Chapter 23

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 give 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 census 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--

Hectares Departments To every 1000 marriages

4 to 5 2 130 3 to 4 3 4372 2 to 3 30 4250 1 to 2 44 4234 .06 to 1 5 4146 .06 1 2657

The two other computations he has given in one table. We subjoin it.

Hect. to each Number of Legit. Births to Legit. Births to Inhabitant Departments 100 Marriages 100 Mar. (1826)

4 to 5 2 497 397 3 to 4 3 439 389 2 to 3 30 424 379 1 to 2 44 420 375 under 1 5 415 372 and .06 1 263 253

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 anything, 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 Lozere to Meuse inclusive, and divide them into two sets of sixteen departments each. The set from Lozere 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 Herault 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--

1st Table 2nd Table 3rd 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 155 people on a square mile................ 4484 4416 3914

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 Lozere, Landes, and Indre. In Lozere, 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--

1st Table 2nd Table 3rd Table

In the three departments in which there are from 68 to 84 people on the square mile............... 4372 4390 3890

In the three departments in which there are from 300 to 417 people on the square mile............... 4457 4510 4060

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 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 Herault. On the one side are the thirty-two departments from Cher to Gironde inclusive. On the other side are the forty-six departments from Herault 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--

1st Table 2nd Table 3rd Table

In the thirty-two departments in which there are from 86 to 132 people on the square mile....... 4210 4199 3760

In the forty-seven departments in which there are from 132 to 417 people on the square mile........ 4250 4224 3766

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 Isle of Wight; in another, a district somewhat less than Yorkshire; in the 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; Worcester 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--

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.

(Here follows a table showing for population on a square mile the proportion of births to 100 marriages, based on figures for the years 1810 to 1821.

100 to 150...396 150 to 200...390 200 to 250...388 250 to 300...378)

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--

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."