Even the question of the ratios was not settled. Godwin had counted his discussion of them the most important part of his book. It gives us his third substantial argument against Malthus. Godwin takes up,[850] what seems to have been a common charge, that the essayist had written a quarto volume to prove that population increases in a geometrical and food in an arithmetical ratio. The essayist had answered, as long ago as 1806,[851] that the first proposition was proved as soon as the facts about America were authenticated, and the second was self-evident; his book was meant less to prove the ratios than to trace their effects. His authorities, as he told Godwin afterwards,[852] were Dr. Price, Styles, Benjamin Franklin, Euler, and Sir William Petty, supplemented, for figures, by Short and Süssmilch and the censuses of the United States and England, and, for principles, by Adam Smith and Hume. We have already seen[853] how far the simile of geometrical and arithmetical ratios was meant to be pressed. Godwin thinks he exposes it by arguing that the increase of population can never be quite exactly geometrical[854] (which Malthus would admit),—that America was an exception[855] (in face of the maxim that the exception tests the rule),—that, in order to suppose population doubling itself in the United States, we must suppose it, as regards births, doing the same in the Old World (in other words, fact is the same as tendency),—that the normal increase is not that of America but that of Sweden,[856] in which case (Malthus would answer) the normal increase must be one that takes place in face of very severe restrictions. To the charge of damaging the borrowed kettle the old Irishwoman had three answers:—It was cracked when I got it; it was whole when I returned it; I never had it. So Godwin’s views of the American colonies vacillated between three inconsistent propositions: the great increase of the numbers is natural (or spontaneous), but that of the food is greater still;[857] the great increase is not natural, but due to immigration;[858] there has been no great increase at all.[859] The reader has three alternative arguments presented to him, and it matters little whereby he is convinced, if only in the end he is persuaded to believe with Godwin, that population requires no checks at all,[860] and is a fitful principle.[861] In history, says Godwin, it seems to operate by fits and starts; and such irregular effects cannot have a uniform cause. It might be replied that in the same sense gravitation is fitful, for we seem to break it by walking upstairs as well as down, by using a siphon as well as a water-jug, or by drying up a drop of ink with blotting-paper instead of letting it sink down into the paper. Yet in these cases the fitfulness is never imputed to the absence of a cause, but to the presence of more causes than one. To believe, as Godwin seems to do, in occult laws which vary with the circumstances is to believe in no laws at all.