( 675 ) 
of the time ¢, of the so-called “local” time t as an independent 
variable, the equation 
1 
t= t — 3 (v2 + pyy + pee) 
serving to define this quantity in terms of ¢ and the coordinates 
x,y,2 with respect to axes fixed in the body. By means of this 
contrivance the electric force, exerted by a small electrically polarized 
particle P on an electron Q, situated at some distance, is made to 
be determined by equations of the same form, whether there be or 
not a common translation of P and Q. 
Let!) m be the electric moment, varying with the time, of P, 
x, y, 2 the coordinates of the kind just mentioned in the surrounding 
field, » the distance to P; then for any point in the field, at its 
own local time f‚ the components of the said electric force will be 
saa 
rere Ga parca aca 
etc., 
provided we take for m,, m,, m, the values corresponding to the 
? 
instant at which the local time in P is t’ — a so that the nume- 
C 
OEM Ue 
rators in the expressions 2, —, —- depend on f', a, y, 2. The 
Di a 2 
differentiations must be performed for a constant f. 
$ 8. We shall now suppose that a dielectric contains a very large 
number of particles, in which electric moments m can be excited, 
that the sole interaction between these consists in the above mentioned 
electric forces, and that for each particle the connexion between its 
moment and the electric force is not altered by a translation. If then, 
in the absence of such a motion, m,, m,, m, for the different parti- 
cles of the body can be certain functions of the time ¢, we shall 
obtain a state that is possible in the moving body, by supposing 
these moments to be exactly the same functions of the local 
time ¢'. This follows at once from what has been said in the 
last §. It is also easily seen that in a point fixed to the ponderable 
matter, the time of vibration will be the same in the two states, and 
that, if the first of these states consists in a propagation of light 
with rotation of the plane of polarization, we shall have in the second 
state a similar propagation, the angle between the vibrations in any 
1) See my vVersuch u, s. w.”, § 33. 
