webster. — planck's radiation formula. 143 



If now the radius of the magneton is about 10~ 9 cm, or 0.1 A, the 

 first two of these values are well within the limits of the possible 

 amplitude of vibration of the center of charge, while the last is com- 

 parable with the radius of the magneton, and therefore suggests the 

 possibility that the disturbance might result in the ejection of the 

 magneton as a thermion. From the form of the expression for £ one 

 would be led to infer that at lower v's this would happen at lower 

 temperatures. We must remember, however, that such speculations 

 are very untrustworthy, because this formula (6) is developed on the 

 hypothesis that the vibration is not disturbed by molecular motions — 

 a hypothesis which we have seen to be incorrect even at the 6000 A, 

 which we have just considered. Hence we may infer that the ampli- 

 tudes required here are probably within the possibilities of this 

 mechanism, and that the results noted above point to a qualitative 

 explanation of the emission of electrons by hot bodies. 



A priori, this mechanism does not seem so good as some scheme for 

 obtaining the quantum from the dimensions and charges of different 

 parts of an atom. Its justification, however, lies in its ability to cor- 

 relate experimental facts which are inconsistent with these other 

 schemes. 



First, by means of this mechanism, we may account for Planck's 

 law of radiation, which, as we have seen, is not given by atomic models 

 in which the atom can hold only a definite number of quanta. 



Second, these assumptions do not, like Planck's, appear to be incon- 

 sistent with observed path differences in interference experiments, or 

 known magnitudes of atoms. 



Third, the magneton has been found by Parson n to be very efficient 

 in explaining not only the periodic table of the elements, but even 

 many of the exceptions to the laws indicated by this table. 



Fourth, since it makes the emission of a quantum take the form of a 

 very energetic oscillation, it gives a good chance for thermal emission 

 of corpuscles, and, at low frequencies, for the interaction between col- 

 liding molecules that is necessary for the interchange of energy be- 

 tween heat and light, or in the absence of collisions for the flourescence 

 of very rarified gases. 12 Moreover, since the amplitude is not 

 dependent on certain equilibrium positions, as in most atomic models 

 giving quanta, these assumptions can give an account of the photo- 

 electric and photo-chemical phenomena at higher frequencies. 



11 1. c. 



12 For a discussion of this point, see Phys. Rev. N. S. 4, 177-94 (1914). 



