Front Page Titles (by Subject) SADLER'S REFUTATION REFUTED. (January 1831.) - Miscellaneous Writings, Vol.2
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SADLER’S REFUTATION REFUTED. (January 1831.) - Thomas Babington, Lord Macaulay, Miscellaneous Writings, Vol.2 
The Miscellaneous Writings of Lord Macaulay, vol. 2, (London: Longman, Green, Longman, and Roberts, 1860).
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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.”
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 as Mr. Sadler will soon be, Robert Heron. His piece was brought upon the stage, and damned, “as it is phrased,” in the second act; but the author, thinking that it had been unfairly and unjustly “run down,” published it, in order to put his critics to shame, with this motto from Swift: “When a true genius appears in the world, you may know him by this mark—that the dunces are all in confederacy against him.” We remember another anecdote, which may perhaps be acceptable to so zealous a churchman as Mr. Sadler. A certain Antinomian preacher, the oracle of a barn, in a county of which we do not think it proper to mention the name, finding that divinity was not by itself a sufficiently lucrative profession, resolved to combine with it that of dog-stealing. He was, by ill-fortune, detected in several offences of this description, and was in consequence brought before two justices, who, in virtue of the powers given them by an act of parliament, sentenced him to a whipping for each theft. The degrading punishment inflicted on the pastor naturally thinned the flock; and the poor man was in danger of wanting bread. He accordingly put forth a handbill, solemnly protesting his innocence, describing his sufferings, and appealing to the Christian charity of the public; and to his pathetic address he prefixed this most appropriate text: “Thrice was I beaten with rods.—St. Paul’s Epistle to the Corinthians.” He did not perceive that, though St. Paul had been scourged, no number of whippings, however severe, will of themselves entitle a man to be considered as an apostle. Mr. Sadler seems to us to have fallen into a somewhat similar error. He should remember that, though Locke may have been laughed at, so has Sir Claudius Hunter; and that it takes something more than the laughter of all the world to make a Locke.
The body of this pamphlet by no means justifies the parallel so modestly insinuated on the title-page. Yet we must own that, though Mr. Sadler has not risen to the level of Locke, he has done what was almost as difficult, if not as honourable—he has fallen below his own. He is at best a bad writer. His arrangement is an elaborate confusion. His style has been constructed, with great care, in such a manner as to produce the least possible effect by means of the greatest possible number of words. Aspiring to the exalted character of a Christian philosopher, he can never preserve through a single paragraph either the calmness of a philosopher or the meekness of a Christian. His ill-nature would make a very little wit formidable. But, happily, his efforts to wound resemble those of a juggler’s snake. The bags of poison are full, but the fang is wanting. In this foolish pamphlet, all the unpleasant peculiarities of his style and temper are brought out in the strongest manner. He is from the beginning to the end in a paroxysm of rage, and would certainly do us some mischief if he knew how. We will give a single instance for the present. Others will present themselves as we proceed. We laughed at some doggerel verses which he cited, and which we, never having seen them before, suspected to be his own. We are now sure that, if the principle on which Solomon decided a famous case of filiation were correct, there can be no doubt as to the justice of our suspicion. Mr. Sadler, who, whatever elements of the poetical character he may lack, possesses the poetical irritability in an abundance which might have sufficed for Homer himself, resolved to retaliate on the person, who, as he supposed, had reviewed him. He has, accordingly, ransacked some collection of college verses, in the hope of finding, among the performances of his supposed antagonist, something as bad as his own. And we must in fairness admit that he has succeeded pretty well. We must admit that the gentleman in question sometimes put into his exercises, at seventeen, almost as great nonsense as Mr. Sadler is in the habit of putting into his books at sixty.
Mr. Sadler complains that we have devoted whole pages to mere abuse of him. We deny the charge. We have, indeed, characterised, in terms of just reprehension, that spirit which shows itself in every part of his prolix work. Those terms of reprehension we are by no means inclined to retract; and we conceive that we might have used much stronger expressions, without the least offence either to truth or to decorum. There is a limit prescribed to us by our sense of what is due to ourselves. But we think that no indulgence is due to Mr. Sadler. A writer who distinctly announces that he has not conformed to the candour of the age — who makes it his boast that he expresses himself throughout with the greatest plainness and freedom — and whose constant practice proves that by plainness and freedom he means coarseness and rancour—has no right to expect that others shall remember courtesies which he has forgotten, or shall respect one who has ceased to respect himself.
Mr. Sadler declares that he has never vilified Mr. Malthus personally, and has confined himself to attacking the doctrines which that gentleman maintains. We should wish to leave that point to the decision of all who have read Mr. Sadler’s book, or any twenty pages of it. To quote particular instances of a temper which penetrates and inspires the whole work, is to weaken our charge. Yet, that we may not be suspected of flinching, we will give two specimens, — the two first which occur to our recollection. “Whose minister is it that speaks thus?” says Mr. Sadler, after misrepresenting in a most extraordinary manner, though, we are willing to believe, unintentionally, one of the positions of Mr. Malthus. “Whose minister is it that speaks thus? That of the lover and avenger of little children?” Again, Mr. Malthus recommends, erroneously perhaps, but assuredly from humane motives, that alms, when given, should be given very sparingly. Mr. Sadler quotes the recommendation, and adds the following courteous comment:—“The tender mercies of the wicked are cruel.” We cannot think that a writer who indulges in these indecent and unjust attacks on professional and personal character has any right to complain of our sarcasms on his metaphors and rhymes.
We will now proceed to examine the reply which Mr. Sadler has thought fit to make to our arguments. He begins by attacking our remarks on the origin of evil. They are, says he, too profound for common apprehension; and he hopes that they are too profound for our own. That they seem profound to him we can well believe. Profundity, in its secondary as in its primary sense, is a relative term. When Grildrig was nearly drowned in the Brobdignagian cream-jug he doubtless thought it very deep. But to common apprehension our reasoning would, we are persuaded, appear perfectly simple.
The theory of Mr. Malthus, says Mr. Sadler, cannot be true, because it asserts the existence of a great and terrible evil, and is therefore inconsistent with the goodness of God. We answer thus. We know that there are in the world great and terrible evils. In spite of these evils, we believe in the goodness of God. Why may we not then continue to believe in his goodness, though another evil should be added to the list?
