﻿Distribution of Electrons in Na and CI Atoms. 447 



X-rays suffer an increased absorption, because a certain 

 fraction of the particles are so set as to reflect them and 

 divert their energy. We made allowance for this type of 

 extinction in our work, and Darwin concludes that our 

 method of allowance, while not rigorously accurate mathe- 

 matically, was sufficiently so for practical purposes. 



Primary extinction arises in another way. The homo- 

 geneous crystals may be so large that, when set at the 

 reflecting angle, extinction in each crystal element shelters 

 the lower layers of that element from the X-rays. Darwin 

 has calculated that this will take place to an appreciable 

 extent for the (100) reflexion if the homogeneous element 

 is more than a few thousand planes in depth. A large 

 homogeneous element such as this does not produce an 

 effect proportional to its volume, since its lower layers are 

 ineffective, and a crystal composed of such elements would 

 give too weak a reflexion. Our method of allowing for 

 extinction will not obviate this effect. 



We cannot be sure, therefore, that we have obtained a 

 true measure of Q for the strong reflexions. The F curve 

 may be too low at small angles. It is just here that its form 

 is of the highest importance in making deductions as to 

 atomic structure. Until this important question of the size 

 of the homogeneous elements has been settled, we must 

 regard our results as provisional. 



(c) The allowance for the thermal agitation of the atom 

 (the Debye factor) is only approximate ; it depends on a few 

 measurements made by W. H. Bragg in 1914. In order to 

 see how much error is caused by our lack of knowledge of 

 the Debye factor, we have calculated the electron distribution 

 without making any allowance for it. The result may appear 

 at first rather surprising ; the electron distribution so calcu- 

 lated is almost indistinguishable from that which we found 

 before, when allowance for the Debye factor had been made. 

 This is so, although the factor is very appreciable for the 

 higher orders of spectra, reducing them at ordinary tem- 

 peratures to less than half the theoretical value at absolute 

 zero. The difference which the factor makes can best be 

 shown by comparing the radii of the shells which give the 

 best fit with (1) the F curve deduced directly from the expe- 

 rimental results, (2) the F curve to which the Debye factor 

 has been applied. 



