X-Rays from Imperfect Crystals, 817 



The extinction factor is perhaps more properly expressed in 

 terms of the depth of the block, rathe/ than the number of 

 its planes, because this will be roughly the same in all direc- 

 tions and so will give rise to a formula suitable for comparing 

 reflexions of different faces of the crystal. Then the 

 extinction factor is 



tanh x /2Qd 2 cot 0/\ 

 \/2Qd 2 cot 0/A, 



1 2 Qd 2 cot 6 t 8 Q 2 ^cot 2 „,„ N 



= 1 ~3— ^-+15 — V (6 ' l0) 



Considering the numerical values in Bragg's experiments, 

 it appears that for a block two thousand layers thick the 

 correction will be about 5 per cent. 



Thus we see that a conglomerate of crystals of size d will 

 give rise to a Q modified by the extinction factor (6'15). 

 This modification is the primary extinction, and as we shall 

 see it is untouched by Bragg's method of eliminating extinc- 

 tion. The secondary extinction arises in considering the 

 action of the transmitted beam on the lower blocks. It may 

 be calculated by allowing for the ordinary absorption of the 

 incident beam and in addition subtracting from it the amount 

 of the reflexion. As this last depends on Q' the secondary 

 extinction will do so too. 



7. Reflexion from a Face. 



Now consider what happens when a beam strikes the face 

 of a thick conglomerate at any angle near the angle of 

 reflexion. Imagine the conglomerate divided into successive 

 layers. In the first layer it will find a few blocks rightly 

 placed, and from each of these a ray will be reflected. In 

 § 6 we saw that extinction would reduce the intensity of the 

 transmitted beam by an amount equal to the intensity of 

 the reflected beam. After traversing the first layer the 

 beam will thus be defective in a few patches, where par- 

 ticular blocks have been able to extinguish it ; but in 

 considering the effect of many layers it will be correct to 

 average the intensity after traversing each and so treat it as 

 uniform for the next. To obtain the power transmitted 

 through a single layer, we shall therefore take the power 

 reflected by it, subtract it from the incident and reduce the 

 result by an amount given by the ordinary absorption. 



The whole reflexion from a deep crystal results from the 

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