How does Mr. Sadler answer this? Merely by telling us that we are too wicked to be reasoned with. He completely shrinks from the question; a question, be it remembered, not raised by us—a question which we should have felt strong objections to raising unnecessarily—a question put forward by himself, as intimately connected with the subject of his two ponderous volumes. He attempts to carp at detached parts of our reasoning on the subject. With what success he carries on this guerilla war after declining a general action with the main body of our argument our readers shall see.
“The reviewer sends me to Paley, who is, I confess, rather more intelligible on the subject, and who, fortunately, has decided the very point in dispute. I will first give the words of the reviewer, who, when speaking of my general argument regarding the magnitude of the evils, moral and physical, implied in the theory I oppose, sums up his ideas thus: — ‘Mr. Sadler says, that it is not a light or transient evil, but a great and permanent evil. What then? The question of the origin of evil is a question of ay or no, — not a question ofmoreorless.’ But what says Paley? His express rule is this, that ‘when we cannot resolve all appearances into benevolence of design, we make thefewgive place to themany,thelittleto thegreat;that we take our judgment from a large and decidedpreponderancy.’ Now in weighing these two authorities, directly at issue on this point, I think there will be little trouble in determining which we shall make ‘to give place;’ or, if we ‘look to a large and decided preponderancy’ of either talent, learning, or benevolence, from whom we shall ‘take our judgment.’ The effrontery, or, to speak more charitably, the ignorance of a reference to Paley on this subject, and in this instance is really marvellous.”
Now, does not Mr. Sadler see that the very words which he quotes from Paley contain in themselves a refutation of his whole argument? Paley says, indeed, as every man in his senses would say, that in a certain case, which he has specified, the more and the less come into question. But in what case? “When we cannot resolve all appearances into the benevolence of design.” It is better that there should be a little evil than a great deal of evil. This is self-evident. But it is also self-evident that no evil is better than a little evil. Why, then, is there any evil? It is a mystery which we cannot solve. It is a mystery which Paley, by the very words which Mr. Sadler has quoted, acknowledges himself unable to solve; and it is because he cannot solve that mystery that he proceeds to take into consideration the more and the less. Believing in the divine goodness, we must necessarily believe that the evils which exist are necessary to avert greater evils. But what those greater evils are we do not know. How the happiness of any part of the sentient creation would be in any respect diminished if, for example, children cut their teeth without pain, we cannot understand. The case is exactly the same with the principle of Mr. Malthus. If superfecundity exists, it exists, no doubt, because it is a less evil than some other evil which otherwise would exist. Can Mr. Sadler prove that this is an impossibility?
One single expression which Mr. Sadler employs on this subject is sufficient to show how utterly incompetent he is to discuss it. “On the Christian hypothesis,” says he, “no doubt exists as to the origin of evil.” He does not, we think, understand what is meant by the origin of evil. The Christian Scriptures profess to give no solution of that mystery. They relate facts; but they leave the metaphysical question undetermined. They tell us that man fell; but why he was not so constituted as to be incapable of falling, or why the Supreme Being has not mitigated the consequences of the Fall more than they actually have been mitigated, the Scriptures did not tell us, and, it may without presumption be said, could not tell us, unless we had been creatures different from what we are. There is something, either in the nature of our faculties or in the nature of the machinery employed by us for the purpose of reasoning, which condemns us, on this and similar subjects, to hopeless ignorance. Man can understand these high matters only by ceasing to be man, just as a fly can understand a lemma of Newton only by ceasing to be a fly. To make it an objection to the Christian system that it gives us no solution of these difficulties, is to make it an objection to the Christian system that it is a system formed for human beings. Of the puzzles of the Academy, there is not one which does not apply as strongly to Deism as to Christianity, and to Atheism as to Deism. There are difficulties in everything. Yet we are sure that something must be true.
If revelation speaks on the subject of the origin of evil it speaks only to discourage dogmatism and temerity. In the most ancient, the most beautiful, and the most profound of all works on the subject, the Book of Job, both the sufferer who complains of the divine government, and the injudicious advisers who attempt to defend it on wrong principles, are silenced by the voice of supreme wisdom, and reminded that the question is beyond the reach of the human intellect. St Paul silences the supposed objector, who strives to force him into controversy, in the same manner. The church has been, ever since the apostolic times, agitated by this question, and by a question which is inseparable from it, the question of fate and free-will. The greatest theologians and philosophers have acknowledged that these things were too high for them, and have contented themselves with hinting at what seemed to be the most probable solution. What says Johnson? “All our effort ends in belief that for the evils of life there is some good reason, and in confession that the reason cannot be found.” What says Paley? “Of the origin of evil no universal solution has been discovered. I mean no solution which reaches to all cases of complaint.—The consideration of general laws, although it may concern the question of the origin of evil very nearly, which I think it does, rests in views disproportionate to our faculties, and in a knowledge which we do not possess. It serves rather to account for the obscurity of the subject, than to supply us with distinct answers to our difficulties.” What says presumptuous ignorance? “No doubt whatever exists as to the origin of evil.” It is remarkable that Mr. Sadler does not tell us what his solution is. The world, we suspect, will lose little by his silence.
He falls on the reviewer again.
“Though I have shown,” says he, “and on authorities from which none can lightly differ, not only the cruelty and immorality which this system necessarily involves, but its most revolting feature, its gross partiality, he has wholly suppressed this, the most important part of my argument; as even the bare notice of it would have instantly exposed the sophistry to which he has had recourse. If, however, he would fairly meet the whole question, let him show me that ‘hydrophobia,’ which he gives as an example of the laws of God and nature, is a calamity to which the poor alone are liable; or that ‘malaria,’ which, with singular infelicity, he has chosen as an illustration of the fancied evils of population, is a respecter of persons.”
