372 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 11, NO. 15 



It will be sufficient for the present purpose to have pointed out a 

 single structure for rock salt, besides the generally accepted one, which 

 is in agreement with the experimental data. There are undoubtedly 

 numerous others which would serve equally well. It is not, however, 

 feasible to indicate even all of the different types of structures that 

 would fulfill the present requirements. This arises in part from the 

 fact that besides those other structures which can be developed from 

 0A^ it is conceivable that such special values could be assigned to the 

 coordinates of arrangements developed from other space groups that 

 the intensity of the reflections from certain types of planes would be 

 either obliterated entirely or would be so weak as to pass detection. 

 As a result the sequence of spacings found for such an arrangement 

 might agree with that for rock salt.^"'^^ 



The wave lengths of the X-rays calculated upon the basis of struc- 

 tures representing sodium chloride but possessing various numbers of 

 molecules in the unit cell must of course differ from one another. 

 For instance the wave lengths of the rays diffracted through the angle 

 6 when calculated upon the assumption of the correctness of the 

 sodium chloride structure and when calculated upon the assumption 

 of the structure just considered which has twenty-four chemical 

 molecules within the unit cell will stand in the ratio of v^i to -s/'IA. 



Quantum calculations of the wave lengths of X-rays. — It was early 

 pointed out that the quantum hypothesis furnishes an independent 

 way of obtaining the wave lengths of X-rays. By identifying the 

 energy of the electrons required to excite either the characteristic 

 X-rays^" or those of the short wave length limit of the continuous 

 spectrum ^^ (as the case may be) with the energy of the rays that are 

 produced, it is possible from the quantum relationship 



E = nhv 



to get the frequency (i^) and hence the wave length of the correspond- 

 ing X-rays.^"* If it is assumed that such X-rays correspond with the 



" This sort of agreement with experiment is illustrated in the course of the treatment 

 of the structure of magnesium oxide. Ralph W. G. Wyckoff. Amer. Journ. Sci. 1: 138. 

 1921. (See the grouping there called (j).) 



" In the light of present knowledge such a structure as we have just discussed need not 

 be immediately disregarded as impracticably complicated, especially when it is borne in 

 mind that it offers the chance of so placing a sodium and a chlorine atom nearer to one 

 another than to other atoms as to preserve, in the existence of a chemical molecule, the 

 older idea of the nature of solid sodium chloride. 



12 W. H. and W. L. Bragg, op. cit., p. 72. 



13 W. DuANE and F. S. Hunt. Phys. Rev. (2) 6: 166. 1915, etc. 

 1* W. DuANE and F. S. Hunt, op. cit. 



