196 R. W. G. Wyckoff — Symmetry and Crystal 



The identification of the secondary spectra on this 

 photograph can be carried ont with the aid of the gno- 

 monic net which has previously been described. 4 The 

 distance from the crystal to the photographic plate can 

 if necessary be accurately calculated from the measure- 

 ment of the principal spectrum (in this case the (100) 

 reflection). It is then a simple matter to prepare a 

 gnomonic ruler 4 for plotting on a radius of five centi- 

 meters the projections of the various secondary spectra. 

 By making the distance from the crystal to the plate 

 exactly five centimeters, it would be possible to use 

 directly the same gnomonic ruler which serves for Laue 

 photographs; by making this distance 10 cm., as is more 

 satisfactory, the same ruler can of course be used by 

 dividing by two the readings of the scale giving distances 

 from the central spot. While, during the course of the 

 experiment, the crystal is rotated back and forth, the 

 gnomonic projections of the various reflecting planes 

 will travel along the hyperbolas of the gnomonic net if 

 it is so placed that the zero degree hyperbola (a straight 

 line) coincides in position with the principal spectrum. 

 By rotating the mean projected positions of these- reflect- 

 ing planes (which in the present instance form a simple 

 square network of points) through the angle of rotation 

 suffered by the crystal, portions of hyperbolas will be 

 decribed which will pass through the gnomonic projec- 

 tions of the observed reflections for those planes that can 

 reflect for this particular setting of the crystal. By 

 superposing, then, the gnomonic projection of the photo- 

 graph over the series of hyperbolic paths obtained in this 

 manner, it is possible to identify the various reflections 

 upon the photograph. Considerable care must be taken 

 in such a determination and some ambiguity may of 

 necessity arise because it frequently happens that reflec- 

 tions from different planes, especially planes in different 

 orders of reflection, give effects at about the same posi- 

 tions upon the plate. 



By making this sort of an interpretation of the trans- 

 mission spectrum photograph from sodium hydrogen 

 acetate, reflections from planes belonging to a number of 

 forms, such as {161}, {721}, and {521}, were observed in 



4 H. Hilton, Min. Mag., 14, 18, 1904; Ralph W. G. Wyckoff, this Journal, 

 50, 317, 1920. 



