110 J. W. Gibbs— Equations of Monochromatic Light 
. Now, on the electrical theory, these motions are excited by 
electrical forces, which are of two kinds, distinguished as elec- 
trostatic and electrodynamic. The electrostatic force is deter- 
i the electrostatic potential. If we write g for the 
actual value of the potential, and [g],,. for its value as aver- 
aged in the manner specified above, the components of the 
actual electrostatic force will be 
di d 
de? dy’ dz’ 
and for the average values of these components in the small 
spaces described above we may write 
als A lave oe AL lave he A dave 
da. > : d > dz ? 
ee 
for it will make no difference whether we take the average 
before or after differentiation. 
5. The electrodynamic force is determined by the accelera- 
tion of electrical flux in all parts of the field, but physicists 
are not entirely agreed in regard to the laws by which it 1s 
determined. This difference of opinion is however of less im- 
portance, since it will not affect the result if electrical fluxes 
are always solenoidal. According to the most simple law, the 
components of the force are given by the volume-integrals 
Wie ihe Ie 
r r r 
where dv represents an element of volume, and 7 the distance 
of this element from the point for which the value of the elee- 
tromotive force is to be determined. In other words, the 
for brevity, 
— Pot &, — Pot 7, Pot & 
for the components of force, using the symbol Pot to denote 
the operation by which the potential of a mass is derived from 
its density. For the average values of these components in the 
small spaces defined above, we may write 
— Pot [é Javes — Pot ne — Pot [2] ave 
