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II, On the Meclianical Effect of Heat and of Chemical Forces, 

 By W. J. Macquorn Kankine, F.R.S.E, &^c. In a Letter 

 to J. P. Joule, F.R.S, §-c.* 



69 St. Vincent Street, Glasgow, 

 My dear Joule, December 11, 1852. 



I RETURN you my best thanks for the papers you have 

 sent me. 

 In that on the " (Economical production of Mechanical Effect 

 from Chemical Forces/^ I am struck in particular with the ana- 

 logy you have pointed out between the functions representing 

 the fractions of the motive power converted into mechanical effect 

 in the electro-dynamic and tHermo-dynamic engines respectively, 

 both being capable of being expressed by the formula 



a-b 

 a 



With respect to the nature of the functions a and b in the case 

 of electricity, it is evident that they are proportional, as you have 

 stated t, to the strengths of the current measured when the 

 engine is at rest and in motion. In fact, ab being the total 

 power expended, b^ is converted into heat, and ab—b'^ remains 

 for the useful effect. 



As to the nature of these functions in the case of heaty they 

 are pi'oportional to the absolute quantities of themiometric heat 

 contained in the body at the temperatures of heating and cooling 

 respectively. 



If we make no definite hypothesis respecting the kind of vis 

 viva which constitutes thermometric heat, then a and b are func- 

 tions of the temperatures, the nature of which has to be deter- 

 mined empirically; and this view constitutes the basis of the 

 theory of Carnot as modified by Clausius and Thomson. 



If we assume the principle (with Mayer) that the specific heat 

 of a perfect gas is constant at all temperatures, or the necessary 

 consequence of this assumption, that the heat developed by 

 compressing a perfect gas is the exact equivalent of the power 

 employed, then the functions a and b become simply proportional 

 to the absolute temperatures as measured by a perfect gas ther- 

 mometer. I see you have adopted this view in your investigations 

 on the air-engine. 



If we adopt, respecting the nature of the vis viva which con- 



* Communicated, with the permission of the Author, by Mr. J. P. Joule. 



t " Experiments and Observations on the Mechanical Powers of Electro- 

 magnetism, Steam, and Horses," by Messrs. Scoresby and Joule, Philoso- 

 phical Magazine, S. 3. vol. xxviii. p. 451, 1846. 



