816 Mr. C. G. Darwin on the Reflexion of 



So we may represent the effect of extinction by introducing 

 a correction factor 



tanhwg , ...... (6-9) 



mq v y 



and this is quite accurate for crystals not so deep that the 

 ordinary absorption would become important, and remains 

 fairly good even for those much deeper. 



Now consider a small block limited in breadth as well as 

 depth and irradiated by plane waves. The multiple internal 

 reflexions will give a complicated system, which will depend 

 on the crystal's shape and will be irregular at its surfaces. 

 But it seems reasonable to represent its effect by calculating 

 the intensity of reflexion as though it were of infinite area, 

 and then selecting from the reflected rays the cross-section 

 which has met the actual crystal. Let d be the mean depth, 

 then Y/d is the area. The cross-section of the rays is there- 

 fore (V/d) sin 0, and so the power reflected is 



\S o \ 2 (V/d)$'m0. 

 Then we have 



E= j |S o | 2 (V/d)sin0dto/a>. 



If we put | T j 3 = J, d=ma, q 2 = 2Qa 2 cot 0/\, 



we thus get Eg>/J = VQ tanh mq/mq, . . . (6'10j 



which shows that on these assumptions the same correction 

 factor is applicable in (4*8) as in (6*8). 



Exactly the same process may be applied to the argument 

 of § 5. For though there the crystal was not rotating, yet 

 the distribution of the blocks was such that there was an 

 integration, equivalent in its effects to the u integration 

 here. We may thus say that the reflexion of a conglomerate 

 at angle (0 + u) is given by 



JVG(w), (6-11) 



provided that 



G(» = Q' I dW Vdm' WF(W, m, m'\ . (6-12) 



— 00 



where Q' = Q tanh mq/mq (6'13) 



In .consequence of this (5*6) becomes 



J 



Gr(u)du=Q' (6-11) 



