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

In virtue of its limitations to Newtonian forces Helmholtz's "Erhaltung der Kraft"
achieved in the second chapter, with the sharp distinction between kinetic and
positional terms, is the fulfilment of the far- reaching plan anticipated in the first
lines of the "Einleitung" : the conservation law just formulated is the
"consequence" (level B) of the two basic physical assumptions (level A:
impossibility of perpetual motion and central forces).
But so far we only have a theoretical framework that has to be applied, i.e. filled
with the specific expressions of the vis viva and tension forces resulting from the
interaction of the principle (level B) with the experimental laws (level C) in the
various realms of natural phenomena (level D). This interaction between levels B
and C will be carried forward in the next four sections.
Nevertheless, Helmholtz's achievements in the Einleitung and in the first two
chapters are impressive. In a limited number of pages a complete reappraisal of
previous traditions in physics has been made, with an original synthesis of
different and previously competing approaches (analytical mechanics, Newtonian
mechanics, Leibnizian philosophy, mechanical engineering ). But the programme
is only at its initial stage : the general framework is going to be applied in the
following four sections to an extremely wide variety of natural phenomena and
empirical laws. It is in this way that the "empty" framework will show its
justificatory and heuristic power, but not without problems. In my view it is
useful to analyse in the following chapters of the Erhaltung the difficulties
Helmholtz had to face in specifying the "energy" equations in the different
branches of natural sciences. This in order to assess the merits and demerits of
his mechanical approach based on the central force assumption, with the resulting
distinction between the two main forms of energy. An evaluation of Helmholtz's
results in the application of the theoretical framework to the empirical laws of
natural phenomena is a kind of analysis well known at the turn of the century,
but forgotten in more recent times.
4 An easy start: Mechanics
In the third chapter of the Erhaltung Helmholtz started to apply the principle to
mechanical theorems, mostly recalling applications already known of vis viva
conservation. That is: in this short and non- mathematical chapter Helmholtz did