( 561 ) 
Then, in what follows, we need only consider the forces due to the 
state of the aether, in so far as it not directly produced by the 
ion itself. 
Since the formulae (2) contain e as a factor, the coefficients a 
and 5 will be independent of the charge; their sign will be the 
same for a negative ion and for a positive one. 
Now, as soon as the ion has shifted from its position of equili- 
brium, new forces come into play. In the first place, the force 
4a V*ed will have changed a little, because, for the new position, 
d will be somewhat different from what it was at the point P. 
We may express this by saying that, in addition to the force (1), 
there will be a new one with the components 
dx Dx dx 
An prol x 0 bs Sy Nd |g | 
dz dy dz 
In the second place, in consequence of the velocity of vibration, 
there will be an electromagnetic force with the components 
etn fie ete.) of oe oe \ ae reen 
If, as we shall suppose, the displacement of the ion be very small, 
compared with the wave-length, the forces (3) and (4) are much 
smaller than the force (1); since they are periodic — with the 
frequency 2, — they will give rise to new vibrations of the particle. 
We shall however omit the consideration of these slight vibrations, and 
examine only the mean values of the forces (3) and (4), calculated for a 
rather long lapse of time, or, what amounts to the same thing, for a full 
278 
eriod ——. 
perl EF 
§ 3. It is immediately clear that this mean force will be 0 if the 
ion is alone in a field in which the propagation of waves takes 
place equally in all directions. It will be otherwise, as soon as a 
second ion @ has been placed in the neighbourhood of P; then, 
in consequence of the vibrations emitted by Q after it has been itself 
put in motion, there may be a force on P, of course in the direction 
of the line QP, In computing the value of this force, one finds 
a great number of terms, which depend in different ways on the 
distance r. We shall retain those which are inversely proportional 
to rorr®, but we shall neglect all terms varying inversely as the 
higher powers of r; indeed, the influence of these, compared with 
dk te 
that of the first mentioned terms will be of the order —, if A is the 
= 
