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

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in a note that he had considered twice every interaction of two electrical particles ( most contemporary textbooks warn the students not to make such a 'mistake' 197) and that the use of other authors to equate potential and work was more appropriate. Still he maintained that his 1847 approach in relating potential and work was basically correct. In my view Helmholtz's claim is based on reasonable grounds: I believe he was among the first to interpret and use "correctly" the "new" mathematical tool (the potential) in physical research 198. Helmholtz thus unified explicitly in this essay the tradition of analytical mechanics (potential function of Gauss, Hamilton and Jacobi) and of engineering (concept of work), but it is noticeable that, at variance with Clausius' more mathematical approach of 1852 199, he arrived at the concept of potential not through the concept of work as a total differential, but straight from the concept of sum of tension forces. The fact that theoretical rather than mathematical physics was at the root of Helmholtz's approach is evident from his attempt to clarify the "mathematical" potential through the introduction of physically sound concepts and not viceversa. Helmholtz introduced 200 first the "equilibrium surfaces", later identified with equipotential surfaces, and second the "free tension", later to be identified by Helmholtz himself with the mathematical reader with a note to the last appendix WA 1 P.75 (the latter in Kahl's translation is simply omitted). 196 Helmholtz WA 1 P.75 197 For instance: Feynman, Richard. The Feynman's Lectures on Physics. 3 vols. Addison Wesley, 1963; vol 2 P.8/15 198 Hoppe's claim that the identification of work and potential started with Riemann is probably due, being Hoppe a committed Weberian, to the lasting effects of the Weber/ Helmholtz controversy; see Hoppe,E. Histoire de la Physique. Paris: Payot, 1928; P.570. 199 Clausius, Rudolf. "Ueber das mechanische Aequivalent einer elektrischen Entladung und die dabei stattfindende Erwärmung des Leitungsdrahtes" Pogg Ann 86, 1852: 337-375; transl in:"On the Mechanical Equivalent of an Electric Discharge, and the Heating of the Conducting Wire which accompanies it." In Tyndall and Francis Scientific Memoirs on Natural Philosophy 1 (1853): 1-32. 200 Helmholtz Erhaltung Pp.40-1 and P.42
potential function 201. It is worth noting that still in 1847 Helmholtz's idea of electric tension was reminiscent of Volta's influential "density of electricity" 202. Helmholtz with great intellectual ingenuity struggled to apply his conceptual framework of living and tension forces to every realm of nature: he did not use mathematical requirements as heuristic tools and thus differed from mathematical physicists such as Clausius and Riemann to a great extent. But he also differed widely from experimentalists such as Joule: in discussing the heat generated in an electrical discharge he stressed the interpretation of the heat as the vis viva produced by a decrease of the quantity of tension forces (i.e. of the potential) and of the discharge as an oscillatory process of alternating currents, more than the search for experimental results. In fact for the mechanical equivalent of heat (whose numerical value enters in the laws expressed, given the electrostatic system of units utilised 203) he asserted that "up to now observations are lacking". Detailed information is instead given on the relation between the heat produced through the discharge of a specific battery and the shape and dimension of the connecting wire 204 (quoting Riess, Vorselman de Heer and Knochenauer). The fact that conceptual explanation played a greater role than empirical corroboration or mathematical formalism is again exemplified in the discussion of galvanism. For Helmholtz 205 the contact law of Volta, if correctly interpreted, is not in disagreement, as often remarked 206, with the impossibility of perpetual motion. 201 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 p.475, P.224. 202 On Volta's influence in Germany see: Teichmann, Jurgen. "L'influenza di A.Volta in Germania." Quaderni del Giornale di Fisica 3 (1977): 43-60. In 1849 Kirchhoff unified the concepts of electric tension, electrostatic and electrodynamic potential : Kirchhoff,Gustav. "On a Deduction of Ohm's Law, in Connection with the Theory of Electrostatics" Phil Mag 3 XXXVII (1850): 463-8; translated from Pogg Ann LXXVIII (1849) P.506; see also : my Energy and Electr Pp.77 and 96-7; Archibald, Thomas. "Tension and Potential from Ohm to Kirchhoff." In Centaurus 31 (1988): 141-63. criticisms. 203 See Planck Princip P.41. 204 Helmholtz Erhaltung Pp.43-4. This was going to be another object of Clausius' 205 Helmholtz Erhaltung P.45. 206 Kuhn seems still to believe it: Kuhn Sim Disc P.73. See above n.20.
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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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Page 11 and 12: the origin and meaning of the princ
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Page 35 and 36: since Leonardo 113; the "ad nihilum
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Page 39 and 40: The principle of conservation of vi
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Page 45 and 46: In virtue of its limitations to New
Page 47 and 48: Helmholtz, while asserting that lig
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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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