We said nothing about this argument, as Mr. Sadler calls it, merely because we did not think it worth while; and we are half ashamed to say anything about it now. But, since Mr. Sadler is so urgent for an answer, he shall have one. If there is evil, it must be either partial or universal. Which is the better of the two? Hydrophobia, says this great philosopher, is no argument against the divine goodness, because mad dogs bite rich and poor alike; but, if the rich were exempted, and only nine people suffered for ten who suffer now, hydrophobia would forthwith, simply because it would produce less evil than at present, become an argument against the divine goodness! To state such a proposition, is to refute it, And is not the malaria a respecter of persons? It infests Rome. Does it infest London? There are complaints peculiar to the tropical countries. There are others which are found only in mountainous districts; others which are confined to marshy regions; others again which run in particular families. Is not this partiality? Why is it more inconsistent with the divine goodness that poor men should suffer an evil from which rich men are exempt, than that a particular portion of the community should inherit gout, scrofula, insanity, and other maladies? And are there no miseries under which, in fact, the poor alone are suffering? Mr. Sadler himself acknowledges, in this very paragraph, that there are such; but he tells us that these calamities are the effects of misgovernment, and that this misgovernment is the effect of political economy. Be it so. But does he not see that he is only removing the difficulty one step farther? Why does Providence suffer men, whose minds are filled with false and pernicious notions, to have power in the state? For good ends, we doubt not, if the fact be so; but for ends inscrutable to us, who see only a small part of the vast scheme, and who see that small part only for a short period. Does Mr. Sadler doubt that the Supreme Being has power as absolute over the revolutions of political as over the organisation of natural bodies? Surely not: and, if not, we do not see that he vindicates the ways of Providence by attributing the distresses, which the poor, as he confesses, endure, to an error in legislation rather than to a law of physiology. Turn the question as we may, disguise it as we may, we shall find that it at last resolves itself into the same great enigma,—the origin of physical and moral evil: an enigma which the highest human intellects have given up in despair, but which Mr. Sadler thinks himself perfectly able to solve.
He next accuses us of having paused long on verbal criticism. We certainly did object to his improper use of the words, “inverse variation.” Mr. Sadler complains of this with his usual bitterness.
“Now what is the Reviewer’s quarrel with me on this occasion? That he does not understand the meaning of my terms? No. He acknowledges the contrary. That I have not fully explained the sense in which I have used them? No. An explanation, he knows, is immediately subjoined, though he has carefully suppressed it. That I have varied the sense in which I have applied them? No. I challenge him to show it. But he nevertheless goes on for many pages together in arguing against what he knows, and, in fact, acknowledges, I did not mean; and then turns round and argues again, though much more feebly, indeed, against what he says I did mean! Now, even had I been in error as to the use of a word, I appeal to the reader whether such an unworthy and disingenuous course would not, if generally pursued, make controversy on all subjects, however important, that into which, in such hands, it always degenerates — a dispute about words.”
The best way to avoid controversies about words is to use words in their proper senses. Mr. Sadler may think our objection captious; but how he can think it disingenuous we do not well understand. If we had represented him as meaning what we knew that he did not mean, we should have acted in a disgraceful manner. But we did not represent him, and he allows that we did not represent him, as meaning what he did not mean. We blamed him, and with perfect justice and propriety, for saying what he did not mean. Every man has in one sense a right to define his own terms; that is to say, if he chooses to call one two, and two seven, it would be absurd to charge him with false arithmetic for saying that seven is the double of one. But it would be perfectly fair to blame him for changing the established sense of words. The words, “inverse variation,” in matters not purely scientific, have often been used in the loose way in which Mr. Sadler has used them. But we shall be surprised if he can find a single instance of their having been so used in a matter of pure arithmetic.
We will illustrate our meaning thus. Lord Thurlow, in one of his speeches about Indian affairs, said that one Hastings was worth twenty Macartneys. He might, with equal propriety, have said ten Macartneys, or a hundred Macartneys. Nor would there have been the least inconsistency in his using all the three expressions in one speech. But would this be an excuse for a financier who, in a matter of account, should reason as if ten, twenty, and a hundred were the same number?
Mr. Sadler tells us that he purposely avoided the use of the word proportion in stating his principle. He seems, therefore, to allow that the word proportion would have been improper. Yet he did in fact employ it in explaining his principle, accompanied with an awkward explanation intended to signify that, though he said proportion, he meant something quite different from proportion. We should not have said so much on this subject, either in our former article, or at present, but that there is in all Mr. Sadler’s writings an air of scientific pedantry, which renders his errors fair game. We will now let the matter rest; and, instead of assailing Mr. Sadler with our verbal criticism, proceed to defend ourselves against his literal criticism.
“The Reviewer promised his readers that some curious results should follow from his shuffling. We will enable him to keep his word.
“ ‘In two English counties,’ says he, ‘which contain from 50 to 100 inhabitants on the square mile, the births to 100 marriages are, according to Mr. Sadler, 420; but in 44 departments of France, in which there are from one to two hecatares [hectares] to each inhabitant, that is to say, in which the population is from 125 to 250, or rather more, to the square mile, the number of births to one hundred marriages is 423 and a fraction.’
“The first curious result is, that our Reviewer is ignorant, not only of the name, but of the extent, of a French hectare; otherwise he is guilty of a practice which, even if transferred to the gambling-table, would, I presume, prevent him from being allowed ever to shuffle, even there, again. He was most ready to pronounce upon a mistake of one per cent in a calculation of mine, the difference in no wise affecting the argument in hand; but here I must inform him, that his error, whether wilfully or ignorantly put forth, involves his entire argument.
“The French hectare I had calculated to contain 107708 English square feet, or 2 acres; Dr. Kelly takes it, on authority which he gives, at 107644 English square feet, or 2 acres. The last French Annuaires, however, state it, I perceive, as being equal to 2 acres. The difference is very trifling, and will not in the slightest degree cover our critic’s error. The first calculation gives about 258 hectares to an English square mile; the second, 258; the last, or French calculation, 258. When, therefore, the Reviewer calculates the population of the departments of France thus: ‘from one to two hectares to each inhabitant, that is to say, in which the population is from 125 to 250, or rather more, to the square mile;’ his ‘that is to say’ is that which he ought not to have said—no rare case with him, as we shall show throughout.”
