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

"The equality that exists between effect and efficient cause confirms what
we have just said. In this equality consists the conservation of forces of bodies
that are in motion" 142.
"Empirical" causality then comes into play here: not causality as a
condition of the possibility of natural laws, but a principle which establishes a
specific link between different realms of phenomena. The "empirical" causality
indicates a quantitative equivalence between phenomena that are qualitatively
different (static and dynamic).
A static cause can generate, as an effect, the movement of a body. This
movement, in its turn the cause, has the power ("motive force") to produce the
effect of bringing the body back to its former position. The quantitative
equivalence of cause and effect is supposed to hold true at every instant of the
process: the interchangeability of the initial and final stage is only an
exemplification of this principle. What is conserved during the process in
Helmholtz as in Leibniz is this specific quantitative equivalence between
qualitatively different phenomena.
But how can we actually measure two qualitatively different phenomena
to establish a quantitative equivalence? A common unit of measurement is
needed. Again a problem already faced by Leibniz, who asserted the relevance of
(what was later defined as) work as a unit of measurement of all natural
phenomena 143. Leibniz had recognised the impossibility of continually creating
work without a corresponding compensation, and also of destroying work, i.e. of
both the "ex nihilo" and "ad nihilum", a necessary condition to guarantee the
invariability of the chosen unit.
142 Johann Bernoulli Discours sur les lois de la communication du mouvement, Paris
1724; chapt.V, par. 8; quoted in Lindsay Hist P.125.
143 Leibniz:"Brevis Demonstratio erroris memorabilis Cartesii et aliorum circa legem
naturalem, secundam quam volunt a Deo eandem semper quantitatem motus conservari, qua et
in re mechanica abutuntur" in Acta Eruditorum, Christofory Guntheri, Lipsiae 1686, Pp.161-3;
repr. in Leibniz Mathematische Schriften, 7 volumes, C.I.Gerhard ed, Berlin: Asher and Halle:
Schmidt, 1849-63; Vol 2, 1860, Pp.117-9; more generally see: Cassirer, Ernst. Leibniz' System
in seinen wissenschaftlichen Grundlagen, Marburg: Elwert, 1902; Substanzbegriff und
Funktionsbegriff, Berlin: B.Cassirer, 1923, Chapt 4, Sect 7, pp.226-48; Das
Erkenntnisproblem in der Philosophie und Wissenschaft der Neueren Zeit , 2 vols. 2nd
revised edition, B.Cassirer: Berlin, 1911; vol 2. P.165.