2 Bateiman, Degrees of Freedom of a Molecule. 



which the energy is governed by the principal tempera 

 ture. To a first approximation* the equation is 



(i) y=i+- 



n 



where n denotes the number of degrees of freedom 



possessed by the type of molecule under consideration. 



The validity of this equation has often been called 

 into question-f- but the principal dbjections brought 

 against it lose their force when the dissipation of energy is 

 taken into account, (Jeans, ^/. cit., pp. 188-196, 210-228.) 



It appears that the degrees of freedom which must 

 be taken into account in calculating the value of n, are 

 those which allow for a permanent increase or decrease in 

 the amount of energy allotted to them, when the state of 

 motion of the molecule is suddenly changed. On this 

 view the degrees of freedom which correspond to damped 

 vibrations are excluded. When the molecule is considered 

 as a dynamical system consisting of a large number of 

 particles, the damped vibrations arise from a set of 

 displacements of the system for which the existing state 

 of motion is stable. The type of displacement which 

 must be considered in calculating the value of n is one 

 for which the motion of the system is either neutral or 

 unstable.^ 



Whatever view be taken with regard to the validity of 

 equation (i) and other equations of a more general char- 

 acter, it is not without interest to examine whether a set 

 of rules can be framed which will lead to a value of;/ for 

 which the calculated value of y agrees roughly with the 

 experimental value. Various attempts have been made 



* A general investigation is given by Jeans, in "The Dynamical Theory 

 of Gases," ch. 10. 



t E.g. Nature, Aug. 13, (1885), vol. 32, pp. 352, 533. 



\ It may be mentioned here that Lord Kelvin was of the opinion that 

 a mode of vibration was not to be considered as a degree of freedom. 



