ON OUR KNOWLliDGK OV THERMODYNAMICS. 87 



the work performed on the system through the coordinates defining the 

 positions of the molecules and not involving —dW, the work performed 

 through the coordinates determining the external configuration of the 

 system. The two portions of the work could only enter together into the 

 equations in the form fZE. 



In other words, it is impossible to deduce the Second Law of Thermo- 

 dynamics from purely mechanical principles without making some 

 axiomatic assumption regarding the nature of the molecules whose motion 

 produces the phenomenon of heat. 



7. The question now arises as to what dynamical quantity represents 

 temperature. We have good reasons for believing that, in gases at least, 

 the absolute temperature is proportional, either to the total mean kinetic 

 energy, or to the mean kinetic energy of translation of the molecules. 

 But if this or indeed any other hypothesis be adopted it will be necessary, 

 before the mechanical theory of heat is complete, to prove that (1) the 

 molecular kinetic energy is an integrating divisor of clQ, ; (2) it deter- 

 mines the thermal state of a body in relation to other bodies. 



Most of the earlier writings are concerned only with the first property. 

 But a complete mechanical proof of the Second Law would involve a 

 mechanical definition of temperature applicable to all kinds and states 

 of matter, together with an explanation on dynamical or statistical laws 

 of the principle of degradation of energy in non-reversible processes; and 

 we are still far from arriving at a satisfactory solution of either of these 

 problems. 



8. It will be convenient to classify the methods by which the problem 

 has been attacked as follows, under three headings corresponding to the 

 three different fundamental hypotheses which underlie them : — 



I. The Hypothesis of ' Stationary ' or ' Quasi-Periodic ' Motions as 

 adopted by Clausius and Szily. 



II. The Hypothesis of ' Monocyclic Systems ' of von Helmholtz, and 

 similar hypotheses. 



III. The Statistical Hypothesis of Boltzmann, Clerk Maxwell, and 

 other writers on the Kinetic Theory of Gases. 



9. Rankine seems to have been the first who attempted to deduce the 

 Second Law from dynamical principles. As early as 1855 he published 

 a paper ' On the Hypothesis of Molecular Vortices,' ' in which he obtained 

 •equations analogous to those of thermodynamics; and in a paper read at 

 the British Association in 1865 - he explained the Second Law on the 

 hypothesis that ' heat consists in any kind of steady molecular motion 

 within limited space.' such as that due to circulating streams. Both of 

 Rankine's hypotheses are special cases of Helmholtz's ' Monocyclic 

 Systems.' 



Boltzmann seems to have been the next to take up the subject, but his 

 •claim to priority has been disputed by Clausius, whose investigations 

 appeared about five years later. Boltzmann was undoubtedly the first to 

 regard the subject from a statistical point of view. 



Szily laid claim to the discovery of the connection of the Second 

 Law with Hamilton's Principle of Least Action, and he may fairly be 

 entitled to the credit of having propounded this connection. But most 

 of his early investigations are not only wanting in rigour, but in many 

 oases so inaccurate that they do not prove the connection at all. 



' Phil. Mac/. 1855, pp. 354, 411. " Ibid. 1865, p. 241. 



