been considering in this particular: that it applies experience about the shape of a plant—which is one circumstance connected with it—to dealings with its medicinal properties, which are other and different circumstances. Again, suppose that you had been frightened by a thunder-storm on land, or your heart had failed you in a storm at sea; if any one then told you that, in consequence of this, you should always cultivate an unpleasant sensation in the pit of your stomach, till you took delight in it—that you should regulate your sane and sober life by the sensations of a moment of unreasoning terror; this advice would not be an example of scientific thought. Yet it would be an application of past experience to new and different circumstances.
But you will already have observed what is the additional clause that we must add to our definition in order to describe scientific thought, and that only. The step between experience about animals and dealings with changing humanity is the law of evolution. The step from errors in the calculated places of Uranus to the existence of Neptune is the law of gravitation. The step from the observed behavior of crystals to conical refraction is made up of laws of light and geometry. The step from old bridges to new ones is the laws of elasticity and the strength of materials.
The step, then, from past experience to new circumstances must be made in accordance with an observed uniformity in the order of events. This uniformity has held good in the past in certain places; if it should also hold good in the future, and in other places, then, being combined with our experience of the past, it enables us to predict the future, and to know what is going on elsewhere, so that we are able to regulate our conduct in accordance with this knowledge.
The aim of scientific thought, then, is to apply past experience to new circumstances: the instrument is an observed uniformity in the course of events. By the use of this instrument it gives us information transcending our experience, it enables us to infer things that we have not seen from things that we have seen; and the evidence for the truth of that information depends on our supposing that the uniformity holds good beyond our experience. I now want to consider this uniformity a little more closely, to show how the character of scientific thought and the force of its inferences depend upon the character of the uniformity of Nature. I cannot, of course, tell you all that is known of this character without writing an encyclopædia, but I shall confine myself to two points of it, about which, it seems to me, that just now there is something to be said. I want to find out what we mean when we say that the uniformity of Nature is exact; and what we mean when we say that it is reasonable.
When a student is first introduced to those sciences which have come under the dominion of mathematics, a new and wonderful aspect of Nature bursts upon his view. He has been accustomed to regard things as essentially more or less vague. All the facts that he has