952 Prof. J. II. Jeans on Non-Newtonian Mechanical 



of matter and aether may be from the standard form, yet 

 when the matter is made to diminish indefinitely in amount, 

 we may sup; ose, without any loss of generality, that the 

 equations of wave-motion are of the standard form, and that 

 the co-ordinates Q, R are the Lagrangian co-ordinates and 

 momenta. Equipartition of: energy follows as a direct 

 consequence. 



12. In the genera] analysis of §7 it was assumed that the 

 whole of the generalized space was Idled with fluid. The 

 fluid must, however, be excluded from any parts which 

 represent physically impossible configurations, and if these 

 parts are of sufficient extent, the exclusion of fluid may affect 

 the final result. Let us examine whether any arrangement 

 of fluid can be found which shall so modify the result as to 

 change the law of equipartition into the widely different law 

 of Planck. 



Lei u- consider X vibrations having Erequencies differing 

 only infinitesimally from 'lirv. Their total energy E must, 

 ling to Planck's law, lie given by 



■-ii5=] m 



where h is Planck's constant. Eliminating the temperature 

 her wren .-his and equation (6), which is true no matter what 

 parts of the generalized .-pace are excluded, we obtain 



as i * f^^^\ 



5B = T = cM 14 ST7" 



This gives on integration 



4 terms arising from the other vibrations. . (15) 



Let W be proportional to the volume of that region of the 

 generalized space (less the excluded parts) in which E lies 

 between E— J-e and E-f ~e. 



On comparison of equations (4) and (15) we have 



i xkt /at E\, / xt E\ E, E , 



If we write P for E///v, and use Stirling's approximation, 



