1919-20.] Note on the Scattering of X-Rays. 
43 
VI. — Note on the Scattering 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 October 14, 1919.) 
§ 1. The scattering of X-rays is one of the most promising methods 
of approaching the constitution of the atom. Sir J. J. Thomson’s theory 
undoubtedly gives the main features of the phenomenon. But there are 
certain facts, namely : 
(i) the increase of scattering with heavy elements for soft rays, 
(ii) the extra-radiation, and 
(iii) the low value of the scattering coefficient for y-rays, 
for which it affords no explanation. It seems worth while trying to extend 
the theory so as to cover these facts also. 
Professor Barkla has suggested that (i) is to be explained by interference 
between the different electrons of the atom, by the atom scattering as a 
whole in the case of the longer wave-lengths. We shall formulate this idea 
mathematically. 
Let us suppose there are n electrons in the atom, and let P denote 
the position of one of them. Take an origin O in the atom, say at its 
centroid, and let a homogeneous radiation be incident in direction ZO. 
The intensity of the radiation scattered by the n electrons is required 
in the direction OQ. Let L ZOQ = 0. P is generally not in the plane 
ZOQ. The intensity of the radiation scattered by a single electron in 
the direction OQ is, in the usual notation, I,/ 2 (l +cos 2 0). 
The length of the actual path taken by the ray HPG varies with the 
position of P. We shall specify it by its difference from the path ZOQ. 
Draw PM perpendicular to ZO and PN perpendicular to OQ. The actual 
