X-Rays from Imperfect, Crystals. 821 



tan 2 u. Then 



Q' Q'* 5Q' 3 

 = *Q'/{/*+*Q'+fo , -&«)^}. • (7-5) 



If the third term is neglected this is in the form used by 

 Bragg, who calls c/ 2 Q! the " extinction coefficient." If we 

 had considered that every incident and every reflected beam 

 had only a single reflexion, then we should have had instead 

 of (7-2) 



E M /I=iG( w )/> + G( w )} 5 



and this would lead to the same first two terms in (7*5). 

 This idea has been used by Sir W. H. Bragg *, and it is 

 clear that there will be a wide region of values in which it 

 will be a very good approximation. 



It is evident that a knowledge of p by itself is not sufficient 

 to determine the value of Q' ; but (7*2) suggests that it may 

 be possible to do so by a study of the shape of the reflexion 

 curve. For if we know E M for all values of u we may solve 

 (7*2) for Gr(u). If the first factor is omitted, we have 



p/ n 2/x,(E„/I) , . 



^^ ~ l-2(F>JI) + (1-cot 2 6 tan* u) (E«/I) 2 ' K } 



A quadrature will then lead to Q' by (6*14), and so the 

 secondary extinction is eliminated. 



It thus appears theoretically possible to determine Q' from 

 observation on a single face. There is, however, a serious 

 objection to the method. It is not reasonable to suppose 

 that Gr(V) is really independent of the depth ; for grinding 

 or even cleaving must necessarily act differently on the 

 surface-layers and interior, and if Gr is an unknown function 

 of c, the data are insufficient for a solution. If, in spite of this, 

 the process should be valid, there would still be the difficulty 

 that Q' may differ from Q. The only possibility of deter- 

 mining Q would appear to lie in finding Q' for several 

 crystals, of which the blocks were scattered in various 

 degrees. If then the results all came the same, there 

 would be a presumption that primary extinction was not 

 present. Of two discordant values the greater is to be 



* W. H. Bragg-, Phil. Mag. vol. xxvii. p. 881 (1914), and Proc. Lond. 

 Pliys. Soc. vol. xxxiii. p. 304 (1921). 



