﻿808 Quaternionic Form of Relativity. 



Now, botli biquaternions, P = OF and GO being transformed 

 by the same Q[ ]Q, this will also be the transformer of their 

 sum, and of their difference, i. e. 3 by (25.) and (26), of P m 

 and of P c . 



Thus we see that not only P but also its constituents P e 

 and P m , taken separately, are cov. q ; and since each of them 

 has also the structure of q *, both P e and P, 71 are physical 

 quaternions, cov. q. 



They are given explicitly by (25e), (25m), and may, by the 



above, be written also 





P e =Hc*-GO} . . 



. . (27e) 



P„ > =-|(CP+GC}. . 



. . (27m) 



It is true that (at least on the ground of the fundamental 

 electronic equations) only P e has an immediate physical 

 meaning, and not P m . But this does not seem to me a dis- 

 advantage. On the contrary ; since our stock of physical 

 quaternions, as the reader will certainly have observed, is as 

 yet not very big, it may be better to have one more. 



P e corresponds to the u Viererkraft" f and might conse- 

 quently be called here the force- quaternion. It has a dynamic 

 vector and an energetic scalar, as observed above. As to 

 P m , it is of no importance to give it (at least for the 

 "vacuum") any special name. On the other hand, the 

 whole P, which may possibly turn out to be more convenient 

 for the quaternionic treatment of Relativity, might be called 

 the dynamical % biquaternion, and be looked on as the standard 

 of physical biquaternions, in the same manner as q, P have 

 been the standards of physical quaternions and of physical 

 bivectors, respectively §. 



Now, using the quaternionic differential equation (VI.), or 

 C = DP, the formula (27 e) for P* may be written 



2P«=DF.F-G.DF, .... (28) 



and similarly (27 m) for P m , the dot being a separator, as 



* Namely an imaginary scalar and a real vector. 



t See Lane, loc. cit., § 15. 



J Notwithstanding that it is partially energetic. 



§ It is worth. noticing again that F (plus an invariant and consequently 

 unessential scalar) and P may be regarded as alternating products of 2 

 and of 3 physical quaternions, respectively. From this standpoint q, F, 

 V and their respective companions might be considered as quaternionic 

 entities of the 1st, 2nd,- and 3rd degree, respectively. 



