Die Erhaltung der Kraft

If medicine was not Helmholtz’s first choice, it nevertheless served him (and he
served medicine) well, even when circumstances were trying. His medical scholarship
stipulated eight years of service as an army surgeon. He tookup this
service without much enthusiasm. Life as surgeon to the regiment at Potsdam
offered little of the intellectual excitement he had found in Berlin. But to an
extraordinary degree, Helmholtz had the ability to supply his own intellectual
stimulation. Although severely limited in resources, and unable to sleep after
five o’clockin the morning when the bugler sounded reveille at his door, he
quickly started a full research program concerned with such topics as the role of
metabolism in muscle activity, the conduction of heat in muscle, and the rate of
transmission of the nervous impulse.
During this time, while he was mostly in scientific isolation, Helmholtz wrote
the paper on energy conservation that brings him to our attention as one of the
major thermodynamicists. (Once again, as in the stories of Carnot, Mayer, and
Joule, history was being made by a scientific outsider.) Helmholtz’s paper had
the title U¨ ber die Erhaltung der Kraft (On the Conservation of Force), and it was
presented to the Berlin Physical Society, recently organized by du Bois-Reymond,
and other students of Mu¨ ller’s, and Gustav Magnus, in July 1847.
As the title indicates, Helmholtz’s 1847 paper was concerned with the concept
of “force”—in German, “Kraft”—which he defined as “the capacity [of matter] to
produce effects.” He was concerned, as Mayer before him had been, with a composite
of the modern energy concept (not clearly defined in the thermodynamic
context until the 1850s) and the Newtonian force concept. Some of Helmholtz’s
uses of the word “Kraft” can be translated as “energy” with no confusion. Others
cannot be interpreted this way, especially when directional properties are assumed,
and in those instances “Kraft” means “force,” with the Newtonian
connotation.
Helmholtz later wrote that the original inspiration for his 1847 paper was his
reaction as a student to the concept of “vital force,” current at the time among
physiologists, including Mu¨ ller. The central idea, which Helmholtz found he
could not accept, was that life processes were controlled not only by physical
and chemical events, but also by an “indwelling life source, or vital force, which
controls the activities of [chemical and physical] forces. After death the free action
of [the] chemical and physical forces produces decomposition, but during
life their action is continually being regulated by the life soul.” To Helmholtz
this was metaphysics. It seemed to him that the vital force was a kind of biological perpetual motion. He knew that physical and chemical processes did not
permit perpetual motion, and he felt that the same prohibition must be extended
to all life processes.
Helmholtz also discussed in his paper what he had learned about mechanics
from seventeenth- and eighteenth-century authors, particularly Daniel Bernoulli
and Jean d’Alembert. It is evident from this part of the paper that a priori beliefs
are involved, but the most fundamental of these assumptions are not explicitly
stated. The science historian Yehuda Elkana fills in for us what was omitted:
“Helmholtz was very much committed—a priori—to two fundamental beliefs: (a)
that all phenomena in physics are reducible to mechanical processes (no one
who reads Helmholtz can doubt this), and (b) that there be some basic entity in
Nature which is being conserved ([although] this does not appear in so many
words in Helmholtz’s work).” To bring physiology into his view, a third belief
was needed, that “all organic processes are reducible to physics.” These general
ideas were remarkably like those Mayer had put forward, but in 1847 Helmholtz
had not read Mayer’s papers.
Helmholtz’s central problem, as he saw it, was to identify the conserved entity.
Like Mayer, but independently of him, Helmholtz selected the quantity “Kraft”
for the central role in his conservation principle. Mayer had not been able to
avoid the confused dual meaning of “Kraft” adopted by most of his contemporaries.
Helmholtz, on the other hand, was one of the first to recognize the ambiguity.
With his knowledge of mechanics, he could see that when “Kraft” was
cast in the role of a conserved quantity, the term could no longer be used in the
sense of Newtonian force. The theory of mechanics made it clear that Newtonian
forces were not in any general way conserved quantities.
This reasoning brought Helmholtz closer to a workable identification of the
elusive conserved quantity, but he (and two other eminent thermodynamicists,
Clausius and Thomson) still had some difficult conceptual ground to cover. He
could follow the lead of mechanics, note that mechanical energy had the conservation
property, and assume that the conserved quantity he needed for his
principle had some of the attributes (at least the units) of mechanical energy.
Helmholtz seems to have reasoned this way, but there is no evidence that he got
any closer than this to a full understanding of the energy concept. In any case,
his message, as far as it went, was important and eventually accepted. “After [the
1847 paper],” writes Elkana, “the concept of energy underwent the fixing stage;
the German ‘Kraft’ came to mean simply ‘energy’ (in the conservation context)
and later gave place slowly to the expression ‘Energie.’ The Newtonian ‘Kraft’
with its dimensions of mass times acceleration became simply our ‘force.’ ”
I have focused on the central issue taken up by Helmholtz in his 1847 paper.
The paper was actually a long one, with many illustrations of the conservation
principle in the physics of heat, mechanics, electricity, magnetism, and (briefly,
in a single paragraph) physiology.