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XL. Relations between the Density, Temperature, and Pressure 

 of Substances. By R. D. Kleeman, D.Sc, B.A., Mackinnon 

 Student of the Royal Society*. 



THE writerj has shown in a previous paper that an 

 infinite number of equations can be found connecting 

 the surface tension or latent heat of evaporation of a liquid 

 with its temperature and density and density of the saturated 

 vapour. These equations correspond to laws of attraction 

 between the molecules, but none of which is necessarily the 

 law that actually exists. Each of these laws can be obtained 

 by giving a definite value to the arbitrary function contained 

 in the general law of attraction that can be deduced from 

 surface tension or latent heat data. This general law of 

 attraction between two molecules of the same kind is 



$2 ( 7" > m" ) • - 5 , where T denotes the temperature of 



the molecules and z their distance of separation, x c denotes 

 their distance of separation in the liquid state at the tempe- 

 rature T c , Xa/ mi denotes the sum of the square roots of the 



/ z T \ 

 atomic weights of the atoms in a molecule, and <j> 2 ( — , rTr ) 



T z \®e I c / 



denotes an arbitrary function of r -p- and — . 



There exists, therefore, an infinite series of equations of 



the form L==^i(/>k p 2i T) = yfr 2 (p 1 , p 2 , T) = , where L 



denotes the internal heat of evaporation of a liquid at the 

 temperature T, and p x and p 2 denote the density of the 

 liquid and that of the saturated vapour respectively. It is 

 obvious that we can obtain from these equations an infinite 

 number of equations containing T, p u or p 2 only. Now eacli 

 of the equations thus obtained must obviously be either an 

 identity or be an equation which has an infinite number of 

 real positive roots lying between certain limits. In practice, 

 however, the equations found in the above way (usually by 

 trial) do not exactly satisfy these conditions. But this is of 

 no consequence, as the equations deduced, containing any 

 two of the quantities p { , p 2 , T, usually agree very well with 

 the facts. It is the object of this paper to point out and 

 discuss some of these equations. 



Mills % has shown that the internal latent heat of 

 evaporation is very approximately given by the equation 

 L = D(/o} /3 — p}J 3 ), where D is a constant depending only on 



* Communicated by the Author. 



t Phil. Mag. Jan. 1911, p. 83. 



X Jouru. of rhys. Chem. vol. viii. p. 40o (1904). 



