210 Mr. E. Buckingham on Certain Difficulties 



place in a certain direction and not in the opposite one. 

 And how does it take this step ? By leaving the solid ground 

 of reversibility and making use of a new theorem — the one 

 under discussion. The new step leads to results which 

 always turn out to be correct ; but it is disquieting ; we feel 

 that we may be making a mistake ; we are not sure of our 

 ground, and why ? Because we demand of the original 

 bases of u reversible thermodynamics " more substance than 

 is in them. It is new substance that we must have, no matter 

 how we get it. 



Professor Orr suggests that we alter the wording of the 

 second law ; in other words, he proposes that we insert the 

 substance of the new proposition into the old principles. To 

 the mathematical mind, the one that regards logic and neat- 

 ness of form as in themselves admirable, this would seem the 

 best way out of our difficulty, as it is certainly the neatest. 

 But does it really do us any good ? It does if we are merely 

 trying to silence criticism, but is it the best way? I think 

 not. 



The immediate object of theoretical physics is to arrange 

 known facts under certain general principles using hypo- 

 theses only when necessary, and making the general prin- 

 ciples and the hypotheses as few, as simple, and as easily 

 comprehensible in statement as possible. We are confronted 

 with the question whether we shall make an addition to one 

 of our generally accepted and familiar principles or set up a 

 new principle. The old principle — Lord Kelvin's or Clausius' 

 statement of the second law — is well established and is 

 familiar to everyone who is interested in thermodynamics. 

 It has been used erroneously in the building up of fallacious 

 proofs. Now it seems to me distinctly better, at the present 

 time, not to change the old statements by adding a little to 

 them, but to act in such a way as shall show clearly our 

 appreciation of their inadequacy to the new needs ; in other 

 words, to set up a new principle and state that it is new, and 

 different from the old. Finally, of course, it is all one : the 

 new substance has to be put in somewhere, and I am quite 

 agreed that in the end a single statement, even if it be a 

 little less simple than the usual statement of the second law, 

 may be preferable to two separate statements. But I think 

 that at the present time we should do well to sacrifice our 

 feeling for neatness in the interest of the advance of the 

 knowledge and use of thermodynamics, an advance which is 

 impeded by the present obscurity of some of the fundamental 

 theorems of the subject. My proposal is in the nature of 

 putting the foundations of thermodynamical reasoning into 



