X-Rays from Imperfect Crystals. 801 



coefficient of the crystal is involved in the formula, and there 

 were indications that the actual absorption was a good deal 

 stronger than usual. This was especially the case in the 

 reflexions at small angles, and these small angles are par- 

 ticularly important, for by them is tested the truth of* the 

 hypothesis that in rock-salt the sodium atoms have passed 

 one electron over to the chlorine. The difficulty was over- 

 come— at any rate, partially — by finding the actual absorption 

 coefficients for the various directions in the crystal, by a 

 study of the reflexions of the internal planes of a set of 

 plates of rock-salt. But even this method has an unsatis- 

 factory feature ; for it was only possible to arrive at a definite 

 result by rejecting the observations from certain of the 

 plates. It is true that the discrepancy was explained by 

 the fact that these had had much rougher treatment 

 than the rest, but still it suggests a certain measure of 

 doubt as to the soundness of the method, or at any rate the 

 necessity for an inquiry into it. It appeared to me therefore 

 to be worth while to re-examine theoretically the reflexion 

 from crystals in general, in the hope of clearing up the 

 difficulties, and also in the hope that theory would indicate 

 some way of obviating them. The whole point evidently 

 lies in the imperfections of the crystals, and this introduces 

 many complications. I am afraid I have not succeeded in 

 welding the parts of the argument rigorously together, but 

 in spite of certain gaps in the theory it seems unlikely that 

 there is serious error in the general views to which it leads. 

 The work has been rather heavy, but the trouble will have 

 been justified, if it helps in determining the positions of the 

 electrons in the atom, one of the supremely important pro- 

 blems in the present condition of physics. 



There will be frequent occasion to refer to the two papers 

 of Bragg, James, and Bosanquet *. When mentioning them 

 in the text, I shall, for short, use only the name of the first 

 of the authors. The papers themselves will be called 

 B.J.B.i. and B.J.B.ii. Similarly, my own former papers f 

 will be denoted D.i. and D. ii. 



2. Previous Theories. 



The theory of the reflexion of X-rays by crystals was 

 discussed by the present writer in the papers D. i. and D. ii. 

 In D. i. it was assumed that each atom scattered X-rays just 

 as though it was alone, and the solution of this interference 



* Locc. citt. 

 t Locc. citt. 



Phil. Mag. S. 6. Vol. 43. No. 257. May 1922. 3 F 



