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

The controversy started with some remarks on Helmholtz's Erhaltung in the
notes of Clausius' 1852 paper on electric discharge. Helmholtz answered in a
note of his 1853 257 paper on the distribution of electrical currents in material
conductors. In the same year 258 Clausius fought back and in 1854 259 Helmholtz
expressed his views at length , in a paper to be reprinted in the energy section in
the first volume of his collected works. A short comment of Clausius in 1854 260
closed the debate. As already seen 261, later on in 1882, in the appendix to the
reprint of the Erhaltung in the same first volume of the collected works,
Helmholtz admitted, in part and without quoting Clausius, that some of his old
objections were correct.
There were three main points of debate and I will deal with them separately: a)
the definition of potential; b) the conceptual model of central forces; c)
accusations of lack of precision.
a) Helmholtz had introduced the concept of Spannkraft (potential energy) without
going into a discussion of the concept of potential. The peculiarity of Helmholtz's
approach is that he jumps from the vis viva theorem to the conservation of
"force" principle, without following the now standard pattern of f x ds = work,
work as total differential = difference of potential. In the case of central
Newtonian forces work is indeed a total differential and thus the two approaches
intersect considerably. In fact, as discussed in the previous section, Helmholtz
introduces in a straightforward way in the second chapter of the Erhaltung the
sum of tension forces (potential energy) and the energy concept (the variation of
vis viva equals the variation of the sum of tension forces, the sum of vis viva and
tension forces is a constant) as conceptual and physical entities. Instead he
introduces the term potential only in the fifth chapter, with a physical grasp not
completely refined and without knowledge of Green's contributions, but "in
257 Helmholtz, Hermann. "Ueber einige Gesetze der Vertheilung elektrischer Ströme
in körperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche." In Pogg Ann
89 (1853): 211-33, 352-77. Repr. in WA 1 pp.475-519; n.1 p.488.
258 Clausius, Rudolf."Ueber einige Stellen der Schrift von Helmholtz "uber die
Erhaltung der Kraft." In Pogg Ann 89 (1853): 568-579.
259 Helmholtz, Hermann. "Erwiderung auf die Bemerkungen von Hrn. Clausius". In
Pogg Ann 91 (1854): 241-60; repr. in WA1, 1882, pp.76-93.
260 Clausius, Rudolf. "Ueber einige Stellen der Schrift von Helmholtz "uber die
Erhaltung der Kraft", zweite Notiz." In Pogg Ann 91 (1854): 601-604.
261 See nn.125, 126, 127 above. Helmholtz WA 1 p.70.