244 Dr. Rankine on the Second Law 



11. In a paper " On the Mechanical Action of Heat," published 

 in the Transactions of the Royal Society of Edinburgh for 1850, 

 the author deduced the Second Law of Thermodynamics, in the 

 form above stated, from the hypothesis of a particular sort of 

 steady molecular motion, viz. revolution in circular streams or 

 vortices. In a paper " On the Centrifugal Theory of Elasticity," 

 published in the same Transactions for 1851, he deduced the 

 same law from the hypothesis of steady molecular motion in 

 circulating streams of any figure whatsoever, being a proposition 

 substantially identical with that set forth in the present paper ; 

 but as the demonstration in the paper of 1851 involved tedious 

 and intricate symbolical processes, he has written the present 

 paper in order to show that the demonstration can be effected 

 very simply. 



12. It is obvious that the steadiness of the supposed molecular 

 motions is the essential condition which makes the Second Law 

 of Thermodynamics deducible from a mechanical hypothesis; 

 and that no kind of unsteady motion, such as vibratory or wave- 

 like motion, would lead to the same results. If, then, it be 

 admitted as probable that the phenomena of heat are due to 

 unseen molecular motions, it must also be admitted, that while 

 the motions which constitute radiance may be vibratory and wave- 

 like, the motions which constitute sensible or thermometric heat 

 must be steady and like those of circulating streams. 



13. The function by which the absolute temperature is mul- 

 tiplied in calculating the conversion of energy between the me- 

 chanical and the thermic forms, is the variation of what the 

 author has called the metamorphic function*, being one term of 

 the thermodynamic function^ which corresponds to what Professor 

 Clausius calls entropie%. 



Glasgow University, 

 September 4, 1865. 



Appendix. 



The following is the symbolical expression of the demonstra- 

 tion given in the paper. 



Let m stand for the specific properties of the sort of matter 

 which is in a state of steady motion within a limited space. 



/for the figures and dimensions of that space, and of the 

 paths described by the particles contained in it, and Bf for any 

 indefinitely small change of such figures and dimensions. 



* See "On the Science of Energetics/' Edinburgh Philosophical Journal, 



t Philosophical Transactions, 1854. 



J Ueber verschiedene fur die Anwendung bequeme Formen der Haupt- 

 gleichungen der mechanischen Warmetheorie, April 1865. 



