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:—