X-Rays from Imperfect Crystals. 825 



However, from these data it is possible to get the numerical 

 values of E u / 1 for all values of u. It is found that the 

 approximation of (8*3) is quite accurate enough, and this 

 equation can be solved for (Jr(u). A quadrature then gives 

 Q'. The results are rather disappointing, for the curve A 

 gi^es Q' = -0119, while B gives Q' = '0146. Moreover, the 

 extinction coefficients g 2 Q? come out as l'Ol and 0*47 respec- 

 tive^, whereas values in the neighbourhood of 5 would have 

 been expected. The discrepancy is exactly the same as in the 

 evaluation of g 2 above. There it was found that the region 

 of reflexion ought to be narrower for the observed extinc- 

 tion, here that the observed reflexion curve implies less 

 extinction than is in fact found. It is, of course, possible 

 that a part of the difference between A and B may be due to 

 a difference of their primary extinctions, and the cause 

 suggested at the end of § 7 may be another source of 

 discrepancy. 



Finally, our results may be applied to some experiments 

 due to Davis and Stempel *. Here the perfection of the 

 calcite crystal was enormously greater than in Bragg's rock- 

 salt, and all the approximations are hopelessly wrong. If, 

 nevertheless, we apply our formulae to the actual curves we 

 may obtain something of an idea of the perfection of the 

 crystal. The data are directly in terms of E M /I. They 

 were dealing with white X-rays, but there was double 

 reflexion in two crystals with parallel faces and it is easy 

 to see that dispersion will play no part, so that the formulae 

 for monochromatic rays are applicable. Taking the most 

 extreme case of all, their fig. 6 (p. 617), we use (7*6) to 

 obtain G(u) and from this we get a scatter a = ±"'§. Now 

 this is only a little greater than what should be the region of 

 complete reflexion in a perfect crystal, and the most remark- 

 able thing about it is that not more than half the incident 

 beam is reflected. This suggests that a part of the breadth 

 of the reflexion is really due to imperfection. It does not 

 appear worth while to carry further the comparison with 

 these experiments, both because our methods are not 

 applicable rigorously, and because there must certainly be 

 a great deal of primary extinction in crystals that are so 

 nearly perfect, so that they would be of little use in a 

 determination of Q. 



* Davis and Stempel, Phys. Rev. vol. xvii. p. 608 (1921). 



