662 Mr. G. H. Livens on the 



6. Larmor' 9 s formulation of the fundamental problem*. 

 An interesting attempt has been made by Prof. Larmor 

 to generalise the basis of the ordinary theory of the con- 

 nexion between probability and entropy, and in applying 

 this generalization to the radiation problem as above he con- 

 cludes that the formula of Planck, although not necessarily 

 requiring an atomic structure for the energy itself, never- 

 theless implies a definite new quality in the radiation which 

 he interprets as a specification of a limiting value for the 

 ratio of the element of energy to extent of the cell reoarded 

 as the receptacle of the particular type of disturbance cor- 

 responding to the wave-length. The generalization he makes 

 involves the fact that in the usual formula 



S = *logW, 



connecting the entropy S and probability W of any state of 

 a system, the constant k, undoubtedly a function of the scale 

 of the statistics, must be of a different order of magnitude 

 for the molecular as opposed to the oscillatory degrees of 

 freedom. In fact, if we take k to be the usual constant for 

 the molecular coordinates, but of the form <xk for the oscil- 

 latory coordinates (a being ultimately zero), then we obtain 

 a formula for the average energy per unit volume in the 

 oscillations corresponding to the wave-lengths X? of the form 



which is again Planck's law if 



LtNx.«=Lt e J±°. 



e=0 €=0 a A * 



If, as Larmor assumes, ex. is constant, then N is also a con- 

 stant, and thus it is now e that is to be taken as different for 

 each type of oscillation (the opportunities or extents of each 

 type being the same), although there is still no limit to its 

 subdivision involved in the final form of the result. 



This view is in some respects analogous to that adopted 

 above, but is distinguished from it by the different physical 

 interpretation placed on the necessary restrictions implied in 

 the analytical discussion. On the present view it appears 

 that the various cells representing receptacles of energy are 

 of different opportunities for the occurrence of a specified 



* Bakerian Lecture, Proc. Roy. Soc. A. lxxxjii. pp. 82-95 (1909). 



