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LVI. On the Discovert/ of the true form of Carnot's Function. 

 By Professor William Thomson. 



To the Editors of the Philosophical Magazine and Journal. 



Oakfield, Moss Side, Manchester, 

 Gentlemen, May 12, 1856. 



MCLAUSIUS, in a letter of date March 20, 1856, ad- 

 • dressed to yourselves, and published this month in 

 yom- Magazine, objects to a statement he supposes me to have 

 made in 1851, and to have frequently repeated since that time, 

 that Mr. Joule had discovered " the theorem, that Carnot's func- 

 tion (c or — ) 'is nothing more than the absolute temperature 



multiplied by the equivalent of heat for the unit of work.' " He 

 attributes the discovery of the true form of Carnot's function to 

 Holtzmann, who gave the formula referred to in a paper which 

 appeared as early as 1845 ; but he believes that in his own paper 

 " On the IMoving Force of Heat," communicated to the Berlin 

 Academy in 1850, the principles upon which that formula is based 

 were first correctly explained. 



Allow me to answer the charge he makes against me by quo- 

 ting what I said with ref^ence to the " discovery " for which 

 M. Clausius claims priority. 



" This formula was suggested to me by Mr. Joule, in a letter 

 dated December 9, 1848, as probably a true expression for fi, 

 being required to reconcile the expression derived from Carnot's 

 theory (which I had communicated to him) for the heat evolved 

 in terms of the work spent in the compression of a gas, with the 

 hypothesis that the latter of these is exactly the mechanical 

 equivalent of the former, which he had adopted in consequence 

 of its being, at least approximately, verified by his own experi- 

 ments. This, which will be called Mayer's hypothesis, from its 

 having been first assumed by Mayer, is also assumed by Clausiua 

 without any reason from experiment ; and an expression for /j,, 

 the same as the preceding, is consequently adopted by him as 

 the foundation of his mathematical deductions from elementary 

 reasoning regarding the motive power of heat*." 



This passage is the sequel to the extract quoted by M. Clausius 

 in his letter to you, and appeared in the same Part of the 'Trans- 

 actions,' and in the same volume of the Philosophical Magazine. 

 When it is read, I think it will be admitted that I did not do 

 injustice to his claims in writing the following sentence two years 



* " On a Method of discovering experimentally the Relation between the 

 Mechanical Work spent, and the Ileat produced by the Compression of a 

 Gaseous Fluid." (Trans. Roy. Soc. Edinb. April 1/, 1H51 ; or Phil. Mag. 

 December 1852.) 



