﻿390 Mr. G. H. Livens on the Law of 



fundamental problem in radiation, we should again fail to 

 obtain anything like the definite radiation formula proposed 

 by Planck, but the result obtained- has now the additional 

 advantage of being extremely indefinite. This indefiniteness 

 is, however, not very surprising seeing that we know so 

 little about the dynamics of the system concerned in radia- 

 tion phenomena, and are therefore quite at a loss to determine 

 anything about the constants « r tentatively introduced in 

 the above analysis, or even the total number m r of the co- 

 ordinates of any particular type. We do know, however, 

 that for instance the possible vibrations, each of which pre- 

 sumably corresponds to a degree of freedom, of the type 

 specified by the fact that the radiation from it has a wave- 

 length lying in the infinitely small range between \ and 

 X-f d\, are infinite in number, but such knowledge is, under 

 the present circumstances, worse than useless. 



We are not, however, prevented from obtaining further 

 information on this subject because there are still two 

 methods of attack open to us. The first, or Planck's method, 

 has been fully discussed in a previous paper, and the con- 

 clusion to be drawn from it is identical with that drawn in 

 the previous paragraph, unless it is preferred to retain in the 

 analysis the hypotheses of a finite limiting ratio between 

 the elements of energy and extent of the elementary cells 

 which form the bases for the application of: the probability 

 calculus, in which case it is possible to obtain Planck's 

 formula. The suggestion that Planck's formula essentially 

 involves an assumption of this kind and nothing else, is due 

 to Larmor*, but I am not yet aware of any plausible 

 physical reason for it t ; some such assumption is, however, 

 necessitated by the requirements of definiteness in the 

 ultimate formula, and it is not inconsistent with any of our 

 usual stock of ideas, so that for the present, at least, some- 

 thing will be gained by retaining it. 



There is yet another method of attack still open and this 

 is the converse one followed by Jeans, but, contrary to the 

 conclusion drawn by Jeans from his work, I cannot agree 

 that anything very definite can be got out of it. The method, 

 exactly reverses the argument of Planck and starts with the 

 assumption that his formula is correct. Let us therefore 

 assume that in any given system in thermal equilibrium the 



* Proc. Roy. Soc. vol. lxxxiii. 19G9. 



t I should like to take this opportunity of applying a reservation to 

 certain remarks bearing on this question which were made in my previous 

 paper. On due consideration of the various possibilities I think it will 

 be difficult to avoid Larnior's suggestion, even if we cannot find a 

 good reason for it. 