We must inform Mr. Sadler, in the first place, that we inserted the vowel which amuses him so much, not from ignorance or from carelessness, but advisedly, and in conformity with the practice of several respectable writers. He will find the word hecatare in Rees’s Cyclopædia. He will find it also in Dr. Young. We prefer the form which we have employed, because it is etymologically correct. Mr. Sadler seems not to know that a hecatare is so called, because it contains a hundred ares.
We were perfectly acquainted with the extent as well as with the name of a hecatare. Is it at all strange that we should use the words “250, or rather more,” in speaking of 258 and a fraction? Do not people constantly employ round numbers with still greater looseness, in translating foreign distances and foreign money? If indeed, as Mr. Sadler says, the difference which he chooses to call an error involved the entire argument, or any part of the argument, we should have been guilty of gross unfairness. But it is not so. The difference between 258 and 250, as even Mr. Sadler would see if he were not blind with fury, was a difference to his advantage. Our point was this. The fecundity of a dense population in certain departments of France is greater than that of a thinly scattered population in certain counties of England. The more dense, therefore, the population in those departments of France, the stronger was our case. By putting 250, instead of 258, we understated our case. Mr. Sadler’s correction of our orthography leads us to suspect that he knows very little of Greek; and his correction of our calculation quite satisfies us that he knows very little of logic.
But, to come to the gist of the controversy. Our argument, drawn from Mr. Sadler’s own Tables, remains absolutely untouched. He makes excuses indeed; for an excuse is the last thing that Mr. Sadler will ever want. There is something half laughable and half provoking in the facility with which he asserts and retracts, says and unsays, exactly as suits his argument. Sometimes the register of baptisms is imperfect, and sometimes the register of burials. Then again these registers become all at once exact almost to an unit. He brings forward a census of Prussia in proof of his theory. We show that it directly confutes his theory; and it forthwith becomes “notoriously and grossly defective.” The census of the Netherlands is not to be easily dealt with; and the census of the Netherlands is therefore pronounced inaccurate, In his book on the Law of Population, he tells us that “in the slave-holding States of America, the male slaves constitute a decided majority of that unfortunate class.” This fact we turned against him; and, forgetting that he had himself stated it, he tells us that “it is as erroneous as many other ideas which we entertain,” and that “he will venture to assert that the female slaves were, at the nubile age, as numerous as the males.” The increase of the negroes in the United States puzzles him; and he creates a vast slave trade to solve it. He confounds together things perfectly different; the slave-trade carried on under the American flag, and the slave-trade carried on for the supply of the American soil, — the slave-trade with Africa, and the internal slave-trade between the different States. He exaggerates a few occasional acts of smuggling into an immense and regular importation, and makes his escape as well as he can under cover of this hubbub of words. Documents are authentic and facts true precisely in proportion to the support which they afford to his theory. This is one way, undoubtedly, of making books: but we question much whether it be the way to make discoveries.
As to the inconsistencies which we pointed out between his theory and his own tables, he finds no difficulty in explaining them away or facing them out. In one case there would have been no contradiction if, instead of taking one of his tables, we had multiplied the number of three tables together, and taken the average. Another would never have existed if there had not been a great migration of people into Lancashire. Another is not to be got over by any device. But then it is very small, and of no consequence to the argument.
Here, indeed, he is perhaps right. The inconsistencies which we noticed were, in themselves, of little moment. We gave them as samples, — as mere hints, to caution those of our readers who might also happen to be readers of Mr. Sadler against being deceived by his packing. He complains of the word packing. We repeat it; and, since he has defied us to the proof, we will go fully into the question which, in our last article, we only glanced at, and prove, in such a manner as shall not leave even to Mr. Sadler any shadow of excuse, that his theory owes its speciousness to packing, and to packing alone.
That our readers may fully understand our reasoning, we will again state what Mr. Sadler’s proposition is. He asserts that, on a given space, the number of children to a marriage becomes less and less as the population becomes more and more numerous.
We will begin with the censuses of France given by Mr. Sadler. By joining the departments together in combinations which suit his purpose, he has contrived to produce three tables, which he presents as decisive proofs of his theory.
The first is as follows:—
“The legitimate births are, in those departments where there are to each inhabitant—
The two other computations he has given in one table. We subjoin it.
These tables, as we said in our former article, certainly look well for Mr. Sadler’s theory. “Do they?” says he. “Assuredly they do; and in admitting this, the Reviewer has admitted the theory to be proved.” We cannot absolutely agree to this. A theory is not proved, we must tell Mr. Sadler, merely because the evidence in its favour looks well at first sight. There is an old proverb, very homely in expression, but well deserving to be had in constant remembrance by all men, engaged either in action or in speculation—“One story is good till another is told!”
We affirm, then, that the results which these tables present, and which seem so favourable to Mr. Sadler’s theory, are produced by packing, and by packing alone.
In the first place, if we look at the departments singly, the whole is in disorder. About the department in which Paris is situated there is no dispute: Mr. Malthus distinctly admits that great cities prevent propagation. There remain eighty-four departments; and of these there is not, we believe, a single one in the place which, according to Mr. Sadler’s principle, it ought to occupy.
That which ought to be highest in fecundity is tenth in one table, fourteenth in another, and only thirty-first according to the third. That which ought to be third is twenty-second by the table, which places it highest. That which ought to be fourth is fortieth by the table, which places it highest. That which ought to be eighth is fiftieth or sixtieth. That which ought to be tenth from the top is at about the same distance from the bottom. On the other hand, that which, according to Mr. Sadler’s principle, ought to be last but two of all the eighty-four is third in two of the tables, and seventh in that which places it lowest; and that which ought to be last is, in one of Mr. Sadler’s tables, above that which ought to be first, in two of them, above that which ought to be third, and, in all of them, above that which ought to be fourth.
By dividing the departments in a particular manner, Mr. Sadler has produced results which he contemplates with great satisfaction. But, if we draw the lines a little higher up or a little lower down, we shall find that all his calculations are thrown into utter confusion; and that the phenomena, if they indicate any thing, indicate a law the very reverse of that which he has propounded.
