24 M. 0. Szily on the Deduction of the Second Proposition 



1850 by Rankino*, according to which the particles of bodies 

 move in circular currents. 



(6) The hypothesis of circulating currents (" circulating 

 streams of any figure whatever "), developed likewise by Ban- 

 kine, in 1851, and considerably simplified by him in 1855 f- 



(7) The hypothesis of periodic motions, made use of by 

 Boltzmann, in 1866, in order to deduce the Second Propo- 

 sition J. 



(8) The hypothesis of quasi-periodic motions, which Clausius 

 first advanced in 1871 §, and has since more fully developed 

 in several large memoirs. 



Of all the above-mentioned hypotheses, the axioms of Clausius 

 and Thomson found the most acceptance, as being the most 

 plausible. 



But now arises the question whether a new hypothesis is 

 needed for the deduction of the Second Proposition, and 

 whether it cannot be deduced with mathematical rigour by 

 means of the First Proposition alone. If this can be done, 

 the theory of heat will be really based on a single proposition, 

 on the universal principle of the conservation of energy. 



At present this problem is not merely unsolved, but has 

 scarcely been taken into consideration. As far as I know, 

 only Bankine and Clausius have expressed any opinion on this 

 question, and the latter merely by the way. Bankine pro- 

 nounces as follows : — " Carnot's law is not an independent 

 principle in the theory of heat, but is deducible as a conse- 

 quence from the equations of the mutual conversion of heat 

 and expansive power " (Phil. Mag. [IV.] vol. vii.), and adds 

 that he has shown this in the first part of his treatise. He 

 forgets, however, that in the part cited he occupies a very 

 hypothetical stand-point, in that, inter alia, he defines tempera- 

 ture thus : — " The temperature is a function of the square of 

 the velocity of the molecular vortices, divided by the coefficient 

 of elasticity of the atmospheres of the atoms." It was very 

 natural that a deduction based on such a complicated hypothesis 

 was accepted by no one. Bankine's consequence is, accord- 

 ingly, a mere assertion, of which he has not furnished the 

 demonstration. 



Clausius alludes to the above question quite incidentally, in 

 a lecture delivered by him at the 41st Meeting of the German 

 Natural Philosophers and Physicians, at Frankfort. He ex- 

 presses himself to this effect : — " Yet there is a second prin- 

 ciple, which is not yet contained in that (the First Proposi- 



* Edinb. Trans, vol. xx. f Phil. Mag. [IV.] vol. xxx. 



% Sitzungsberichte der Wiener Akademie, vol. liii. 

 § Pogg. Ann. vol, cxlii. 



