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

The relevance of the first question can be better understood if we remember that Helmholtz's
sharp distinction between a positional and a kinetic energy was the result of the privilege he
had attributed to central Newtonian forces. It was not a result of the other basic hypothesis of
the impossibility of peprpetual motion. Thus alternative expression of the principle of
conservation were possible and were in fact given (correlation, generalised potentials). In
which way then was Helmholtz's approach superior? Were electromagnetic phenomena better
explained if interpreted in terms of the two forms of energy?
The second question does not deal with the superiority of one or the other
expression of the principle but with the possibility of the theoretical principles to
provide new knowledge; in a way it questions the basis of the new theoretical
physics: can the energy terms in a specific situation be provided by a theoretical
analysis based on the principle alone or is experimental knowledge of that
situation needed for a correct application of the principle? In this second case
what is the advantage of using the principle?
An answer to these questions can be obtained through a discussion of two of the
four cases analysed in this section of the Erhaltung.
The first case discussed refers to a system consisting in a magnet moving under
the effect of a current 216. Helmholtz identified the tension forces with the ones
utilised in the current : aAJdt (in mechanical units, with a = mechanical
equivalent of heat, A = the electromotive force of a single cell, J= the current),
that is, (following the result of the section on galvanism in the previous chapter),
with the heat generated in the chemical process inside the battery. The living
force is supposed to be composed of two parts: one, as before, is the heat
generated in the circuit (W= the resistence of the circuit) by the current:
the other is the living force acquired by the magnet under the effect of the
current. This is identified with:
J dV
dt dt
where V is the potential of the magnet towards the conductor carrying a unitary
current (accepting Ampère's view that the electrodynamic effects of a closed
current are equivalent to those of a magnetic double layer). Thus:
A−
J =
1
a dV
dt
W
The term
1
a
dV
dt
216 Helmholtz Erhaltung Pp.64-5.