164 PROCEEDINGS OF THE AMERICAN ACADEMY. 



volume does not appear to tend to become zero at the zero of tempera- 

 ture, but rather to approach as a limit some definite volume. As the 

 kinetic forces become less there must be some other force wliich enters 

 to oppose the attraction between the molecules. If it is permissible 

 to consider the limiting case where the motion of the molecules ceases, 

 there must exist at the absolute zero a condition in which the total ex- 

 ternal pressure and all the attractive forces between the molecules are 

 together balanced by some sort of outward force which is equal to their 

 sum. This would be greater than the attractive forces alone, and the 

 difference would depend upon the external pressure. In other words, 

 there would be a resultant repulsive force equal to the external pressure. 

 As to whether this force is of the nature of elasticity, or of some action 

 at a distance, it would be presumptuous to speculate. From these con- 

 siderations, which must be admitted to be very hypothetical, it would 

 seem that at ordinary temperatures there should be analogous conditions 

 in which the repulsive forces would be greater the higher the pressure. 

 According to equation (16), in all liquids the resultant attractive pressure 

 diminishes with increasing external pressure, and finally changes sign at 

 the point where on the P F diagram the equation of condition cuts the 

 hyperbola of thermal pressure ; that is, at the point where the volume is 

 the same as it would be if the substance were to behave as a perfect gas 

 under the same pressure. Similarly, at high pressures probably all gases 

 have a greater volume than corresponds to the gas law, and according to 

 our theory their particles repel each other under these conditions. At 

 atmospheric pressure, on the other hand, almost all gases have too small 

 a volume, but hydrogen still has a volume which corresponds in our 

 theory to an mtermolecular repulsion. It is iyteresting, therefore, to 

 note that in the experiments of Joule and Thomson, while other gases 

 showed an increase of internal energy on expansion, hydrogen showed a 

 slight decrease. Helium is in all probabilit}^ another gas which has too 

 great a volume ; and it has been shown by Donnan * from his experiments 

 on the eff'usion of gases, that probably helium also has a heating effect on 

 free expansion, like hydrogen. Such a heating effect can be explained 

 in no other way so simply as by assuming that there is a repulsion 

 between the molecules in both helium and hydrogen. Finally, a similar 

 repulsion could explain the phenomenon observed in the experiments 

 of Ramsay f on the distribution of hydrogen between two spaces, one of 

 which contained hydrogen alone, the other hydrogen and nitrogen. lie 



* Pliil. Mag., XLIX. 423 (1900). t Pliil. Mag., XXXVIII. 206 (1894). 



