138 Dr. L. Silberstein on 



(gp) its activity ; then 



'-(Sp) = -iSG[D]F=i| I (GP)-idivVGP, . (5) 



g=-±VG[D]F, (6) 



whence 



(gp) = - \\ t (GP) + -|div VGF = - |? -div % 

 the scalar u and the vector 9j$ being given by 



$=-~VGF = e-VEM ) 



Thus, the scalar part of the equation (XV.) expresses the 

 conservation of energy, leading to the flux of energy or the 

 Poynting-vector, 9j$, and to the density of electromagnetic 

 energy, u. 



Both of the equations (7) may be condensed into one single 

 quaternionic formula 



AGF= -i<+-$*, . . . (XVI. a) 

 c 



thus giving us one of the properties of G[ ]F. 



To obtain another property of this operator develop the 

 vector part of (XV.), i. e. (6). Then 



g=-iVG[|jF-|VG[V]F; 



here, the first term on the right is seen, by (2), to be simply 

 identical with 



so that we have only to develop the second term, which (since 

 it will turn out to be the Maxwellian ponderomotive force) 

 we shall denote by F M x W .- Thus 



S = S M xw"" ( 7i §p ( 8 ) 



where we recognize already in ty/c 2 the electromagnetic 

 momentum (per unit volume) and where 



g Ml w = -i VG [V]P (9) 



* It is hardly necessary to warn the reader that GF is not a physical 

 quaternion. 



