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LXXXVII. On the Radius of the Sphere of Action of a 

 Molecule. By R. D. Kleeman, D.Sc, B.A., Mackinnon 



Student of the Royal Society ; Emmanuel College, Cam- 

 bridge *. 



rjlHE writer f has shown that two molecules a given 

 JL distance apart attract one another, apart from their 

 gravitational attraction, with a force proportional to the 

 product of the two sums of the square roots of the atomic 

 weights of the atoms of the molecules. This attraction gives 

 rise to the surface tension of liquids, and the work done 

 against it in evaporating a liquid is the internal heat of 

 evapoi'ation ; there is also evidence that it is the attraction 

 which produces chemical combination. It was also shown 

 that for distances of separation of the order of those of the 

 molecules in a liquid the force of attraction between two 

 molecules varies approximately inversely as the fifth power 

 of their distances of separation. 



Physicists usually use the term "radius of the sphere of 

 action " in connexion with the field of force surrounding a 

 molecule. The attractive force, however, in reality does 

 probably not end abruptly at a certain distance from the 

 molecule ; but there is a distance corresponding to which 

 the energy necessary to move another atom to infinity is small 

 in comparison with the energy expended when the atoms are 

 initially in contact; and in this sense we will use the term in 

 this paper. 



If we take the attraction between two molecules as in- 

 versely proportional to the fifth power of their distance of 

 separation, the energy expended in separating them by an in- 

 finite distance when they are initially separated by 10~ 8 cm., 



the average diameter of a molecule, is proportional to 40 . 



And when they are initially separated by a distance of 

 5xl0" 8 cm., which is of the same order as the diameter 



of a molecule, the energy expended is fi9 ^ -m-40 * wmcn * s 



a small fraction of the foregoing value. This shows that the 

 radius of the sphere of action of a molecule is of the same 

 order of magnitude as its diameter. 



The object of this paper is to give a definite expression for 

 the radius of sphere of action in terms of other quantities. 

 It will be seen that further properties of this quantity are 

 brought to light by means of this expression, 



* Communicated by the Author. 



t Phil, Mag, May 1910. p, 783, 



