PROCEEDINGS 



THE ROYAL IRISH ACADEMY 



PAPERS READ BEFORE THE ACADEMY 



ON THE APPLICATION OF QUATERNIONS TO SOME EECENT 

 DEVELOPMENTS OF ELECTRICAL THEORY. 



By ARTHUR W. CONWAY, M.A. (Oxon. and R.U.I.), D.Sc, 

 Professor of Mathematical Physics, University College, Dublin. 



Read Febbuauy 13. Published March 22, 1911. 



CONTENTS. 



I. Introduction, ..... 1 

 II. Fundamental Formulae and examples, 2 



in. On Fredholm Solutions, . 

 IV. On the Relativity Principle, 



Page 

 . 6 

 . 7 



§ 1. Introduction. 



The development of the mathematical theory of electrons has, in the hands 

 of various continental mathematicians, been largely expressed in some notation 

 of vector algebra.* Although (necessarily from the algebra employed) no 

 use is made of quaternion products, still the results are distinguished by a 

 conciseness and clearness, both of which often disappear on translation to the 

 Cartesian form. It so happens, however, that two of the most recent 

 developments are such that if one attempts to treat them by vector methods 

 (without the use of quaternions), it leads to expressions more complicated 

 than the ordinary scalar methods. I refer to Poincare'sf FredhoLm solutions 

 of the electrodynamic equations, and to the transformation connected with 



• Of. Abraham and Fbppl's Theorie der Electricitat. For quaternion treatments reference 

 might be made to the Proceedings of the Royal Irish Academy, vol. xxvii., Sect. A, No. 8, and 

 vol. xxviii., Sect. A, No. 1. 



t Poincare : Comptes Rendus Nos. S, 13, 15, 23 (1909), and Reudiconti del' Civcolo Matematico 

 di Palermo, tomo xxix., p. 169. 



K.I.A. PKOC, VOL. XXCX., SECT. A. [1] 



