Relation of Mass to Energy. 7 
except that we here have to deal with, besides the forces in 
the constraint, only the electromagnetic force on electricity- 
embedded in the constraint, and we have nothing to do with 
hypothetical stresses in the free aether. 
If (p) represents the electric density and ($x) the ^-com- 
ponent of the total electromagnetic force on unit charge 
embedded in the constraint, Ave have 
3.r + W **~ p *\ 
= -pX-(Jyy-*«0) ; 
where (k) is the density of convection current caused by the 
movement with velocity (y) of the electricity of density (p). 
Making use temporarily of the vector terminology for the 
sake of brevity and calling the electric force (E), the mag- 
netic (H), and the sign [ ] denoting the vector product, we 
have 
Since divE = 47rp and curl H— ^ ° =4tt&, 
= -^{E,divE + [curlH, H].-[P|, H]J. (7) 
Now it is an easilv verifiable identity that 
E* div E - [E, curl E]* + H. Y div H + [curl H, H> 
= ^ {KE/-E/-E/)+i(H, 2 -fl/-H/)} 
+ ^-(EJE y + H*H,) + ^(E,E, + H r H s ); . . (8) 
and hence, remembering that div H = 0, equation (7) becomes 
+ £ (E,E„ + H,H y ) -i- ^ (E,E, + H„H S ) 
+ [E, curlE]. r -[^, H]J (9) 
