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



energy o£ radiation is to be distinguished from the energy 

 which belongs to matter. For in the electromagnetic theory 

 the material energy too is localized in the " aether " and the 

 distinction to be made is practical and approximate, not 

 absolute and uniquely definable. I have assumed that the 

 electric charges constituting the material system move with 

 velocities much smaller than the velocity o£ light or move 

 in a steady distribution. Complete radiation is then shown 

 to involve the interaction of two dynamical systems — the 

 material system on the one side, and the field of -radiation 

 on the other. 



For the motion of such material systems as are defined 

 by Hamilton's equations 



dt~~d P ; dt~ dq r • • • • u 

 (r=l, 2 . . . n) : II is the total energy. 



(1) it is to be noticed refers to the motion such as it 

 would be if undisturbed by the radiation. q x q 2 ...q n nre 

 coordinates defining the distribution. pip 2 . . . p« are the 

 momenta. 



Write 



dY 2n =dq 1 dq 2 ... dq n dp l dp 2 ... dp n ... (2) 



Let the probability of a distribution in which the 

 coordinates and momenta lie in the 2?i'ple volume element 

 dV 2n be 



fdYto (3) 



And let the energy of complete radiation per unit volume 

 whose wave-length lies between X and \ + d\ be 



E x dX (4) 



It is shown in this paper that 



= - 16tt A~ 5 ((/$, f ' <f>(t - OCos (=^ e) de dY,„ ; . (5) 

 the Poisson-bracket expression. <f>t is a linear function of 



