The Distribution of Molecular Energy. 237 



is shown by direct methods that the energy will, after an infinite 

 time, distrib\ite itself equally between the five degrees of freedom, 

 but when a wave of sound is passed through the gas, the energy will 

 never have sufficient time to attain to its equilibrium distribution. It 

 is shown that sounds of different period will be propagated with appre- 

 ciably different velocities, except in the extreme case in which the ratio 

 of r to a is almost, but not necessarily quite, zero. In this case, the 

 ratio of the two specific heats, as determined from indirect experiments 

 on the velocity of sound, would be If, while direct experiments might 

 give any value from 1 to If, the value varying with the duration of 

 the experiment. 



It is suggested that an escape from this dilemma is made possible by 

 regarding the molecules as forming an incomplete dynamical system, 

 of which the ether is the remaining part. For purposes of illustration, 

 it is imagined that the interaction between the two parts of this com- 

 plete system consists of a frictional force which retards the rotation of 

 the molecules. A steady state is now impossible, but it is shown that 

 when the energy (i.e., temperature) of the gas is sufficiently low, the 

 gas tends to assume an approximately steady state, in which the energy 

 of rotation vanishes in comparison with that of translation. 



It is then shown that these conclusions may be generalised, so as to 

 apply to a more complex system of molecules, these molecules possess- 

 ing an indefinite number of degrees of freedom, and internal potential 

 energy as well as kinetic. The molecules exert forces on one another 



O/ 



at any. distance, and the radiation is of a more general type than 

 before. 



In Part III some of the "physical consequences of the view here put 

 forward are examined. The final conclusions are briefly as follows : 



The degrees of freedom must be weighted, not counted. The weight 

 of a degree of freedom may be anything between unity and zero, and 

 may vary with the temperature. A degree of freedom which does not 

 radiate energy will always be of weight unity ; for a non-luminous 

 gas, one which does radiate energy when the gas is heated is of weight 

 zero. 



As the gas is heated, the radiation and internal energies will in- 

 crease much more rapidly than the temperature, until finally, at infinite 

 temperature, the energy is distributed equally between all degrees of 

 freedom. 



Finally, it is pointed out that this view is in accordance with ordin- 

 ary thermodynamics for a non-luminous gas, but that the ordinary 

 thermodynamics must be supposed to break down above the tempera- 

 ture of incandescence, a view which has already been put forward, in a 

 modified form, by Wiedemann. 



