94 THE PROBLEM OF PARTITION OF 



partitioning of energy amongst wave-lengths which is expressed 

 by Planck's well-corroborated law. A third method, that of 

 Planck, locates the source of non-equipartition in the intrinsic 

 nature of energy itself, which is postulated to be atomic, the 

 ultimate unit being so large that it may only be manifested in 

 relation to many degrees of freedom, some freedoms absorbing 

 no units, others one unit, and so on. 



2. Planck's postulate has the merit of leading to a well- 

 supported expression for the distribution of energy amongst 

 the various wave-lengths in ' natural ' radiation ; it has the 

 possible demerit of necessitating discontinuities of motion on 

 molecular, atomic, or, at any rate, on ' freedomal ' scale. Yet 

 it may be that the seeming demerit is not real, the discontinu- 

 ities vanishing as a matter of statistics. 



Sir J. Larmor, in his recent Bakerian Lecture (Proc. R.S., 

 1909, vol. Ixxxiii.), modifies and amplifies Planck's treatment 

 in such a way as to get rid of the assumption of the finitely 

 atomic nature of energy. Indivisibility of an element of 

 energy is replaced by an unalterable ratio of the element of 

 energy of any one type to the extent of a ' cell,' of correspond- 

 ing type, in which that element is contained. The actual 

 element itself may be infinitesimal, so motional discontinu- 

 ities become infinitesimal. A ' cell ' replaces the ' degree 

 of freedom ' of the previous treatment, and each cell is of 

 equal opportunity or extent as regards an element of disturb- 

 ance, which may pass from one cell to another of a different 

 type, the amount of energy associated with it being possibly 

 altered in the process. Thus in analogy with the passage of 

 heat energy in diminished (or increased) amount from a region 

 of high to one of low temperature (or conversely), in association 

 with the necessary performance (or absorption) of external 

 work we have the transformation of radiation from one 

 wave-length to another in association with the performance 

 or absorption of work. These postulates lead to Planck's law, 

 the constants only having important modifications of meaning. 



