﻿172 Lorentz 9 s Theory of Long Wave Radiation. 



kinetic principles. The method followed by Thomson is 

 analogous to that of Lorentz, but it avoids the probability 

 considerations involved in that author's theory. He views, 

 with Lorentz, the radiation as a result o£ the changes of 

 velocity produced in the collisions of the electrons against 

 the molecules, and he concludes that the manner in which 

 these changes take place must, as stated above, ultimately be 

 of influence on the final formula for the radiation. Assuming, 

 then, as possible arbitrary types of acceleration of an electron 

 during a collision functions of the time of the form 



(I-) A."*, (II.) —j? 



in which A and a are constants, he arrives at forms of 

 F(X, T) of the following types respectively, 



(I.) F(X,T)=55gj-« -sr, 



(II.) F(X,T)=^<V^, 

 which give for the total energy radiated respectively 

 (I.) — j o e ^-—^ e *>dx, 



9 — -llTCX -. 



x"e ax. 



and 



Smuj C™ ~^d\_Smujr 

 C } 3 J e V 3a* J 



wherein each integral on the right we have written x=a/~k. 



Now in each of the two cases here illustrated the con- 

 stant a turns out to be approximately equal to the time of 

 duration of an encounter of an electron with an atom, so 

 that if we assume this time to be infinitely small both forms 

 of Thomson's theory agree in giving 



-H x > - 1 -) = — VT~ 



as the complete radiation formula all along the spectrum, but 

 in both cases the total energy is infinite of the order (1/rt 3 ). 

 It would thus appear, both from these two examples and 

 also from the more general case discussed above, that any 

 general theory which leads to the Rayleigh-Jeans formula 

 as the formula generally applicable all along the spectrum 

 must involve some assumption which essentially implies that 

 the total amount of energy radiated is infinite, so that it 