Let us take, for example, the thirty-two departments, as they stand in Mr. Sadler’s table, from Lozére to Meuse inclusive, and divide them into two sets of sixteen departments each. The set from Lozére and Loiret inclusive consists of those departments in which the space to each inhabitant is from 3·8 hecatares to 2·42. The set from Cantal to Meuse inclusive consists of those departments in which the space to each inhabitant is from 2·42 hecatares to 2·07. That is to say, in the former set the inhabitants are from 68 to 107 on the square mile, or thereabouts. In the latter they are from 107 to 125. Therefore, on Mr. Sadler’s principle, the fecundity ought to be smaller in the latter set than in the former. It is, however, greater, and that in every one of Mr. Sadler’s three tables.
Let us now go a little lower down, and take another set of sixteen departments—those which lie together in Mr. Sadler’s tables, from Hérault to Jura inclusive. Here the population is still thicker than in the second of those sets which we before compared. The fecundity, therefore, ought, on Mr. Sadler’s principle, to be less than in that set. But it is again greater, and that in all Mr. Sadler’s three tables. We have a regularly ascending series, where, if his theory had any truth in it, we ought to have a regularly descending series. We will give the results of our calculation.
The number of children to 1000 marriages is—
We will give another instance, if possible still more decisive. We will take the three departments of France which ought, on Mr. Sadler’s principle, to be the lowest in fecundity of all the eighty-five, saving only that in which Paris stands; and we will compare them with the three departments in which the fecundity ought, according to him, to be greater than in any other department of France, two only excepted. We will compare Bas Rhin, Rhone, and Nord, with Lozére, Landes, and Indre. In Lozére, Landes, and Indre, the population is from 68 to 84 on the square mile, or nearly so. In Bas Rhin, Rhone, and Nord, it is from 300 to 417 on the square mile. There cannot be a more overwhelming answer to Mr. Sadler’s theory than the table which we subjoin:
The number of births to 1000 marriages is—
These are strong cases. But we have a still stronger case. Take the whole of the third, fourth, and fifth divisions into which Mr. Sadler had portioned out the French departments. These three divisions make up almost the whole kingdom of France. They contain seventy-nine out of the eighty-five departments. Mr. Sadler has contrived to divide them in such a manner that, to a person who looks merely at his averages, the fecundity seems to diminish as the population thickens. We will separate them into two parts instead of three. We will draw the line between the department of Gironde and that of Hérault. On the one side are the thirty-two departments from Cher to Gironde inclusive. On the other side are the forty-six departments from Hérault to Nord inclusive. In all the departments of the former set, the population is under 132 on the square mile. In all the departments of the latter set, it is above 132 on the square mile. It is clear that, if there be one word of truth in Mr. Sadler’s theory, the fecundity in the latter of these divisions must be very decidedly smaller than in the former. Is it so? It is, on the contrary, greater in all the three tables. We give the result.
The number of births to 1000 marriages is—
This fact is alone enough to decide the question. Yet it is only one of a crowd of similar facts. If the line between Mr. Sadler’s second and third division be drawn six departments lower down, the third and fourth divisions will, in all the tables, be above the second. If the line between the third and fourth divisions be drawn two departments lower down, the fourth division will be above the third in all the tables. If the line between the fourth and fifth division be drawn two departments lower down, the fifth will, in all the tables, be above the fourth, above the third, and even above the second. How then has Mr. Sadler obtained his results? By packing solely. By placing in one compartment a district no larger than the the Isle of Wight; in another, a district somewhat less than Yorkshire; in a third, a territory much larger than the island of Great Britain.
By the same artifice it is that he has obtained from the census of England those delusive averages which he brings forward with the utmost ostentation in proof of his principle. We will examine the facts relating to England, as we have examined those relating to France.
If we look at the counties one by one, Mr. Sadler’s principle utterly fails. Hertfordshire with 251 on the square mile; Worcestershire with 258; and Kent with 282, exhibit a far greater fecundity than the East-Riding of York, which has 151 on the square mile; Monmouthshire, which has 145; or Northumberland, which has 108. The fecundity of Staffordshire, which has more than 300 on the square mile, is as high as the average fecundity of the counties which have from 150 to 200 on the square mile. But, instead of confining ourselves to particular instances, we will try masses.
Take the eight counties of England which stand together in Mr. Sadler’s list, from Cumberland to Dorset inclusive. In these the population is from 107 to 150 on the square mile. Compare with these the eight counties from Berks to Durham inclusive, in which the population is from 175 to 200 on the square mile. Is the fecundity in the latter counties smaller than in the former? On the contrary, the result stands thus:
The number of children to 100 marriages is—
Take the six districts from the East-Riding of York to the County of Norfolk inclusive. Here the population is from 150 to 170 on the square mile. To these oppose the six counties from Derby to Worcester inclusive. The population is from 200 to 260. Here again we find that a law, directly the reverse of that which Mr. Sadler has laid down, appears to regulate the fecundity of the inhabitants.
The number of children to 100 marriages is—
But we will make another experiment on Mr. Sadler’s tables, if possible more decisive than any of those which we have hitherto made. We will take the four largest divisions into which he has distributed the English counties, and which follow each other in regular order. That our readers may fully comprehend the nature of that packing by which his theory is supported, we will set before them this part of his table.
These averages look well, undoubtedly, for Mr. Sadler’s theory. The numbers 396, 390, 388, 378, follow each other very speciously in a descending order. But let our readers divide these thirty-four counties into two equal sets of seventeen counties each, and try whether the principle will then hold good. We have made this calculation, and we present them with the following result.
The number of children to 100 marriages is—
The difference is small, but not smaller than differences which Mr. Sadler has brought forward as proofs of his theory. We say, that these English tables no more prove that fecundity increases with the population than that it diminishes with the population. The thirty-four counties which we have taken make up, at least, four-fifths of the kingdom: and we see that, through those thirty-four counties, the phenomena are directly opposed to Mr. Sadler’s principle. That in the capital, and in great manufacturing towns, marriages are less prolific than in the open country, we admit, and Mr. Malthus admits. But that any condensation of the population, short of that which injures all physical energies, will diminish the prolific powers of man, is, from these very tables of Mr. Sadler, completely disproved.
