214 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1920. 



methods of projection familiar to the crystallographer. Likewise 

 the distance between like planes in terms of the indices of these 

 planes for each of the units of structure which underlie crystals can 

 be obtained from geometrical considerations alone. Furthermore 

 the distance from the crystal to the photographic plate and the dis- 

 tance of a reflection from the central spot give the angle of its reflec- 

 tion. Then with the aid of expression (1) it is possible to get a 

 value for rik, the product of the order of the reflection into the wave 

 length of the reflected X rays, after one of the absolute dimensions in 

 the crystal has been obtained from an X-ray spectrum measurement. 

 By tilting the crystal so that the X rays do not pass through it along 

 some important axis, different planes of the same form are inclined 

 at different angles to the incident beam and consequently must reflect 

 X rays of different wave lengths. By plotting the intensity of the 

 reflection from planes belonging to the same form against the 

 wave lengths of the X rays they are reflecting, points of a curve 

 will be obtained which represents the effect of the X rays upon 

 the plate. The curves thus arising, one for each different kind of 

 reflecting plane, can be compared in the same wave length. The data 

 so obtained 22 are serviceable in distinguishing between the possible 

 arrangements of atoms for the crystal under investigation. 



Resume. — A brief outline has now been given of the essential 

 features of the three ways, as they exist at the present time, of 

 attacking the problem of the structure of crystals. It may be well 

 to collect the outstanding features of these methods to show how 

 they are related to one another and to indicate again the present 

 status of the work in this field. 



The start toward determining the arrangement of the atoms in 

 crystals was made by looking around in each case for a structure 

 which would explain the relative distances apart of planes of atoms 

 in directions normal to a few crystal faces. Several chemically 

 and crystallographically simple compounds — the alkali halides, zinc 

 blende, the diamond, fluorspar — were thus studied. Assuming, then, 

 that the structures thus obtained actually represent the arrangement 

 of atoms within these crystals, the wave length of X rays was 

 deduced with the aid of expression (1) from a knowledge of the 

 density of the crystals and the number Of molecules in the gram 

 molecule. Further, taking this as the proper value for the wave 

 length of X rays, we have proceeded to use it to determine the 

 amount of mass to be associated with the unit of structure of every 

 crystal which has subsequently been studied. The objection to this 



a 2 S. Nishikawa, op. cit. Ralph W. G. Wyckoff, J. Am. Chem. Soc, 42, 1100, 1920; Phys. 

 Rev., 16, 149, 1920 ; Am. J. Sci., 50, 317, 1920. 



