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VII. On the Importance of Quaternions in Physics. 

 By Professor Tait*. 



MY subject may usefully be treated under three heads, 

 viz.: — 



1. The importance of mathematics, in general, to the pro- 

 gress of physics. 



2. The special characteristics required to qualify a calculus 

 for physical applications. 



3. How quaternions meet these requirements. 



The question has often been asked, and frequently answered 

 (one way or other) in the most decided manner : — Whether 

 is experiment or mathematics the more important to the pro- 

 gress of plrysics ? To any one who really knows the subject, 

 such a question is simply absurd. You might almost as well 

 ask : — Whether is oxygen or hydrogen the more necessary to 

 the formation of water ? Alone, either experiment or mathe- 

 matics is comparatively helpless : — to their combined or alter- 

 nate assaults everything penetrable must, some day, give up 

 its secrets. 



To take but one instance, stated as concisely as possible : — 

 think of the succession of chief steps by which Electromag- 

 netism has been developed. You had first the fundamental 

 experiment of Oersted: — next, the splendid mathematical work 

 of Ampere, which led to the building up of a magnet of any 

 assigned description by properly coiling a conducting wire. 

 But experiment was again required, to solve the converse 

 problem: — and it was by one of Faraday's most brilliant dis- 

 coveries that we learned how, starting with a magnet, to 

 produce an electric current. Next came Joule and v. Helm- 

 holtz to show (the one by experiment, the other by analysis) 

 the source of the energy of the current thus produced: — in 

 the now-a-days familiar language, why a powerful engine is 

 required to drive a dynamo. Passing over a mass of import- 

 ant contributions mathematical and experimental, due to 

 Poisson, Green, Gauss, Weber, Thomson, &c, which, treated 

 from our present point of view, would furnish a narrative of 

 extraordinary interest, w T e come to Faraday's Lines of Force. 

 These were suggested to him by a long and patient series of 

 experiments, but conceived and described by him in a form 

 requiring only technical expression to become fully mathe- 

 matical in the most exclusive sense of the word. This 



* Abstract of an Address to the Physical Society of the University of 

 Edinburgh, November 14, 1839. See the Author's Address to Section A 

 at the British Association, 1871. 



