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LV. On Hamilton's Dynamic Principle in Thermodynamics. 

 By C. Szily*. 



IN a memoir published not long since f, I have maintained 

 that the equation which expresses the second proposition 

 of the mechanical theory of Heat is in complete agreement with 

 the dynamical equation which is named after Hamilton, and 

 that, accordingly, in reply to the question " To which equation 

 in dynamics can the second proposition of thermodynamics be 

 reduced?" we must point directly to Hamilton's equation. 



I was moved to the publication of my considerations on this 

 subject chiefly by the circumstance that neither Boltzmann nor 

 Clausius, in their memoirs J, has once mentioned Hamilton's 

 principle ; and they are the only writers who up to that time 

 had occupied themselves with the above question. Both seem 

 to consider that, in order to bring in accordance, it was neces- 

 sary to deduce an equation yet unknown in dynamics; both 

 remark that the equations deduced by them exhibit a certain 

 affinity with the principle of least action ; but neither of these 

 two philosophers has taken any notice of Hamilton's principle 

 and its close relations to the equations in question. 



Hereupon M. Clausius published a memoir § which refers ex- 

 clusively to mine above mentioned; and at the very commence- 

 ment he therein readily acknowledges that the connexion sought 

 becomes much more striking when one compares the proposition 

 in question, not (as he and Boltzmann had done) with the prin- 

 ciple of least action, but with Hamilton's. At the same time 

 Clausius suggests the cause which prevented him from turning 

 his attention to Hamilton's principle when treating upon the 

 above-mentioned connexion. Namely, in many text -books of 

 dynamics (for instance, Jacobi's Vorlesungen uber Dynamik) Ha- 

 milton's equation is cited in a form which differs essentially from 

 the original, in consequence of the peculiar variation. Now, if 

 Jacobi's form only be kept in view instead of the primitive form, 



* Translated from a separate impression, communicated by the Author, 

 from Poggendorff's Annalen, vol. cxlix. pp. 74-86. 



t "Hamilton's Principle and the Second Proposition of the Mechanical 

 Theory of Heat," Phil. Mag. S. 4. vol. xliii. p. 339. Pogg. Ann. vol. cxlv. 

 p. 295. 



X Boltzmann, " Ueber die mechanische Bedeutung des zweiten Haupt- 

 satzes der Warmetheorie," Sitzungsberichte der Wiener Akademie, vol. liii. 

 p. 210. R. Clausius, "Ueber die Zuriickfiihrung des zweiten Haupt- 

 satzes der mechanischen Warmetheorie auf allgemeine mechanische Prin- 

 cipien," Pogg. Ann. vol. cxlii. p. 433 ; Phil. Mag. S. 4. vol. xlii. p. 161. 



§ Pogg. Ann. vol. cxlvi. p. 585. " On the Connexion of the Second 

 Proposition of the Mechanical Theory of Heat with Hamilton's Principle/' 

 Phil. Mag. S. 4. vol. xliv. p. 365. 



