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XX. On Certain Difficulties which are Encountered in the 

 , Study of Thermodynamics. By Edgar Buckingham*. 



THERE are three main difficulties which one meets when 

 trying to develop the theory of Thermodynamics logi- 

 cally. Any one who has tried \o get the subject ordered in 

 his mind with the clearness and precision which are necessary 

 if it is to be presented to students sufficiently advanced to be 

 really critical, must have been impressed by the manner in 

 which so many writers dodge these three difficulties, and will 

 be glad that Professor Orr, in his very interesting article in the 

 October number of the Philosophical Magazine, has pointed 

 them out so distinctly. These three points are: — (1) the 

 definition of temperature ; (2) the definition of quantity of 

 heat: and (3) the statement of the theorem of Clausius for 

 irreversible processes. The last of these is ostensibly the 

 subject of Prof. Orr^s paper; but he touches critically on so 

 many other points that his article should prove of great 

 benefit, even to people who have reached a state of mind 

 which satisfies themselves, at any rate, regarding the parti- 

 cular subject of the inequality of Clausius. 



Aside from these three difficulties, the rest of '• classical 

 thermodynamics," as M. Duhem has named it, seems to be a 

 fairly logical and satisfactory whole, but discussion on these 

 points seems to me useful. 



There are three things in Prof. Orr's article which stand 

 out as of particular importance. 



(1) He says in substance, though with great moderation, 



that all proofs of the (heorem that I — <0, when the in- 

 tegral is taken round an irreversible cycle, are rubbish, if 

 based on the two laws of thermodynamics as usually stated 

 and on the usual definition of reversibility. 



(2) He proposes a way to avoid the difficulty by a modifi- 

 cation of the wording of the second law, as stated by Lord 

 Kelvin or by Clausius. 



(3) He makes a plea for the use, wherever it is practicable, 

 •of Carnot cycles, instead of entropy, free energy, or thermo- 

 dynamic potentials, which are, mathematically at any rate, 

 secondary ideas to the derivation of which the use of cycles 

 is a necessary antecedent. 



As regards the first of these points, any logical physicist 



always finds these so-called proofs worthless, and he always 



will so long as they rest on the bases mentioned. I say this 



with the fullest confidence and the most complete generality. 



* Communicated bv the Author. 



