﻿434 Prof. W. L. Bragg and Messrs. James and Bosanquet : 



concentrated in a region whose dimensions were small com- 

 pared with the wave-length of the rays, then the resultant 



Z e 2 

 amplitude would be equal to ^ — ^ smce the scattered 



_tx Tnc 



wavelets would be in phase with each other in all directions. 



It is found experimentally that the measured amplitude 



tends to a value which is in agreement with the formula 



at small angles of scattering, but that at greater angles it 



falls to a very much smaller value. This is to be accounted 



for by the action of interference between the waves scattered 



by the electrons in an atom, which are distributed throughout 



a region whose dimensions are large compared with the 



X-ray wave-length. 



It is an easy matter to calculate the average amplitude 

 scattered in any direction by a given distribution of electrons 

 around the nucleus. Here we are attempting to solve the 

 reverse of this problem. The experimental results tell the 

 amplitude of the wave scattered by the sodium and chlorine 

 atoms through angles between 10° and 60°. We wish to 

 use these results in order to get some idea of the manner 

 in which the electrons are distributed. 



2. In addition to Darwin's original mathematical treat- 

 ment, the question of the effect on X-ray reflexion of the 

 distribution of electrons around the atom has been dealt 

 with by W. H. Bragg *, A. H. Compton f , and P. Debye 

 and P. Scherrerif. 



W. H. Bragg considered the interpretation of the diminu- 

 tion in the intensities of reflexion by a crystal as the 

 glancing angle is increased, due allowance being made for 

 the arrangement of the atoms. He concluded that "an 

 ample explanation of the rapid diminution of intensities 

 •is to be found in the highly probable hypothesis that the 

 scattering power of the atom is not localized at one central 

 point in each, but is distributed through the volume of the 

 atom." He did not regard the experimental data then 

 available as sufficient to justify making an estimate of the 

 distribution of the electrons. These data indicated that the 



intensity of reflexion fell off roughly as . 2 ~ (0 being 



the glancing angle), and he showed that a density of 

 distribution of the electrons could be postulated which 



* W. H. Bragg, Phil. Trans. Roy. Soc. Series A, vol. ccxv. 

 pp. 253-274, July 1915. 



t A. H. Compton, Phys. Rev. vol. ix. no. 1, Jan. 1917. 



t P. Debye and P. Scherrer, Phys, Zeit. pp. 474-483, July 1918. 



