On the Proof of a Theorem in Wave-motion. 99 



when it is illustrated only by the rough geometrical concep- 

 tions ordinarily employed. 



Another distinctive feature of the Dublin School of Mathe- 

 matics of those decades — one which was perhaps peculiar to 

 that school — was the large introduction of these same accurate 

 methods into the study of the various branches of Physics. 

 This was chiefly due to the influence of MacCullagh on the 

 teaching of the University ; and his suggestions were being 

 actively developed and extended in the instruction given to 

 undergraduates in the student days of the present writer — 

 from 1844 to 1847 — which were the last years of MacCullagh's 

 life. 



Some years afterwards a change was made in the curri- 

 culum of Trinity College, Dublin, which had the effect of 

 diminishing the stress which the College until then had laid 

 upon the earlier and necessary steps of the training of the 

 mind for such pursuits ; and as a consequence the attention 

 paid by schools preparing for the University, to developing 

 the geometrical insight and skill of their pupils, gradually 

 fell off. One result, probably unforeseen and certainly Tin- 

 fortunate, has been that much valuable unrecorded work that 

 was done in the University of Dublin in those earlier times 

 was not followed up; and has been, or is in risk of being, lost. 

 Circumstances have occurred within the last few months, 

 culminating in Mr. Preston's announcement in the June 

 number of the Philosophical Magazine, which have brought 

 forcibly to the knowledge of the present writer that methods 

 of great value which were then employed in physics have 

 become a lost art, unknown to the present teachers and 

 students of the University. 



In what I have written within the last nine months about 

 wave-motion, and especially in the paper at p. 273 of the 

 April number of the Philosophical Magazine, I applied what 

 used to be called " MacCullagh/s method," or " Proof by the 

 Principle of Reversal," to the study of wave-motion, for 

 which it is in a special degree adapted. In doing this I 

 assumed that my readers understood the fundamental prin- 

 ciples upon which all accurate geometrical proofs in this 

 branch of physics ultimately rest ; but the doubts expressed 

 and the questions put by Mr. Preston on p. 460 of the June 

 number of the Philosophical Magazine, show that these as 

 they used to be studied in the University of Dublin are now 

 forgotten, and that even so well-informed a reader as Mr. 

 Preston is unacquainted with them. Accordingly explana- 

 tions must now be given which would have been superfluous 

 forty years ago. I am endeavouring to do this in a paper I 



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