It is scarcely worth while to proceed with instances, after proofs so overwhelming as those which we have given. Yet we will show that Mr. Sadler has formed his averages on the census of Prussia by an artifice exactly similar to that which we have already exposed.
Of the census of 1756 we will say nothing, as Mr. Sadler, finding himself hard pressed by the argument which we drew from it, now declares it to be grossly defective. We confine ourselves to the census of 1784: and we will draw our lines at points somewhat different from those at which Mr. Sadler has drawn his. Let the first compartment remain as it stands. Let East Prussia, which contains a much larger population than his last compartment, stand alone in the second division. Let the third consist of the New Mark, the Mark of Brandenburg, East Friesland and Guelderland, and the fourth of the remaining provinces. Our readers will find that, on this arrangement, the division which, on Mr. Sadler’s principle, ought to be second in fecundity stands higher than that which ought to be first; and that the division which ought to be fourth stands higher than that which ought to be third. We will give the result in one view.
The number of births to a marriage is —
We will go no farther with this examination. In fact, we have nothing more to examine. The tables which we have scrutinised constitute the whole strength of Mr. Sadler’s case; and we confidently leave it to our readers to say, whether we have not shown that the strength of his case is weakness.
Be it remembered too that we are reasoning on data furnished by Mr. Sadler himself. We have not made collections of facts to set against his, as we easily might have done. It is on his own showing, it is out of his own mouth, that his theory stands condemned.
That packing which we have exposed is not the only sort of packing which Mr. Sadler has practised. We mentioned in our review some facts relating to the towns of England, which appear from Mr. Sadler’s tables, and which it seems impossible to explain if his principles be sound. The average fecundity of a marriage in towns of fewer than 3000 inhabitants is greater than the average fecundity of the kingdom. The average fecundity in towns of from 4000 to 5000 inhabitants is greater than the average fecundity of Warwickshire, Lancashire, or Surrey. How is it, we asked, if Mr. Sadler’s principle be correct, that the fecundity of Guildford should be greater than the average fecundity of the county in which it stands?
Mr. Sadler, in reply, talks about “the absurdity of comparing the fecundity in the small towns alluded to with that in the counties of Warwick and Stafford, or in those of Lancaster and Surrey.” He proceeds thus—
“In Warwickshire, far above half the population is comprised in large towns, including, of course, the immense metropolis of one great branch of our manufactures, Birmingham. In the county of Stafford, besides the large and populous towns in its iron districts, situated so close together as almost to form, for considerable distances, a continuous street; there is, in its potteries, a great population, recently accumulated, not included, indeed, in the towns distinctly enumerated in the censuses, but vastly exceeding in its condensation that found in the places to which the Reviewer alludes. In Lancashire again, to which he also appeals, one-fourth of the entire population is made up of the inhabitants of two only of the towns of that county; far above half of it is contained in towns, compared with which those he refers to are villages; even the hamlets of the manufacturing parts of Lancashire are often far more populous than the places he mentions. But he presents us with a climax of absurdity in appealing lastly to the population of Surrey as quite rural compared with that of the twelve towns, having less than 5000 inhabitants in their respective jurisdictions, such as Saffron-Walden, Monmouth, &c., Now, in the last census, Surrey numbered 398,658 inhabitants, and, to say not a word about the other towns of the county, much above two hundred thousands of these are within the Bills of Mortality! ‘We should, therefore, be glad to know’ how it is utterly inconsistent with my principle that the fecundity of Guildford, which numbers about 3000 inhabitants, should be greater than the average fecundity of Surrey, made up, as the bulk of the population of Surrey is, of the inhabitants of some of the worst parts of the metropolis? Or why the fecundity of a given number of marriages in the eleven little rural towns he alludes to, being somewhat higher than that of an equal number, half taken for instance, from the heart of Birmingham or Manchester, and half from the populous districts by which they are surrounded, is inconsistent with my theory?
“Had the Reviewer’s object, in this instance, been to discover the truth, or had he known how to pursue it, it is perfectly clear, at first sight, that he would not have instituted a comparison between the prolificness which exists in the small towns he has alluded to, and that in certain districts, the population of which is made up, partly of rural inhabitants and partly of accumulations of people in immense masses, the prolificness of which, if he will allow me still the use of the phrase, is inversely as their magnitude; but he would have compared these small towns with the country places properly so called, and then again the different classes of towns with each other; this method would have led him to certain conclusions on the subject.”
Now, this reply shows that Mr. Sadler does not in the least understand the principle which he has himself laid down. What is that principle? It is this, that the fecundity of human beings on given spaces, varies inversely as their numbers. We know what he means by inverse variation. But we must suppose that he uses the words, “given spaces” in the proper sense. Given spaces are equal spaces. Is there any reason to believe, that in those parts of Surrey which lie within the bills of mortality there is any space, equal in area to the space on which Guildford stands, which is more thickly peopled than the space on which Guildford stands? We do not know that there is any such. We are sure that there are not many. Why, therefore, on Mr. Sadler’s principle, should the people of Guildford be more prolific than the people who live within the bills of mortality? And, if the people of Guildford ought, as on Mr. Sadler’s principle they unquestionably ought, to stand as low in the scale of fecundity as the people of Southwark itself, it follows, most clearly, that they ought to stand far lower than the average obtained by taking all the people of Surrey together.
The same remark applies to the case of Birmingham, and to all the other cases which Mr. Sadler mentions. Towns of 5000 inhabitants may be, and often are, as thickly peopled, “on a given space,” as Birmingham. They are, in other words, as thickly peopled as a portion of Birmingham, equal to them in area. If so, on Mr. Sadler’s principle, they ought to be as low in the scale of fecundity as Birmingham. But they are not so. On the contrary, they stand higher than the average obtained by taking the fecundity of Birmingham in combination with the fecundity of the rural districts of Warwickshire.
