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

Poincarè agrees that the electrodynamic potential of a system of currents is the
kinetic energy of the ether 425.
In contrast to the great interest in energy theories, little room is left for Hertz’s
experiments.
Analysing Weber’s theory, Poincarè asserts that it agrees with PCE, as far as the
work of electrodynamic repulsion is equal to the differential - dc of the potential
c. 426 In this case Poincarè is using the potential law as PCE, but somewhere else
he adopts Helmholtz’s PCE, and clearly refers to the distinction between kinetic
and potential energy. In the analysis of Helmholtz’s theory the expression of PCE
is the following: the variation of T+U must be equal to the work performed by the
external electromotive forces (chemical, thermoelectrical, etc.) minus the Joulean
heat 427. The need for the distinction of T and U appears relevant in the subsequent
analysis of the different theories: Weber’s is rejected, despite its fulfilment of
PCE, because of the negative value of the constant K in Helmholtz’s general
potential. In fact K < O leads to negative kinetic energy and instabilities 428. The
relevance for Poincarè of PCE and, moreover, his specific preference for a PCE
involving T and U has already been outlined. His preference for Maxwell was a
result of this choice. Equally remarkable is that Poincarè’s made a link between
PCE (with T and U sharply divided) and the Lagrangian derivation: he never
considered the possibility of a Lagrangian derivation with an electrokinetic
potential, and thus refers the possibility of a mechanical explanation (given by the
Lagrangian derivation) to the possibility of dividing T and U.
Poincarè’s ideas on energy are clarified in a work of 1892 429. The principle of
conservation is called here Mayer’s principle and Poincarè wonders at the
success it has among other physical laws. A reason cannot be found in its
connections with the impossibility of perpetual motion (from which it can be
derived only in the case of reversible phenomena). Moreover the attempts at a
clear definition are useless: "it is impossible to find a general definition of it". The
principle disappears when generalised and applied to the universe. The only
425 Poincarè El et Opt p.169 (par.152).
426 Poincarè, Henry. Electricité et Optique. II. Les Theories de Helmholtz. Paris:
Carré, 1891; p.31, 41 (par.18-20).
427 Poincarè El et Opt 2 p.69 (par.31).
428 Poincarè El et Opt 2 p.75 (par.34).
429 Poincarè, Henry. Thermodynamique. Paris: Carré, 1892; p.IX. Repr. in Poincarè
La Science pp.144-9.