THE ELECTRIC AND LUMINIFEROUS MEDIUM, 
803 
109'‘\ When however we consider the case of conductors ii\ motion, so that their 
current sheets, instead ot being referred to fixed axes, are carried on along with them, 
we shall have to refer the medium and therefore also the above variational operation 
to a moving scheme of axes or more generally to a moving space; and this will be 
accomplished if we include in djdt (F, G, H) not only ordinary partial differential 
coefficients with respect to the time, but also the rate of change due to alteration of 
position of the point considered owing to the movement of tiie space to which it is 
referred. 
The result of this reference to moving space, for the case in which it moves like 
a body of invariable form, is worked out as in Maxwell, ‘ Treatise,’ § 600, and leads 
to his well-known equations of electric force. These equations are however expressed 
with equal generality by eliminating the adjustable quantity if/, thus obtaining for any 
complete circuit, with this extended meaning djdt, 
|(P dx 4- Q + P dz) = — |(F t/x -f G dij + H dz) 
la + mb + nc) dS. 
As this relation retains the same form whether referred to fixed or to imjving 
space, it expresses the Faraday-Maxwell law that under all circumstances the 
electromotive force referred to a circuit, fixed or moving, is equal to the rate of 
duninution of the magnetic induction through its aperture. 
The expressions for the electric force thus determined are merely formidce for the 
kinetic reaction of the disturbed medium, which must be at each instant balanced by 
the forces of the elastic strain which is the other aspect of the efficient cause of 
the phenomena. Thus they do not imply any conclusion that in all material dielectrics, 
whether gaseous or liquid or solid, the motion of the matter produces an electric effect 
which is objectively the same for all; the equations referred to moving space apply in 
fact quite as readily to the free rnther itself as to a moving material medium, provided 
the currents as well as the electric force are referred to the moving space. 
In any actual problem, the quantity xjj, which enters into the electric force, is made 
determinate by means of the circuital condition to be satisfied by the currents 
throughout the dielectric : as a matter of convention we may if we please take i// to 
include the electric potential of charges on the conductors which are the terminal 
aspects of the elastic strain in the dielectric, but nothing essential is peiliaps gained 
by such a course, unless in the case of slow movements. 
110. If however we were to adopt, on the lines of Helmholtz’s theory of 1870, a 
different procedure and assume that the vector (F, G, H) is a physical entity as 
distinct from a mathematical expression, and so assign a definite physical formula for 
it, which must from our actual knowledge be of the type 
5 K 2 
