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LIV. On the Dissipation of Energy. By Prof. P. G. Tait. 



To Sir W. Thomson, F.R.S. 



My dear Thomson, — 



I ADDRESS you as one of the Editors of the Philoso- 

 phical Magazine^ but also specially as the first pro- 

 pounder of the doctrine of the Dissipation of Energy. I do 

 so because Prof. Clausius, in the second part of the new- 

 edition of his work on Thermodynamics, has challenged your 

 claim to the well-known expression for the amount of heat dis- 

 sipated in a non-reversible cycle. I think that the time has 

 come for you to speak out on the subject, so as, if possible, to 

 prevent further unnecessary discussions. 



I shall endeavour, so far as I can, to keep to matters of 

 scientific importance ; but I must introduce the subject by a 

 reference to the comments made by Prof. Clausius upon a 

 somewdiat slipshod passage (§ 178) of my little work on 

 ' Thermodynamics.' That passage refers to the integral 



P 



to which I believe Rankine first called attention, but which is 

 essentially connected with your doctrine. 



I cannot altogether complain of Prof. Clausius's comments, 

 because I cannot account for my having called the above in- 

 tegral (in the way in w T hich I have employed it) a positive 

 quantity, except by supposing that in the revision of the first 

 proof of my book I had thoughtlessly changed the word 

 " negative" to "positive." This might easily happen from 

 my having used a novel term, " practical value," in a somewhat 

 ambiguous manner, at one place confounding it wdth " realized 

 value." That the wdiole section was meant to bear the con- 

 struction forced on it by Prof. Clausius is, I think, sufficiently 

 disproved by its opening sentence, not to speak of the fact that 

 no one in this country has so interpreted it. 



But there is a graver matter involved than any such mere 

 slips of the pen ; for Prof. Clausius asserts that the method I 

 employ (and which I certainly obtained from your paper of 

 1852) is inapplicable to any but reversible cycles. This, I 

 think, is equivalent to denying altogether your claims in the 

 matter. I therefore quote the whole passage, correcting, 

 however, the above-mentioned slip, and slightly extending the 

 latter part to make my meaning perfectly clear. 



" § 178. The real dynamical value of a quantity, dg, of 

 " heat is Jdq, whatever be the temperature of the body which 