The plain fact is, that Mr. Sadler has confounded the population of a city with its population “on a given space,”—a mistake which, in a gentleman who assures us that mathematical science was one of his early and favourite studies, is somewhat curious. It is as absurd, on his principle, to say that the fecundity of London ought to be less than the fecundity of Edinburgh, because London has a greater population than Edinburgh, as to say that the fecundity of Russia ought to be greater than that of England, because Russia has a greater population than England. He cannot say that the spaces on which towns stand are too small to exemplify the truth of his principle. For he has himself brought forward the scale of fecundity in towns, as a proof of his principle. And, in the very passage which we quoted above, he tells us that, if we knew how to pursue truth, or wished to find it, we “should have compared these small towns with country places, and the different classes of towns with each other.” That is to say, we ought to compare together such unequal spaces as give results favourable to his theory, and never to compare such equal spaces as give results opposed to it. Does he mean anything by “a given space?” Or does he mean merely such a space as suits his argument? It is perfectly clear that, if he is allowed to take this course, he may prove anything. No fact can come amiss to him. Suppose, for example, that the fecundity of New York should prove to be smaller than the fecundity of Liverpool. “That,” says Mr. Sadler, “makes for my theory. For there are more people within two miles of the Broadway of New York, than within two miles of the Exchange of Liverpool.” Suppose, on the other hand, that the fecundity of New York should be greater than the fecundity of Liverpool. “This,” says Mr. Sadler again, “is an unanswerable proof of my theory. For there are many more people within forty miles of Liverpool than within forty miles of New York.” In order to obtain his numbers, he takes spaces in any combinations which may suit him. In order to obtain his averages, he takes numbers in any combinations which may suit him. And then he tells us that, because his tables, at the first glance, look well for his theory, his theory is irrefragably proved.
We will add a few words respecting the argument which we drew from the peerage. Mr. Sadler asserted that the Peers were a class condemned by nature to sterility. We denied this, and showed, from the last edition of Debrett, that the Peers of the United Kingdom have considerably more than the average number of children to a marriage. Mr. Sadler’s answer has amused us much. He denies the accuracy of our counting, and, by reckoning all the Scotch and Irish Peers as Peers of the United Kingdom, certainly makes very different numbers from those which we gave. A member of the Parliament of the United Kingdom might have been expected, we think, to know better what a Peer of the United Kingdom is.
By taking the Scotch and Irish Peers, Mr. Sadler has altered the average. But it is considerably higher than the average fecundity of England, and still, therefore, constitutes an unanswerable argument against his theory.
The shifts to which, in this difficulty, he has recourse, are exceedingly diverting. “The average fecundity of the marriages of Peers,” said we, “is higher by one-fifth than the average fecundity of marriages throughout the kingdom.”
“Where, or by whom did the Reviewer find it supposed,” answers Mr. Sadler, “that the registered baptisms expressed the full fecundity of the marriages of England?”
Assuredly, if the registers of England are so defective as to explain the difference which, on our calculation, exists between the fecundity of the peers and the fecundity of the people, no argument against Mr. Sadler’s theory can be drawn from that difference. But what becomes of all the other arguments which Mr. Sadler has founded on these very registers? Above all, what becomes of his comparison between the censuses of England and France? In the pamphlet before us, he dwells with great complacency on a coincidence which seems to him to support his theory, and which to us seems, of itself, sufficient to overthrow it.
“In my table of the population of France, in the forty-four departments in which there are from one to two hectares to each inhabitant, the fecundity of 100 marriages, calculated on the average of the results of the three computations relating to different periods given in my table, is 406. In the twenty-two counties of England, in which there is from one to two hectars to each inhabitant, or from 129 to 259 on the square mile, — beginning, therefore, with Huntingdonshire, and ending with Worcestershire, —the whole number of marriages during ten years will be found to amount to 379,624, and the whole number of the births during the same term to 1,545,549 — or 407 births to 100 marriages! A difference of one in one thousand only, compared with the French proportion!”
Does not Mr. Sadler see that, if the registers of England, which are notoriously very defective, give a result exactly corresponding almost to an unit with that obtained from the registers of France, which are notoriously very full and accurate, this proves the very reverse of what he employs it to prove? The correspondence of the registers proves that there is no correspondence in the facts. In order to raise the average fecundity of England even to the level of the average fecundity of the peers of the three kingdoms, which is 3·81 to a marriage, it is necessary to add nearly six per cent. to the number of births given in the English registers. But, if this addition be made, we shall have, in the counties of England, from Huntingdonshire to Worcestershire inclusive, 4·30 births to a marriage or thereabouts; and the boasted coincidence between the phenomena of propagation in France and England disappears at once. This is a curious specimen of Mr. Sadler’s proficiency in the art of making excuses. In the same pamphlet he reasons as if the same registers were accurate to one in a thousand, and as if they were wrong at the very least by one in eighteen.
He tries to show that we have not taken a fair criterion of the fecundity of the peers. We are not quite sure that we understand his reasoning on this subject. The order of his observations is more than usually confused, and the cloud of words more than usually thick. We will give the argument on which he seems to lay most stress in his own words:
“But I shall first notice a far more obvious and important blunder into which the Reviewer has fallen; or into which, I rather fear, he knowingly wishes to precipitate his readers, since I have distinctly pointed out what ought to have preserved him from it in the very chapter he is criticising and contradicting. It is this: — he has entirely omitted “counting” the sterile marriages of all those peerages which have become extinct during the very period his counting embraces. He counts, for instance, Earl Fitzwilliam, his marriages, and heir; but has he not omitted to enumerate the marriages of those branches of the same noble house, which have become extinct since that venerable individual possessed his title? He talks of my having appealed merely to the extinction of peerages in my argument; but, on his plan of computation, extinctions are perpetually and wholly lost sight of. In computing the average prolificness of the marriages of the nobles, he positively counts from a select class of them only, one from which the unprolific are constantly weeded, and regularly disappear; and he thus comes to the conclusion, that the peers are ‘an eminently prolific class!’ Just as though a farmer should compute the rate of increase, not from the quantity of seed sown, but from that part of it only which comes to perfection, entirely omitting all which had failed to spring up or come to maturity. Upon this principle the most scanty crop ever obtained, in which the husbandman should fail to receive ‘seed again,’ as the phrase is, might be so ‘counted’ as to appear ‘eminently prolific’ indeed.”
