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

with impacts, for them work was not a total differential and the concept of
potential, which was being developed, not only in France 107, in the tradition of
analytical mechanics, was not generally admitted 108. On the other side in the
analytical tradition, up to a certain date, the quantity that is now called potential
was not meant to be work stored in the system at a certain position, but, despite
formal equivalence, was understood only as a mathematical function of the
positions from which the forces could be derived. Force by displacement in the
direction of force was in this tradition a total differential but did not receive a
physical interpretation. Helmholtz very subtly and skilfully here unified the two
approaches, that is, the concept of work with the function of positions (but not
without problems in defining potential 109). Now work cannot be created and
cannot be destroyed, it is a state function (of the positions). Discussions in the
1880's outlined clearly that with this new "representation" of the principle of
impossibility of perpetual motion a relevant modification had been achieved 110.
The relevance of the innovation just introduced was made explicit by
Helmholtz himself in 1884 111; he asserted that there are two philosophical roots
of the principle of conservation: the "ex nihilo nil fieri" and the "nil fieri ad
nihilum". The first is connected with the impossibility of creating work ( and thus
with the impossibility of perpetual motion) and the second with the impossibility
of destroying it. Helmholtz in 1884, looking back, asserted that a big difficulty
he had to overcome in the formulation of energy conservation was the acceptance
of the "ad nihilum", while the first root was part of shared knowledge 112. The "ex
nihilo" is based on an inductive assumption, already made by a qualified minority
nn.71-4.
107 see for instance the contributions of Green, Hamilton, Gauss, F.Neumann: above
108 Grattan-Guinness, Ivor. "Work for the Workers: Advances in Engineering
Mechanics and Instruction in France, 1800-1830". In Annals of Science 41 (1984):1-33. P.
32.
109 See chapter 5 of the Erhaltung
110 Planck Princip P. 37.
111 In an appendix to the reprint of the famous talk on the Interaction of Natural
Forces: Helmholtz, Hermann. "Robert Mayer's Priorität". In Vorträge und Reden. 2 vols.
Braunschweig: Vieweg, 1884.
112 Both had been already explicitly recalled by Mayer in 1842.