

230 Dr. G, Green on a Method of 



Let the gas consist of molecules having internal modes of 

 vibration which are identical with the modes of vibration 

 of unit volume of pother. 



Let no molecule emit radiation in any mode until the total 

 energy in that mode is hf; h being a constant, and /'the 

 frequency of the mode. When the limiting energy is 

 reached let the whole quantity hf or any portion of it be 

 emitted at a discharge. 



Let Maxwell's law of distribution of velocities hold 

 throughout the gas. This implies an equilibrium condition 

 within the enclosure maintained by collisions, statistically 

 regular absorption, and sudden emission in each mode when 

 the limiting energy is reached. 



Consider now the energy distribution amongst the N mole- 

 cules per unit volume in a single vibrational mode. If we 

 adopt the view that each internal mode corresponds to the 

 motion of an electron in an orbit whose plane is fixed relative 

 to each molecule, the velocities to be considered in estimating 

 the kinetic energy of a molecule in a given mode are clearly 

 velocities relative to the centroid of each molecule. Hence, 

 in assigning for any mode the number of vibrators having a 

 given velocity, we have only to consider all phases in a plane 

 orbit as equally possible — and we are not concerned with the 

 directions of the velocities in space or with the orientation of . 

 the orbital planes. On the above view, or on any other which 

 allows us to deal with the velocities in any internal mode as a 

 two-dimensional system, we have according to MaxwelPs law 



A'e ke vdv ) for any assigned vibrational mode, 



Number of molecules having energy in range (e— de. e) 



_ e 



= Ae tide, . . (1) 



where A depends on the number of molecules and on the 

 temperature of the enclosure, and kO is the mean total 

 energy of a molecule in any mode, assuming all velocities 

 from zero to infinity to be possible in that mode. In the 

 above equation, since in each mode the potential energy is 

 on the average equal to the kinetic, we may take e to represent 

 total energy, instead of kinetic energy alone. This involves 

 only an alteration in the value of A, which we now determine 

 to suit the case where e represents total energy of a molecule 

 in a given mode. Integration of (1) gives 



Number of molecules in energy range (0, e) 



= Ak6\l-e *V). 



(2) 



