050 On the Theoretical Evaluation of '7. 



Moreover, the radiation at a given temperature would be 

 proportional to El, and this is not in agreement with 

 experiment. 



§ 12. Now two molecules must repel one another as soon 

 as their centres are at a sufficiently small distance apart. In 

 nature, this repulsion must vary continuously with the dis- 

 tance apart. Let us, as a first approximation to a represen- 

 tation of this, suppose each molecule surrounded by an 

 imaginary sphere S, such that an amount of work 12 must 

 be expended in bringing the spheres of two molecules into 

 contact. Let us make the assumption that the internal 

 vibrations of two molecules are affected by collision to an 

 appreciable extent, only when the spheres of the two molecules 

 intersect. 



At low temperatures,, only a very small fraction of the 

 whole number of molecules will possess sufficient energy to 

 penetrate at collision to the surrounding spheres of other 

 molecules, and therefore the mean energy of internal vibra- 

 tion will be affected by collisions only to an infinitesimal 

 extent. Jt can be shown* that our present assumptions can 

 be represented mathematically by supposing a in equation 

 (22) to contain a factor of the form e~ SQ/E . Thus it appears 

 that the reconciliation of theory with experiment depends 

 mainly on the possibility of attributing to II a sufficiently 

 great value f. If we may regard 12 as large in comparison 

 with the value of E at normal temperatures, then the dis- 

 turbance of F at collisions will be infinitesimal. Any internal 

 vibrations which may be excited are dissipated by radiation 

 into the aether. As soon as we reach temperatures at which 

 E becomes comparable with 12, the increase of F caused by 

 collisions becomes appreciable, and as a consequence both F 

 and the amount of radiation will become appreciable. It 

 appears, therefore, that the point at which E becomes com- 

 parable with 12 will be the point at which the gas becomes 

 incandescent. 



In equation (23), a must now be regarded as a function 

 of E. Differentiating this equation logarithmically we shall 



* ' Distribution of Molecular Energy/ § 29. 



f We must, in fact, suppose the vibratory mechanism of a molecule 

 to he sheltered by a held of repulsive force. Thus the " effective size'" 

 of a molecule will be large compared with the dimensions of the vibra- 

 tory structure. This view finds a certain amount of confirmation in the 

 discrepancy between the two values of the radius of an atom fouid (i.J 

 by kinetic theory methods (10-7 cm.), and (ii.) by methods of ionization 

 (10- 9 cm.). 



