﻿Quaternionie Form of Relativity. 801 



or the transformer of Y is Q[ ]Q e . Here the meaning of 

 Do is o£ course, according to (11), 



D = &-? w 



Notice that Xa nd Y may be but are not necessarily full 

 quaternions'* ; they can be, for example, pure vectors, either 

 real (or ordinary vectors) or complex, i. e. biveetors, if we are 

 to retain Hamilton's terminology. 



Let us now pass to consider the fundamental electro- 

 magnetic equations " for the vacuum/' as they are recently 

 called, i. e. the system of differential equations 



BE 



-^r- +pp = c. curlM, divE = p 



1 = -c.curlE, divK[ = 



(18) 



where E, M are the electric and magnetic vectors of the field, 

 respectively, p the volume-density of electricity and p the 

 vectorial velocity o£ its motion, both p and p being given 

 functions of space and time. 



First, to condense these equations, put together the electric 

 and the magnetic vectors to make up the electromagnetic 

 bivector (or the bivector of the field) 



F=M-iE (19) 



and write again l — ict. Both curl and div being distributive, 

 this will give us instead of the four vector equations (18) the 

 two bivectorial equations f 



?^F 1 



■^j + curl F = - pp ; divF= — ip, 



or, using Hamilton's symbols, 



* This has no influence on their transformational peculiarities as 

 expressed in the above quaternionie form. 



t The reader will find these equations together with the corresponding' 

 bivectorial form of the density of energy and the Poynting flux in my 

 paper published in 1907 in the Annalender Physik, vol. xxii., and (supple- 

 ment) vol. xxiv. I was then unaware of their possible application to the 

 present purpose. (The rj of that paper is the above »F.) 



PML Mag. S. 6. Vol. 23. No. 137/3% 1912. 3 G 



