"It may at once be denied," says he, "that human increase proceeds geometrically; and for this simple but decisive reason, that the existence of a geometrical ratio of increase in the works of nature is neither true nor possible. It would fling into utter confusion all order, time, magnitude, and space." This is as curious a specimen of reasoning as any that has been offered to the world since the days when theories were founded on the principle that nature abhors a vacuum. We proceed a few pages further, however; and we then find that geometric progression is unnatural only in those cases in which Mr Malthus conceives that it exists; and that, in all cases in which Mr Malthus denies the existence of a geometric ratio, nature changes sides, and adopts that ratio as the rule of increase. Mr Malthus holds that subsistence will increase only in an arithmetical ratio. "As far as nature has to do with the question," says Mr Sadler, "men might, for instance, plant twice the number of peas, and breed from a double number of the same animals, with equal prospect of their multiplication." Now, if Mr Sadler thinks that, as far as nature is concerned, four sheep will double as fast as two, and eight as fast as four, how can he deny that the geometrical ratio of increase does exist in the works of nature? Or has he a definition of his own for geometrical progression, as well as for inverse proportion? Mr Malthus, and those who agree with him, have generally referred to the United States, as a country in which the human race increases in a geometrical ratio, and have fixed on thirty-five years as the term in which the population of that country doubles itself. Mr Sadler contends that it is physically impossible for a people to double in twenty-five years; nay, that thirty-five years is far too short a period,--that the Americans do not double by procreation in less than forty-seven years,--and that the rapid increase of their numbers is produced by emigration from Europe. Emigration has certainly had some effect in increasing the population of the United States. But so great has the rate of that increase been that, after making full allowance for the effect of emigration, there will be a residue, attributable to procreation alone, amply sufficient to double the population in twenty-five years. Mr Sadler states the results of the four censuses as follows:-- "There were, of white inhabitants, in the whole of the United States in 1790, 3,093,111; in 1800, 4,309,656; in 1810, 5,862,093; and in 1820, 7,861,710. The increase, in the first term, being 39 per cent.; that in the second, 36 per cent.; and that in the third and last, 33 per cent. It is superfluous to say, that it is utterly impossible to deduce the geometric theory of human increase, whatever be the period of duplication, from such terms as these."