Certain Difficulties in the Study of Thermodynamics. 209 



There may have been hundreds of these " proofs " published, 

 and I have probably not waded through more than a dozen 

 or two at most, but T have reached the same state of mind 

 that the French Academy reached about perpetual motion 

 machines. They did not prove, and we cannot to-day prove, 

 that no perpetual motion machine can ever be devised: 

 but we have all stopped believing that it can, and we have 

 taken the further step of concluding that there is a reason 

 in the nature of things why it cannot be done. A man who 

 reads thermodynamics only because he wants to follow the 

 literature may not care much about the origin or the justifi- 

 cation of a given theorem, if he finds it generally used and 

 never with disastrous results. But the man who works up 

 his thermodynamics for presentation in convincing form to a 

 critical audience, has a different task ; and such a man, if he 

 be honest with himself, necessarily reaches the same conclu- 

 sion as Professor Orr, namely, that the inequality of Clausius 

 for irreversible cycles not only has not been, but cannot be 

 deduced from the accepted forms of the second law. 



The question at once arises : what are we to do about it ? 

 Probably no one doubts either the usefulness or the truth of 

 i he theorem, and no one, certainly, has ever found a case in 

 which the correct application of it led to results which were 

 contradicted by experiment — the final test. The theorem is 

 correct for practical purposes and everyone knows that it is 

 just as he knows that the principle of the conservation of 

 energy is correct. What then? The proposition is true: 

 the proofs of it are fallacious : shall we insist upon having a 

 proof at all ? To my mind it is very doubtful whether there 

 is any advantage to be gained by having the proof. 



At present, thermodynamics deals successfully and logically 

 with states of equilibrium: it has advanced in a reasonably 

 secure and satisfactory way over a field similar in extent to 

 the -tatics of frictionless systems in pure dynamics. It has 

 done this by means of reversible processes, first by using 

 reversible (Jarnot cycles and later by using entropy, free 

 energy, and thermodynamic potentials in perfectly legitimate 

 way- and by using reasoning which is logical and satisfying 

 when we have in view only reversible changes of state. The 

 theory up to this point rests on the principle of the conser- 

 vation of energy and on the second law as formulated by 

 Lord Kelvin or by Clausius. 



Thermodynamics now takes, or attempts to take, another 

 step forward. Leaving pure statics, it attempts to say that 

 if equilibrium does not subsist, whatever change takes place 

 in the state of the system under consideration must take 



Phil. Mag. S. 6. Vol. 9. No. 50. Feb. 1905. P 



