84:4 Dr. R. D. Kleeman on the Radius of 



a paper by Mills * who has calculated the internal heat of 

 evaporation at different temperatures for a number of liquids 

 by means of Clapeyron's equation. The values of h x p were 

 formed for temperature intervals of 10 degrees, and the 

 differences plotted, and a smooth curve drawn through the 



points obtained. From these curves the values of n 



for different temperatures were obtained, being given by the 

 ordinates corresponding to the given temperature abscissae. 



In a similar way the values of -^-were obtained, the values 



of X used being taken from the tables given by Ramsay and 

 Shields f . In the deduction of the above equation the effect 

 of the vapour surrounding the liquid is neglected, and it 

 therefore applies only to a liquid whose density is large in 

 comparison with that of the surrounding vapour. The 

 calculations have therefore not been carried out up to the 

 critical point. The table gives the diameters of the spheres 

 of action of a number of molecules, and the radii are there- 

 fore obtained by halving these values. 



It will be seen that the diameter of the sphere of action is of 

 the same order of magnitude as the usually accepted diameter 

 of a molecule. It is very nearly of the same magnitude as 

 the distance of separation of the molecules in a liquid : this 

 for example in the case of ether at 311 c, 7 C. is equal to 

 4'24xl0 -8 cm., if the mass of a hydrogen atom is taken 

 equal to 7*1 X 10~ 25 gram. The effects produced by these 

 intermolecular forces can therefore be of considerable mag- 

 nitude only when the molecules are at a distance from one 

 another of the same order as their diameters. 



There is a slight but unmistakable decrease of the radius 

 of the sphere of action with the temperature. It is impossible 

 to say whether this is due to a decrease of the force of attrac- 

 tion of the atoms with rise of temperature, or to an alteration 

 in the configuration of the atoms in the molecules. The 

 observed decrease of the heat of formation of a molecule with 

 increase of temperature, however, makes it appear probable 

 that the force of attraction decreases slightly with increase of 

 temperature. 



The radius of the sphere of action does not vary very much 

 with the nature of the molecule. It would be the same for 

 all kinds of molecules if the function which expresses the 

 force of attraction between two molecules in terms of their 

 distance of separation is the same for all molecules multiplied 



* Jour, of Phys. Chem. vol. viii. p. 405 (1904). 



f Phil. Trans, of the Roy. Society, A. vol. clxxxiv. p. 647 (1893). 



