204 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1920. 



sodium atom. The atoms N and P are each shared by two cubes ; both 

 together then supply another sodium atom within our cube. The two 

 remaining sodium atoms are furnished by L and M and by Q and R. 

 In a similar fashion it can be shown that four chlorine atoms are as- 

 sociated with this unit. 



The volume of the cube can be written : 



v _mM 



P 

 where 



Fmthe volume, 



m, the number of molecules of sodium chloride within the unit,=4, 



p, the density of sodium chloride,=2.17. 



i¥, the mass of a single molecule of sodium chloride, equals the 

 molecular weight multiplied by the weight of an atom whose 

 atomic weight is unity, roughly equal to the weight of a single 

 atom of hydrogen,=58.5Xl-64Xl0" 24 grams. 

 From these, d, the length of a side of the cube, 1/17— 5.60 X 10~ 8 

 centimeters. If the reflection is taken from the face CDI1G, then the 

 distance d between like cube planes is the distance between the plane 

 CDHG and the plane BAEF. The reflection from planes of such 

 a spacing would be of the first order. But it will be seen that the 

 plane QLRM has exactly the same composition as these other two 

 planes and is spaced midway between them. The waves reflected 

 from it will then be exactly out of phase with those from the other 

 planes and, having the same amplitude, will blot them out completely. 

 The first reflection to be found from the cube face of this arrange- 

 ment of atoms is thus of the second order. If X rays from a tube 

 having a palladium target are used, the angle of this reflection is 

 found to be 5.9°. In equation (1) we now have— 



n=2, 



d=5.QOXlO s cm., 

 6=5.90°. 



Consequently X is equal to 0.576X10" 8 centimeters. 12 



The obvious objection to this determination lies in the fact that 

 though this particular structure for sodium chloride agrees with the 

 experimental data just mentioned, there may be, for aught it tells, 

 a myriad of other structures which are in equally good agreement. 

 The large amount of data, however, agreeing with this structure and 

 the value of the wave length of X rays derived from it that has since 

 been obtained from different sources make their truth seem highly 

 probable. 



Using this same method of procedure, W. H. and W. L. Bragg and 

 others have found structures which will account for the positions of 



" W. FI. and W. L. Bragg, op. cit., chap. vil. 



