“The preceding definition may be thus amplified and explained. Premising, as a mere truism, that marriages under precisely similar circumstances will, on the average, be equally fruitful everywhere, I proceed to state, first, that the prolificness of a given number of marriages will, all other circumstances being the same, vary in proportion to the condensation 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 {223}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 is 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.