babington Macaulay (best e reader for epub .txt) π
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be denied," says he, "that human increase proceeds geometrically; and for this simple but decisive reason, that the existence of a geometrical ratio of increase in the works of nature is neither true nor possible. It would fling into utter confusion all order, time, magnitude, and space."
This is as curious a specimen of reasoning as any that has been offered to the world since the days when theories were founded on the principle that nature abhors a vacuum. We proceed a few pages further, however; and we then find that geometric progression is unnatural only in those cases in which Mr Malthus conceives that it exists; and that, in all cases in which Mr Malthus denies the existence of a geometric ratio, nature changes sides, and adopts that ratio as the rule of increase.
Mr Malthus holds that subsistence will increase only in an arithmetical ratio. "As far as nature has to do with the question," says Mr Sadler, "men might, for instance, plant twice the number of peas, and breed from a double number of the same animals, with equal prospect of their multiplication." Now, if Mr Sadler thinks that, as far as nature is concerned, four sheep will double as fast as two, and eight as fast as four, how can he deny that the geometrical ratio of increase does exist in the works of nature? Or has he a definition of his own for geometrical progression, as well as for inverse proportion?
Mr Malthus, and those who agree with him, have generally referred to the United States, as a country in which the human race increases in a geometrical ratio, and have fixed on thirty-five years as the term in which the population of that country doubles itself. Mr Sadler contends that it is physically impossible for a people to double in twenty-five years; nay, that thirty-five years is far too short a period,-that the Americans do not double by procreation in less than forty-seven years,-and that the rapid increase of their numbers is produced by emigration from Europe.
Emigration has certainly had some effect in increasing the population of the United States. But so great has the rate of that increase been that, after making full allowance for the effect of emigration, there will be a residue, attributable to procreation alone, amply sufficient to double the population in twenty-five years.
Mr Sadler states the results of the four censuses as follows:-
"There were, of white inhabitants, in the whole of the United States in 1790, 3,093,111; in 1800, 4,309,656; in 1810, 5,862,093; and in 1820, 7,861,710. The increase, in the first term, being 39 per cent.; that in the second, 36 per cent.; and that in the third and last, 33 per cent. It is superfluous to say, that it is utterly impossible to deduce the geometric theory of human increase, whatever be the period of duplication, from such terms as these."
Mr Sadler is a bad arithmetician. The increase in the last term is not as he states it, 33 per cent., but more than 34 per cent. Now, an increase of 32 per cent. in ten years, is more than sufficient to double the population in twenty-five years. And there is, we think, very strong reason to believe that the white population of the United States does increase by 32 per cent. every ten years.
Our reason is this. There is in the United States a class of persons whose numbers are not increased by emigration,-the negro slaves. During the interval which elapsed between the census of 1810 and the census of 1820, the change in their numbers must have been produced by procreation, and by procreation alone. Their situation, though much happier than that of the wretched beings who cultivate the sugar plantations of Trinidad and Demerara, cannot be supposed to be more favourable to health and fecundity than that of free labourers. In 1810, the slave-trade had been but recently abolished; and there were in consequence many more male than female slaves,-a circumstance, of course, very unfavourable to procreation. Slaves are perpetually passing into the class of freemen; but no freeman ever descends into servitude; so that the census will not exhibit the whole effect of the procreation which really takes place.
We find, by the census of 1810, that the number of slaves in the Union was then 1,191,000. In 1820, they had increased to 1,538,000. That is to say, in ten years, they had increased 29 per cent.-within three per cent. of that rate of increase which would double their numbers in twenty-five years. We may, we think, fairly calculate that, if the female slaves had been as numerous as the males, and if no manumissions had taken place, the census of the slave population would have exhibited an increase of 32 per cent. in ten years.
If we are right in fixing on 32 per cent. as the rate at which the white population of America increases by procreation in ten years, it will follow that, during the last ten years of the eighteenth century, nearly one-sixth of the increase was the effect of emigration; from 1800 to 1810, about one-ninth; and from 1810 to 1820, about one-seventeenth. This is what we should have expected; for it is clear that, unless the number of emigrants be constantly increasing, it must, as compared with the resident population, be relatively decreasing. The number of persons added to the population of the United States by emigration, between 1810 and 1820, would be nearly 120,000. From the data furnished by Mr Sadler himself, we should be inclined to think that this would be a fair estimate.
