Theory of X- Ray Reflexion, 689 



of the electrons were crowded together in a region of the 

 order of 10 ~ 9 cm., and this they certainly will be for the 

 heavier elements. But if this is so there is a certain amount 

 of difficulty with regard to Bragg's second experimental 

 result. From measurements of crystals of a good many 

 substances, he concludes that on the average the relative 

 strengths of reflexion of the several orders for monochro- 

 matic radiation are as the numbers 100, 20, 7, 3, 1. After 

 allowing for the temperature corrections these numbers are 



fairly well expressed by the formula — 2 ; but since the 



radiation is not appreciably dispersed they are to be com- 

 pared not with (14) but with (13), and in this formula the 



reflexion is proportional to — . Thus, we must attribute a 



factor - to / 2 , the coefficient for the scattering of a single 



atom. Now we saw in the earlier paper* that f 2 will 

 certainly decrease with the order of reflexion, and the expres- 

 sion there found seems capable of accounting for the excess 

 scattering from amorphous substances, as in this case experi- 

 ments have only been concerned with light atoms where 

 there is no great concentration of electrons ; but when we 

 are dealing with heavier atoms we have seen that Bragg's 

 first result points to a considerable crowding of electrons 

 in a small space, and in this case it would hardly be expected 

 that the excess effect should be so great as to give a factor 



-. Involving as it does a knowledge of the arrangement of 



n ° 



the electrons in the atom, it does not seem possible at present 

 to make any better progress in discussing this question. 



Summary. 



The paper attempts a more accurate solution than was 

 given in the first part of the problem of X-ray reflexion, on 

 the basis of allowing for the mutual influences of the scattering- 

 atoms . 



(i.) It is shown that the mutual influences of the atoms in 

 a plane together are unimportant. 



(ii.) The interactions of the separate planes are allowed 

 for, and revised reflexion formulae are deduced. The re- 

 flexion is found to be practically perfect for a certain range 

 of angles. The transmitted beam is extinguished much 

 * Loc. cit. p. 329. 



