676 Mr. 0. G. Darwin on the 



of atoms in a plane. Let 6 be the glancing angle between 

 the direction of incidence and the plane. Then* 



_Mo/(2M) 

 q ~ ksm0 ...... U; 



As long as the atoms are supposed not to influence one 

 another's motion, every plane however deep in the crystal 

 scatters the same amount of radiation, and if no allowance 

 were made for the absorption of the transmitted wave the 

 reflexion would become indefinitely large. Now an atom in 

 rocksalt may be supposed to have about 10 electrons, and so 



/ is probably about 10 ~\. Taking N = 4'50 x 10 22 , 



a = 2'81xl0~ 8 and reflexion in the first order so that 

 k sin = 7r/a, we find that q is about 2 x 10" 4 . According to 

 the assumptions of the earlier paper, the amplitude of the 

 wave is reduced by absorption in passing through one plane 

 by an amount \pa cosec 0, and for soft X-rays this is 1 x 10 ~ 6 . 

 Thus we should expect reflexion to be much more efficient 

 than absorption in extinguishing the transmitted wave. 

 Indeed, we shall find that over a certain small range of 

 angles of incidence the reflexion is practically complete and 

 does not depend on the absorption coefficient. 



In the earlier paper the coefficient of reflexion q was cal- 

 culated by considering a spherical wave coming from a point 

 source. In view of the greater complexity of the present 

 problem it is more convenient to deal with plane waves, and 

 we must therefore first observe that the evaluation of q could 

 have been done equally well with these. It is only necessary 

 to find the amplitude of reflexion at a point so distant from 

 the crystal, that in the principal part of the field the phases 

 of waves from adjacent atoms are sensibly the same — 

 this permits the summation to be replaced by an integration 

 — while yet the point is not so distant that the crystal has to 

 be regarded as finite — this introduces the Fresnel factors in 

 the integral and makes it converge. There can be little 

 doubt that the procedure gives the right value, though it is 

 not of course mathematically rigorous. It has the great 

 advantage that the formulae do not involve the exact number 

 of atoms in the whole plane, which is obviously quite 

 irrelevant to the final results. 



The formula for q cannot be quite general, if /is supposed 

 to depend only on the atom itself. For we might then make 



* Loc. cit. pp. 319-320. 

 t Loc. cit. pp. 326-329. 



