Forces of Attraction between Atoms and Molecules. 799 



Dividing each value of c a bv the corresponding value of V ' m 

 we obtain the ratios H = l, C = 1'53, = 1*49, F = 1'32, 

 01=1-41, Br =1-19, Sn = l*35, 1 = 1*38. It will be seen 

 that the value of c a for hydrogen is in comparison with the 

 other atoms about 30 per cent. Jess than it should be accord- 

 ing to the square root law, which fits in, according to the 

 above, with what one would expect from chemical con- 

 siderations. 



Let us now investigate the conditions when the interaction 

 of the molecules or screening effect in different systems of 

 molecules produces the same proportional change in the 

 attraction, &c. Let A, B, C, be three molecules not neces- 

 sarily of the same kind. Remove the molecule A to an 

 infinite distance and let the work done be denoted by Fa. 

 The work is being done against the attraction of the mole- 

 cule A by B and C modified by the interaction of the mole- 

 cules on one another. Next remove the molecule B and 

 let the work done be denoted by F. Now the removal of A 

 and B may be carried out in a different way. Remove the 

 molecule B first and let the work done be Fa'. Then remove 

 the molecule A and let the work done be F'. Then we have 

 Fa + F = Fa' + F / . Now suppose that the mass of each 

 molecule is m times as great, the position of each molecule 

 remaining the same. Let F become nF, then F' will become 

 nF'. According to the above equation (Fa— Fa') will 

 therefore become »(Fa — Fa r ). This shows that the per- 

 centage diminution of the attraction between the molecules 

 in a system of molecules is the same as that in another 

 system if the distances between the molecules and their 

 arrangement is the same in both cases and the mass of each 

 molecule in one system is the same fraction or multiple of 

 that of the corresponding molecule in the other system. 

 This is realized for different liquids at different temperatures 



when their values of — are equal to one another. 



m l 



It does not seem improbable that the effect of a molecule 

 A in diminishing the attraction of a molecule C on B is 

 proportional to the attraction A exerts on B. In that case, 

 the magnitude of the diminution of the attraction of the 

 molecules on one another can be calculated if we are given 

 the law of attraction that would exist if there were no inter- 

 action between the molecules. Let us, for example, see what 

 the attraction between two atoms of mass wij, m 2 , becomes if 

 they influence one another in that way. The force of attrac- 

 tion of the atom m 1 at the point occupied by the other atom 



