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

methodology. Dühring claimed the character "a priori" of the conservation law
and was one of those who recognised in Mayer "a hero in the field of pure
thought" 361.
Helmholtz after these controversies shows a second shift from his own
positions of 1847: now not only the conceptual explanation of central forces is
given up, but also the theoretical character of the conservation principle: the
empirical component acquires greater and greater importance.
In fact the judgement on Mayer is radically different. Mayer's papers'
weakness is exactly what is praised by metaphysicians:
"the illusory demonstration, metaphysically formulated, of the a priori
necessity of this law".
The law 's success was due to Joule's results. Only then was attention
paid to Mayer's work. The origins of the law, even those of the theoretical
demonstration, are inductive: they came from the empirical acknowledgement of
the impossibility of perpetual motion. The (1775) statement of the Paris Academy
was based on such a probable inductive "conviction" (and not on a
demonstration). The conviction was largely shared. Helmholtz himself, he recalls,
since his school years, had heard discussions 362 on the problems of proving
perpetual motion. His target in writing the Erhaltung was not to propose an
original idea but to carry out a critical work, and he was thus surprised that only
Jacobi, "the mathematician", received it well.
Later, in 1883, while asserting, against Dühring, that he had been the
first in 1854 to recognize Mayer's priority, Helmholtz again attacks the
metaphysicians, who believe the conservation law to be an a priori knowledge.
This is the real point of the debate, not Mayer's priority: the problem is the old
fight between "speculation and empiricism", deduction and induction. In this
light, any special concern for Mayer's personal difficulties should be overcome
and the history of the law of conservation of force clearly stated. The
impossibility of perpetual motion had already been stated in the last century for
"conservative forces" after the works of Leibniz and Daniel Bernoulli. Helmholtz
agrees explicitly with Mayer's identification of the two philosophical roots of the
conservation principle: the "ex nihilo nil fit " and the "nil fieri ad nihilum". He
asserts that the first was thus already accepted in the previous century, and that
the second, equivalent to the assertion that work could not be destroyed, despite
361 Helmholtz WA 1 p.
362 See also Koenigsberger H v H p.8 and 25-6.