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XXXIX. Elasticity of Vapours. By W. J. Macquorn Rankine, 

 C.E., LL.D., ER.SS.L. $ E. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



1. TV/fR. ALEXANDER, quoted by Professor Potter in the 

 -LtA Philosophical Magazine for February, was surely 

 mistaken when he claimed as new, in 1848, the formula 



p={a + bT) 6 



for the pressures of saturated vapours. The general formula of 

 which it is a particular case, p = (a + bT)™, was first proposed by 

 Dr. Thomas Young nearly sixty years ago. The same formula, 

 with the index n — 5, was used by Arago and Dulong in 1829*, 

 and with the index n — Q, by Tredgold about 1828j\ 



2. The history of that and many other formulae is given by 

 M. Regnault in his Relation des Experiences fyc, vol. i. pp. 582 

 et seqq. He gives the preference, for purposes of interpolation, 

 to the formula proposed by Biot in 1844, 



log p = a + baf + cB T , 



the five constants a } b, c, a., /3 being deduced from five experi- 

 mental data for each fluid. 



3. Young's formula, it is true, contains three constants only, 

 a, b, and n; but, as M. Regnault has shown, it is deficient in 

 exactness. It has, in particular, two faults, — that for a certain 



temperature, T= — y, it makes the pressure of the fluid disap- 

 pear, and become negative below that temperature, which is 

 exceedingly improbable ; and that it makes the pressure of every 

 vapour increase without limit as the temperature rises — a result 

 contradicted by the experiments of M. Regnault, which (as he 

 states in vol. ii. p. 647) point to the conclusion, that "the elastic 

 force of a vapour does not increase indefinitely with the temperature, 

 but converges towards a limit which it cannot exceed" 



4. The first of those faults, but not the second, exists in 

 Roche's formula, 



AT 



l0 ^ =ffl -TT^r 



5. So far as I am aware, no formula has yet appeared, con- 

 taining three constants only, which agrees so closely with experi- 

 ment as that which I proposed in the Edinburgh Philosophi- 



* Memoires de VIntut. 



f Treatise on the eam-Engine. 



U2 



