PAPERS 



or THE 



ROYAL SOCIETY OF TASMANIA, 



1914. 



QUATERNIONS APPLIED TO PHYSICS 

 IN NON-EUCLIDEAN SPACE. 



I.— THE MATHEMATICAL METHODS. 



By Alex. McAulay, M.A., Professor of Mathematics 

 in the University of Tasmania. 



(Received 25th March, 1914; read 15th April, 1914; issued 

 separately 18th May, 1914.) 



§L The utility of quaternions in matliematical physics 

 in non-Eiiclidean space is much the same as in Euclidean, 

 that is to say they are suitable for establishing funda- 

 mental relations. Details must be worked out by some 

 system of scalar coordinates. It is hoped that the 

 applications, to Physics, for which the methods of this 

 paper have been prepared, will appear in subsequent 

 papers ; but, quite naturally, it has been found that the 

 methods alone demand for exposition more space than 

 can be placed at the writer's disposal for the first paper 

 of the series. As probably considerable intervals of 

 time will elapse between the publication of successive 

 papers, it is well to state at the outset that the founda- 

 tions of the following have already been treated : — 

 particle dynamics, rigid dynamics, hydrodynamics, elastic 

 solids and electrodynamics in free ether ; and also four 

 types of wave-motion, (1) in elastic fluids, (2) and (3) 

 the two types in elastic isotropic solids, (4) in free ether. 

 As examples of the kind of results that emerge we may 

 mention (1 ) that in fluids the famous vortex-motion 



