If, however, reasoning from an analogy may be fallacious when inferences are drawn from the fact that two things possess the same attributes in common, it is, I think, a safer guide when it is used to suggest a new hypothesis; a corpuscular theory of light may be suggested by the analogy between the reflexion of light and the rebounding of elastic bodies; an undulatory theory by the analogy of a wave propagated along a string or on the surface of water. The one theory may be found to fit the facts and the other may be condemned; but without some analogy as a guide how are such theories to be devised? What we require in science are continual stimuli to start us on new experiments, new observations, and new ideas, and prevent us, especially those who are teachers, from constantly repeating the old ones. I shall be satisfied if the present lecture is regarded as a plea for the use of reasoning from analogy, and as an illustration of its value. Let me, then, after this exhortation, return to my problem of the growth of crystals, and show how I still think that we may be guided by analogy in seeking to understand it. So far from regarding the growth of a crystal as of no further importance after it has been proved to be quite different from the growth of a plant, we must still think of it as one of the most interesting and mysterious events, and the one through which we may hope to get the clearest insight into the nature of the crystal itself. For, after all, when after making physical experiments upon the solid crystal and studying its action upon heat and light we are led to speculate upon the manner in which it is constructed, we must not forget that it grew, and that the material was laid down under conditions which we can only understand by studying what happens on the surface as it grows. LORD CURZON devoted his ROMANES Lecture to the consideration of Frontiers, and explained their interest and importance in the growth of nations. In the study of Science also nothing is more interesting and important than frontier problems. In two senses is this true. The problems which lie on the borderland between two sciences are the most fruitful of all, because they throw light upon each science, and, by bringing into harmony things that were previously distinct and separate, lead to an immediate extension of knowledge. And also in a more restricted sense. You will find, I think, that the scenes of the most interesting events in Nature are generally those places where different things come into contact and where there is consequently stir and action; where two substances meet to form a new chemical compound; where two bodies touch and react upon each other; at the surface of a solid or a liquid; these are the regions in which events are taking place that we can study and measure with the prospect of discovery.