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V. On the Criterion by which the Critical Point of a Gas may 

 be determined. By J. Douglas Hamilton Dickson, M.A., 

 F.R.S.E., Tutor of St. Peters College, Cambridge*. 



IT is generally assumed that at the critical point of a gas 

 the internal latent heat, X, vanishes. From the known 

 equation for the internal latent heat, 



X-}(„-.)(Tf^), 



we get the condition Ty- — p=0* In order to support this, 



Avenarius has made experiments on ether to show that u is 

 not equal to v at the critical point. 



On the assumption, however, of the correctness of the 

 formula given by Clausius in the last Number of this Maga- 

 zine (June 1880, p. 401), viz. 



_ KT _c__ 



p- v-u^Ttv+py ' • • • w 



where, for carbonic acid, 



R= -003688,-| 



c =2*0935, I ' 



a = -000843, J l ' 



/5= -000977/ 



the pressure being reckoned in atmospheres, and the unit 

 volume being that of carbonic acid at one atmosphere at the 

 freezing-point ; the critical point may be determined by assu- 

 ming James Thomson's form of an isothermal below the cri- 

 tical point, and in the cubic (1) for v (p and T being constant), 

 putting v 1 (the volume of the liquid) equal to v 3 (the volume of 

 the gas) — and therefore, by the Theory of Equations, making 

 its roots equal. This is in opposition to what Avenarius wished 

 to establish by his experiments on ether. 

 Eewriting (1) as a cubic for v, it becomes 



t 3 - (— -2£+«) v 2 + (^ -2/8— -2«£ + /8»)t> 



-(«^ f +/3 2 y+W3 2 )=0. • • (3) 

 The conditions for the roots of this being equal maybe written 

 * Communicated by the Author. 



