384 



Distribution of Scattered Rontgen Radiation . 



plane for the point considered. The area of such a zone is 

 inversely proportional to cos i. Hence the energy per sq. cm. 

 in the reflected rays is inversely proportional to cos 2 i. The 

 total energy in the reflected ray is therefore inversely pro- 

 portional to cos i and also directly proportional to the intensity 

 of the radiation from a single electron. The intensity of the 

 radiation to be expected from a body entirely composed of 

 small crystals orientated at random is therefore, since 6 = 2i, 



LI 



I fl = ± 



cos 2 <9 



cos 0/2 ' 



this makes 1^ 



When 9 is nearly equal to it this makes Iq very large. 

 However, in this case the Fresnel's zones will be too large 

 to be included in the planes in the crystals, so that the energy 

 will not increase further after 6 reaches a value near to it. 



Even in the amorphous parts of the metal it will be pos- 

 sible to draw small planes each containing a number of 

 electrons, so that we should expect the scattered radiation 

 from the amorphous part not to follow exactly the law 

 I = I 9O (l + cos 2 #), but in the amorphous parts the planes 

 will contain very few electrons, so that in most cases they 

 will not be big enough to fill up several Fresnel's zones. 



We should therefore expect to be able to represent the 

 distribution of the scattered radiation except very near to 

 6 = rjr bv the formula 



I = A 



1 + cos 2 



-f B(l + cos 2 <9), 



cos 0/2 



in which the first term represents the scattered radiation due 

 to crystals and the second that from electrons distributed at 

 random. 



The following table gives values of Iq/1qo calculated by 

 means of the equation just found and the values observed 

 by Crowther * for a thin plate of aluminium. 



9. 



Observed. 



Calculated. 



B=0. 



A=B. 







30 



60 



90 



120 



150 



i 



1-8 

 1-7 

 1-4 

 10 

 1-8 

 3-8 



1-4 



1-3 

 10 



1-0 

 1-8 



4-8 



1-7 

 1-5 

 11 



ro 



1-6 



3-5 



* Proc. Roy. Soc. A. vol. lxxxv. p. 40 (1911). 



