» 
ON ELECTRICAL THEORIES, 113 
Riemann’s law, if we make 
fH L{unuy + (vv) + (ww); 
r 
Clausins’ law, if we make 
.— t {uu’ + vo’ + ww'}; 
r 
and that we cannot get Gauss’s law in this way; this is in accordance 
with the fact that Gauss’s law does not satisfy the principle of the 
conservation of energy. This way of considering the theories enables us 
to see that neither Weber’s nor Riemann’s formule can be right, for if 
they were, an electrified body, when in presence of another, would, under 
certain circumstances, behave as if its mass were negative. Thus take 
Weber’s law as an example: let us suppose that two electrified bodies are 
moving along the line joining them, which we may take as the axis of a; 
then the expression for the kinetic energy, putting in the value of f which 
corresponds to Weber’s law, is 
/ 
mg? + 4mq’? + ae?g? + Bel2q/? + — {y-—q}%, 
«pp! 
so that if dm + ae? 4 82 
be negative, then the coefficient of q* in the kinetic energy will be nega- 
tive, and the body will behave as if its mass were negative; and, by 
sufficiently increasing e’ or diminishing r, we can make this expression 
negative, so that Weber’s law leads to results which are inconsistent with 
experience. This result of Weber’s law was first pointed out by Helmholtz. ! 
Exactly the same objection applies to Riemann’s theory, and indeed 
we see that it will apply to any theory which makes the force between 
two electrified bodies depend on relative velocities and accelerations. 
The same objection need not apply to Clansius’ theory, for substitut- 
ing the value of f belonging to his theory, the kinetic energy equals 
(dm + aet)y?+ (Lm! + fe?)q!? + ee! M1 008 «, 
so that the kinetic energy will be always positive if 
2 o2 p/2 2 
(4m + ae’) (4m! + Be!2)> a 
This condition will evidently be satisfied if 
2 
10g 
and this relation does not involve the electrification. We cannot assume 
that we can make r so small that this condition is not satisfied, for r has 
a minimum value depending upon the shape and size of the electrified 
bodies. For example, if these are spheres, 7 cannot be less than the 
sum of their radii. On the other hand, a and f may be functions of the 
1 Ueber die Theorie der Elektrodynamik. Crelle, vol. Ixxv. p. 535; Collected 
Works, Bd. 1, S. 647. 
1885. 
