﻿538 Mr. S. B. McLaren on Emission and Absorption 



of freedom, is to make the problem practically insoluble. 

 The first alternative is no longer open. The reasoning of 

 the kinetic theory is soundly based on the laws of dynamics, 

 and the postulate of an essentially positive energy. 



Of those who have chosen the second of our three 

 alternatives and deny the reality of temperature equilibrium, 

 it is scarcely unjust to say that they prefer the dynamical 

 theory to the physical facts it has failed to explain. I 

 do not understand their theory. Wherever there is 

 less energy than Rayleigh's formula would require they 

 suspect that it escapes all enclosures designed to trap it 

 and never appears in what is falsely supposed to be the 

 complete black body radiation. Then, of course, the Fourth 

 Power law and Wien's law deduced by thermo-dynamics 

 have no rational basis, the success of the reasoning by which 

 they were reached is a mere accident. For complete 

 radiation as ordinarily understood is not radiation in 

 temperature equilibrium at all. This is bad enough in 

 theory, but further it is contrary to fact to say that the 

 defect of radiation for ordinary light-waves is due to 

 the transparency of the enclosure to them. It is due to the 

 enormously greater absorbing power of the body which 

 emits these waves than we should expect were the ratio of 

 absorption to emission given by Rayleigh's formula. (See 

 Phil. Mag. xxii. pp. 71, 72, 1911). The light-waves are 

 absorbed and the energy reappears at once as heat, the 

 complete radiation is what it is always assumed to be — 

 the result of a balanced radiation and absorption. If we 

 postulate some process by which the absorption is effected 

 which is not equally involved in the radiation then we are 

 resigning dynamics. I have shown in this paper and in my 

 last that the pressure of radiation for example will produce 

 no deviation from the formula (76). 



There remains, it appears to me, nothing but to embrace 

 the last alternative and resign our belief in the universal 

 validity of dynamics. Jeans (Phil. Mag. xx. p. 943, 1910) 

 has indeed argued that any system of laws of motion 

 involves the doctrine of equipartition. I offer the following 

 equations of motion as a test of his conclusion. 



Let qi ... q 2 ... q n be the coordinates of position of a 

 dynamical system and pi...p 2 ...p n be the momenta. The 

 equations which replace Hamilton's are to be 



dq r dH dp dH , ., N /QJO 



H may be any function not containing the time explicitly ; 



