822 Mr. C. a. Darwin on the Reflexion of 



preferred, and it would be expected that this greater value 

 would be associated with a greater scattering among the 

 blocks — that is, a broader region of reflexion. 



8. Reflexion through a Plate. 



To overcome the difficulty of the unknown extinction 

 Bragg «ent X-rays through a crystal plate and observed 

 the reflexion from the interior planes. In this case the 

 equations for the multiple reflexions take quite a different 

 form from (7*1). Suppose the crystal cut into layers 

 parallel to its faces, the breadth of a layer being Bx. 

 Let l u (x) be. the power of the incident beam at depth x 

 from the front face, E u (w) of the reflected beam. Let 

 B be the area of the face on which the rays fall. The 

 incident beam now makes angle 6 + u with the normal to B, 

 and so the intensity is I„ (x) / B cos (6 •+- it) . The power 

 reflected in the volume BSx is I«(a?) Sx G(u) sec [0-\~u) and 

 the incident ray is reduced by an amount 



I u (x) 8x {/jt + Q(u)} sec (6 + it). 



Similarly for the reflected rays. The differential equations 

 now are 



aw _ _ /*+G(tQ j , x , aw v (rA } 



-dx ~ wstf + u)^ } <x>*(*^») W { (S . ±) 



The end condition is that E w (#)=() for x=0. If E tt is the 

 power of the emerging reflected beam, the solution gives 



_. ._ G(u) sinh tx x {ll -f G(u)\ cos cos u 



E 1 = r \' v exp xr t v ( } — ^ v , 



u ' cos(u + u) T r cos (v-{-u)cos(6 — 11) 



. ... (8-2) 



where 



\/G 2 cos (0 + m) cos (0-<O + (^+G) 2 sin 2 0sin 5 



w 



cos (0 + u) cos (6 — u) 



Apart from the first factor in (82), u only occurs as a 

 square. So, as in § 7, an averaging with the reversed 

 beam will eliminate the effect of untrue faces. In most 

 cases this will be far less important than it was in § 7, 

 because the factor occurs as a cosine and in the important 

 cases 6 will be fairly small. 



