214 EQUATIONS OF MONOCHROMATIC LIGHT IN MEDIA 



2 , 



where t denotes the time, p the period, and a lf a 9) functions of the 

 coordinates. It follows that 



47T 2 , 



etc. 



JT 



(2) 



4. Now, on the electrical theory, these motions are excited by 

 electrical forces, which are of two kinds, distinguished as electro- 

 static and electrodynamic. The electrostatic force is determined by 

 the electrostatic potential. If we write q for the actual value of the 

 potential, and [<7JAve f r i^ 8 value as averaged in the manner specified 

 above, the components of the actual electrostatic force will be 



dq dq dq 



dx' dy' dz' 



and for the average values of these components in the small spaces 

 described above we may write 



dx 



dy 



dz 



for it will make no difference whether we take the average before 

 or after differentiation. 



5. The electrodynamic force is determined by the acceleration of 

 electrical flux in all parts of the field, but physicists are not entirely 

 agreed in regard to the laws by which it is determined. This 

 difference of opinion is however of less importance, 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 



-flj$* -ffl> -IIF 



where dv represents an element of volume, and r the distance of this 

 element from the point for which the value of the electromotive 

 force is to be determined. In other words, the components of the 

 force at any point are determined from the components of acceleration 

 in all parts of the field by the same process by which (in the theories 

 of gravitation, etc.) the value of the potential at any point is deter- 

 mined from the density of matter in all parts of space, except that 

 the sign is to be reversed. Adopting this law, provisionally at least, 

 we may express it by saying that the components of elecfcrodynamic 

 force are equal to the potentials taken negatively of the components 

 of acceleration of electrical flux. And we may write, for brevity, 



-Pot -Pot;/, -Potf, 



for the components of force, using the symbol Pot to denote the 

 operation by which the potential of a mass is derived from i 



