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XII. On the Proof of a Theorem in Wave-motion. 



To the Editors of the Philosophical Magazine. 



Gentlemen, 



WERE it not for the unexpected avowal made by Mr. 

 Preston on p. 460 of the June number of the Philo- 

 sophical Magazine, that he " feels bound " to " protest 

 against " MacCullagh's method of investigating wave-motion 

 (which is the method I had employed), I should scarcely 

 have felt it incumbent on me to trouble you with any com- 

 ments upon his letter: for though there are fallacies in its 

 earlier paragraphs, they seem sufficiently transparent not to 

 need formal reply. Nevertheless I will further on briefly 

 refer to them. However, what I desire chiefly to do is to 

 apply myself to the more important task of rescuing from 

 oblivion one of the several additions to the resources of 

 mathematics in its application to physical science which were 

 made by MacCullagh, and which, to my surprise, seem now 

 to be forgotten in his own University. 



For about thirty years — that is, in the thirties, the forties, 

 and most of the fiities of the present century — the University 

 of Dublin was a great school of geometrical teaching. It 

 had risen to this position owing to the profound reform in 

 the teaching of the University which had been effected by 

 Provost Bartholomew Lloyd in the twenties. As a school of 

 geometry Dublin had then no rival except Paris. And 

 perhaps there are no greater names among those who have 

 advanced geometry, treated as a branch of Pure Mathematics, 

 than those of the great Frenchman Chasles, of Sir William 

 Hamilton, and of Dr. Salmon the present venerable Provost 

 of Trinity College. The last two received their training in 

 the University of Dublin at the time above referred to. The 

 great feature of the methods then pursued was the close inter- 

 leaving of analytical and geometrical conceptions and methods 

 of treatment, often with a preponderance of the contribution 

 from geometry. Where such a combination was not practi- 

 cable the geometrical method was advanced side by side with 

 the analytical. But where the intimate union of the two could 

 be effected it furnished tools for discovery more effective 

 than those of either method handled separately, and at the 

 same time kept before the mind of the inquirer a clearness of 

 vision in regard to what was being done, which was more 

 continuous and of an altogether higher order than can be 

 reached by the analytical treatment applied separately or 



