Part 22

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--

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 {285}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. Malthas 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, {286}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 Lozère to Meuse inclusive, and divide them into two sets of sixteen departments each. The set from Lozère 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--

First Table. Second Table. Third Table. In the sixteen departments where there are from 68 to 107 people on a square mile 4188 4226 3780 In the sixteen departments where there are from 107 to 125 people on a square mile 4374 4332 3855 In the sixteen departments where there are from 134 to 125 people on a square mile 4484 4416 3914 {287}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 Lozère, Landes, and Indre. In Lozère, 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--

Take the whole of the third, fourth, and fifth divisions into which Mr. Sadler has 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 MV. 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--

In the thirty-two departments in whieh there are from 86 to 13.2 people on the square mile 4210 4199 3760 In the forty-seven departments in whieh there are from 132 to 41.7 people on the square mile....

This fact is alone enough to decide the question. Yet it is only one of a crowd of similar facts. If the {289}line between Mr. Sadler’s second and third divisions 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 he 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 divisions 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 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 F rance.

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 {290}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--

In the eight counties of England, in which there are from 107 to 146 people on the square mile 388 In the eight counties of England, in which there are from 175 to 200 people on the square mile 402 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--

In the six counties in which there are from 150 to 170 people on the square mile. . . 392

In the six counties in which there are from 200 to 260 people on the square mile. . . 399

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.

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.

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, {295}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 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 oui’ 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_?”

{296}”_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 hint 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, {297}and to all the other eases 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 {298}any thing 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 any thing. 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 {299}know Letter 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. In the twenty-two counties of England, in which there is from one to two hectares to each inhabitant, or {300}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 379,024, 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 l’aise 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.