"Dr Seybert says, that the passengers to ten of the principal ports of the United States, in the year 1817, amounted to 22,235; of whom 11,977 were from Great Britain and Ireland; 4164 from Germany and Holland; 1245 from France; 58 from Italy, 2901 from the British possessions in North America; 1569 from the West Indies; and from all other countries, 321. These, however, we may conclude, with the editor of Styles's Register, were far short of the number that arrived."
We have not the honour of knowing either Dr Seybert or the editor of Styles's Register. We cannot, therefore, decide on their respective claims to our confidence so peremptorily as Mr Sadler thinks fit to do. Nor can we agree to what Mr Sadler very gravely assigns as a reason for disbelieving Dr Seyberts's testimony. "Such accounts," he says, "if not wilfully exaggerated, must always fall short of the truth." It would be a curious question of casuistry to determine what a man ought to do in a case in which he cannot tell the truth except by being guilty of wilful exaggeration. We will, however, suppose, with Mr Sadler, that Dr Seybert, finding himself compelled to choose between two sins, preferred telling a falsehood to exaggerating; and that he has consequently underrated the number of emigrants. We will take it at double of the Doctor's estimate, and suppose that, in 1817, 45,000 Europeans crossed to the United States. Now, it must be remembered that the year 1817 was a year of the severest and most general distress all over Europe,-a year of scarcity everywhere, and of cruel famine in some places. There can, therefore, be no doubt that the emigration of 1817 was very far above the average, probably more than three times that of an ordinary year. Till the year 1815, the war rendered it almost impossible to emigrate to the United States either from England or from the Continent. If we suppose the average emigration of the remaining years to have been 16,000, we shall probably not be much mistaken. In 1818 and 1819, the number was certainly much beyond that average; in 1815 and 1816, probably much below it. But, even if we were to suppose that, in every year from the peace to 1820, the number of emigrants had been as high as we have supposed it to be in 1817, the increase by procreation among the white inhabitants of the United States would still appear to be about 30 per cent. in ten years.
Mr Sadler acknowledges that Cobbett exaggerates the number of emigrants when he states it at 150,000 a year. Yet even this estimate, absurdly great as it is, would not be sufficient to explain the increase of the population of the United States on Mr Sadler's principles. He is, he tells us, "convinced that doubling in 35 years is a far more rapid duplication than ever has taken place in that country from procreation only." An increase of 20 per cent. in ten years, by procreation, would therefore be the very utmost that he would allow to be possible. We have already shown, by reference to the census of the slave population, that this doctrine is quite absurd. And, if we suppose it to be sound, we shall be driven to the conclusion that above eight hundred thousand people emigrated from Europe to the United States in a space of little more than five years. The whole increase of the white population from 1810 to 1820 was within a few hundreds of 2,000,000. If we are to attribute to procreation only 20 per cent. on the number returned by the census of 1810, we shall have about 830,000 persons to account for in some other way;-and to suppose that the emigrants who went to America between the peace of 1815 and the census of 1820, with the children who were born to them there, would make up that number, would be the height of absurdity.
We could say much more; but we think it quite unnecessary at present. We have shown that Mr Sadler is careless in the collection of facts,-that he is incapable of reasoning on facts when he has collected them,-that he does not understand the simplest terms of science,-that he has enounced a proposition of which he does not know the meaning,-that the proposition which he means to enounce, and which he tries to prove, leads directly to all those consequences which he represents as impious and immoral,-and that, from the very documents to which he has himself appealed, it may be demonstrated that his theory is false. We may, perhaps, resume the subject when his next volume appears. Meanwhile, we hope that he will delay its publication until he has learned a little arithmetic, and unlearned a great deal of eloquence.
...
SADLER'S REFUTATION REFUTED.
(January 1831.)
"A Refutation of an Article in the Edinburgh Review (No. CII.) entitled, 'Sadler's Law of Population, and disproof of Human Superfecundity;' containing also Additional Proofs of the Principle enunciated in that Treatise, founded on the Censuses of different Countries recently published." By Michael Thomas Sadler, M.P. 8vo. London: 1830.
"Before anything came out against my Essay, I was told I must prepare myself for a storm coming against it, it being resolved by some men that it was necessary that book of mine should, as it is phrased, be run down."-John Locke.
