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XIV. — On the Density of Steam. By W. J. Macquorn Rankine, C.E., LL.D., 



F.R.SS. Lond. and Edin., &c. 



(Read 28th April 1862.) 



1. The object of the present paper is to draw a comparison between the 

 results of the meclianical theory of heat, and those of the recent experiments of 

 Messrs Fairbairn and Tate on the density of steam, published in the " Philoso- 

 phical Transactions" for 1860. 



General Equation of Thermodynamics. 



2. The equation which expresses the general law of the relations between 

 heat and mechanical energy in elastic substances was arrived at independently 

 and contemporaneously by Professor Clausius and myself, having been published 

 by him in Poggendorff's " Annalen" for February 1850, and communicated by 

 me to the Royal Society of Edinburgh, in a paper which was received in Decem- 

 ber 1849, and read on the 4th of February 1850. The processes followed in the 

 two investigations were very different in detail, though identical in principle and 

 in results; Professor Clausius having deduced the law in question from the 

 equivalence of heat and mechanical energy as proved experimentally by Mayer 

 and Joule, combined with a principle which had been prev^iously applied to the 

 theory of substantial caloric by Sady Carnot, while by me the same law was 

 deduced from the " hypothesis of molecular vortices," otherwise called the " cen- 

 trifugal theory of elasticity." 



3. Although, since the appearance of the paper to which I have referred, the 

 notation of the general equation of thermodynamics has been improved and 

 simplified in my own researches, as well as in those of others, I shall here pre- 

 sent it, in the first place, precisely in the form in which I first communicated it 

 to this Society, in order to show the connection between that equation in its 

 original form, and the law of the density of steam, which has since been verified 

 by the experiments of Messrs Fairbairn and Tate. The equation, then, as it 

 originally appeared in the twentieth volume of the " Transactions of the Royal 

 Society of Edinburgh," p. 161, is as follows: — 



uV^KY-dv) -^^rf?j' • • • • a-) 



^ CnM 



in which the symbols have the following meanings : — 



T, the absolute temperature of an elastic substance as measured from the 

 zero of gaseous tension, a point which was then estimated to be at 



VOL. XXIII. PART I. 2 S 



