Scattering of Rontgen Radiation. 235 



of the excess radiation is the same as that of the primary 

 from which it is produced. 



" (4) If Efl8# is the intensity of the excess radiation between 

 the angles 6 and 6 + h6 with the primary beam 



E^^f Ee-* 2 / 6 0$0, 

 o 



where E is the whole intensity of the excess radiation round 

 the radiator, and b is a constant depending only on the 

 quality of the primary beam and the substance of the radiator. 



w * (5) The value of 6 decreases as the primary beam becomes 

 harder, and increases with the atomic weight of the radiator. 

 It is independent of the thickness of the radiator," 



In Mr. Crowther's first paper these effects were explained 

 by the hypothesis that each molecule refracted part of the 

 rays falling on it through a certain small angle, and the dis- 

 tribution of the excess radiation was shown to agree with the 

 distribution calculated on this hypothesis by Prof. Thomson. 

 But in the second paper another explanation, on the basis of 

 radiation from the stoppage of secondary cathode particles, 

 was put forward. 



The purpose of the present paper is to revise the original 

 formula without the hypothesis that each electron scatters 

 energy exactly as if it were alone, and to show how the 

 re-enforcement of the radiation from one electron by that 

 from another may produce the " excess radiation " that 

 Mr. Crowther has observed. 



For this purpose, we may first consider a single, polarized, 

 primary pulse, specified by the formula 



H.=*E.=0, E y =E f(^y • • . (1) 



where t is the time, considered equal to the distance light has 

 gone since the time t = 0. Let f{s) be zero except in the 

 interval — ^<s< +i, over which the average value of its 

 square is 1, so that E is the square root of the mean square 

 of Ey. Let there be n electrons per unit volume in the 

 radiator, each with a <harp;e e and mass m * ; and let the 

 origin of coordinates be the position of one of the electrons 

 at the time t = 0. 



At the point r, 0, , in the x, z plane, where r is very large 



compared with the distance of any electron in the radiator 



* It must be noticed here that with the time unit used in this paper, 

 to make force equal to mass times acceleration, the mass of any body 

 must be c 2 times the mass in units in which the velocity of light is C. 



R2 



