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

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In 1876 Clausius, discussing 253 his own electrodynamic law of the previous year, clarified his interpretation of the conservation principle, in a way that is strongly connected with the approach of his early works on electricity: the only condition needed to fulfil the principle of conservation is that the work done by the forces is a total differential. No physical interpretation of potential energy or of the energy concept is given, conservation is still defined along the lines of the analytical tradition as vis viva conservation. Clausius' approach derives from his committment to mathematical potential theory 254 and to his identification of work with the difference of potential. All this shows that Clausius' 1852 remarks on Helmholtz's results were by no means casual, but originated and deeply rooted in Clausius' research programme. A main difference in the interpretation of the energy concept was to create a lifelong barrier between these two champions of the mechanical view of nature: Helmholtz believed in two forms of energy sharply divided and based on central forces depending only on distance, while Clausius admitted forces that were not central and depended also on velocities and accelerations as far as they admitted a potential; the fact that in this (kinetic) potential appeared terms including both positions and velocities was not seen as a problem by Clausius . The existence itself of a potential was considered as the fulfilment of the impossibility of perpetual motion. The whole controversy of 1852-54 took place in the pages of the Annalen der Physik 255, a clear indication that both Clausius' and Helmholtz's theoretical contributions were now fully accepted by Poggendorff 256. 253 Clausius, Rudolf. "Ueber das Verhalten des elektrodynamischen Grundgesetzes zum Prinzip von der Erhaltung der Energie und über eine noch weitere Vereinfachung des ersteren." In Pogg Ann 157 (1876):489-94; tr.in Phil Mag s5 1 (1876): 218-21. 254 Clausius published many editions of his textbook on the Potential and the Potential Function starting from 1859. A French translation of the second German edition of 1866 appeared in 1870: Clausius, Rudolf. De la fonction potentielle et du potentiel. Tr by F.Folie. Paris:Gauthier-Villars, 1870. 255 Comments on this controversy are in Planck Prinzip Pp.48-50, Koenigsberger H v H Pp.115-20, Heimann "Helmholtz and Kant" Pp.234-7, Jungnickel,C. and McCormmach, R. Intellectual Mastery p.163. 256 On the cultural policy of the journal see: Jungnickel,C. and McCormmach, R. Intellectual Mastery Vol.1, Pp. 113-128.
The controversy started with some remarks on Helmholtz's Erhaltung in the notes of Clausius' 1852 paper on electric discharge. Helmholtz answered in a note of his 1853 257 paper on the distribution of electrical currents in material conductors. In the same year 258 Clausius fought back and in 1854 259 Helmholtz expressed his views at length , in a paper to be reprinted in the energy section in the first volume of his collected works. A short comment of Clausius in 1854 260 closed the debate. As already seen 261, later on in 1882, in the appendix to the reprint of the Erhaltung in the same first volume of the collected works, Helmholtz admitted, in part and without quoting Clausius, that some of his old objections were correct. There were three main points of debate and I will deal with them separately: a) the definition of potential; b) the conceptual model of central forces; c) accusations of lack of precision. a) Helmholtz had introduced the concept of Spannkraft (potential energy) without going into a discussion of the concept of potential. The peculiarity of Helmholtz's approach is that he jumps from the vis viva theorem to the conservation of "force" principle, without following the now standard pattern of f x ds = work, work as total differential = difference of potential. In the case of central Newtonian forces work is indeed a total differential and thus the two approaches intersect considerably. In fact, as discussed in the previous section, Helmholtz introduces in a straightforward way in the second chapter of the Erhaltung the sum of tension forces (potential energy) and the energy concept (the variation of vis viva equals the variation of the sum of tension forces, the sum of vis viva and tension forces is a constant) as conceptual and physical entities. Instead he introduces the term potential only in the fifth chapter, with a physical grasp not completely refined and without knowledge of Green's contributions, but "in 257 Helmholtz, Hermann. "Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche." In Pogg Ann 89 (1853): 211-33, 352-77. Repr. in WA 1 pp.475-519; n.1 p.488. 258 Clausius, Rudolf."Ueber einige Stellen der Schrift von Helmholtz "uber die Erhaltung der Kraft." In Pogg Ann 89 (1853): 568-579. 259 Helmholtz, Hermann. "Erwiderung auf die Bemerkungen von Hrn. Clausius". In Pogg Ann 91 (1854): 241-60; repr. in WA1, 1882, pp.76-93. 260 Clausius, Rudolf. "Ueber einige Stellen der Schrift von Helmholtz "uber die Erhaltung der Kraft", zweite Notiz." In Pogg Ann 91 (1854): 601-604. 261 See nn.125, 126, 127 above. Helmholtz WA 1 p.70.
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Fabio Bevilacqua Conservation and I
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different formulations 4 and priori
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and interesting results, despite th
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principle of correlation is express
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principle to the existing empirical
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the origin and meaning of the princ
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Whether physiological research, apa
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In a discussion on the origins of a
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his "Wärme" that one of the differ
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generate a determined equivalent of
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meaning left is: "There is somethin
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interpretations at the beginning of
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while fighting metaphisicians, he w
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literature 456. There is an intrins
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assertion is surprising: it has lon
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Kant was a Naturphilosophe 480. The
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condition that work done by the for
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histories cites these (Hirn's) arti
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) the experimental determinations o
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force principle 522. Elkana tried t
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Blüh, Otto. "The Value of Inspirat
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Graetz, L. "Das Mechanische Wärme
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Helmholtz, Hermann. "Bericht über
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Helmholtz, Hermann. Wissenschaftlic
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Madison: Wisconsin U.P., 1959. Pp.
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Poincarè, Henry. Electricité et O
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Yagi, Eri."Clausius's Mathematical
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