84 Dr. L. Vegard on 



Let the face considered have a spacing d . A length 

 equal to d on the normal to the face will be cut by a 

 number of point-planes (r) with numbers of atoms per unit 

 area fi l9 fi 2 ... fi r . 



We select an arbitrary point (0) on the normal, and call 

 the distances from this point to the (r) planes 



d 1 d 2 ...di ...d r . 



The intensity of the reflected wave from such a face has 

 been calculated by Bragg in the case of r = 2 and a general 

 geometrical method is given *. 



The general analytical expression for the intensity will be 



\ = KK 2 (10) 



k n is a factor which W. H. and W. L. Bragg put pro- 

 portional to the intensities of the normal spectrum, and they 

 give the following values 



n= \ 1 | 2 ! 3 | 4 | 5 



K n = | 100 | 20 | 7 | 3 | 1 



An is the calculated amplitude which is given by the 

 formulae : 



i-r L l . 



f\(n) = 2 Ui cos n 2ir-~ 



«=* d o y . . . (ii) 



%=r . d 



i=l « 



In a great number of cases we can give the point such 

 a position that the r planes are symmetrically arranged 

 with regard to this point, and as sin (—a) =— sin a, the 

 quantity / 2 (n) =0. 



The lattice of the zircon group as given in Table IV. will 

 give the spacing shown in fig. 6 for the five faces experi- 

 mented upon. Of these the face (001) has identical and 

 equidistant planes and should give a normal spectrum which 

 is also in agreement with experiments. The intensities of 

 the spectra of the four other faces should be given by the 

 following expressions for f\(n) and/ 2 (7z) : — 



* W. L. Bragg, Pivc. Roy. Soc. lxxxix. p. 483 (1914). 



