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 favorable 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 iniles 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 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 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 a unit with that obtained from the registers of France, which are notoriously very full and ac

curate, 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 mar

riages 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 honors are, for the most part, limited to heirs male.

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"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 characterized as arrant nonsense, it is this that an honor limited to males alone is more likely to become extinct than an honor which, like the crown of England, descends indifferently to sons and daughters. We have heard of, 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 adıniration, that, though in families the