It may be safely asserted …that population, when unchecked, increases in a geometrical progression of such a nature as to double itself every twenty-five years. . . . If, setting out from a tolerably well peopled country such as England, France, Italy, or Germany, we were to suppose that, by great attention to agriculture, its produce could be permanently increased every twenty-five years by a quantity equal to that which it at present produces, it would he allowing a rate of increase decidedly beyond any probability of realization. . . . Yet this would be an arithmetical progression, and would fall short, beyond all comparison, of the natural increases of population in a geometrical progression.