110 PROCEEDINGS OF THE AMERICAN ACADEMY. 



ated with a representative molecule which undergoes periodic changes 

 from kinetic to potential and back to kinetic. In complicated cases 

 where the transformation from kinetic to potential does not take 

 place simultaneously in all parts of the atom, an equivalent generali- 

 zation is: Temperature is the difference between the maximum and 

 minimum potential energy of a representative molecule. This evi- 

 dently applies to both the extreme cases above; the one for which 

 temperature is proportional to kinetic translational energy, and the 

 one for which it is proportional to internal energy. In one respect 

 these two extreme cases are not entirely unlike; in accordance with 

 the law of equipartition, only a certain proportion of the total energy 

 communicated to a molecule of a gas becomes kinetic; the rest goes 

 to the internal degrees of freedom. So that an increase of tempera- 

 ture always carried with it an increase of the internal energy of the 

 molecule. Whether this internal energy also oscillates in character 

 between kinetic and potential is not obvious. 



Of course the justification of this proposed general definition of 

 temperature must be furnished by experiment. It does have the 

 advantage, however, of being ai^plicable at high pressures where the 

 ordinary definition breaks down completely, and it does agree with 

 our physical feeling of what temperature must be in the case of one 

 very simple model of a substance under high pressure. 



The effect of this conception of temperature on our conception of 

 the equipartition of energy between the different degrees of freedom 

 is interesting. At high pressures, where the molecules press on each 

 other from all sides, one degree of freedom has been lost (or more 

 properly three) namely, the possibility of motion of the molecule as a 

 whole. We may suppose, if we like, that under these circumstances 

 the total energy is equally divided between the remaining degrees of 

 freedom. Now at any instant in a liciuid, there are molecules with 

 varying degrees of freedom, according to the kind of collision in which 

 they are entangled. Furthermore, the same molecule at different 

 stages of its career may enjoy a different number of degrees of freedom. 

 When the degrees of freedom change, there must follow a redistribu- 

 tion of the total energy among the remaining degrees of freedom, and 

 this process takes time. The result is that we cannot ascribe to the 

 average molecule of the substance any definite number of degrees of 

 freedom. The number cannot be an integer in the first place, and in 

 the second place must vary continuously as pressure varies. 



The idea that the temperature of a substance need not be propor- 



