260 Mr. W. Sutherland on Molecular 



into one another at the critical point. When the points of 

 mean density are marked they yield a straight line inclined 

 to the axes. The mean density is a linear function of the 

 temperature. That is the discovery made by Cailletet and 

 Mathias. S. Young (Phil. Mag. [5] 1. 1900, p. 291) has 

 shown that there is a small departure from linearity. The 

 relation of Cailletet and Mathias is expressed completely by 

 the equation 



pH-p 2 -2/>c=2c(T c -T), .... (14) 



to which S. Young adds on the right a small term in T c — T 2 . 

 By the principle of corresponding states c is a parameter 

 such that cT c /p c =l, the actual values calculated by S. Young 

 ranging from 0*932 for fluorbenzene to 1*06" 1 for ethyl 

 formate. For C 2 H 4 the value rises to 1*30, and for N 2 to 

 1*49. For Cl 2 it falls to 0*7675. If we return to equation 

 (10) with our interpretation of it, we can write it 



[U(MI(>y^ = 4(p s -p c )el4W^ (15) 



= 1*46 (or 2*12) (T,-T). 



Since by the principle of corresponding states we derive 

 from this (o 1 -fp 2 -2^.)/2 Pc =(T c -T)/T c which is the law of 

 Cailletet and Mathias, it follows that 



^ = 3x1*46 (or 2*12) T c jSp c W^ . . . (16) 



The law of Cailletet and Mathias is identical with that of 

 Eotvos by virtue of the relations which we have adopted 

 between R lt 2 R 2 , R 2 on the one hand and densities on the 

 other. The equations just given contain the fourth and fifth 

 methods of calculating the attractional virial parameter I as 

 developed in "The Laws of Molecular Force" (Phil. Mag. 

 [5] xxxv. 1893, p. 211), namely, from the data of the critical 

 point and from surface tension. 



9. The surface energy of mixed liquids. 



Here an interesting kinetic point is raised in connexion 

 with our principle that molecules can be treated as though 

 each attracted only its six immediate neighbours. Consider 

 a mixture of liquids 1 and 2 containing 100 molecules of 1 

 to 1 of 2. Then in a permanent uniform distribution of the 

 molecules, no molecule of 2 has another molecule of 2 amongst 

 its six immediate neighbours, for it is surrounded by more 

 than 100 molecules of 1. In a puiely statical theory with 

 the assumption of permanent uniform distribution the mutual 



