A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 561 



In isotropic substances, which alone we shall here consider, if p is the specific 

 resistance referred to unit of volume, we may write the 



Equations of Electric Resistance, 



P=-pp] 



Q=-pq\ (F). 



R=-pr\ 



Electric Quantity. 



(68) Let e represent the quantity of free positive electricity contained in 

 unit of volume at any part of the field, then, since this arises from the electri- 

 fication of the different parts of the field not neutralizing each other, we may 

 write the 



Equation of Free Electricity, 



e+ df + dff + dh = /Q\ 



dx eZy dz 



(69) If the medium conducts electricity, then we shall have another con- 

 dition, which may be called, as in hydrodynamics, the 



Equation of Continuity, 



(70) In these equations of the electromagnetic field we have assumed twenty 

 variable quantities, namely, 



For Electromagnetic Momentum F G H 



,, Magnetic Intensity a /3 y 



Electromotive Force P Q R 



Current due to true Conduction p q r 



Electric Displacement f g h 



Total Current (including variation of displacement) p' q' r' 



Quantity of Free Electricity e 



Electric Potential 



VOL. I. 71 



