110 Dr. J. E. Mills on the Relation of 



by each system is the same and the amount given up is the 

 same. In order, therefore, to reduce either system to an 

 unstable configuration the same amount of energy would 

 have to be added, and it would seem that the systems must 

 be equally stable. The area of the circle is ira 2 and the area 

 of the ellipse is irab. The volumes of the corresponding- 

 sphere or ellipsoids of revolution are 4/o7ra 3 , and A/'dirab 2 or 

 4:/o7ra 2 b. Now b is less than a, and if we consider the system 

 to occupy the corresponding solids of revolution, the energy of 

 the circular system takes up more space than the energy of the 

 elliptical system. This will appear yet more clear if wo 

 consider that the limit of the elliptical orbit, as b approaches 

 zero, is the linear orbit. 



The energy retained by the system per unit of space is 

 therefore greater the more elliptical the orbit. In a system 

 of n particles it seems to me therefore that if we have a system 

 with a certain amount of energy the orbits will be circular if 

 the endeavour is to have the energy as little concentrated per 

 unit of space as possible. If the system endeavours to concen- 

 trate the energy per unit of space as much as possible then 

 elliptical orbits will result. 



Increase of temperature might be viewed as an increased 

 concentration of kinetic energy in space, and we have seen 

 that the more elliptical the orbit the more concentrated the 

 energy per unit of volume. Apparently, therefore, only in 

 one way could the addition of energy cause an increase of 

 kinetic energy per unit of volume in the system and yet 

 cause a decrease in the mean orbital energy, and that is by 

 causing an increased ellipticity of orbit. 



A rise or fall of temperature does not change the nature or 

 the amount of the molecular attractive force. It merely deter- 

 mines the orbit that the molecules will follow in obedience to the 

 attractive force. 



22. Some light is thrown upon the relation between 

 temperature and molecular attraction by a study of the 

 relations at the critical temperature. In a gas indefinite 

 expansion takes place as the pressure is decreased. This 

 shows that the attraction between the molecules cannot be 

 great enough to make the paths of the molecules closed 

 curves. In a liquid, while undoubtedly many molecules 

 whose velocity is above the average molecular velocity are 

 continually flying away from the surface, yet it must certainly 

 be the case that most of the molecules are drawn back by 

 the molecular attraction. There must be for each substance 

 a certain temperature at which the molecules attain suf- 

 ficient velocity to fly apart to an infinite distance, without 



