Conservation and Innovation : Helmholtz's Struggle with Energy ...

means taking into account the actual bodies and not "purely imaginary systems of
coordinates" 283. Helmholtz admits that he assumed that the vis viva depends only
on the positions of the points and thus only on their distance. If this version of the
principle is accepted Helmholtz can derive, through a massive use of
mathematics, both the hypotheses leading to central forces (the intensity depends
on the distance and the direction is in the joining line) also for the case in which
there is a point moving under the action of a material element. In this case, in
principle, the vis viva of the point should depend on the orientation of the
distance. Furthermore, Helmholtz explicitly asserts that the only implicit
principle used, the superposition of the effects for the force, if accepted
reinforces his conclusions 284.
Clausius quick answer is very short, he denied that in the Erhaltung the concern
was only with relative positions and reasserted his views on the impossibility of a
mathematical deduction of the central forces 285.
In 1882 once more Helmholtz had to accept the criticism, but with some
qualifications: he now admits that the demonstration in the second chapter needs
a restriction, that is: forces that depend also on velocities and accelerations are in
agreement with the vis viva theorem, but not with the principle of action and
reaction 286. Nevertheless they are in agreement with the impossibility of perpetual
motion. Helmholtz asserts in appendix 2 that this point was clarified for him by
Lipschitz. He does not quote the controversy with Clausius, and in appendix 3
while quoting Clausius' electrodynamic law does not quote Weber's.
In a section below I will analyse the role of Helmholtz's expression of the energy
concept and of the conservation principle in the electromagnetic debate of the
70's. It is sufficient for the moment to point out that the root of the problem, the
supposed necessity for energy conservation of central forces, was already explicit
after Weber's 1848 expression of a kinetic potential and Clausius' 1853
criticisms.
c) Other minor points were part of the controversy: Clausius in 1852 287, while
praising Helmholtz's Erhaltung, claims that some parts were incorrect; he
283 Helmholtz "Erwiderung" p.82.
284 Helmholtz "Erwiderung" Pp.88-9.
285 Clausius "Zweite Notiz" p.604.
286 Helmholtz WA 1. Appendix 2 and 3 to the Erhaltung; pp.68-70.
287 Clausius "Electrical Discharge" p.6