202-205] Dissipation of Energy 173 



gases and in no case is 7 equal to unity within the limits of experimental 

 error. Our theory has, then, led to a result which is in flagrant opposition 

 to experiment. ~f 



Dissipation of Energy. 



204. An explanation is not difficult to find. The whole discussion has 

 rested upon the Law of Equipartition of Energy, expressed by equation (161). 

 Now in arriving at equation (161) it was assumed that the molecules of the 

 gas together formed a conservative dynamical system, whereas the very fact 

 of our observing spectral lines shews that the molecules are radiating energy 

 into the ether, and therefore do not form a conservative system. The 

 application of the Law of Equipartition or of equation (161) to the energy 

 represented by spectral lines is therefore illegitimate. In the next chapter 

 we shall apply the general dynamical methods of Chapter V. to the motion 

 of a gas in which the conservation of energy does not hold, and shall return ./ 

 later to a mathematical investigation of the question of the ratio of the 

 specific heats of such a gas. 



205. We may conclude the present chapter by giving a brief forecast of 

 the results of this investigations The energy of those degrees of freedom 

 which are represented by the lines of the spectrum are, it will be seen, 

 subject to losses from two causes and to gain from one. In the first place 

 there is the continual radiation into the surrounding ether. This results in 

 a loss which may be referred to as a. Secondly at each collision the 

 vibrations of the molecule are disturbed, so that a collision may either 

 increase or decrease the energy of a particular vibration. The collisions 

 which occur during a specified small interval of time may therefore be 

 supposed to result in a loss /3 and a gain 7 to any particular degree of 

 freedom. The total decrease in the energy of this degree of freedom may 

 therefore be written symbolically as 



a + - 7, 

 and when the energy remains steady, we must have 



a+y g_ 7 = (420). 



In the previous investigations, there has been no radiation so that a = 0, 

 and in the normal or steady state @ = y. Equation (420) was therefore 

 satisfied in this case by the solutions 



a = 0, = 7 (421). 



