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

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force. Lagrange himself in the Mechanique Analitique from the principle of virtual work deduced the vis viva principle outlining that the name conservation of vis viva is given because the sum of the vis viva expressions of the bodies of the system is the same when the bodies revert back to their original positions, independently of the trajectories followed. Thus, for Lagrange, conservation of vis viva is, after Huygens, conservation at specific positions 117 and not conservation during a process. In Lagrange's formulation 118: the stress is on the vis viva term: the factor 2 is with the second member; the function of the positions (the potential term) and the constant F are not given special relevance and do not acquire physical meaning, despite the fact that, from a contemporary point of view, the two terms on the right side of the equation are easily identified with total energy and potential energy of the system 119. My third remark outlines the criticisms to Helmholtz's "demonstration"of the equivalence of the two initial assumptions. This "wrong" demonstration plays a vital role in Helmholtz's research program: the generalisation of the principle of conservation of vis viva into Helmholtz's principle of conservation of "force", that is, into a principle where the kinetic and positional terms can be sharply split, is only possible if the forces depend solely on distances. While this applies to Newton's, Coulomb's and Ampere's forces, it does not apply to Weber's electrodynamic ones, not a minor problem for Helmholtz. It being impossible at the time to oppose Weber's law on empirical grounds 120, it was important for Helmholtz to demonstrate that empirical laws which admitted forces different from the central ones violated the conservation of vis viva and the impossibility of perpetual motion. 117 This particular meaning of conservation surprises some commentators: Lindsay (unhistorically) wonders why the name of conservation of vis viva is given if vis viva is conserved only in the specific case of constant potential energy: Hist Devel Pp. 167-9. 118 Lagrange Mech An P.208. 119 The same can be said of other expressions of vis viva conservation typical of analytical mechanics: P.S.Laplace, Pierre Simon.Traité de la Mécanique Celeste . 5 vols. Paris, 1799-1825. Vol I, P. 52; Hamilton "On a General Method in Dynamics" Phil Tr Roy Soc Pt II 1834: 247-57. P.250; in: Lindsay Hist P.264. 120 Helmholtz will try that in the seventies.
But unfortunately for the whole strategy this was an impossible task. Helmholtz's demonstration was based on a wrong assumption: even if the components of the vis viva depend on the positions only, the same does not necessarily follow for the force components. In fact it was possible to show that forces depending on velocities and accelerations, like Weber's, do not violate the conservation of vis viva or the impossibility of perpetual motion: Weber in 1848 was to show that his own force admitted a potential, even if a kinetic one 121. But all the same Helmholtz's approach had for twenty years an incredible success: in the British literature the point that Weber's force law denied conservation of vis viva and energy conservation was maintained by Maxwell 122 in 1865, Tait and Thomson in 1867 123 and Tait in 1868 124, and finally refused by Maxwell in 1873 only after Helmholtz's own retreat in 1870. Helmholtz himself acknowledged in 1882 125 that a flaw in the 1847 demonstration had been shown by Lipschitz (he still did not mention Clausius' criticisms 126). Nevertheless he had to agree that he 121 The first to explicitly criticise the limitations of the validity of the principle of vis viva to central forces was Clausius in 1852 and 1854. 122 Maxwell, James Clerk. "A Dynamical Theory of the Electromagnetic Field". Repr. in: Scientific papers. 2 Vols. Cambridge: Cambridge U.P., 1890. Vol.1 Pp.526-597; at pp.526-7. 123 Thomson,W. and Tait, P.G. Treatise on Natural Philosophy. , Clarendon Press, Oxford, 1867. Par. 385. P.311-2. 124 Tait,P.G. Sketch of Thermodynamics., Edmonston and Douglas, Edinburgh, 1868. P.76. See also C.Neumann's defense of Weber : Neumann, Carl. Die Gesetze von Ampére und Weber. Leipzig: Teubner, 1877. Pp.322-4; for a discussion see my Energy and Electr Pp.122- 3 and133-6. 125 Helmholtz WA 1 P.70. 126 Clausius, Rudolf. "Ueber das mechanische Aequivalent einer elektrischen Entladung und die dabei stattfindende Erwärmung des Leitungsdrahtes" In Pogg Ann 86 (1852): 337-375 Clausius, Rudolf."Ueber einige Stellen der Schrift von Helmholtz "uber die Erhaltung der Kraft." In Pogg Ann 89 (1853): 568-579. Clausius, Rudolf. "Ueber einige Stellen der Schrift von Helmholtz "uber die Erhaltung der Kraft", zweite Notiz." In Pogg Ann 91 (1854): 601-604.
Page 1 and 2: Fabio Bevilacqua Conservation and I
Page 3 and 4: different formulations 4 and priori
Page 5 and 6: and interesting results, despite th
Page 7 and 8: principle of correlation is express
Page 9 and 10: principle to the existing empirical
Page 11 and 12: the origin and meaning of the princ
Page 13 and 14: Whether physiological research, apa
Page 15 and 16: In a discussion on the origins of a
Page 17 and 18: his "Wärme" that one of the differ
Page 19 and 20: generate a determined equivalent of
Page 21 and 22: "Bericht", despite the application
Page 23 and 24: experiments in the most disparate b
Page 25 and 26: The premise reveals that the struct
Page 27 and 28: intelligible if it can be referred
Page 29 and 30: elevant consequence of the deductio
Page 31 and 32: Needless to say the plan was to be
Page 33 and 34: and from here that the direction an
Page 35: since Leonardo 113; the "ad nihilum
Page 39 and 40: The principle of conservation of vi
Page 41 and 42: different from the one joining the
Page 43 and 44: "The equality that exists between e
Page 45 and 46: In virtue of its limitations to New
Page 47 and 48: Helmholtz, while asserting that lig
Page 49 and 50: the temperature of 1 Kg of water ca
Page 51 and 52: In his search for a mechanical equi
Page 53 and 54: had already been achieved in the Be
Page 55 and 56: approach is discussed at length and
Page 57 and 58: and unaware of Green's results190,
Page 59 and 60: potential function 201. It is worth
Page 61 and 62: and judged unreliable, despite prov
Page 63 and 64: The relevance of the first question
Page 65 and 66: principle taking this potential int
Page 67 and 68: Finally we get to the real conclusi
Page 69 and 70: conservation 234, on the theory of
Page 71 and 72: for the mechanical equivalent of he
Page 73 and 74: The controversy started with some r
Page 75 and 76: where μ are immovable masses, m th
Page 77 and 78: demonstration criticised by Clausiu
Page 79 and 80: directions that join them and whose
Page 81 and 82: quotes 288 and criticises a proposi
Page 83 and 84: motion to all natural forces, the k
Page 85 and 86: measure this expenditure and compar
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" ...the quantity of force in natur
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forces is constant: but it relates
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experiences in general laws of unli
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"a series of important and difficul
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the Discontinuous Movements of Flui
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methodology. Dühring claimed the c
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The first history of the conservati
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while in Britain for the above talk
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apply it to acoustics (1859), hydro
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magnetic intensity. Maxwell realize
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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
Page 117 and 118:
while the electromagnetic and the s
Page 119 and 120:
can modify its specific theoric for
Page 121 and 122:
considered relevant. In Poincarè
Page 123 and 124:
meaning left is: "There is somethin
Page 125 and 126:
interpretations at the beginning of
Page 127 and 128:
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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