216 Prof. J. H. Jeans on Temperature-Radiation 



moving molecules: the latter regards the energy as that of a 

 vibrating medium. Each law of distribution is that of the 

 normal state. From the second, it follows at once (cf. equa- 

 tion (15)) that the law of partition of energy between 

 vibrations of different wave-lengths is 



2UTX~ 2 dX, 



and it is easily seen that in the three-dimensional problem, 

 the corresponding law is 



■iTrRTX-^dX. 



These formulae are of course true only for waves of length 

 great compared with molecular distances. They require 

 modification as we approach wave-lengths comparable with 

 molecular distances. 



III. A Mechanical Model of the JEther. 



21. There appears to be no reason why the energy of the 

 electromagnetic field cannot be treated similarly to that of 

 a gas, except for the simplification that, so far as we know, 

 no limitations need be introduced by the coarsegrainedness 

 of the structure of the medium. 



For simplicity let us consider a rectangular enclosure, and 

 imagine it divided into equal cubical cells, each of edge I 

 and volume co. Let these cells be denoted by the numbers 



000,001, 002, ...010, 011, ... 



the cell pqr having as its Cartesian coordinates relative to 

 the cell 000, 



a;— pi, y = ql, z-rl. 



With any cell pqr we associate three coordinates g pqri 

 Vpqr, Inn and the three corresponding velocities j; pqr , r} pgr , £ pqr . 

 We examine the motion of the system of which the energy 

 function is given by 



+ ~jj [(&,« + !■<— Ip.l.r — Vp,i,,<-+1+Vp,<,,r) 2 +(.■■)'+ {■■■y~\ j- 



. . . (29) 



This function E is of course identical with the Hamiltonian 

 function L' of § 8, so that the equations of motion of the 

 system can be written down at once (cf. equations (5)). 



