Mr. L. Fletcher's CrystallogmpMc Notes. 281 



one hand, a face of {1 1} be both twin-plane and composition- 

 plane, the adjacent tetrahedron-faces form small salient or re- 

 entrant angles ; if, on the other hand, the composition-plane 

 be perpendicular to the twin-plane, the tetrahedron-faces of 

 the one are coincident with the adjacent faces of the other." 

 The probability is that both are mentioned, not because Sade- 

 beck believed them to be both true, but merely to show that 

 in either case the position then being contended for was a 

 tenable one ; and in fact the position of the composition-plane 

 has no further bearing on the argument of that paper. 



It would at first sight appear that a difference of a right 

 angle in the position of the plane of composition would mani- 

 fest itself by angular differences in the twin sufficient to render 

 any difficulty of distinction impossible ; we shall therefore 

 attempt to make quite clear what differences would be ob- 

 served in growths characterized by such different laws. 



Fig. 2 represents an octahedron {111} of copper pyrites in 

 equipoise, abed being one set of similar alternate faces, and 

 cc/3y8 the other set respectively parallel to the first. This figure 

 approaches very nearly to the regular octahedron of geometry 

 and of the Cubic system, of which the faces are all equilateral 

 triangles and the sections through the edges all squares : the 

 difference therefrom was first made known by Haidinger in the 

 memoir of 1822. Though ABAB, the basal section of an 

 octahedron of copper pyrites, is a square, the sections C A C A, 

 CBCB through the terminal edges are merely rhombs, the 

 angles in the vertical axis being 90° 51', and in the horizontal 

 axes 89° 9 r ; the triangular faces are only isosceles, the vertical 

 angle of each being 60° 29' and the basal angles 59° 45^'. 



In fig. l,abcd and ufiyS are the stereographic projec- 

 tions of the points in which lines drawn through the centre 

 parallel to the normals of the faces of the octahedron of fig. 2 

 would meet the sphere. 



The faces of the form {101} truncate the terminal edges 

 of the octahedron {111}; T T Q Q, four of the poles of this 

 form, are shown in fig. 1. 



According to Haidinger's measurement, 2 Qa is 108° 40', 

 whence tan qq = tan Qri cog q Qa = fan Qa CQS ^ 



Thus 



QC = 44° 34^, Q T = 90° 51', and Q a = 35° 3f ' : 

 also 



cos Ta = cos Q a cos Q T ? 

 and 



Ta = T/3 = 90°41| / , 



T« = T6 =180°- 90° 41f= 89 c 18±'. 



