t 291 ] 



XXVII. On the Law of Cailletet and Mat Mas and the Critical 

 Density. By Sydney Young, D.Sc, F.R.S., University 

 College, Bristol*. 



IN a very interesting paper {Mem. de la Soc. Roy. des Sci. 

 de Liege, ser. 3, ii. 1899) M. E. Mathias discusses the 

 law of the Rectilinear Diameter, discovered in 1886 by 

 M. Cailletet and himself, and the law of the corresponding 

 states of matter. The law of Cailletet and Mathias may be 

 stated simply in this wayr — The means of the densities of 

 liquid and saturated vapour for any stable substance are a 

 rectilinear function of the temperature. 



It has been shown (Mathias, Ann. de la Fac. des Sci. de 

 Toulouse, 1892 ; Young, Phil. Mag. Dec. 1892, p. 506) that 

 if the generalizations of van de YYaals regarding corre- 

 sponding temperatures, pressures, and volumes are correct, 

 the angular coefficient a [D ? =D + a^ where D t and D are 

 the means of the densities at t° and 0° respectively] of the 

 diameters of different substances should be directly propor- 

 tional to their critical densities, and inversely proportional to 

 their absolute critical temperatures ; or that for any substance 



, Do 

 a = const. X ttt j 



thus -=p = const. = a. 



M. Mathias points out that in order to test the truth of the 

 law of corresponding states, it is only necessary to ascertain 

 whether a is really a constant. He then discusses the con- 

 ditions necessary for the determination of a. 



For a certain number of substances the critical temperature 

 and the densities of liquid and saturated vapour from about 

 the ordinary boiling-point to the critical point have been 

 determined ; and in these cases there is no difficulty. From 

 the mean densities at a series of temperatures a is found, and 

 D c is then calculated from the formula 



D c =D + «(T c -273). 



In the great majority of cases, however, the only density 

 determinations that have been made are those of the liquid 

 below the boiling-point. We may, however, calculate the 

 densities of saturated vapour at these low temperatures if the 

 vapour-pressures are known on the assumption that the 

 vapour-density is practically normal ; and thus the mean 

 densities of liquid and saturated vapour may be ascertained. 



* Communicated by the Physical Society : read June 22nd, 1900. 



