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

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On this point Clausius, who had given 186 in 1850 a mechanical equivalent of 421 Kgm, in 1854 moved a serious objection, asserting that Helmholtz had misunderstood Holtzmann's law, in which the caloric concept played a role which cannot be eliminated. This was among the very few criticisms that Helmholtz accepted during the controversy 187. In 1882 in an appendix to this chapter, Helmholtz discussed the priority problem 188. 6 Electricity, galvanism and thermo-electric currents: Helmholtz and the batteries The fifth and the longest chapter of the Erhaltung is dedicated to applying the law of conservation of force to static electricity, galvanism and thermo-electric currents 189. Once again Helmholtz displayed an extraordinarily detailed knowledge of empirical laws of physics in his attempt at further theoretical applications of his principle. The first application is an easy one: Coulomb's law, being a strictly central force law with attractive and repulsive forces, offers the best possible example of how to formulate a sum of tension forces, to be equated with an increase of vis viva. But the difficulties do not wait for long: Helmholtz, explicitly referring to Gauss 186 Clausius, Rudolf "Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen" Annalen 79 (1850): 368-97, 500-24. 187 Helmholtz, Hermann. "Erwiderung auf die Bemerkungen von Hrn. Clausius". In Pogg Ann 91 (1854): 241-60; repr. in WA1, 1882, pp.76-93. P.90. Still Truesdell believes that Helmholtz's approach in 1847, while wrong in other aspects, in this was consistent: Truesdell, Clifford. The Tragicomic History of Thermodynamics. 1822-1854. New York: Springer,1980, P.162; Truesdell believes that the Erhaltung is "Helmholtz's weakest work" ibid. P.161. 188 Helmholtz WA 1 Pp.71-4. 189 Given that most of the chapter (from P. 48 to P. 58) deals with a careful analysis of batteries, Kuhn's remark (Kuhn Sim Disc P.73) that Helmholtz did not discuss batteries in his Erhaltung is difficult to understand.
and unaware of Green's results190, introduced the concept of electric potential. He defined the quantity ⎛ eieii − ⎝ r ⎠ ⎞ corresponding to the sum of the tension forces consumed, and also of course to the living forces acquired in the motion of the two charges from an infinite distance to the distance r, as the potential of the two electrical elements for the distance r 191. The principle of conservation can thus be expressed in a new way: "the increase of vis viva in whichever movement must be considered equal to the difference of the potential at the end of the trajectory respect to the potential at the beginning" 192 (the sign of the potential is opposite to that of modern convention). The potential as defined by Helmholtz is equivalent but for the sign to what later was to be called potential energy. He showed a good grasp in setting the relations between potential and work, for instance in the case of the potential of one body with respect to another193. Here in fact he precisely stated the equivalence between potential and work. But problems occur in the definition of the potential of a body on itself (the sum of the potentials of an electric element of a body with respect to all the other electrical elements of the same body): in this case Helmholtz's definition is double the modern convention, but what mostly matters, does not correspond to the work done194 (the potential is supposed to be double the work done). This shows the "independence" of the two concepts in Helmholtz's approach. In the original 1847 edition of the Erhaltung there is a final correction (the only one) referring exactly to these problems. This is a clear indication of the incertitudes and difficulties faced by Helmholtz with concepts that in 1847 were by no means common195. Helmholtz in 1882 196 acknowledged 190 According to Koenigsberger, Helmholtz knew of Green's theorem later, in Koenigsberg, partially through F.Neumann: Koenigsberger H v H P.100. Erhaltung 191 Helmholtz Erhaltung P.38. 192 Helmholtz Erhaltung P.39. 193 Helmholtz Erhaltung Pp.39-40 194 Helmholtz Erhaltung Pp.42-3. Clausius was the first to criticise this part of the 195 In the 1882 reprint of the Erhaltung in WA 1 the correction is incorporated in the text (as in the English translations of Tyndall, Kahl and Lindsay), and Helmholtz warned the
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Fabio Bevilacqua Conservation and I
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different formulations 4 and priori
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Page 47 and 48: Helmholtz, while asserting that lig
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Page 51 and 52: In his search for a mechanical equi
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and the electrostatic In modern not
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of conservation of energy: it is re
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efuted. But again in 1881 Helmholtz
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But was important here is that desp
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The second (1892-94), follows the i
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while the electromagnetic and the s
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can modify its specific theoric for
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considered relevant. In Poincarè
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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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