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 in the least populous part of England, would be, 246 X 4000 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 { 226}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 two hundred-thousand-fold, the fecundity decreases by little more than one-half.