﻿Distribution of Electrons in Na and CI Atoms. 437 



between his results and ours is accounted for by the extinction 

 or increased absorption of the rays at the reflecting angle. 

 Compton pointed out that the reflexion factor was of the 

 order to be expected from Darwin's formula, but did not 

 use the value he obtained to solve the electron-distribution 

 problem. 



3. For the sake of convenience of reference, the formula 

 which forms the basis of all the calculations is quoted below. 

 Let the intensity I of a beam of homogeneous X-rays, at a 

 given point, be defined as the total energy of radiation falling 

 per second on an area of one square centimetre at right 

 angles to the direction of the beam. If a crystal element of 

 volume dV, supposed to be so small that absorption of the 

 rays by the crystal is inappreciable, be placed so that it is 

 bathed by the X-rays, and if it is turned with angular 

 velocity co through the angle at which some plane in it 

 reflects the X-rays about an axis parallel to that plane, the 

 theoretical expression for the total quantity of energy of 

 radiation E reflected states that 



■^ = NV F «.4- 4 i±^.-B-n-»iV . (2) 



I sin 2d m 2 c 4 2 v ' 



= QdV. 

 In this expression 



N= Number of diffracting units per unit volume*. 



A, = Wave-length of X-rays. 



6 = Glancing angle at which reflexion takes place. 



e = Electronic charge. 



m = Electronic mass. 



c = Velocity of light. 



The factor e~ Bsm " (the Debye factor) represents the effect 

 of the thermal agitation of the atoms in reducing the 

 intensity of reflexion. 



The factor F depends on the number and arrangement of 

 the electrons in the diffracting unit. At = it would have 

 a maximum value equal to the total number of electrons in 

 the unit, and it falls off owing to interference as 6 increases. 



The experimental observations have as their object the 

 determination of Q in absolute units. In practice we cannot 

 use a single perfect crystal so small that absorption is 



* Xo account is taken here of the " structure factor." The diffracting 

 units are supposed to be spherically symmetrical as regards their 

 diffraction effects. 



