﻿56 Prof. G. A. Schott on the 



understand this better we must examine the energy relations 

 of the electron. 



From (11) we obtain by means of (18) and (33) 



T=cosh % -l=Ftf (31) 



This equation shows that the whole of the work done by 

 the external field is converted into kinetic energy of the 

 electron, just as if there had been no radiation at all. None 

 of it is radiated. 



Again, from (12) we find by means of (33) and (34) 



Q = T' = sinh x • X = FH = Ul • • • ( 35 ) 



Thus we see that the energy radiated by the electron is 

 derived entirely from its acceleration energy ; there is as it 

 were an internal compensation amongst the different parts 

 of the radiation pressure, which causes its resultant effect to 

 vanish. 



The total energy radiated is on the present hypothesis 

 only a very small fraction of the kinetic energy, unless the 

 external force be exceptionally large. From (33) ... (35) we 

 find by means of (18) 



Rt Fsinh % / lH-*/( l-t 2 ) 



T - cosh x- IV 1-4/(1- v 2 )' 



(36) 



In applying this equation we must bear in mind that we 

 are using the new units of § 3 ; hence when we return to 

 C..G.S. units we must replace F by 2<? 2 F/3c 4 m 2 = 2e 3 X/3c 4 m 2 , 

 where X is the electric force in E.S.U. From the value of 

 the new unit of force given in § 3, viz. 4*3 . 10 6 dyne, and 

 that of e, viz. 4'65 . 10' 10 E.S.U., we find that F in (36) 

 is equal to 1*08. 10" 14 , and that R^/T is about 4*03 . 10" 14 

 when X is 30,000 volt/cm. and v or ft is 0*5. 



9. In order to test the truth of the hypothesis of § 3 we 

 must examine what happens when it fails. Still confining 

 our attention to the case of an electron moving in a uniform 

 electric field along the line of motion, let us return to equa- 

 tions (18) and (23) ... (25), which are true quite independently 

 of the hypothesis in question. Bearing in mind that F as 

 well as B is a constant, we see that we may write instead 

 of (28) 



B=F(l4-S), (37) 



where 8 is another constant, i. e. a quantity independent ot 

 X or v, but generally a function of F. We may regard 8 as 

 a measure of the deviation of our hypothesis from the truth. 



