Systems, and Planch* & Theory of Radiation. 

 this becomes 



W==Cj( ^FT L! (1G) 



where C is a constant. This is of course Planck's formula 

 obtained bj working backwards from Planck's law. What 

 is important is that (16) follows inevitably from (14) ; in 

 other words, formula (14) can only be true in a generalized 

 space in which the regions excluded are such that the 

 remaining volume is given by (16). Furthermore, the 

 necessity for an indivisible unit of energy follows inevitably 

 from (16), for Planck's assumption of this indivisible unit is 

 known to lead to formula (16), and there can be only one 

 way of distributing the fluid in the generalized space so that 

 W is a given function of E for all values of E. 



The analysis has, however, shown that the truth of Planck's 

 law requires something more than appeared in Planck's 

 original papers. It is now apparent that it is not enough 

 to postulate systems of vibrators capable only of holding 

 definite multiples of a fixed unit of energy ; we see that the 

 energy in the aether itself must also be atomic. Moreover, 

 it is not sufficient that the energy should always in nature 

 occur in complete atoms ; what is required is that it should 

 be physically impossible to divide these atoms. For instance, 

 the requirements of this condition are not met by imagining 

 a system of radiators which always give off energy in 

 complete units ; we must also have an sether structure such 

 that no vibrations can possibly exist in it except in atomic 

 amounts. If it is agreed that these conditions do not hold 

 in nature, then we are driven to supposing that the state of 

 the aether represented by Planck's law is not a final steady 

 state, or in other words that there is not thermodynamicai 

 equilibrium between the matter and the different vibrations. 



13. In conclusion, it may be worth noting an alternative 

 method of arriving at Planck's law. 



Other things being equal, if a vibration can have energies 

 0, e, 2e, . . ., then the ratio of the probabilities of these events 

 as in the usual gas-theory calculations, is 



where A = 1/2RT ; or, replacing h by its value, 



1 : e~ e ^ T : e~ 2e ^ T (17) 



If out of N vibrations under consideration, M have zero 

 Phil. Mag. S. 6. Vol. 20. No. 120. Dec. 19.10. 3 R, 



