478 Mr. A. M c Aulay on Quaternions as a 



expressing the results obtained by the old-fashioned and 

 artificial methods — but there their admiration would stop. 

 The stern work, say they, of advancement into the unknown 

 regions must be made by the clumsier but stronger means. 

 When the country has been reduced to order and civilization, 

 let quaternions be introduced as a luxury conducing to the 

 recreation of the exhausted toilers. Nevertheless there is a 

 small minority among these workers that venture to deny this 

 slur on the character of their favourite implement. They 

 assert that it has only to be used to be appreciated, and this 

 to such an extent that all other geometrical implements are, 

 or ought to be, cast aside in favour of it. I confess myself to 

 be one of the extremest parti zans of this sect. When directly 

 I proceed, however, to state exactly what I believe to be the 

 mission of quaternions in the domain of Physics, it will appear 

 that in a short paper it is impossible to establish the conten- 

 tions. The chief object of the present paper is to shake the 

 belief of mathematical physicists. It is too much to hope to 

 overturn that belief. 



The first question to answer is the one already put — Can the 

 apathy of physicists with regard to quaternions be accounted 

 for if it be not that quaternions are unsuitable for their pur- 

 poses ? I confess that the more I think of this apathy the 

 more extraordinary does it appear, and, as already hinted, 

 it will probably prove an insoluble problem to the future 

 historian of Mathematics. But reasons can be given, though 

 not perfectly satisfactory — at least to my mind — for this 

 almost criminal negligence. 



Let us state the case against us. It can be put in very 

 few words as follows — Not much advance in Physics has been 

 made by the aid of Quaternions. I do not for a moment ques- 

 tion this. It is too evident even for an advocate to blink. 

 In all sincerity, however, I believe that this is all that can be 

 assigned as reason for believing that quaternions do not pro- 

 vide means for extending the bounds of the known in the 

 domain of Physics. Probably through the minds of more 

 than one who listen to this is passing the thought — " But 1 

 have tried quaternions and /have found them wanting. I 

 came to the subject unprejudiced, but I could produce nothing 

 out of it." Perhaps it is to the point to say that the present 

 writer has passed through this phase. He, too, found that 

 though quaternions were a fascinating study, they seemed to 

 fail, for some inscrutable reason, to furnish the means for any 

 real advance. Looking back, I think I can see the reason for 

 this. 



Maxwell, I fear, is responsible to a large extent for the 



