114 REPORT—1885. 
sizes of the electrified bodies, and the geometrical relations may be such 
that the condition written above must be always satisfied. 
Physical reasons why the force between two electrified bodies should depend 
on their velocities and accelerations. 
If we assume Maxwell’s hypothesis that a change in the electric 
polarisation produces the same effect as an electric current, then we see 
that the kinetic energy of an electrified body must be different from the 
kinetic energy of the same body moying at the same rate but not electri- 
fied. For let us suppose that we have an electrified body at rest, and 
consider the amount of work necessary to start it with a velocity g. It 
is evident that it will be greater than when it is not electrified, for when 
it is electrified and in motion the electric polarisation in the surrounding 
dielectric will be in changing, and so in addition to starting the body 
with a velocity g we have, if Maxwell’s hypothesis be true, to establish 
what is equivalent to a field full of electric currents. The production of 
these currents of course requires work, so that more work is required to 
start the body with a velocity g when it is electrified than when it is not ; 
in other words, the kinetic energy of a moving electrified body is greater 
than that of one not electrified, but under similar conditions as to mass and 
velocity. In fact in this case electricity behaves as if it possessed inertia. 
In a paper published in the ‘ Philosophical Magazine,’ April 1881, I 
have shown that the kinetic energy of a charged sphere of radius a and 
niass m moving at a velocity q 
2 
é 
— 4mq? + 2 B ig 
where j: is the magnetic permeability of the surrounding dielectric and 
e the charge on the sphere. If there are two spheres in the field, then 
I have shown in the same paper that the kinetic energy 
e? ve!? ee! 
=imq?+ 75 ~ q’? + 4m'q? + 25 =n q? + ae) qq’ COS €, 
where corresponding quantities for the two spheres are denoted by plain 
and accented letters. We see from this expression that the forces 
between the spheres are exactly the same as those given by Clausius’ 
formule. It would not, however, be legitimate to go and develope the 
laws of electrodynamics from this result in the way that Clausius does, 
as Clausius’ conception of an electric current does not accord with that 
of the displacement theory. We may remark that in this case the part 
of the kinetic energy due to the electrificaticn is always positive. 
On theories which are based on dynamical considerations, but which 
neglect the action of the dielectric. 
F, E. Neumann! was the first to develope a theory founded on the 
principles of the Conservation of Energy. His theory was based upon 
the assumption that two elements of circuit ds, ds’, traversed by currents 
«, ’ possess an amount of energy equal to 
/ 
cv cose 
, ee sates OLE 
a 
1 ‘Die mathematischen Gesetze der inducirten electrischen Stréme,’ Schriften der 
Berliner Academie der Wissensch., 1845. 
