I have alluded to laws of crystalline structure, to which LORD KELVIN had directed attention: these are the laws of geometrical arrangement which prove crystals to be constructed in an entirely different manner from the living plants which they may so closely resemble; these laws, however, were not established by observations or experiments upon the growth of crystals. They were the result of a century of patient measurements of the external shape of countless crystals; more than a century of accurate determinations of what happens when heat and light are transmitted through them and of numberless other experiments made by physicists; and, added to this, the labours of mathematicians who studied the manner in which solid particles could be arranged so as to correspond to the geometrical and physical proportions thus determined by experiment. But all these were experiments and reasoning upon matter which appears to be as nearly as possible inert; they entirely ignore the power of growth possessed by crystals; indeed, no such power is contemplated by the ordinary theories of crystal structure or could be predicted from them. So far, then, we may regard the comparison of crystals with plants and all the fanciful ideas concerning their connexion with the origin of life which were suggested by that comparison as only one more example of the dangers of reasoning from analogy. The recollections that I retain of the allusions to that process—in text-books of logic and treatises on Science alike—give me the impression that examples of reasoning from analogy are generally quoted only as instances of its danger and futility. That, indeed, might seem to be the conclusion of my own inaugural lecture; for, when we come to examine the growth and structure of crystals, so far from finding that there is any real likeness to the life and structure of the plants which they resemble, we find nothing but a profound difference. That, however, is not my real opinion, and was not my opinion fifteen years ago. On the contrary, I have the greatest belief in analogy as one of the most useful guides to discovery, and as the means by which in practice new lines of investigation are most frequently opened and new hypotheses suggested. In fact, I think that most of the advances which are made in science, and especially in scientific theory, have been made with the help of analogies.