X-Rays from Imperfect Crystals. 805 



and amplitude will be the square root of intensity. In the 

 example above we should thus speak of the " reflected 

 power." This necessitates a slight alteration from Bragg's 

 terminology. He calls a certain quantity (of zero dimen- 

 sions) the "reflecting power." To avoid confusion we shall 

 here call it the " integrated reflexion." 



The course of the paper is as follows : — 



§ 4 treats of the reflexion from a small perfect crystal of 

 any shape and belonging to any of the crystal classes. In 

 § 5 there is found the reflexion from a conglomerate com- 

 posed of a large number of small crystals orientated nearly 

 in the same direction. In both these sections the crystals 

 are supposed so thin that absorption and extinction are 

 negligible. In § 6 there is a discussion of extinction. In 

 § 7 all the results are combined so as to give the reflexion 

 formula for a deep conglomerate, and in § 8 the same pro- 

 cesses are applied to reflexion through a plate — the method 

 of B.J.B.ii. In § 9 there is a short discussion of the rather 

 few experimental results by which the theory can be tested. 

 For the sake of completeness, the formula for reflexion 

 from a powder of crystals is worked out in § 10. The paper 

 concludes with a short general discussion and a summary. 



4. Reflexion from a Small Perfect Crystal. 



We shall first consider the reflexion from a single perfect 

 crystal which is so small that absorption and extinction may 

 be completely neglected. Apart from this condition there 

 is no restriction on its size or shape, and it may belong to 

 any of the crystal classes. Let it be divided into its funda- 

 mental lattice. Call the group of atoms in each element of 

 the lattice a molecule. We are not here concerned with 

 symmetry, and there is a certain amount of arbitrariness 

 about the choice of lattice and molecule. For example, in 

 rock-salt it is indifferent whether we take the face-centred 

 cubic lattice, with molecules composed of a sodium atom and 

 one of its chlorine neighbours, or the cubic lattice, containing 

 four atoms of each kind. According to the choice the 

 answer will take a different form, but it is an elementary 

 matter to reconcile the difference. 



Take an origin in the crystal, and draw the z axis perpen- 

 dicular to the planes of which the reflexion is to be studied. 

 Let xz be the plane of incidence of the rays, and let the 

 positive directions of x and z be away from the source. The 

 three primitive translations of the lattice may then be 

 taken as a x , a y , a; b X} fry, 0; Cx, c y , 0. The determinant of 



