434 SCIENCE PROGRESS 



wave-lengths, and that the law of radiation given by Planck may 

 be a statement of the distribution of energy per wave-length in a 

 series of similar pulses which constitute the radiation, that is, 

 without actual wave motion. 



To test this idea, let^us take the case of two pulses follow- 

 ing each other in close succession, and let us assume, as is 

 generally done in connection with light pulses, that the com- 

 ponent pulses are equal and opposite. If we consider the effect 

 of the combined pulses at a point very distant from the source, 

 the predominant wave-lengths at the point belonging to the 

 positive and negative parts of the original disturbance will be 

 very nearly equal. Thus for the case of the long waves, the theory 

 of group-velocity indicates that the wave-length X,, and therefore 



k, varies very slowly with % and therefore 3- is nearly zero. 



Accordingly we may take as the expression representing the 

 displacement due to the combined pulse 



^ - k sin [k { x - tf(k)} ± zr] 

 U = d^ = V + 2irt{2f'(k) + kf"(k)} 



The energy corresponding to the region of wave-lengths from 

 X to X + S\, estimated exactly as in the case of a single pulse, 

 is now 



E8X = constant x k 2 Sk : or, E8X = constant x -n 



' A 4 



This is of course the law of radiation arrived at by Lord 

 Rayleigh by an application of the Boltzmann-Maxwell theorem 

 of partition of energy to the ether in a closed rectangular space 

 containing radiant energy. Again the result is true for any 

 form of pulse consisting of equal and opposite parts, as has been 

 proved by E. T. Whittaker in Monthly Notices, Astr. Soc, 1906. 

 The same note explains how, by an application of thermo- 

 dynamics, we can deduce from the above that the radiation of a 

 body at temperature T absolute is proportional to TX _4 S\. 

 Thus, so far, the pulse form of radiant energy satisfies the 

 requirements. It is impossible to proceed further without 

 introducing some speculation as to the mechanism of radiation. 



A prominent feature of modern doctrine with respect to the 

 mechanism of radiation is the idea that the emission of energy 

 takes place, not gradually, but in a statistically regular sequence 

 of finite and perhaps nearly equal quantities, or quanta ; and it 

 is suggested by some that the absorption of energy likewise 



