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VII. 



THE EELATIOX OF MATHEMATICS TO PHYSICAL SCIEXCE. 



Ax Addeess deliykeed to the Academy, Decembee 9. 1907. 

 By FEANCIS ALEXAXDER TAELETOX, LL.D., Sc.D., President. 



Published December 28, 1907. 



It has iDeeu the usual custom for each President of the Eoyal Irish Academy 

 to deliYer an address to the Academy ; aud as I should be most unwilling 

 to show any want of appreciation of the high honour which the Academy 

 has done me in electing me as its President, I shall try to carry out this 

 somewhat difficult undertaking — difficult on account of the eminence and 

 skill of those who haYe preceded me, and who haYc exhausted so many topics 

 of interest ; and difficult because it is hard, without entirely exhausting your 

 patience, to say anything which is intelligible and yet not altogether trite 

 and commonplace. 



As the Academy did me the honour of selecting me as a representative of 

 its seientifie side, I have thought that I might offer for your consideration 

 some thoughts on the relation between Mathematics and Physical Science. 



To an audience so learned as the present I = cannot hope to present 

 anything absolutely new ; but I may be able to direct your attention to some 

 matters of interest in reference to which many entertain opinions which 

 cannot, I think, be regarded as correct. 



The splendid discoYeries wliich have been made by obserYation and 

 experiment during the last 120 years have led to such an exaltation of these 

 modes of procedure that it has become common to limit the term " Science " 

 to their study and practice. This seems to me extremely incorrect. A mere 

 knowledge of facts, apart from their causal connexion, can scarcely be called 

 Science ; and the more completely this connexion is traced out and known, 

 the more scientific does our knowledge become. It can scarcely be doubted 

 that, in the last resort, all the phenomena of the material uniYcrse depend on 

 mathematical relations — a knowledge of which is impossible without a 

 knowledge of ]\Iathematics itself. It seems, therefore, to follow that 

 Mathematics is not merely a department of Science, but is an essential 

 requisite for a scientifically complete knowledge of natural phenomena ; and 



