Results of Crystal Analysis. 407 



I£ we consider the expressions of A„ for the two faces 

 (001) and (111), and compare them with the observed 

 maxima of these faces, we can draw some very important 

 conclusions. 



The first point we notice is that the third-order spectrum 

 of (111) almost vanishes. Now 



cos (3 x 33) = —cos 81 



is a very small quantity ; and, as the last term of A„ will 

 be dominating, we must have 



cos 3C nearly equal to 0, or 3C = 90 or 270. 



The last possibility is excluded because it would make 

 cos C a very small quantity, and we should not be able to 

 explain the very strong first-order spectrum of this face. 



C near to 30 c 



Hence we conclude 



Now, also, the third-order spectrum of the (001) face is 

 very small ; consequently, as cos 30 is small, 



cos 3B must be nearly equal to zero, 

 or 3B nearly equal to 90° or 270°. 



The latter possibility is excluded because the first-order 

 spectrum of (001) is to be quite small and cos B must have 

 a fairly large positive value. 

 Thus we get 



B nearly equal to 30°. 

 Thms we find 



B nearly = 30° nearly = C. 



In order to find the best values of A, B 5 and 0, we should 

 have to give B and C values near to 30° and determine the 

 amplitudes for the faces (111), (101), and (001) for various 

 values of A. 



If we carry out such a calculation, we find that we get 

 the best possible agreement between calculated and observed 

 values when we put 



A = B = C = (about) 35° (13) 



The amplitudes calculated with this value of A, B, and C 

 are given in Table IV., and also the values calculated from 

 the observed intensities by means of the relation J n = k n A n 2 , 

 where &i=l, ^2 = 3? £3 = 7? &4=v2- We see that the agree- 

 ment is quite satisfactory. 



