W. G.Brown — Quartz-twin from Yirginia. 193 



allel juxtaposition have the face opposite «, over the apex of 

 the crystal, in common, along with a third sub-individual 

 in part shown in the figure on the lower left, hand side of a. 

 These three sub-individuals have also the ooR plane parallel to 

 that under a, seen in the figure in common. The second individ- 

 ual b is also composed of three sub-individuals in juxtaposition 

 with the principal axes parallel. Using a to indicate one 

 individual and b the other, it is seen that a 

 and b are in a twinned position. The faces 

 R of both individuals which are perpendicu- 

 lar to the plane of the paper give a single 

 reflection and the faces of the sub-individuals 

 a and b lie nearly in the same plane, not par- 

 allel planes which is the general case and 

 which is represented by the faces R of c 

 and b. The faces R which lie nearly in one plane, indeed all 

 the well developed faces in the group, are slightly curved and 

 striated so that a sharp reflection cannot be obtained for the 

 purpose of exact measurement. Such being the case the fol- 

 lowing details are given. 



The faces E are not absolutely in one plane, careful examina- 

 tion showing that the faces are inclined at an angle a little less 

 than 180°. Further, when one face is horizontal the other is 

 very slightly twisted around an axis joining the apices of the 

 two crystals. Moreover the faces R and — R of the two individ- 

 uals are not exactly in a zone, or what is the same thing the 

 planes normal to R containing the principal axis in each indi- 

 vidual would form a very small angle at their intersection. So 

 nearly do the individuals approach the theoretical conditions 

 that these points are mentioned to avoid giving the impression 

 that the group possesses ideal symmetry. 



The two conditions are practically fulfilled : 



1. The faces R parallel to the same plane. 



2. Principal axes contained in a plane perpendicular to R. 

 Under these conditions the angle between the principal axes 



would be 103° 34/ (the supplement of the angle between R 

 and — R over the apex) and the twinning plane perpendicular 

 to R, which is — ■§• R. 



Supposing — fR to be the twinning plane and calculating 

 backwards it is found the faces R, of the two crystals, would 

 form an angle at their common intersection of 179° 34:' an 

 angle a little less than 180° which is the case with the group 

 here described, and that the inclination of the principal axes 

 of the two crystals would be 104°. 



It may be stated that the lower portion of the group, rep- 

 resented in the figure by irregular lines, consists mostly of planes 

 having a definite orientation to the dominant individuals. 



