Scattering of Rontgen Radiation, 237 



I£ we knew the equation of this spheroid, we might now 

 calculate the volume, Y, that lies at the same time within the 

 spheroid and between the planes of equations (4). But any 

 accuracy in such a calculation would be worthless when com- 

 bined with the approximations already made, and a qualitative 

 analysis of the behaviour of V as a function of 6 is more 

 useful. 



As the thickness, T, of the primary pulse may be supposed 

 fairly small compared with any radius of the spheroid, at least 

 if the material is not too dense and n not too large, V may 



be considered as the product of the distance T/2 sin ~, between 



the planes by the mean area of the sections of the spheroid 

 parallel to the planes and included between them. Since 



Q 



the inclination of the planes to the x axis is ^, this mean area 



will be a maximum when 6 is 180°, and will decrease, slowly 

 at first, then more rapidly, as 6 decreases. But since the 

 thickness of the segment increases, slowly at first, and then 

 more rapidly, Y may change very slowly until 6 is fairly 

 small. At this stage of the process the rate of change of the 

 mean area will diminish, while the thickness continues to 

 increase faster than before. The volume will now begin 

 to increase and continue to do so until the whole spheroid is 

 included between the planes, and no further increase is 

 possible. 



From the experimental fact that the scattered radiations 

 are about as hard as the primary, we may be sure that, when 

 is large, Y must be small enough to contain rarely more 

 than one electron, or cluster of electrons, if they are in compact 

 clusters ; for if there were many electrons, or clusters, radiating 

 only slightly out of phase, the resultant radiation would 

 appear as a pulse thicker than the primary. If there are 

 such clusters, the charge, e, and mass, w, must be the charge 

 and mass of the whole cluster. 



In either case, if one such charge is known to be in the 

 volume Y, the probability of there being no other there 

 is e~ nY ; so that of all the secondary pulses scattered per unit 

 volume of the radiator, ne~ nY may be supposed to have 

 electric vectors specified by expression (2), and to scatter 

 energy per unit area at the distance r equal to 



+ 00 



Ef„ e -nTj[/(^] 2 rtt= EfT ne - v . . . (5) 



