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

considered relevant. In Poincarè’s view, the demonstration of the possibility of a
mechanical explanation i.e. the fulfillment of Lagrange equations, is the main
point in Maxwell’s analysis. This allows him to accept the difficulties and
contradictions that sometimes blemish the British masterpiece. In my analysis,
Poincarè’s remarks are fundamental for two reasons: first, because they show the
importance of PCE and PLA, i.e. of regulative principles, as grounds of debate;
second, because they show that Maxwell’s merit was considered to be the
application of Helmholtz's PCE, a specific PCE with a sharp distinction of T and
U. Thus Poincarè is not concerned, unlike Planck, with the local conservation in
Poynting’s sense, but still judges Maxwell's theory on the basis of Helmholtz's
PCE, the same that Maxwell adopts. For Poincarè in 1890, the sharp distinction
between T and U is still very important, and we are going to see that he will
consider it basic in later works too. But still this is not Poincarè only meaning of
conservation: in 1890 he asserts that a consequence of the assumed conservation
of energy is the existence of a force function (= - U, where U is the potential
energy) so that the equations of movement can be expressed as 421:
etc. Sometimes Poincarè asserts that one of the expressions of conservation of
energy is the existence of a potential depending only on positions 422; in the case
of two electric circuits the terms expressing an exchange of energy are:
where is the electric energy provided by two batteries;
is the Joulean heat produced in the circuit and dT is the part of the variation of
the electrodynamic potential in itself of the system of the two circuits due to the
displacement of the circuits. Now PCE asserts that the previous expression has to
be zero for a closed cycle or to be an exact differential in other cases 423. In this
last example, reference to potential and kinetic energy in the expression of PCE is
avoided. Other relevant passages of this first edition are the statements of the
existence of two electrostatic theories deducible from Maxwell’s and that in the
first theory electrostatic energy cannot be considered as potential 424. Instead
421 Poincarè El et Opt p.X.
422 Poincarè El et Opt p.117 (par.106).
423 Poincarè El et Opt p. 165 (par.149).
424 Poincarè El et Opt p.92 (par.84).