Of the former class we have a typical example in mathematics, and in those exact sciences which make use of mathematics as their instrument of proof; but even in these, it is common sense which affords not only the basis, but the materials of the fabric. For while the axioms of geometry are self-evident truths which not only do not require proof, but are not capable of being proved in all their universality, every step of a demonstration is an assertion of which our acceptance depends on our incapability of conceiving either the contrary or anything else than the thing asserted. And thus the certain assurance of the proof felt by every person capable of understanding a mathematical demonstration, depends upon the conclusive self-evidence of each step of it. But we not unfrequently meet with individuals, not deficient in ordinary common sense, who cannot be brought to see this self-evidence; whilst, on the other hand, the advanced mathematician, when adventuring into new paths of inquiry, is able to take a great deal for granted as self-evident, which at an earlier stage of his researches would not have so presented itself to his mind. The deliverances of this acquired intuition can in most cases be readily justified by the reasoning process which they have anticipated. But the genius of a mathematician--that is, his special aptitude developed by special culture--will occasionally enable him to divine a truth, of which, though he may be able to prove it experientially, neither he nor any other can at the time furnish a logical demonstration. In this divining power we have clear evidence of the existence of a capacity which cannot be accounted for by the mere co-ordination of antecedent experiences, whether of the individual or of the race; and yet, as already shown, such co-ordination has furnished the stimulus to its development. Of those departments of science, on the other hand, in which our conclusions rest (like those of ordinary common sense) not on any one set of experiences, but upon our unconscious co-ordination of the whole aggregate of our experiences,--not on the conclusiveness of any one train of reasoning, but on the convergence of all our lines of thought towards one centre,--geology may be taken as a typical example. For this inquiry brings (as it were) into one focus, the light afforded by a great variety of studies,--physical and chemical, geographical and biological; and throws it on the pages of that great stone book in which the past history of our globe is recorded. And its real progress dates from the time when that common sense method of interpretation came to be generally adopted, which consists in seeking the explanation of past changes in the forces at present in operation, instead of invoking (as the older geologists were wont to do) the aid of extraordinary and mysterious agencies.