34 
Proceedings of the Royal Society of Edinburgh. [Sess. 
V. — The Absorption of X-Rays. By Dr R. A. Houstoun, Lecturer 
on Physical Optics in the University of Glasgow. 
(MS. received April 19, 1919. Read June 2, 1919. Revised MS. received October 14, 1919.) 
§ 1. Let us suppose that a light wave is being propagated and absorbed 
in a homogeneous medium. Take OY as the direction of propagation, and 
consider a slice of the medium bounded by two planes at right angles to 
the direction of propagation and distant dy apart; dy is small in com- 
parison with the wave-length. Let x=f(t) denote the mean displacement 
of the electrons, and let X = A cos gt denote the electric intensity of the light 
wave in the slice, measured in electrostatic units. Then the average rate 
at which work is being done on an electron is 
-Xe^ = - A ef\t) cos gt. 
Let there be N electrons per unit volume. Then if a portion of the slice of 
unit cross-sectional area is considered, the average rate at which work is 
done in it in time r is 
NAecfyD /x 
— — — — I / ( t ) cos gt dt. 
The average rate at which energy flows through unit area is by Poynting’s 
theorem ci/A 2 /8tt, where c is the velocity of light in vacuo and v the 
index of refraction, provided that the absorption is small. Hence if 
E = E 0 e" 4mc!//X represents the rate of diminution of energy in the wa ve 
where A is the wave-length in vacuo , the average value of k during r is 
given by 
4:7TK 8 7rYe [ T .. . . 
— =-^l)/^ cos ^ dt ••••(!) 
Let us suppose that the electrons are subject to an equation of the type 
d 2 x dx 
m ~d^ + (dt Jr f x= ~ cos 
and that the free vibrations have died down. Then 
— Ae cos (gt - tan -1 hg[(f - mg 2 )) 
X ~ ((/- mg 2 ) 2 + h 2 g 2 y 
Differentiate x with respect to t, substitute the result for f'(t) in (1), and we 
obtain 