We have, in violation of our usual practice, transcribed Mr Sadler's title-page from top to bottom, motto and all. The parallel implied between the Essay on the Human Understanding and the Essay on Superfecundity is exquisitely laughable. We can match it, however, with mottoes as ludicrous. We remember to have heard of a dramatic piece, entitled "News from Camperdown," written soon after Lord Duncan's victory, by a man once as much in his own good graces as Mr Sadler is, and now as much forgotten
This is as curious a specimen of reasoning as any that has been offered to the world since the days when theories were founded on the principle that nature abhors a vacuum. We proceed a few pages further, however; and we then find that geometric progression is unnatural only in those cases in which Mr Malthus conceives that it exists; and that, in all cases in which Mr Malthus denies the existence of a geometric ratio, nature changes sides, and adopts that ratio as the rule of increase.
Mr Malthus holds that subsistence will increase only in an arithmetical ratio. "As far as nature has to do with the question," says Mr Sadler, "men might, for instance, plant twice the number of peas, and breed from a double number of the same animals, with equal prospect of their multiplication." Now, if Mr Sadler thinks that, as far as nature is concerned, four sheep will double as fast as two, and eight as fast as four, how can he deny that the geometrical ratio of increase does exist in the works of nature? Or has he a definition of his own for geometrical progression, as well as for inverse proportion?
Mr Malthus, and those who agree with him, have generally referred to the United States, as a country in which the human race increases in a geometrical ratio, and have fixed on thirty-five years as the term in which the population of that country doubles itself. Mr Sadler contends that it is physically impossible for a people to double in twenty-five years; nay, that thirty-five years is far too short a period,-that the Americans do not double by procreation in less than forty-seven years,-and that the rapid increase of their numbers is produced by emigration from Europe.
Emigration has certainly had some effect in increasing the population of the United States. But so great has the rate of that increase been that, after making full allowance for the effect of emigration, there will be a residue, attributable to procreation alone, amply sufficient to double the population in twenty-five years.
Mr Sadler states the results of the four censuses as follows:-
"There were, of white inhabitants, in the whole of the United States in 1790, 3,093,111; in 1800, 4,309,656; in 1810, 5,862,093; and in 1820, 7,861,710. The increase, in the first term, being 39 per cent.; that in the second, 36 per cent.; and that in the third and last, 33 per cent. It is superfluous to say, that it is utterly impossible to deduce the geometric theory of human increase, whatever be the period of duplication, from such terms as these."
Mr Sadler is a bad arithmetician. The increase in the last term is not as he states it, 33 per cent., but more than 34 per cent. Now, an increase of 32 per cent. in ten years, is more than sufficient to double the population in twenty-five years. And there is, we think, very strong reason to believe that the white population of the United States does increase by 32 per cent. every ten years.
Our reason is this. There is in the United States a class of persons whose numbers are not increased by emigration,-the negro slaves. During the interval which elapsed between the census of 1810 and the census of 1820, the change in their numbers must have been produced by procreation, and by procreation alone. Their situation, though much happier than that of the wretched beings who cultivate the sugar plantations of Trinidad and Demerara, cannot be supposed to be more favourable to health and fecundity than that of free labourers. In 1810, the slave-trade had been but recently abolished; and there were in consequence many more male than female slaves,-a circumstance, of course, very unfavourable to procreation. Slaves are perpetually passing into the class of freemen; but no freeman ever descends into servitude; so that the census will not exhibit the whole effect of the procreation which really takes place.
We find, by the census of 1810, that the number of slaves in the Union was then 1,191,000. In 1820, they had increased to 1,538,000. That is to say, in ten years, they had increased 29 per cent.-within three per cent. of that rate of increase which would double their numbers in twenty-five years. We may, we think, fairly calculate that, if the female slaves had been as numerous as the males, and if no manumissions had taken place, the census of the slave population would have exhibited an increase of 32 per cent. in ten years.
If we are right in fixing on 32 per cent. as the rate at which the white population of America increases by procreation in ten years, it will follow that, during the last ten years of the eighteenth century, nearly one-sixth of the increase was the effect of emigration; from 1800 to 1810, about one-ninth; and from 1810 to 1820, about one-seventeenth. This is what we should have expected; for it is clear that, unless the number of emigrants be constantly increasing, it must, as compared with the resident population, be relatively decreasing. The number of persons added to the population of the United States by emigration, between 1810 and 1820, would be nearly 120,000. From the data furnished by Mr Sadler himself, we should be inclined to think that this would be a fair estimate.
"Dr Seybert says, that the passengers to ten of the principal ports of the United States, in the year 1817, amounted to 22,235; of whom 11,977 were from Great Britain and Ireland; 4164 from Germany and Holland; 1245 from France; 58 from Italy, 2901 from the British possessions in North America; 1569 from the West Indies; and from all other countries, 321. These, however, we may conclude, with the editor of Styles's Register, were far short of the number that arrived."
