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

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surveying the region of electromagnetics, and working out the distinctive consequences of the various theories, in order, wherever that was possible, to decide between them by suitable experiments." 382. In fact, in 1870, he started publishing a series of papers that constituted a comprehensive study of electrodynamics. "With the object of clearing up this confusion", he gave a theory, whose mathematical version included Weber, F. Neumann and Maxwell’s theory as limiting cases. Helmholtz’s starting point is relevant: it is the assumption of the existence not only of a force between current elements but of a force and a torque. Both these assumptions contrast with Ampére’s theory. Ampére admitted a potential only for closed currents and only a central force between current elements. Helmholtz’s starting point was a generalisation of F. Neumann’s theory: he gave the most general expression for the energy of two current elements, consistent with the condition that the force between two closed circuits should be the one given by Ampere: where A is a constant depending on the unit of current, r the distance between the elements of circuit Ds and Dσ traversed by the currents i and j. K too is a constant, for K=+1 Helmholtz’s potential reduces to F. Neumann’s; for K=-1, Weber’s potential is obtained; for K=0 plus a dielectric medium, Maxwell’s theory can be obtained 383. An expression giving both F. Neumann’s and Weber’s electrodynamic energies is: where h is an arbitrary constant. The first term is Neumann’s value. The second term is the difference between Weber’s and Neumann’s values. The second term vanishes for closed currents, the only case analysed by F. Neumann 384. In the fourth paragraph Helmholtz analyses the different theories with respect to energy values 385. The whole energy Φ is the sum of the electrodynamic 382 Ibidem 383 Helmholtz, Hermann. "Ueber die Bewegungsgleichungen der Elektricität für ruhende leitende Körper." In Borchardt's Journ 72 (1870): 57-129; repr. in WA 1 pp.545-628. Pp. 549 and 567. 384 Ibidem pp.565-6. 385 Ibidem pp.579-85.
and the electrostatic In modern notation 386: In the absence of electromotive forces external to the system: is essentially negative. In this case, if K is negative Φ might be negative and thus a perturbation of the system might lead away from equilibrium. That is, the equilibrium is unstable for K
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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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Page 67 and 68: Finally we get to the real conclusi
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Page 129 and 130: literature 456. There is an intrins
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Page 133 and 134: Kant was a Naturphilosophe 480. The
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Page 143 and 144: Blüh, Otto. "The Value of Inspirat
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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