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

and from here that the direction and magnitude of the force must be
function of the position of m and thus of its distance from the attracting point a.
Helmholtz synthesized in this chapter many elements deriving from
different traditions and introduced many novelties sometimes implicitly and not
always with success.
The first remark to be made concerns the formulation of the impossibility
of perpetual motion: Helmholtz introduced specific mechanical concepts (work,
velocity, force) that did not belong to the Carnot-Clapeyron expression. There is
thus an attempt at framing the impossibility of perpetual motion in a mechanical
world view 102: an (implicit) step in the methodological strategy tending to show
that the two initial assumptions belong to the same conceptual scheme.
My second remark deals with the relevant innovation introduced by
Helmholtz, that is the interpretation of the term work ("Arbeit") as a total
differential in the (new) expression of the impossibility of perpetual motion. Here
Helmholtz unified two different traditions in mechanics, analytical mechanics
and mechanical engineering 103, and an old philosophical principle, partially
already recalled in the physiological discussions of the "Bericht": "nothing comes
out of nothing and nothing is destroyed" 104.
In the French tradition of mechanical engineering, which, as seen, was
well known to Helmholtz, the term "travail" had received full importance: the
principle of conservation of vis viva became the principle of transmission of
work 105; but while accepting the impossibility of creating work the French
engineers did not exclude that work could be lost 106. Being mostly concerned
102 Helm's criticism on this point is very sharp: he summarised the mechanical
hypothesis with the statement that "all the events can be explained in terms of forces that
originate accelerations". He warned that with Helmholtz's reformulation of the principle of
impossibility of perpetual motion and of the subsequent expression of the vis viva principle,
whenever the last one is applied we will be "obliged to imagine forces and velocities involved
in every experimental application, for instance in electrical or thermal phenomena". For Helm
the two roots of Helmholtz's Erhaltung are basically different and the one based on
Newtonian forces has to be rejected, together with the mechanical formulation of energy.
Helm Energetik P.41.
103 for a classification see: Grattan-Guinness "The varieties of mechanics"
104 WA 1 P.6
105 Rühlmann Maschinenlehre ; Haas Entwickl. Pp.73-83.
106 Haas: ibidem P.81.