Mr. L. Fletcher's Crystallographic Notes. 285 



the twin- growths; and the angles of the upper half of fig. 6 

 are exactly equal to the similarly disposed angles of the upper 

 half of fig. 7, and the angles of the lower half of fig. 6 to the 

 similarly disposed angles of the lower half of fig. 7, the only 

 difference in the growths being the relation of the upper to 

 the lower half. 



Of the specimens of copper pyrites in this collection, one 

 figured by Haidinger himself in the ' Catalogue of the Allan- 

 Greg Collection ' (now in the possession of the British 

 Museum), though probably not one of the original specimens 

 of the memoir of 1822, offered itself as the most likely to 

 afford a satisfactory solution of the difficulty. In this speci- 

 men, which comes from Freiberg, the twin-growths are dis- 

 posed parallel to each other on galena, and are associated with 

 quartz, chalybite, and calcite. The length of a side of the 

 triangular faces is about 1*5 millim. Haidinger's drawing to 

 illustrate this specimen is virtually the same as fig. 9 (copied 

 from his paper of 1825), the only difference being that the 

 faces of e {1 1} being almost linear are not shown in the Cata- 

 logue. This figure represents the rotation as taking place about 

 each of the normals to the four upper faces of { 1 1 } of the 

 central individual, of which both the upper and the lower halves 

 are present. We may remark that a complex growth of this 

 perfect kind would be explained by the law of Naumann equally 

 with that of Haidinger, seeing that in the lower half of the 

 regular composition the various planes of junction are repre- 

 sented as parallel to the corresponding twin-planes, and in the 

 upper half as perpendicular to them. As none of the growths 

 have an all-round development, the figure represents the 

 growth in theoretical perfection rather than as actually ex- 

 istent; in fact the actual habit is more nearly shown in fig. 10, 

 which at the same time will serve to give an idea of the stria- 

 tion to be observed on the faces. 



A crystal from this specimen appeared to show that the triad of 

 octahedron-faces o o x o 2 did not quite coincide, as according to 

 Haidinger's explanation'should be the case; but still no satis- 

 factory measurement of the angle could be obtained. The re- 

 entrant angle lying in the zone c c x at the junction of two 

 individuals could, however, be determined with very fair pre- 

 cision, although the faces are finely striated parallel to their 

 edge of intersection with each other. These planes were sup- 

 posed by Haidinger to belong to the common form s{2 1 } ; and 

 as the angle made by a plane of this octahedron with the adja- 

 cent nice of the form {101} is 18° 31', the reentrant angle 

 according to his theory should be 37° 2'. Actual measurement, 



