408 VAN DEU WAALS OX THE CONTINUITY 



fraction of them are in the act of encountering each other. We know that 

 during an encounter action and reaction are equal and opposite, and -we assume, 

 with Clausius, that on an average of a large number of encounters the pro- 

 portion in which the kinetic energy of a molecule is divided between motion 

 .f translation of its centre of mass and motions of its parts relative to this 

 point approaches some definite value. This amount of knowledge is by no moans 

 sufficient as a foundation for a complete dynamical theory of what takes ]>la.o 

 during each encounter, but it enables us to establish certain relations between 

 the changes of velocity of two molecules before and after their encounter. 



While a molecule is describing its free path, its centre of mass is moving 

 witli constant velocity in a straight line. The motions of parts of the molecule 

 relative to the centre of mass depend, when it is describing its free path, only 

 on the forces acting between these parts, and not on the forces acting between 

 them and other molecules which come into play during an encounter. Hence 

 the theory of the motion of a system of molecules is very much simplified if 

 we suppose the space within which the molecules are free to move to be so 

 large that the number of molecules which at any instant are in the act of 

 encountering other molecules is exceedingly small compared with the number of 

 molecules which are describing their free paths. The dynamical theory of such 

 i\ system is in complete agreement with the observed properties of gases when 

 in an extremely rare condition. 



But if the space occupied by a given quantity of gas is diminished more 

 and, more, the lengths of the free paths of its molecules will also be diminished, 

 and the number of molecules which are in the act of encounter will bear a 

 larger proportion to the number of those Avhich are describing free paths, till at 

 length the properties of the substance will be determined far more by the 

 nature of the mutual action between the encountering molecules than by the 

 nature of the motion of a molecule when describing its free path. And \\e 

 actually find that the properties of the substance become very different alter 

 it has reached a certain degree of condensation. In the rarefied state its pro- 

 ])erties may be defined with considerable accuracy in terms of the laws of Boyle, 

 Charles, Gay-Lussac, Dulong and Petit, &c., commonly called the " gaseous 

 laws." In the condensed state the properties of the substance are entirely 

 different, and no mode of stating these properties has yet been discovered 

 having a simplicity and a generality at all approaching to that of the " gaseous 

 laws." According to the dynamical theory this is to be expected, because in 





