49 
1919-20.] Note on the Scattering of X-Rays. 
Let 
cfix 
m-—- +fx= -eA cos gt . 
at 2 
• (7) 
represent the equation of motion of the electron under the influence of 
the impressed wave. Assume that the vibration is forced. Then 
6-A_ 
x = - . s cos gt. 
f-mg 2 
If we apply the usual formula for a Hertzian doublet, the rate of 
radiation from this electron is found to be 
o 4 c e 4 A 2 
3 (f-mg 2 )* 
By means of Poynting’s theorem the amount of energy flowing through 
unit area in unit time is cA 2 /8tt, where A is measured electrostatically. 
Hence the fraction radiated is 
eV 
87 r 
3 (/-mg 2 ) 2 
If there are N electrons per unit volume, the fraction radiated becomes N 
times as great. Hence, if E = E 0 e _7t2/ represents the diminution of energy 
in the wave, 
Ne-y 
3 (f-mg 2 ) 2 
8tt Ne 4 
3 
(8) 
1- 
X 2 
where A 0 is the wave-length of the free vibration of the electron. This 
expression reduces to the usual formula when A 2 /^ 0 2 * s small in comparison 
with I. This assumption is justified for the regions of the spectrum 
in which the scattering has been investigated. 
It has been assumed above for simplicity that all the electrons in the 
atom have the same free period. If each electron has its own free period, 
a 2 must be prefixed to the expression in (8) and the summation taken 
over all the electrons in the atom ; N is then the number of atoms per 
unit volume. According to my paper on the absorption of X-rays, there is 
one K electron in each atom which vibrates about a position of equilibrium 
in the atom, its period coinciding with the period of the K absorption band. 
As we approach the K absorption band from the side of shorter wave- 
lengths, the A 2 in the denominator of (8) increases and the denominator 
decreases in value. Consequently the scattering due to this electron 
should increase. As a matter of fact, the scattering increases as we 
VOL. XL. 4 
