X-Rays from Imperfect Crystals. 827 



those in § 4. The result is * 



iJVcosfl.Q (10-4) 



This must then be multiplied by a numerical factor given 

 by the symmetry of the crystal according to the following 

 rule. If the crystal has no centre of symmetry, add one on 

 to its symmetry elements. Now construct the " form" corre- 

 sponding to the planes that are being studied. The number 

 of its faces is the required numerical factor for (J 0'4) ; by 

 virtue of the centre of symmetry it must always be an even 

 number. For example, in rock-salt the form for (1, 0, 0) is 

 a cube and the factor is 6 ; for (1, 1, 0) it is a rhombic 

 dodecahedron and the factor is 12 ; for most planes the 

 number is 48. It may sometimes be necessary to apply a 

 correction for absorption. This will depend on the shape of 

 the powder and is a matter of simple geometry. It should 

 not be necessary to make any allowance for secondary ex- 

 tinction, but if it were needed it could be calculated on the 

 principles of §§ 7, 8. 



11. Discussion of Results. 



The tests in § 9 were rather unsuccessful, but I do not 

 think sufficiently so to condemn our theory out of hand. 

 Should further tests prove that the discrepancy is real, it 

 appears to me that it would throw doubt, not only on my 

 own work, but also on the validity of the deduction of Q in 

 B. J.B. ii. ; for that deduction can only be founded on some 

 theory which must be the same as the present one in 

 principle. 



It is of course possible that a crystal, imperfect by warping 

 instead of cracking, should obey a different rule, but I should 

 judge this to be very unlikely. For (5*5) may be used to 

 define a function Gr{u) for such a crystal, though its expres- 

 sion in terms of the imperfection will not be so easy as for a 

 cracked crystal. With this Q(u). the work of §§ 7, 8 will 

 all stand good, and will determine the relation between the 

 extinction and the breadth of the reflexion region, without 

 touching the question of the meaning of G(w). As to this 

 last, it is a most natural conjecture that (5*6) will be true 

 fo^ it, in view of the generality which that equation has 

 already been proved to possess, and so will lead to the right 

 value for Q. If, as appears probable, rock-salt is warped 

 rather than cracked, this will have the advantage that 

 primary extinction is unlikely to be important, and so the 



* The expression does not vanish for 9 = ir/2 on account of the factor 

 cosec 29 in Q. 



