140 PROCEEDINGS OF THE AMERICAN ACADEMY. 



the line is due only to the Doppler effect. Thus we may conclude 

 that in such cases, at least, the time required for an emission is really 

 quite considerable, and that Planck's assumption of practically in- 

 stantaneous emission must be abandoned. 



One way to evade this difficulty in the derivation of Planck's law is 

 to assume that the radiation takes place at a constant rate until the 

 whole energy, n h v, is emitted. This, however, is easier said than 

 done; and one would be strongly tempted to look for some other 

 radiation law, if Planck's had not been so well confirmed by direct 

 experiments, not only those quoted in his book (p. 169) but also those 

 published more recently by Coblentz, 8 and indirectly by the appear- 

 ance of his constant h is the laws of so many other phenomena, such as 

 specific heats and photo-electric effects. 



This constant rate of radiation cannot be obtained by making the 

 effect of the vibrating charge on the ether suddenly become some con- 

 stant multiple of that which the classical theory would give, because 

 it is well known that any such law would make the amplitude die out 

 exponentially, rather than linearly, and approach a finite value, 

 rather than zero. For the same reason, it cannot be obtained by 

 having the absorbed energy stored as potential energy of an electron 

 transferred from one equilibrium position in the atom to another, and 

 re-emitted when the electron is jarred out of the latter position and 

 falls back, with oscillations, into the former. Such models, moreover, 

 would also be open to the objection to Planck's oscillator, that, to give 

 a single quantum, they require too great an amplitude of vibration. 



Another serious difficulty for such models of the oscillator is the 

 fact that an essential point in the derivation of the law is the assump- 

 tion that an oscillator may acquire an amount of energy that is any 

 integral multiple of the quantum before it radiates. This applies, 

 for example, to Bohr's atom, in which the transition from one equili- 

 brium position to another makes the electron give out just one quan- 

 tum, and the transitions between all other such positions will give 

 different frequencies. 



Still another point where such models are apt to be insufficient is in 

 the explanation of photo-electric phenomena. For if, in the "lower" 

 equilibrium, the electron is in a region of positive potential, and in the 

 "higher" one it is either in such a region or removed to infinity, then, 

 when it escapes from the higher position, it will either not leave the 

 atom at all or else leave with an infinitesimal velocity. The only way 



8 Bull. Bur. Stan., Jan. 15 (1914). 



