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XXXVI. On some Applications of the Law of the Recti- 

 linear Diameter. By H. Da vies, B.Sc, Bead of Physics 

 Department^ Municipal College, Portsmouth *. 



1THE law o£ the rectilinear diameter was published by 

 Cailletet and Mathias f in 188G. With temperatures 

 as abscissae and densities as ordinate?, they plotted a curve 

 including liquid and vapour densities up to the critical point. 

 The two branches merged into one another at the critical 

 point. The points of mean density were found to lie on a 

 straight line. The mean density is then a linear function of 

 the temperature and can be expressed as 



D, + D„=a-&T, 



or D|+D.-2D c =c(T c -T). 



S. Young { has shown that there is a slight departure 

 from linearity, and adds a term containing T c 2 — T 2 as a small 

 correction to the right-hand side of the second expression. 

 In a previous note § the author has shown from the first 

 expression that the coefficient of expansion of a liquid is 

 closely related to the critical temperature. Some further 

 relations are obtained in the present paper by the use of this 

 principle. In the first two sections the value of K is taken 

 instead of n 2 , owing to the difficulty of access to values of n 2 

 for infinite wave-length without much laborious calculation, 



1. On the Matio of the Volume at the Absolute Zero of 

 Temperature to the Peal Volume of the Molecules in a 

 Unit Mass. 



Stefan ||, in his memoir on the theory of diffusion of gases, 

 drew attention to a simple relation between the refractive 

 index of a gas and the mean free path of the molecules. 

 He gave the relation in the form (n — 1)L = constant. 

 ClausiusU developed the idea on the lines of Maxwell's and 



Helmholtz's theories, and showed that the expression ^f — - 



represents the ratio of the real volume of the molecules of a 

 substance to the volume they actually occupy, K being the 



* Communicated by Prof. A. W. Porter, F.R.S. 



t Corny. Rend. cii. 1886. 



\ Phil. Mag. (5) 1900, p. 291. 



§ Phil. Mag. April 1912. 



|| Wien. Sitzimgsher. lxv. (1872). 



% Mechamsche Warmetheprie, 1879. 