If we understand this passage rightly, it decisively proves that Mr. Sadler is incompetent to perform even the lowest offices of statistical research. What shadow of reason is there to believe that the peers who were alive in the year 1828 differed as to their prolificness from any other equally numerous set of peers taken at random? In what sense were the peers who were alive in 1828 analogous to that part of the seed which comes to perfection? Did we entirely omit all that failed? On the contrary, we counted the sterile as well as the fruitful marriages of all the peers of the United Kingdom living at one time. In what way were the peers who were alive in 1828 a select class? In what way were the sterile weeded from among them? Did every peer who had been married without having issue die in 1827? What shadow of reason is there to suppose that there was not the ordinary proportion of barren marriages among the marriages contracted by the noblemen whose names are in Debrett’s last edition? But we ought, says Mr. Sadler, to have counted all the sterile marriages of all the peers “whose titles had become extinct during the period which our counting embraced;” that is to say, since the earliest marriage contracted by any peer living in 1828. Was such a proposition ever heard of before? Surely we were bound to do no such thing, unless at the same time we had counted also the children born from all the fruitful marriages contracted by peers during the same period. Mr. Sadler would have us divide the number of children born to peers living in 1828, not by the number of marriages which those peers contracted, but by the number of marriages which those peers contracted added to a crowd of marriages selected, on account of their sterility, from among the noble marriages which have taken place during the last fifty years. Is this the way to obtain fair averages? We might as well require that all the noble marriages which during the last fifty years have produced ten children apiece should be added to those of the peers living in 1828. The proper way to ascertain whether a set of people be prolific or sterile is, not to take marriages selected from the mass either on account of their fruitfulness or on account of their sterility, but to take a collection of marriages which there is no reason to think either more or less fruitful than others. What reason is there to think that the marriages contracted by the peers who were alive in 1828 were more fruitful than those contracted by the peers who were alive in 1800 or in 1750?
We will add another passage from Mr. Sadler’s pamphlet on this subject. We attributed the extinction of peerages partly to the fact that those honours are for the most part limited to heirs male.
“This is a discovery indeed! Peeresses, ‘eminently prolific,’ do not, as Macbeth conjured his spouse, ‘bring forth men-children only;’ they actually produce daughters as well as sons!! Why, does not the Reviewer see, that so long as the rule of nature, which proportions the sexes so accurately to each other, continues to exist, a tendency to a diminution in one sex proves, as certainly as the demonstration of any mathematical problem, a tendency to a diminution in both; but to talk of ‘eminently prolific’ peeresses, and still maintain that the rapid extinction in peerages is owing to their not bearing male children exclusively, is arrant nonsense.”
Now, if there be any proposition on the face of the earth which we should not have expected to hear characterised as arrant nonsense, it is this,—that an honour limited to males alone is more likely to become extinct than an honour which, like the crown of England, descends indifferently to sons and daughters. We have heard, nay, we actually know families, in which, much as Mr. Sadler may marvel at it, there are daughters and no sons. Nay, we know many such families. We are as much inclined as Mr. Sadler to trace the benevolent and wise arrangements of Providence in the physical world, when once we are satisfied as to the facts on which we proceed. And we have always considered it as an arrangement deserving of the highest admiration, that, though in families the number of males and females differs widely, yet in great collections of human beings the disparity almost disappears. The chance undoubtedly is, that in a thousand marriages the number of daughters will not very much exceed the number of sons. But the chance also is, that several of those marriages will produce daughters, and daughters only. In every generation of the peerage there are several such cases. When a peer whose title is limited to male heirs dies, leaving only daughters, his peerage must expire, unless he have, not only a collateral heir, but a collateral heir descended through an uninterrupted line of males from the first possessor of the honour. If the deceased peer was the first nobleman of his family, then, by the supposition, his peerage will become extinct. If he was the second, it will become extinct, unless he leaves a brother or a brother’s son. If the second peer had a brother, the first peer must have had at least two sons; and this is more than the average number of sons to a marriage in England. When, therefore, it is considered how many peerages are in the first and second generation, it will not appear strange that extinctions should frequently take place. There are peerages which descend to females as well as males. But, in such cases, if a peer dies, leaving only daughters, the very fecundity of the marriage is a cause of the extinction of the peerage. If there were only one daughter, the honour would descend. If there are several, it falls into abeyance.
But it is needless to multiply words in a case so clear; and indeed it is needless to say anything more about Mr. Sadler’s book. We have, if we do not deceive ourselves, completely exposed the calculations on which his theory rests; and we do not think that we should either amuse our readers or serve the cause of science if we were to rebut in succession a series of futile charges brought in the most angry spirit against ourselves; ignorant imputations of ignorance, and unfair complaints of unfairness,—conveyed in long, dreary, declamations, so prolix that we cannot find space to quote them, and so confused that we cannot venture to abridge them.
There is much indeed in this foolish pamphlet to laugh at, from the motto in the first page down to some wisdom about cows in the last. One part of it indeed is solemn enough, we mean a certain jeu d’esprit of Mr. Sadler’s touching a tract of Dr. Arbuthnot’s. This is indeed “very tragical mirth,” as Peter Quince’s playbill has it; and we would not advise any person who reads for amusement to venture on it as long as he can procure a volume of the Statutes at Large. This, however, to do Mr. Sadler justice, is an exception. His witticisms, and his tables of figures, constitute the only parts of his work which can be perused with perfect gravity. His blunders are diverting, his excuses exquisitely comic. But his anger is the most grotesque exhibition that we ever saw. He foams at the mouth with the love of truth, and vindicates the Divine benevolence with a most edifying heartiness of hatred. On this subject we will give him one word of parting advice. If he raves in this way to ease his mind, or because he thinks that he does himself credit by it, or from a sense of religious duty, far be it from us to interfere. His peace, his reputation, and his religion are his own concern; and he, like the nobleman to whom his treatise is dedicated, has a right to do what he will with his own. But, if he has adopted his abusive style from a notion that it would hurt our feelings, we must inform him that he is altogether mistaken; and that he would do well in future to give us his arguments, if he has any, and to keep his anger for those who fear it.