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

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historical study of this tradition is still wanting 484, but its relevance for the "energy" conservation debates is great. Not only in fact in the works of Poisson 485, Green 486, Hamilton 487, Gauss 488, Jacobi, F.Neumann 489 did it precede Helmholtz's essay (who in 1847 did not know of Green but quoted Gauss), but also followed it. Helmholtz's remarks on Jacobi's appreciation of the Erhaltung for recognising its links with the older tradition are well known 490, but also I want to stress that Clausius, Weber, Kirchhoff, Riemann, C.Neumann, Sturm kept talking of "vis viva conservation" well after the "discovery" of "energy" conservation 491. To formulate a conservation principle they thought sufficient the 484 But see: Auerbach, F. "Potentialtheorie". In Handbuch der Physik. A.Winkelmann ed.2nd ed. Leipzig: Barth, 1908. 1st vol. Pp. 179-210. Hoppe, E. Histoire de la Physique . Paris: Payot,1928. Pp.566-74; Kline, Morris. Mathematical Thought From Ancient to Modern Times Pp.522-31 and 681-87. 485 see Wise quoted above. 486 Green, George: Mathematical Papers of the late George Green . N.M.Ferrers ed. London: Mac Millan, 1871."Editor's Preface" Pp.VIII-IX; "On the Laws of the Reflection and Refraction" P.245, 248. P.264. 487 Hamilton "On a General Method in Dynamics" 1834. Rep in Lindsay Histor 488 Gauss, C.F."On General Propositions Relating to Attractive and Repulsive Forces Acting in the Inverse Ratio of the Square of the Distance". In Taylor's Scientific Memoirs Vol.II Part X. Pp.155-7. 489 Neumann, Franz. Die mathematischen Gesetze der Inducirten Elektrischen Ströme C.Neumann ed. Leipzig: Engelmann, 1889. See: Olesko "Neumann". Sketch . P.12. 490 Helmholtz WA1 Appendix to the Erhaltung P.74; Helmholtz Autobiographical 491 Weber, Wilhelm. "Elektrodynamische Maassbestimmungen, insbesonder uuber das Prinzip der Erhaltung der Energie." 1871. In Werke 6 vols. Berlin, 1892-4. Vol.4. Pp. 247-99. Tr. in Phil Mag 43 (1872): 1-20 and 119-49; Clausius, Rudolf. De la fonction potentielle et du potentiel. Tr. by F.Folie. Paris: Gauthier-Villars, 1870; 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; Clausius, Rudolf. Die Mechanische Wärmetheorie 2nd ed. 2nd vol. Braunschweig,1879; Sturm, Jacques. Cours de Mécanique , M.Prohuet ed. Vols. 2. Paris: Mallet-Bachelier, 1861; Riemann, Bernhard. Schwere, Elektricität und Magnetismus, nach den Vorlesungen von B.Riemann . Karl Hattendorff (ed). Hannover: Carl Rumpler,1876. P.156;
condition that work done by the forces be a total differential. This means that "energy" was not stressed as an autonomous physical concept but that what was really supposed to be important was a formal condition on the work done by the forces. An analysis of this tradition and of its relations with Helmholtz's Erhaltung and later works ( Helmholtz's attempted in Königsberg at convincing F.Neumann of energy conservation 492, while was actually F.Neumann who taught the potential theory to Helmholtz 493) would outline some interesting differences between mathematical and theoretical approaches to energy conservation. Once that we recognise that something relevant happened in the history of conservation ideas in the 40's and 50's of last century more and more compelling appears that to try to clarify what happened the stress should be put on differences rather than on similarities. This leads to reexamine Kuhn's choice of the twelve "pioneers" and the three groupings. The exclusion from group one of Clausius 494, Rankine 495 and Kirchhoff: see Hoppe Histoire P.99; Neumann, Carl. Die Gesetze von Ampére und Weber. Leipzig: Teubner, 1877. 492 Koenigsberger HvH P.64 493 Koenigsberger HvH . Pp.100-1. Helmholtz in his two main papers in hydrodynamics (Helmholtz, Hermann. "Ueber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen." In Journ. f. d. reine u. angewandte Mathematik 55 (1858): 25-55; rep. in W A 1 pp.101- 134; "Ueber discontinuirliche Flüssigkeitsbewegungen." In Berliner Monatsberichte (1868): 215-28; rep. in W A 1 pp.146- 157) and in his electrodynamics works of the seventies drew more on potential theory than on his 1847 version of "energy" conservation. 494 On Clausius see: Helm Energetik Pp.70-80; Daub, Edward." Atomism and Thermodynamics." In Isis 58 (1967): 293-303; Clark, Peter. "Atomism versus Thermodynamics." In Method and Appraisal in the Physical Sciences: The Critical Background to Modern Science, 1800-1905. Colin Howson ed. Cambridge: Cambridge U.P., 1976, pp.41-105; Truesdell, Clifford. The Tragicomic History of Thermodynamics. 1822- 1854. New York: Springer,1980; Yagi, Eri."Clausius's Mathematical Method and the Mechanical Theory of Heat." In HSPS 15 (1984): 177-95; Wolff "Clausius". 495 On Rankine see: Hutchinson, Keith."W.J.M. Rankine and the Rise of Thermodynamics." In Brit J Hist Sci 14 (1981): 1-26; see also Bevilacqua En and Electr . Pp.80-90.
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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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"Bericht", despite the application
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experiments in the most disparate b
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The premise reveals that the struct
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intelligible if it can be referred
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elevant consequence of the deductio
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Needless to say the plan was to be
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and from here that the direction an
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since Leonardo 113; the "ad nihilum
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But unfortunately for the whole str
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The principle of conservation of vi
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different from the one joining the
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"The equality that exists between e
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In virtue of its limitations to New
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Helmholtz, while asserting that lig
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the temperature of 1 Kg of water ca
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In his search for a mechanical equi
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had already been achieved in the Be
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approach is discussed at length and
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and unaware of Green's results190,
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potential function 201. It is worth
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and judged unreliable, despite prov
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The relevance of the first question
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principle taking this potential int
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Finally we get to the real conclusi
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conservation 234, on the theory of
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for the mechanical equivalent of he
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The controversy started with some r
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where μ are immovable masses, m th
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demonstration criticised by Clausiu
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directions that join them and whose
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quotes 288 and criticises a proposi
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Page 133: Kant was a Naturphilosophe 480. The
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Page 145 and 146: Graetz, L. "Das Mechanische Wärme
Page 147 and 148: Helmholtz, Hermann. "Bericht über
Page 149 and 150: Helmholtz, Hermann. Wissenschaftlic
Page 151 and 152: Madison: Wisconsin U.P., 1959. Pp.
Page 153 and 154: Poincarè, Henry. Electricité et O
Page 155: Yagi, Eri."Clausius's Mathematical
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