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

efuted. But again in 1881 Helmholtz criticised Weber on the grounds of a
possible physical case in which the law would have given an imaginary value of
the velocity 398. Hoppe noted other aspects of the controversy: C. Neumann in
1871, 1875 and 1877 and Zoellner in 1876 published in favour of Weber and
against Helmholtz. Helmholtz in 1876 recognized that Rowland’s experiments on
convection were not in disagreement with Weber’s law. In 1887 Budde made a
very sophisticated analysis of the theories of Weber, Clausius and Riemann, and
planned a series of experiments "in order to prove their validity" 399. C.
Neumann’s contributions of 1877 and 1898 are extremely interesting for an
objective judgment of this long dispute. C. Neumann in fact was a defender of
Weber’s position. Still in 1877 he answered Helmholtz’s criticism of 1872
against Weber in the following terms: "The objection that follows (in Helmholtz’s
argument ) does not bear on the usual principle of energy, but on a completely
novel principle which is here pronounced for the first time. While the usual
principle of energy demands for each system the existence of an energy function,
i.e. the existence of a function which has the quality to increase in each time
interval by the same amount as is the work which is being performed on the
system from the outside - this new principle demands not only the existence of
such a function, but at the same time a very specific feature of it, in as much as it
asserts that the kinetic part of this function must invariably be positive." 400 In
Weber’s approach the electrokinetic potential has terms containing squared
velocities like the kinetic energy ones. But in contrast with standard kinetic terms
which are multiplied by a positive coefficient like m, these new terms can be
multiplied by negative coefficients, like electric charges. The sum of the resulting
positive and negative terms containing squared velocities can be negative. From
Helmholtz’s point of view, this sum represents a negative kinetic energy and thus
the new requirement of positive T was postuled . C. Neumann explicitly asserts
that physical principles are not to be considered established once and for all.
Modifications are possible and the one just introduced by Helmholtz must be
carefully analysed. C. Neumann outlines three shifts in PCE: the principle of
conservation of vis viva, the principle of conservation of energy, and Helmholtz’s
new principle of positive kinetic energy. Being a new principle, for Neumann it
cannot be considered a secure ground for debate. Helmholtz’s objections against
398 Hoppe Histoire p.591.
399 Hoppe Histoire p.592.
400 C.Neumann Amp and Web p.322.