661 Prof. W. Peddie on the 



in the case of even monatomic gases, make the fact of extreme 

 deviation from equipartition very evident. 



It is fully recognized that, in very many special cases, dyna- 

 mical freedoms may be entirely inoperative. So one way of 

 avoiding the difficulty consists in asserting that the special 

 freedoms made evident in radiational phenomena are inope- 

 rative in ordinary thermal phenomena. Such a mode is unsa- 

 tisfactory apart from the specification, by analogy at least, of an 

 appropriate mechanism ; for the doctrine of equipartition does 

 not permit mere partial inoperativeness — the inoperativeness 

 must be total. Another method, adopted by Jeans, consists in 

 regarding a final condition of statistical equilibrium between 

 matter and sether, with consequent equipartition of energy 

 amongst the freedoms, as unattainable in finite time ; so that 

 the practical " steady " conditions, which subsist in experi- 

 mental tests, and are the result of a steady supply of energy 

 in one form compensating an equal steady loss in another 

 form, give rise to that non-equable 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, 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 discon- 

 tinuities vanishing as a matter of statistics. 



Sir J. Larmor, in his recent Bakerian Lecture (Proc. P. 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 corre- 

 sponding type, in which that element is contained. The 

 actual element itself may be infinitesimal ; so motional dis- 

 continuities 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 disturbance, which may pass from one cell to another of a 

 different type, the amount of energy associated with it being 



