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what follows, before passing to considerations of a different order 
(§5), I shall explain the reasons for which this theory of rapid 
vibrations as a cause of gravitation can not be accepted. 
§ 2. Let an ion carrying a charge e, and having a certain 
mass, be situated at the point P(2, y, 2); it may be subject or not 
to an elastic force, proportional to the displacement and driving it 
back to P, as soon as it has left this position, Next, let the aether 
be traversed by electromagnetic vibrations, the dielectric displacement 
being denoted by 5, and the magnetic force by 5, then the ion will 
be acted on by a force 
An Ved, 
whose direction changes continually, and whose components are 
Xr /Vrebsy Vase Veet, LAT Veet... su 
In these formulae V means the velocity of light. 
By the action of the force (1) the ion will be made to vibrate 
about its original position P, the displacement (x, y, z) being deter- 
mined by well known differential equations. 
For the sake of simplicity we shall confine ourselves to simple 
harmonie vibrations with frequency n. All our formulae will then con- 
tain the factor cos zt or sin nt, and the forced vibrations of the ion 
may be represented by expressions of the form 
x= aed, — beds, 
y = aebdy —bdedy, ik hia js 
z= aed, — beds, 
with certain constant coefficients a and b. The terms with dx, dy 
and ò, have been introduced in order to indicate that the phase of 
the forced vibration differs from that of the force (X, Y, Z); this 
will be the case as soon as there is a resistance, proportional to 
the velocity, and the coefficient b may then be shown to be positive. 
One cause of a resistance lies in the reaction of the aether, called 
forth by the radiation of which the vibrating ion itself becomes the 
centre, a reaction which determines at the same time an apparent 
increase of the mass of the particle. We shall suppose however that 
we have kept in view this reaction in establishing the equations of 
motion, and in assigning their values to the coefficients a and b, 
