tion of the population, so that that prolificness shall be greatest where the numbers on an equal space are the fewest, and, on the contrary, the smallest where those numbers are the largest.'

Mr Sadler, at setting out, abuses Mr Malthus for enouncing his theory in terms taken from the exact sciences. Applied to the mensuration of human fecundity,' he tells us, the most 'fallacious of all things is geometrical demonstration;' and he again informs us that those act an irrational and irreverent 'part who affect to measure the mighty depth of God's mercies by their arithmetic, and to demonstrate, by their geometrical ' ratios, that it is inadequate to receive and contain the efflux of that fountain of life which is in Him.'

It appears, however, that it is not to the use of mathematical words, but only to the use of those words in their right senses, that Mr Sadler objects. The law of inverse variation, or inverse proportion, is as much a part of mathematical science as the law of geometric progression. The only difference in this respect between Mr Malthus and Mr Sadler is, that Mr Malthus knows what is meant by geometric progression, and that Mr Sadler has not the faintest notion of what is meant by inverse variation. Had he understood the proposition which he has enounced with so much pomp, its ludicrous absurdity must at once have flashed on his mind.

Let it be supposed that there is a tract in the back settlements of America, or in New South Wales, equal in size to London, with only a single couple, a man and his wife, living upon it. The population of London, with its immediate suburbs, is now probably about a million and a half. The average fecundity of a marriage in London is, as Mr Sadler tells us, 2.35. How many children will the woman in the back settlements bear according to Mr Sadler's theory? The solution of the problem is easy. As the population in this tract in the back settlements to the population of London, so will be the number of children born from a marriage in London to the number of children born from the marriage of this couple in the back settlements. That is to say

2: 1,500,000::2.35:1.762,500.

The lady will have 1,762,500 children: a large efflux of the ' fountain of life,' to borrow Mr Sadler's sonorous rhetoric, as the most philoprogenitive parent could possibly desire.

But let us, instead of putting cases of our own, look at some of those which Mr Sadler has brought forward in support of his theory. The following table, he tells us, exhibits a striking proof of the truth of his main position. It seems to us to prove

only that Mr Sadler does not know what inverse proportion

Is 1 to 160 as 3.66 to 5.48? If Mr Sadler's principle were just, the number of children produced by a marriage at the Cape would be not 5.48, but very near 600. Or take America and France. Is 4 to 140 as 4.22 to 5.22? The number of births to a marriage in North America ought, according to this proportion, to be about 150.

Mr Sadler states the law of population in England thus:Where the inhabitants are found to be on the square mile,

From 50 to 100 (2 counties) the births to 100 marriages are 420

396

500 to 600 (2 counties)

4000, and upwards (1 county)

Now, I think it quite reasonable to conclude, that, were there not another document in existence relative to this subject, the facts thus deduced from the census of England are fully sufficient to demonstrate the position, that the fecundity of human beings varies inversely as their numbers. How, I ask, can it be evaded?'

What, we ask, is there to evade? Is 246 to 420 as 50 to 4000? Is 331 to 396 as 100 to 500? If the law propounded by Mr Sadler were correct, the births to a hundred marriages 246 × 4000

in the least populous part of England, would be 50 that is 19,680,-nearly two hundred children to every mother. But we will not carry on these calculations. The absurdity of Mr Sadler's proposition is so palpable that it is unnecessary to select particular instances. Let us see what are the extremes of

population and fecundity in well-known countries. The space which Mr Sadler generally takes is a square mile. The population at the Cape of Good Hope is, according to him, one to the square mile. That of London is two hundred thousand to the square mile. The number of children at the Cape, Mr Sadler informs us, is 5.48 to a marriage. In London, he states it at 2.35 to a marriage. Now how can that of which all the variations lie between 2.35 and 5.48 vary either directly or inversely, as that which admits of all the variations between one and two hundred thousand? Mr Sadler evidently does not know the meaning of the word proportion. A million is a larger quantity than ten. A hundred is a larger quantity than five. Mr Sadler thinks, therefore, that there is no impropriety in saying that a hundred is to five, as a million is to ten, or in the inverse ratio of ten to a million. He proposes to prove that the fecundity of marriages varies in inverse proportion to the density of the population. But all that he attempts to prove is that, while the population increases from one to a hundred and sixty on the square mile, the fecundity will diminish from 5.48 to 3.66; and that again, while the population increases from one hundred and sixty to two hundred thousand on the square mile, the fecundity will diminish from 3.66 to 2.35.

The proposition which Mr Sadler enounces, without understanding the words which he uses, would indeed, if it could be proved, set us at ease as to the dangers of over-population. But it is, as we have shown, a proposition so grossly absurd, that it is difficult for any man to keep his countenance while he repeats it. The utmost that Mr Sadler has ever attempted to prove is this, that the fecundity of the human race diminishes as population becomes more condensed,-but that the diminution of fecundity bears a very small ratio to the increase of population,-so that while the population on a square mile is multiplied twohundred-thousand-fold, the fecundity decreases by little more than one-half.

