112 J. W. Gibbs— Equations of Monochromatic Light 
ered. We have already seen that the forces and the displace- 
ments are harmonic functions of the time having a common 
eriod. 
A little consideration will show that if the average electro- 
motive force in the sphere is given as a function of the time, 
the displacements in the sphere, both average and actual, must 
be entirely determined. Especially will this be evident, if we 
consider that since we have made the radius of the sphere very 
(Slaves Li aves ic lives [& dives [lave [lave 
at any one instant. For the same reason the average electro- 
motive force is entirely determined for the whole time by the 
values of the six quantities 
LA lives EX lave LZ aves iS live iY lave [Z]ave 
for the same instant. The first six quantities will therefore be 
functions of the second, and the principle of the superposition 
of motions requires that they shall be homogeneous functions 
of the first degree. And the second six quantities will be 
homogeneous functions of the first degree of the first six. 
coefficients by which these functions are expressed will depend 
ufion the nature of the medium in the vicinity of the point 
considered. They will also depend upon the period of vibra- 
tion, that is, upon the color of the light.* 
* The relations between the displacements in one of the small spaces considered 
and the average electromotive force is mathematically analogous to the relation 
