( 610 ) 

 rot b = I), (VI) 



f = M--[^^.()] (VII) 



c 

 In connexion willi tlie lasl fornuila i( may be remarked that b is 

 the electric force that would act on an immo\'able charge. 

 The electric energy per nnit-volume is gi\'en by 



h; = 4- ^' ' ^^'"^^ 



the magnetic eiiergy per unit-\'olume by 



Jï'.< = y(^^ (IX) 



and Poynting's flnx of energy by 



3=:'M/^.M (X) 



We shall fiirlluM- u i-ite l' for the total cUnMric and 7' for the 

 total magnetic energy of a system. 



The equations. (IV) and (V) suiïice for the determination of tlie 

 magnetic force f\ as soon as the current I is given in c\ery point. 

 11 „i is tiien knowji l)y (IX) and 7' loUous l)y integi-ation. In this 

 sense, every motion of electricity may be said to be accompanied 

 by a definite amouiit of magnetic energy. 



Soilor jxttrnliiil <ii)d vcc/cr-po/i'/ififr/. 



§ 2. The equations of § I apjtly to every system in which 

 charged matter moves Uu'ough tlie aether, whether tiie charge be 

 confined to cei-tain extremely small parts of space (electrons) or 

 otherwise distributed. 3Ioreover, the motions may be of any kind ; 

 the electroJis may have a pure traiislatoiy motion, or a I'otation 

 at the same time, and we may even supjjose their form to change 

 iji the coui-se of time. For the validity of the formulae it is however 

 re({uired that each element of volume whose points move with the 

 charged matter should [>reserve its charge, though its form and 

 dimensions may change. This is expressed by the equation (II) and 

 it is on this ground that the electric cnrrent I, as defined by (III), 

 (the resultant of the displacement-current b and the convection-cur- 

 rent Q\:) may ahvays be said to be solenoidally distributed, so that 



iJir ! =: 0. 



If now the motion of the charged matter is given, the electro- 

 magnetic field in the aether, within and without that matter, has 



