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 THE HISTORICAL METHOD. 205 science, and consider briefly how far it is true that they have been "invaded " by the Historical Method. To begin : it is obvious that no such invasion has taken place, or is threatened, in the department of pure mathema- tics the sciences of space, number, abstract quantity. The objects of these sciences, the relations which they investigate are, of course, independent of time : they cannot be con- ceived as having had a past different from the present. Our conceptions, no doubt, of these relations have had a history ; and in the general increase of historic interest, which is certainly characteristic of our age, this branch, among others, has received its share of attention. But whatever philosophic aim the students of the past history of mathe- matics may propose to themselves, they certainly do not propose to modify the received method of mathematical reasoning by the introduction of a historical element, or to support the fundamental assumptions of mathematics by arguments drawn from history, or to explain anything that may seem unexplained or arbitrary in these assumptions by a reference to the process of development through which they have passed. Much the same may be said of the fundamental universal premisses which we use in our general reasonings about the material world the laws of motion, or the law of gravita- tion. We conceive such laws to have operated unchanged through all conceivable time ; and whatever doubts and dis- putes may exist either as to the exact way in which such laws should be formulated, or the exact nature of the evi- dence on which they rest, no one supposes that this doubt and conflict admit of being solved by any knowledge of the process of development through which our physical concep- tions have come to be what they are. The case is different when we contemplate the physical universe as a particular concrete fact, and seek for an explanation of its concreteness and particularity : when we ask why there should be sixty-four or more different kinds of matter, distributed so apparently arbitrarily and irregularly through the spherical mass on which we are carried about in space, and why there should be as astronomy declares a no less irregular and arbitrary distribution of this or other matter through the rest of space. Here no doubt we have a pro- blem for which many inquiring minds have sought a solution in history in the wide sense in which I am now using the term : they have hoped to find by studying the processes of change through which the physical universe has passed an explanation of the complex of irregular differences which its