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



explained by considering the absorption of the emergent 

 beams in the two cases. His argument leads to the same 

 factor. The influence of the vicinal face can be completely 

 eliminated by averaging for both sides, and we shall suppose 

 this done. There is then no need to consider the first 

 factor in (7*2) at all. 



Bragg's "reflecting power" (which we are here calling 

 the integrated reflexion) was defined by him as E<w/I, where 

 the crystal was turned with angular velocity co through the 

 reflecting angle and E was the total energy obtained, while I 

 was the power of the incident beam. His I is the same as 



ours, his E is our l ~Ei u du/co. So we have for the integrated 

 reflexion 



p = i G(u)dul | fi + G(u) 



— + V[/A + GI-(w)] 2 -[GrW] 2 (l-cot s ^tan s M) } .(7*3) 



If G(w) is small compared with p, for every value of u, then 

 neglecting the small terms of the denominator and using 

 (6-4) we have p = Q'/2p. 



Apart from the difference between Q' and Q, this is the 

 equation used in B.J.B.i. 



If G(u) is not always small enough to justify this approxi- 

 mation, it may still be small enough to admit of expansion 

 in powers of Gr(u)/fi. Then we have 



G\u)du 



_00 



!f« s c«)( 



— 00 



Let rG 2 (^=# 2 Q' 2 "! 



— 00 



G 3 (u)(j--cot s 0tan s i*)rf M . 



u. 



(7-4) 



then g 2 and g z will be constants of the crystal. For most 

 crystals it will be legitimate to neglect the term involving 



