98 PROBLEM OF PARTITION OF ENERGY 



the expression (5) reduces to Ay~ l . Px~ 4 , which is the form 

 given by Rayleigh as applicable when Px is sufficiently large 

 while X is not too large. When X is very large with P not too 

 small, (5) takes the form Aa~ l . Px~ 5 . 



6. The distinction between energy transmitted by, and 

 energy stored in, definite freedoms is of fundamental import- 

 ance. The equation (4a) shows that there is not universal equi- 

 partition of the energy allotted to all freedoms except under 

 the condition that fir m is negligible relatively to a ; while, on 

 the other hand, there is equipartition universally amongst the 

 energies transmitted per unit of time if /3r m is large relatively 

 to a and small relatively to P. 



The ratio of the energy transmitted per unit of time per 

 degree of freedom to the energy stored in that freedom takes 

 here the place of the element of energy, and there is no limita- 

 tion upon its finitude. There is necessarily equipartition of 

 energy amongst all freedoms for which it has one and the same 

 value. 



WILLIAM PEDDIE 