We have not the honour of knowing either Dr Seybert or the editor of Styles's Register. We cannot, therefore, decide on their respective claims to our confidence so peremptorily as Mr Sadler thinks fit to do. Nor can we agree to what Mr Sadler very gravely assigns as a reason for disbelieving Dr Seyberts's testimony. "Such accounts," he says, "if not wilfully exaggerated, must always fall short of the truth." It would be a curious question of casuistry to determine what a man ought to do in a case in which he cannot tell the truth except by being guilty of wilful exaggeration. We will, however, suppose, with Mr Sadler, that Dr Seybert, finding himself compelled to choose between two sins, preferred telling a falsehood to exaggerating; and that he has consequently underrated the number of emigrants. We will take it at double of the Doctor's estimate, and suppose that, in 1817, 45,000 Europeans crossed to the United States. Now, it must be remembered that the year 1817 was a year of the severest and most general distress all over Europe,-a year of scarcity everywhere, and of cruel famine in some places. There can, therefore, be no doubt that the emigration of 1817 was very far above the average, probably more than three times that of an ordinary year. Till the year 1815, the war rendered it almost impossible to emigrate to the United States either from England or from the Continent. If we suppose the average emigration of the remaining years to have been 16,000, we shall probably not be much mistaken. In 1818 and 1819, the number was certainly much beyond that average; in 1815 and 1816, probably much below it. But, even if we were to suppose that, in every year from the peace to 1820, the number of emigrants had been as high as we have supposed it to be in 1817, the increase by procreation among the white inhabitants of the United States would still appear to be about 30 per cent. in ten years.
Mr Sadler acknowledges that Cobbett exaggerates the number of emigrants when he states it at 150,000 a year. Yet even this estimate, absurdly great as it is, would not be sufficient to explain the increase of the population of the United States on Mr Sadler's principles. He is, he tells us, "convinced that doubling in 35 years is a far more rapid duplication than ever has taken place in that country from procreation only." An increase of 20 per cent. in ten years, by procreation, would therefore be the very utmost that he would allow to be possible. We have already shown, by reference to the census of the slave population, that this doctrine is quite absurd. And, if we suppose it to be sound, we shall be driven to the conclusion that above eight hundred thousand people emigrated from Europe to the United States in a space of little more than five years. The whole increase of the white population from 1810 to 1820 was within a few hundreds of 2,000,000. If we are to attribute to procreation only 20 per cent. on the number returned by the census of 1810, we shall have about 830,000 persons to account for in some other way;-and to suppose that the emigrants who went to America between the peace of 1815 and the census of 1820, with the children who were born to them there, would make up that number, would be the height of absurdity.
We could say much more; but we think it quite unnecessary at present. We have shown that Mr Sadler is careless in the collection of facts,-that he is incapable of reasoning on facts when he has collected them,-that he does not understand the simplest terms of science,-that he has enounced a proposition of which he does not know the meaning,-that the proposition which he means to enounce, and which he tries to prove, leads directly to all those consequences which he represents as impious and immoral,-and that, from the very documents to which he has himself appealed, it may be demonstrated that his theory is false. We may, perhaps, resume the subject when his next volume appears. Meanwhile, we hope that he will delay its publication until he has learned a little arithmetic, and unlearned a great deal of eloquence.
...
SADLER'S REFUTATION REFUTED.
(January 1831.)
"A Refutation of an Article in the Edinburgh Review (No. CII.) entitled, 'Sadler's Law of Population, and disproof of Human Superfecundity;' containing also Additional Proofs of the Principle enunciated in that Treatise, founded on the Censuses of different Countries recently published." By Michael Thomas Sadler, M.P. 8vo. London: 1830.
"Before anything came out against my Essay, I was told I must prepare myself for a storm coming against it, it being resolved by some men that it was necessary that book of mine should, as it is phrased, be run down."-John Locke.
We have, in violation of our usual practice, transcribed Mr Sadler's title-page from top to bottom, motto and all. The parallel implied between the Essay on the Human Understanding and the Essay on Superfecundity is exquisitely laughable. We can match it, however, with mottoes as ludicrous. We remember to have heard of a dramatic piece, entitled "News from Camperdown," written soon after Lord Duncan's victory, by a man once as much in his own good graces as Mr Sadler is, and now as much forgotten
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