332 R. W. G. Wyckoff — Crystal Structures of 



the following procedure was used. First a gnomonic 

 projection of the pattern was prepared in the customary 

 manner (fig. 3). The position of the (110) plane (crystal- 

 lographic axes) is readily found from a knowledge of the 

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

 lographic data. If now the plane of the projection is ro- 

 tated through an angle sufficient to throw the projection of 

 this plane to infinity, a symmetrical pattern will be ob- 

 tained from which the indices of a majority of the planes 

 may be readily obtained (fig. 9). It will be observed that 

 this pattern is really the specialized case of a triclinic pat- 

 tern in which the axes are of equal length. The indices of 

 those planes which pass off the projection when it is ro- 

 tated can afterwards be determined on the original pro- 

 jection from their zonal relations. 



The Data from the Laue Photographs. — The spacing 

 between like planes in the rhombohedral lattice is given by 

 the expression 15 



7 _ c^/1 + 2 cos 3 a — 3cos 2 a 



<sj (A 2 + ¥ 4- V) sin 2 a + 2 {fik + hi + hi) (cos 2 a - cos a) 



where d = the spacing, 



c = length of the side of the unit rhombohedron, 

 a = the angle between the trigonal axes, and 

 hkl — the Miller indices of a plane. 

 a is here to be taken for the^ second set of axes ; c, the 

 length of the side of the corresponding unit, is readily ob- 

 tained from the spacing measurements. Since the dis- 

 tance of any reflection from the central spot on the pho- 

 tographic plate has been measured and since the distance 

 from the crystal to the plate is known, sin <9, where 6 is the 

 angle of reflection, can be obtained. Consequently n\, 

 where n is the order of the reflection and A = the wave 

 length of the reflected X-rays, can be determined for each 

 spot by using the customary expression, nk = 2d sin 0. 

 When the values of nX y so obtained, were plotted against 

 the estimated intensities of the spots, and those points 

 which correspond with planes of the same form were con- 

 nected together, a series of curves, one above another, 

 was obtained. It was thus possible to compare many 

 planes of different forms in the same wave length. These 

 curves are portions of curves which represent in shape the 



13 A. W. Hull, Phys. Rev., (2) 10, 661, 1917. 



