138 PROCEEDINGS OF THE AMERICAN ACADEMY. 



be constant. This result, which is attained in Planck's theory by the 

 prohibition of all re-radiation or external influences, is quite necessary 

 for the derivation of his law. 



This accumulation of energy, moreover, must continue until the 

 energy stored in the oscillator reaches some integral multiple of h v, 

 so that even at the shortest wave lengths or lowest temperatures it 

 must always be able to attain the value h v at least. At longer wave 

 lengths or higher temperatures, the oscillator will accumulate many 

 quanta. It is, therefore, important to see how this energy will affect 

 its properties. 



If the oscillator is the classical electron, 5 the energy must all be 

 stored in its vibration, so that for an amplitude £o to hold a quantum, 

 we must have the energy 



l , y , , h COO 



2 ZTV 



or 



\ 2 7T m c 



This value, being proportional to VX, will be greatest for the longest 

 waves for which the oscillator may safely be assumed to be an electron 

 in a non-vibrating atom. Since the values of the Zeeman separations 

 lead to this assumption certainly throughout the visible spectrum, we 

 may apply this forumla for X = 8000 A finding 



£o = 3.1 A. 



Comparing this with the distance between carbon atoms in diamond, 

 found by W. H. and W. L. Bragg 6 to be 1.52 A, we find that the length 

 of the whole vibration would have to be over four times the diameter 

 of the atom. 



This is another serious difficulty in the way of Planck's theory. 

 For even if the oscillation consists of all the electrons in the atom mov- 

 ing together, so that the amplitude required is reduced in proportion 

 to the square root of their number, the distance which the group may 

 go before some of them get outside the atom is also greatly reduced. 

 Moreover if the positive sphere is not absolutely uniform in density, 

 the distance they can go before the frequency of vibration is changed 

 is even less. 



5 Planck does not specify the charge or mass of the oscillator: this paragraph 

 therefore starts with the most plausible assumption as to its nature. 



6 Nature 91, 557 (1913). 



