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

expression provided for the conservation principle 380. This is already a
methodological shift of great interest in scientific debates. But the interest is
augmented by the fact that it implied the formulation of more sophisticated
versions of the principle itself. The admissibility of Weber's law had been
questioned on the grounds that his force law did not match Helmholtz's criterion
of central forces. Accepting the supposed equivalence of 1847 between central
Newtonian forces and the impossibility of perpetual motion, the conclusion was
drawn that Weber's law clashed with this basic assumption. Remarks of this kind
were still put forward in the sixties in Britain by Maxwell (1864), W.Thomson
and Tait (1867), Tait (1868). The above mentioned fact that Weber's force
admitted a potential was unnoticed, or, given that this potential included both
kinetic and positional terms, was still considered to violate the requirement of a
sharp distinction between kinetic and potential energy. Finally both Helmholtz
(1870 and 1872) and Maxwell (1873) agreed that Weber's law was not in
contradiction with the impossibility of perpetual motion. But Helmholtz, who
himself had proposed a very general potential law for electrodynamics, kept
criticizing Weber on energy grounds: in Weber's theory energy could become
infinite (1870), kinetic energy could become negative (1872) and so forth till
1882. Weber defended himself vigorously in 1871, reformulating the principle of
conservation of energy and explicitly stating he did not necessarily have to fulfil
Helmholtz's version. He received Carl Neumann's (1871, 1875, 1877) reasonable
support and Zöllner's unreasonable one ( 1876). On another side Clausius very
plainly states that the only condition to fulfil energy conservation is that the work
produced by the force be a total differential (1876) and not that forces be central
or that kinetic and positional terms of energy be sharply split. It is to be noted
that Clausius' target was not so much Helmholtz, but Weber, an indication of the
latter's important role in electrodynamics. Helmholtz's electrodynamic potential
law, based on action at a distance and on the polarization of an interposed
dielectric, in the seventies began to be seen as an understandable translation of
Maxwell's difficult and sometimes contradictory approach. An example of the
difficulties of Maxwell's Treatise (1873) are the many different concepts of
energy presented: as potential energy (electrostatic) and kinetic (electromagnetic)
or as the product of an intensity by a quantity factor; electrostatic energy seen as
charge by scalar potential or as the square of the electric intensity;
electromagnetic energy seen as current by vector potential or as the square of the
380 See my Energy and Electr