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

are considered equivalent. Still, the separation of energy into two main forms,
potential and kinetic, is attributed to Rankine and W.Thomson, following a
British nationalist historiographic tradition. In any case Tait's stress is on the
empirical elements of Helmholtz's approach: even the assumption of the
impossibility of perpetual motion for the whole of natural forces is judged an
experimental result.
This insistence on the historiographical revaluation of the experimental
elements in the various formulations of the principle is shared in the early eighties
by Helmholtz himself, as seen in the previous section. This is, in my view, owing
to some concrete difficulties faced by Helmholtz in applying his 1847 formulation
of the principle to actual physical research in the late sixties and seventies.
A new tool : potential theory (1852-72)
Helmholtz's Erhaltung did not withstand the criticisms pointed out by
Clausius on the definition of potential and on the privilege accorded to central
Newtonian forces. Its electrodynamic part was also "for the most part
defective" 378 for its lack of terms referring to energy stored with the circuits. The
very derivation of Neumann's law of induction, for which Helmholtz and
W.Thomson had received so much credit (not the least from Tait in 68-69 and
Maxwell in 1873), was not correct 379.
Helmholtz realized this before his critics. He acknowledged the
weakness of the electrodynamic aspects of the Erhaltung during the controversy
with Clausius and defended his own theoretical approach with the introduction
of some new energy terms, but from that moment on his research in the field of
energy shifted a great deal. He was in fact more inclined towards the physicomathematical
problems connected with Green's theorem and with the
mathematical theory of potential as heuristic tools, rather than with the
theoretical applications in the 1847 style. Helmholtz worked hard to master
potential theory, and in the end achieved an extraordinary success: he was able to
378 Whittaker, E. A History of the Theories of Aether and Electricity 2nd ed. New
York: Harper, 1960; p.218.
379 See nn.217-221.