Page:Popular Science Monthly Volume 2.djvu/742

722 before to see that Deductive Logic is a science of the relations implied by the inclusions, exclusions, and overlappings of classes. Even were this all, the instalment of progress would be large for a single generation. But it is by no means all. In the work by Prof. Boole, "Investigation of the Laws of Thought," the application to Logic of methods like those of Mathematics, constitutes another step far greater in originality and in importance than any taken since Aristotle. So that, strangely enough, the assertion quoted above, that "we are backward in appreciating and pursuing abstract knowledge," and this complaint of Mr. Arnold that our life is wanting in ideas, come at a time when we have lately done more to advance the most abstract and purely-ideal science than has been done anywhere else, or during any past period!

In the other division of Abstract Science—Mathematics—a recent revival of activity has brought results sufficiently striking. Though, during a long period, the bias of patriotism and an undue reverence for that form of the higher calculus which Newton initiated, greatly retarded us; yet since the recommencement of progress, some five-and-twenty years ago, Englishmen have again come to the front. Sir W. R. Hamilton's method of Quaternions is a new instrument of research; and, whether or not as valuable as some think, undoubtedly adds a large region to the world of known mathematical truth. And then, more important still, there are the achievements of Cayley and Sylvester in the development of the higher algebra. From competent and unbiassed judges I learn that the Theory of Invariants, and the methods of investigation which have grown out of it, constitute a step in mathematical progress larger than any made since the Differential Calculus. Thus, without enumerating the minor achievements of others, there is ample proof that abstract science, of this order also, is flourishing among us in great vigor.

Nor, on passing to the Abstract-Concrete sciences, do we find any better ground for this belief entertained by Mr. Arnold and others. Though Huygens conceived of light as constituted of undulations, yet he was wrong in conceiving the undulations as allied in form to those of sound; and it remained for Dr. Young to establish the true theory. Respecting the principle of interference of the rays of light propounded by Young, Sir John Herschel says: "Regarded as a physical law [it] has hardly its equal for beauty, simplicity, and extent of application, in the whole circle of science;" and of Young's all