Degradation of Gamma-Ray Energy. 765 



shown that for an electron whose acceleration is unpolarized 

 relative to the observer *, and which is travelling at a 

 velocity /30, the mean square of the electric vector at a great 

 distance r is t 



e 2 F' 2 

 E 2 



167T 2 CV 2 



( l-Bcos0) 2 -i(l-l3 2 )sm 2 + ±cos0(2j3-cos 0-/3 2 cos0) 



(l-/3cos0) 6 ' {o) 



where V 2 is the mean square of the acceleration relative to 

 the observer at the moment the pulse under observation left 

 the electron, e is the charge of the oscillator^ C is the 

 velocity of light, and is the angle between the direction of 

 motion of the particle and the observed beam. Thus the 

 ratio of the intensity of the radiation at an angle 0i to that 

 at an angle 2 * s given by the expression 



Ii __ f l~-/3cosflo | 6 (l-/3cos^) 2 -i(l-/3 2 )sin 2 fl 1 

 I 2 ~ \l-/3cos^i (l_/5cos6> 2 ) 2 -i(l-ye 2 )sin 2 ^ 2 



+ Icqs0 1 (2@- cosfl 1 -/3 2 cos6> 1 ) 



+ ^cos# 2 (2/3-cos6' 2 -/3 2 cos0 2 )' W 



Assuming that all the radiating particles are moving in 

 the same direction, the ratio of the intensity of the fluores- 

 cent radiation at the angle 45° to that at 135° has been 

 calculated from this expression, with the results shown in 

 figure 2. It will be seen that it is possible on this view to 

 account for any reasonable degree of asymmetry of the 

 secondary radiation. In the case of paraffin, in which the 

 least scattering of the beta particles occurs, the observed 

 ratio of the intensities at 45° and 135° was about 20. In 

 addition to the effect of the scattering of the secondary beta 

 rays, experimental errors arise because much of the soft 

 radiation at 135° is absorbed before it enters the ionization 

 chamber, while a considerable part of the hard radiation at 

 45° traverses the ionization chamber without being absorbed. 

 The rapid increase of R with/9, however, makes it reasonably 

 certain, on the present view, that the average speed of the 

 oscillators which emit the secondary gamma radiation does 

 not differ greatly from half the speed of light. 



* Of course such an oscillator will not be unpolarized relative to an 

 observer moving with it. A slight polarization will not, however, make 

 any great difference in the value of the ratio (4). 



f The values of the three components of the electric vector from 

 which this expression is derived may be found, e,g. in 0. W. Richardson's 

 1 Electron Theory,' p. 256. 



Phil Mag. S. 6. Vol. 41. No. 245. May 1921. 3 E 



