772 Prof. A. H. Compton on the 



scattered at an angle 6 with the primary heam whose intensity 

 is I is *, 



. fItt . 01 



IiSS 



Lx- wsin 2j 



where X is the wave-length and I x is the intensity of the rays 

 scattered by a single electron. This expression supposes 

 that the forces holding the electrons in position are negligible 

 in comparison with the forces due to the traversing radiation — 

 an hypothesis supported by experiments on the scattering of 

 X-rays. If p mn . ds is the probability that the distance s mn 

 will lie between s and s -f ds, the average value of the intensity 

 for all possible arrangements of the electrons in the atoms is, 



• r s5n °i 2 i i 



- . 4-7T S mn 



J e = *' ? ?J sind/2 , P™ ds * 



or 



i- 9 =F(N, P , s in^/2/\). 



Since for any particular atom the quantities N and p remain 

 constant, for an atom of atomic number N this ratio may be 

 written, 



T f) 



F f-=^(sin I ,a). 



If the quantitjr sin (6/2)/\ is sufficiently large, it will be 

 se^n that cO-operation in the scattering by different electrons 

 will be almost wholly a matter of chance, and the " excess 

 scattering" function -^ will become practically unity. On 

 the other hand, for very small values of this quantity co- 

 operation between the electrons will be almost complete and 

 the value of the function ^ will approach N. For inter- 

 mediate values of sin (0/2)/\ the function will have a different 

 value for every atom, since for no two atoms will the 

 probabilities p mn be identical. The experimental values of 

 ^=I e /Ii . N for different materials, as measured by Barkla 

 and Dunlop f, together with the values calculated for certain 



* P. Debye, Ann. d. Phys. xlvi. p. 809 (1915). 



t Bavkla'and Dunlop, Phil. Mag. xxxvii. p. 222 (1916). 



