Applications of Quaternions to Theory of Relativity. 439 



the important factor (y(u)) seems to leave no escape. The 

 (superficially) uncoordinated employment of the Lagrange 

 function which proves a salient characteristic of relativity ; 

 that is, making a new zero for each frame; as in the 

 elementary case of a lifted body and its weight, would in 

 effect disregard that factor (j[u)). But, as we see, to 

 eliminate that factor is detrimental to the full attainment of 

 symmetry. Logarithmic fundamental relations prevent the 

 mere " butt-joint " arrangement that is allowed for vertical 

 intervals and weight. A discontinuity of energy values is 

 avoidable only by some form of agreement that has for 

 corollaries: Invariant transition at the "junction " with a 

 new frame ; and then equal activity reckoned for the same 

 time-unit. Relativity contrives to satisfy these conditions 

 however indirectly ; at times its perhaps unavowed goal 

 is masked behind an almost opaque veil of four-dimensional 

 mathematics. Yet no just mind would endure cancelling 

 anything of that brilliant achievement of expansion. Once 

 more in physics an inestimable service had its source seemingly 

 in a misapprehended premiss — about Newton's second law 

 and vis viva. 



The matter is weighty enough, if it resolves a puzzling- 

 riddle, to call for immediate publishing in condensed outline 

 of the line of varied attack. A prepared paper discussing 

 the subject less summarily cannot appear for several months. 



University ^f California. 

 September 12, 1919. 



XLIU. Applications of Quaternions to the Theory of Relativity . 

 By EL T. Flint, M.Sc, Lecturer in Physics, University 

 College, Reading *. 



Introduction. 



IN this paper it is proposed to express the results of 

 Relativistic Dynamics by means of quaternions. It 

 amounts to expressing the Minkowski four-vector as a qua- 

 ternion, and bringing about its transformation by a certain 

 operator introduced by Silberstein f . It is shown in the 

 paper, of which the reference is given, that the Lorentz- 

 Einstein transformation is equivalent to 



?'=Q[?]Q. 



q' is a quaternion considered in a system of reference S' 



* Communicated by Processor TV. G. Duffield, D.Sc. 

 t Phil. Mag. May 1912. 



