116 DIRECT PROPERTIES OF MOLECULES 323 



find this constancy when we proceed to calculate the path- 

 volume for a series of gases from the foregoing numbers. 



It therefore follows that we cannot hold ourselves justi- 

 fied in taking the calculated values of * as representing the 

 actual diameters of the gaseous molecules. The reason that 

 we may not do so is obvious. There can be no doubt that the 

 molecules are not spheres in shape ; for, as we concluded in 

 112 from a large number of facts, they are more probably, 

 without exception, flattish discs of very small thickness. We 

 therefore cannot arrive at true values of their diameter and 

 volume by looking on them as spheres. At most we may 

 expect ( 113) to obtain from this calculation an estimate of 

 the volume of a larger sphere which the flat disc describes 

 when it rotates, and the mean diameter of a molecule must 

 be less than the diameter of this sphere. We may not, 

 therefore, take the values calculated for * as giving the true 

 size of the molecules, but may see in them only a superior 

 limit which the size of the molecules does not attain. 



From these considerations we can conclude only that the 

 gaseous molecules are smaller than a sphere whose diameter 

 is one-millionth of a millimetre. But we may add as very 

 probable that the size of the gaseous molecules will in no 

 way appear to be vanishingly small when compared with 

 that small sphere. This is justified on many other grounds, 

 which we have still to mention. 



117. Calculation of the Size of Molecules from th 

 Deviations from Boyle's Law 



The above calculated numbers obtain a remarkably good 

 confirmation from the values which we obtain for the same 

 magnitude by a different mode of calculation first given by 

 vander Waals. 1 In the theory explained in Chapter IV. 

 of this book, by which van der Waals sought to explain 

 the deviations of actual gases from the Boyle-Gay Lussac 

 law, the grounds of these deviations were found partly in 



1 ' Over de continuiteit van den gas- en vloeistof-toestand,' Leiden 1873, 

 transl. by Phys. Soc. London, 1890, Chap. VI. p. 384. Abstracted in Beibl. to 

 Pogg. Ann. 1877, i. p. 10. 



Y 2 



