WEBSTER. — PLANCK'S RADIATION FORMULA. 139 



If one could assume without conflict with measurements of the 

 Zeeman effect that the atom itself takes an appreciable part in the 

 motion at such frequencies, then the amplitude required for this 

 energy would be less than what we have found. In this case, however, 

 the electron would have to be able to distinguish carefully between 

 the part of the atom's energy that it could include in the quantum and 

 the part due to heat motions and vibrations with other frequencies. 



There is, furthermore, another difficulty caused by the fact that the 

 transfer of energy to heat motion of the molecules would increase 

 rapidly with the amplitude of the oscillator, so that the rate of increase 

 of the vibratory energy would diminish, rather than remain constant 

 as it must for Planck's law. 



These difficulties are all avoided by the magneton, because of its 

 storing its energy in its steady current, and thus making the oscillation, 

 as we have noted above, independent of the amount already stored. 

 The smallness of the increase of the steady current that is required 

 for this is evident from the fact that mc 2 , which gives the order of 

 magnitude of the magnetic energy, is 7.9 X 10~ 7 erg, while even at 

 lOOOA, where the oscillator practically never holds more than one 

 quantum, the quantum is only 2 X 10~ 11 erg. 



Another point that is as necessary for the derivation of Planck's 

 law as a satisfactory method of absorbing and storing the energy is a 

 satisfactory law of emission. For this Planck assumes p. 153, "that 

 the emission does not take place continuously, as does the absorption, 

 but that it occurs only at certain definite times, suddenly, in pulses, 

 and in particular we assume that the oscillator can emit only at the 

 moment when its energy of vibration, U, is an integral multiple » of the 

 quantum of energy, e = hv." 



Just how a sudden pulse can have a definite frequency is difficult 

 to imagine, and is not stated in his book. 



The experimental facts, moreover, are against the assumption that 

 the emission is absolutelv instantaneous. For Fabry and Buisson, 7 

 have found that the path difference for interference observable in 

 spectrum lines from the inert gases at low temperatures is often a very 

 considerable fraction of a meter, and in the case of Krypton, with the 

 tube immersed in liquid air, the path difference for wave length 5576 A 

 is 53 cm. or 950000 wave lengths. These path differences, moreover, 

 are given within the limits of experimental error by Schonrock's 

 formula derived from the kinetic theory, on the assumption that the 

 light of each oscillator is really monochromatic and that the width of 



7 C. R. 154, 1224-7 (1912;, or J. de Phys. 2, 5, 442-64 (1912). 



