Energy and Radiation Theory. 79 



could be expressed as the sum or! terms depending on the 

 individual coordinates peculiar to the normal functions. 

 The application of statistical reasoning to the problem, 

 subject to the constancy of the total energy, and to the 

 restricting conditions which provide for the permanence 

 of the electrons, would then lead to the law of partition 

 of energy between the individual terms in the expression 

 for the energy, provided that, by means of the electro- 

 magnetic equations, the laws governing the changes of the 

 coordinates could be thrown into the Hamiltonian form. 

 This is, of course, only a rather more precise method of 

 formulating the problem outlined above, but it serves to 

 show how, in an exact specification of this kind, the 

 electron, as such, would disappear from the analysis, its 

 sole representative being the restricting conditions which 

 provide for the permanence of its existence. 



In spite of all that has been written above concerning the 

 objections to connecting the gas constant R with the radiation 

 formula through the medium of arguments such as those 

 which have been here reviewed, there remains the remark- 

 able fact that the R which occurs in the equipartitional 



£ormula ' E X = fcrBT/V, 



a formula true for long wave-lengths, is found to be 

 actually equal to the gas constant experimentally obtained 

 in other ways. The difficulty presents itself as to how it is 

 that, if the arguments accounting for the presence of R in 

 the radiation formula are wrong, as they appear to be, they 

 nevertheless do predict the presence of the correct constant. 

 The analogous difficulty is not avoided in the arguments 

 which purport to explain the presence of the gas constant in 

 the more exact formula of Planck; and although it would 

 appear impossible to import complete precision into the 

 problem without a knowledge of the mode of interaction 

 between the molecules and the radiation, the following 

 tentative considerations may nevertheless be of interest. 



Relation between the radiation formula and the average 



energy of a gas molecule. 



Suppose that although we may not know the reasons 



underlying the radiation formula, we nevertheless know 



that the value of E^ is determined as a function of \ 



and of the temperature T by the formula 



.JBx-S-T*-, (4) 



,AT 



-1 



