4 8 2 SCIENCE PROGRESS 



of matter. Further, an inverse fourth power law means that 

 the force of attraction dies away very rapidly as we pass out 

 from the molecule. A rough estimate of this may be made 

 in the following way. Knowing the number of molecules in 

 a given volume of a normal liquid, that is, a liquid in which 

 the molecules have not coalesced to form double molecules, 

 etc., and also knowing the average size of each molecule, it is 

 an easy matter to determine the average distance apart of 

 any two contiguous molecules. The distance from centre to 

 centre is about 5 x io" 8 to 1 x io -7 cm. Now by means of a 

 thermodynamical relation, into which it is unnecessary to go, 

 it is possible to calculate the heat which would be absorbed if 

 we could imagine one cubic centimetre of the liquid extended 

 until it occupied just twice its original volume. The writer (6) 

 has calculated the values of these heat absorptions in the case 

 of a number of normal liquids and has found that they are 

 quantitatively very similar to the internal latent heats of 

 vaporisation per unit volume, that is the amount of heat which 

 is absorbed in transforming one c.c. of liquid into the state of 

 vapour. The fact, that the energy absorbed in the two pro- 

 cesses is practically the same, means that by distending the 

 liquid to twice its former size we have already practically 

 overcome the forces of cohesion, for the much greater dis- 

 tension involved in the act of vaporisation requires practically 

 no further addition of energy. If r=i x io" 7 cm., is the 

 distance apart of two molecules in the original state, then the 

 distance apart when the volume is doubled is about 1*3 xr. 

 Hence on increasing the distance of the molecules apart in 

 the ratio of 1*3 : 1, we infer from what has been said that 

 the internal cohesion has now dropped to small dimensions. 

 We conclude, therefore, that the effective range of molecular 

 attractions, that is, the range throughout which the attractive 

 force is still sensible, is of the order 1 x io' 7 cm., a very small 

 quantity indeed. 



Although the effective range of molecular attraction is 

 small, it must not be inferred that attraction itself is small. 

 Quite the reverse is the case. Naturally the magnitude of the 

 force varies with the distance from the molecule, but we can 

 get some idea of the quantity by taking the actual case of some 

 liquid substances as they exist under ordinary conditions. 

 The values given below can only be regarded as approximately 



