Miscellaneous Writings and Speeches — Volume 2

The number of children to 100 marriages is—

In the seventeen counties of England in which there

are from 100 to 177 people on the square mile..........387

In the seventeen counties in which there

are from 177 to 282 people on the square mile..........389

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.

Demonstrating the Law of Population from the Censuses of Prussia at two several Periods.

(Here follows a table showing for inhabitants on a square league the average number of births to each marriage from two different censuses.)

1756     1784

832 to  928...4.34 and 4.72

1175 to 1909...4.14 and 4.45 (including East Prussia at 1175)

2083 to 2700...3.84 and 4.24

3142 to 3461...3.65 and 4.08

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—

In those provinces of Prussia where there are fewer than

1000 people on the square league.......................4.72

In the province in which there are 1175 people on the

square league..........................................5.10

In the provinces in which there are from 1190 to 2083

people on the square league............................4.10

In the provinces in which there are from 2314 to 3461

people on the square league............................4.27

We will go no further 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, etc. 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 7/10. In the twenty-two counties of England in which there is from one to two hectares 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 1/10 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.