346 . EEPOET— 1888. 



and in like manner 



d^"=.tdri"-pdv". 



If we substitute tliese values, the equation becomes 



d^ = {i—ri")dt (10) 



"We have already seen that »;' - t]" represents the integral -t-^ of equations (2) 



and (4), which by equation (2) is equal to the reversible heat evolved, — Q, divided 

 by the temperature of the cell, which we now call t. Substitution of this value 

 gives 



effi__Q 



-Jt- T ^"^ 



which is Helmholtz's equation. 



These results of the second law of thermo-dynamics are of course not to be 

 applied to any real cells, except so far as they approach the condition of reversible 

 action. They give, however, in many cases limits on one side of which the actual 

 values must lie. Thus, if we set < for = in equations (2), (4), (5), (6), and 



> for = in (8), the formula will there hold true without the limitation of reversi- 

 bility. But we cannot get anything by differentiating an inequality, and it does 

 not appear d, prion which side of (10) is the greater when the condition of rever- 

 sibility is not satisfied. The term-? in (11) is certainly not greater than r)" -rj', 



for which it was substituted. But this does not determine which side of (11) is 

 the greater in case of irreversibility. It is the same with Helmholtz's method of 

 proof, which is quite different from that here given, but indicates nothing except 

 so far as the condition of reversibility is fulfilled. (See ' Sitzungsberichte, Berl. Acad.,' 

 1882, pp. 24, 25.) 



I fear that it is a poor requital for the hind wish which you expressed at Man- 

 chester, that I were present to explain and support my position, ibr me to impose 

 so long a letter upon you. Trusting, however, in your forbearance, I remain yours 

 faithfully, 



J. WiLLAED GiBBS. 



AutJwrsMp of Electrolytic Theory. (Translation of a Letter from Professor 

 Clausius, received by the Secretary of the Electrolysis Committee of the 

 British Association.') 



Bonn : October 2, 1887. 



Dear Sir, — While I render you my best thanlis for kindl}' sending me the 

 Report of the E.O.B.A., which I have read with much interest, I should like to be 

 allowed to make a remark on one point arising in it. You mention the theory of 

 electrolytic conduction, started by me in the year 1857, by the name, ' the old 

 Williamson-Clausius hypothesis ; ' and in similar terms my tlaeory is referred to in 

 other parts of the circular you have been good enough to send me. 



This nomenclature must arouse in the minds of readers not fully conversant 

 with the literature of the subject a question as to whether Williamson has not also 

 devised a theory to explain electrolj'tic conduction. 



This, however, is not the case. Williamson was only considering a purely 

 chemical process — namely, the formation of ether, and his theory relating to this 

 was contributed to the British Association in Edinburgh. On electrolytic con- 

 duction he had not spoken a single word. I am quite convinced that he himself 

 has not the least intention of claiming the merit of having started an hypothesis for 

 the explanation of electrolytic conduction. 



By other authors the theory of electrolytic conduction is continually referred 

 to as mine. Of English authors I will only mention Maxwell, who, in his 