Does this principle vindicate the honour of God? Does it hold out any new hope or comfort to man? Not at all. We pledge ourselves to show, with the utmost strictness of reasoning, from Mr Sadler's own principles, and from facts of the most notorious description, that every consequence which follows from the law of geometrical progression, laid down by Mr Malthus, will follow from the law, miscalled a law of inverse variation, which has been laid down by Mr Sadler.

London is the most thickly-peopled spot of its size in the known world. Therefore the fecundity of the population of London must, according to Mr Sadler, be less than the fecun

dity of human beings living on any other spot of equal size. Mr Sadler tells us, that the ratios of mortality are influenced by the different degrees in which the population is condensated; and that, other circumstances being similar, the relative number of deaths in a thinly-populated, or country district, is less than that which takes place in towns, and in towns of a moderate size, less again than that which exists in large and populous cities. Therefore the mortality in London must, according to him, be greater than in other places. But though, according to Mr Sadler, the fecundity is less in London than elsewhere, and though the mortality is greater there than elsewhere, we find that even in London the number of births greatly exceeds the number of deaths. During the ten years which ended with 1820, there were fifty thousand more baptisms than burials within the bills of mortality. It follows, therefore, that, even within London itself, an increase of the population is taking place by internal propagation.

Now if the population of a place in which the fecundity is less and the mortality greater than in other places still goes on increasing by propagation, it follows that in other places the population will increase, and increase still faster. There is clearly nothing in Mr Sadler's boasted law of fecundity which will keep the population from multiplying till the whole carth is as thick with human beings as St Giles's parish. If Mr Sadler denies this, he must hold, that in places less thickly peopled than London, marriages may be less fruitful than in London, which is directly contrary to his own principles; or that in places less thickly peopled than London, and similarly situated, people will die faster than in London, which is again directly contrary to his own principles. Now if it follows, as it clearly does follow, from Mr Sadler's own doctrines, that the human race might be stowed together by three or four hundred to the acre, and might still, as far as the principle of propagation is concerned, go on increasing, what advantage, in a religious or moral point of view, has his theory over that of Mr Malthus? The principle of Mr Malthus, says Mr Sadler, leads to consequences of the most frightful description. Be it so. But do not all these consequences spring equally from his own principle? Revealed religion condemns Mr Malthus. Be it so. But Mr Sadler must share in the reproach of heresy. The theory of Mr Malthus represents the Deity as a Dionysius hanging the sword over the heads of his trembling slaves. Be it so. But under what rhetorical figure are we to represent the Deity of Mr Sadler?

A man who wishes to serve the cause of religion ought to hesitate long before he stakes the truth of religion on the event of

a controversy respecting facts in the physical world. For a time he may succeed in making a theory which he dislikes unpopular, by persuading the public that it contradicts the Scriptures, and is inconsistent with the attributes of the Deity. But if at last an overwhelming force of evidence proves this maligned theory to be true, what is the effect of the arguments by which the objector has attempted to prove that it is irreconcilable with natural and revealed religion? Merely this, to make men infidels. Like the Israelites, in their battle with the Philistines, he has presumptuously, and without warrant, brought down the ark of God into the camp, as a means of ensuring victory:—and the consequence of this profanation is, that, when the battle is lost, the ark is taken.

In every age the Church has been cautioned against this fatal and impious rashness by its most illustrious members,-by the fervid Augustin, by the subtle Aquinas, by the all-accomplished Pascal. The warning has been given in vain. That close alliance which, under the disguise of the most deadly enmity, has always subsisted between fanaticism and atheism, is still unbroken. At one time, the cry was,- If you hold that the earth 'moves round the sun, you deny the truth of the Bible.' Popes, conclaves, and religious orders, rose up against the Copernican heresy. But, as Pascal said, they could not prevent the earth from moving, or themselves from moving along with it. One thing, however, they could do, and they did. They could teach numbers to consider the Bible as a collection of old women's stories, which the progress of civilisation and knowledge was refuting one by one. They had attempted to show that the Ptolemaic system was as much a part of Christianity as the resurrection of the dead. Was it strange, then, that, when the Ptolemaic system became an object of ridicule to every man of education in Catholic countries, the doctrine of the resurrection should be in peril? In the present generation, and in our own country, the prevailing system of geology has been, with equal folly, attacked on the ground that it is inconsistent with the Mosaic dates; and here we have Mr Sadler, out of his especial zeal for religion, first proving that the doctrine of superfecundity is irreconcilable with the goodness of God, and then laying down principles, and stating facts, from which the doctrine of superfecundity necessarily follows. This blundering piety reminds us of the adventures of a certain missionary, who went to convert the inhabitants of Madagascar. The good father had an audience of the king, and began to instruct his majesty in the history of the human race as given in the Scriptures. Thus, 'sir,' said he, was woman made out of the rib of man, and ever