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

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are considered equivalent. Still, the separation of energy into two main forms, potential and kinetic, is attributed to Rankine and W.Thomson, following a British nationalist historiographic tradition. In any case Tait's stress is on the empirical elements of Helmholtz's approach: even the assumption of the impossibility of perpetual motion for the whole of natural forces is judged an experimental result. This insistence on the historiographical revaluation of the experimental elements in the various formulations of the principle is shared in the early eighties by Helmholtz himself, as seen in the previous section. This is, in my view, owing to some concrete difficulties faced by Helmholtz in applying his 1847 formulation of the principle to actual physical research in the late sixties and seventies. A new tool : potential theory (1852-72) Helmholtz's Erhaltung did not withstand the criticisms pointed out by Clausius on the definition of potential and on the privilege accorded to central Newtonian forces. Its electrodynamic part was also "for the most part defective" 378 for its lack of terms referring to energy stored with the circuits. The very derivation of Neumann's law of induction, for which Helmholtz and W.Thomson had received so much credit (not the least from Tait in 68-69 and Maxwell in 1873), was not correct 379. Helmholtz realized this before his critics. He acknowledged the weakness of the electrodynamic aspects of the Erhaltung during the controversy with Clausius and defended his own theoretical approach with the introduction of some new energy terms, but from that moment on his research in the field of energy shifted a great deal. He was in fact more inclined towards the physicomathematical problems connected with Green's theorem and with the mathematical theory of potential as heuristic tools, rather than with the theoretical applications in the 1847 style. Helmholtz worked hard to master potential theory, and in the end achieved an extraordinary success: he was able to 378 Whittaker, E. A History of the Theories of Aether and Electricity 2nd ed. New York: Harper, 1960; p.218. 379 See nn.217-221.
apply it to acoustics (1859), hydrodynamics (1859 and 1868) and electrodynamics (1861, but mainly from 1869-1870 on) in works that became masterpieces in their fields. _______________________ In the German-speaking world the mathematical potential (potential function) and the physical potential (potential) spread rapidly and were widely used. Clausius had a prominent role in this, through the different editions of his treatise on "Potential and Potential function", but already F.Neumann in 1845, Weber and Kirchhoff in 1848 and Riemann had made various use of these concepts. C.Neumann too followed this line of thought; in the sixties and seventies delayed potentials and generalised potentials were also introduced. Given the now generally applied identification of potential with the work done, in this tradition all that was required to satisfy energy conservation was to show that the force in question (the problems were mainly connected with the attempt to formulate a general electrodynamic force) admitted a potential, that is that the work done by the force was a total differential. This in fact is equivalent to admitting the impossibility of perpetual motion. In Britain the situation was somewhat different. Despite the early and important contributions to potential theory by Green, Hamilton, W.Thomson and Stokes, priority was in general given to the "classic" concept of energy, implying the clear distinction between potential and kinetic parts. Of these two the kinetic was to be seen as basic : J.J.Thomson among others attempted to show this supposed priority, while Maxwell in 1873 had defined the idea of a delayed potential as "inconceivable". An energy battlefield for the electrodynamic debate (1870-75) In Electrodynamics Helmholtz opposed the views of Weber, who since 1846 had given a force law depending not only on distances but also on velocities and accelerations, and of Clausius who in 1875-6 published a contribution along similar lines. Various physicists contributed to various aspects of the debate, but here we will only refer to the role of the energy principle. Not a minor one indeed, but rather the main battleground. Given the mathematical equivalence of the competing theories and the difficulties in experimenting with open currents, the acceptance of one law or the other began to be evaluated in relation to the
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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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Page 67 and 68: Finally we get to the real conclusi
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Page 121 and 122: considered relevant. In Poincarè
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Page 129 and 130: literature 456. There is an intrins
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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.
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Poincarè, Henry. Electricité et O
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Yagi, Eri."Clausius's Mathematical
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