108 J. W. Gibbs—Equations of Monochromatic Light 
the hypothesis of Maxwell that electrical fluxes are solenoidal.* 
Our results, however, will be such as to require us to admit the 
substantial truth of this hypothesis, if we regard the processes 
involved in the transmission of light as electrical. 
ith regard to the undetermined questions of electrodyna- 
mic induction, we shall adopt provisionally that hypothesis 
which appears the most simple, yet proceed in such a manner 
that it will be evident exactly how our results must be altered, 
if we prefer any other hypothesis. 
Electrical quantities will be treated as measured in electro- 
magnetic units. 
2. We must distinguish, as before, between the actual elec- 
trical displacements, which are too complicated to follow in 
detail with analysis, and which in their minutiz elude experi- 
mental demonstration, and the displacements as averaged for 
. 
point considered. 
Whatever may be the quantities considered, such averages 
will be represented by the notation 
io” 
i) 
[ dave 
If, then, €, 7, € denote the components of the actual displace- 
ment at the point considered, 
[& loves [7 aves [Clave 
will represent the average values of these components in the 
small sphere about that point. These average values we shall 
matical physics, must nevertheless, by its wide departure from ordinary methods, 
have tended to repel such as might not make it a matter of serious study. 
*A flux is said to be solenoidal when it satisfies the conditions which charac 
terize the motion of an incompressible fluid,—in other words, if u, v, w are the 
rectangular components of the flux, w 
and the normal component of the flux is the same on both sides of any surfaces 
ist. 
This is rather to fix our ideas, than on account of any mathematical necessity. 
For the space for which the average is taken may in general be considerably 
varied without sensibly affecting the value of the average. 
