722 THE POPULAR SCIENCE MONTHLY. 



before to see that Deductive Logic is a science of the relations implied 

 by the inclusions, exclusions, and overlappings of classes. 1 Even were 

 this all, the instalment of progress would be large for a single genera- 

 tion. But it is by no means all. In the work by Prof. Boole, " In- 

 vestigation 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 back- 

 ward in appreciating and pursuing abstract knowledge," and this com- 

 plaint 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 re- 

 search ; and, whether or not as valuable as some think, undoubtedly 

 adds a laroje 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 oth- 

 ers, 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 Huyghens 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 pro- 

 pounded by Young, Sir John Herschel says : " Regarded as a physical 

 law [it] has hardly its equal for beauty, simplicity, and extent of ap- 

 plication, in the whole circle of science ; " and of Young's all-impor- 



1 Most readers of logic will, I suppose, be surprised on missing from the above sen- 

 tence the name of Sir W. Hamilton. They will not be more surprised than I was myself 

 on recently learning that Mr. George Bentham's work, " Outline of a New System of 

 Logic," was published six years before the earliest of Sir W. Hamilton's logical writings, 

 and that Sir W. Hamilton reviewed it. The case adds another to the multitudinous ones 

 in which the world credits the wrong man ; and persists in crediting him in defiance of 

 evidence. 



