X-Rays from Imperfect Crystals. 803 



radiation — that in which the crystal turns during the expe- 

 riment with a constant angular velocity, so as to integrate the 

 effect o£ the crystal. His results were substantially the same 

 as those of! the present writer, though naturally in a form 

 more convenient for comparison with recent experiments. 

 From a mathematical point of view his method has the 

 advantage that he had no need to consider Fresnel integrals, 

 whereas in my method they were necessary in order to 

 secure convergence. I think the identity of results depends 

 on the fact that if an integral nearly converges, and is made 

 to converge by the introduction of a slight convergency 

 factor, then the consequent value is independent of the 

 form of that factor. My factor was the Fresnel term, 

 Compton made his expression converge by cutting it off 

 at the end. As the present paper deals only with small 

 crystals, the case will be analogous to Compton's, the con- 

 vergence will be assured, and therefore no use will be made 

 of the Fresnel terms. 



The same reflexion formula is worked out in B.J.B.i. It 

 is designed to meet the exact requirements of the work, and, 

 though implicitly using the Fresnel integrals, it is free 

 from much of the mathematical complication of the earlier 

 derivations. 



3. General Exposition of the Problem, 



The imperfection of crystals ma}' take either of two forms, 

 warping or cracking. Either the atoms may be arranged on 

 surfaces which are not quite flat, or else they may be arranged 

 in blocks, each block a perfect crystal, but adjacent blocks 

 not accurately fitted together. An examination of the sur- 

 faces of rock-salt crystals suggests that the first is probably 

 more the nature of its imperfection, but the second is 

 much more tractable to mathematics and so has been adopted 

 here. 



The whole question turns on the phenomenon of extinc- 

 tion, which may be roughly described as the diminution in 

 the reflected beam due to the fact that when one part of a 

 crystal has reflected some of the radiation, there is less for 

 the parts behind it to reflect. In Bragg's work observation 

 was made on the total ionization as the crystal turns through 

 the reflecting angle. Now, at each instant of the rotation 

 there will be a different amount reflected and therefore a 

 different extinction, and consequently it will not suffice to 

 treat of the mean effect of extinction, without first deter- 

 mining it at every setting of the crystal. As will be 



3 F 2 



