436 
Proceedings of the Royal Society of Edinburgh. [Sess. 
(2) the twins of monoclinic amphiboles and pyroxenes on 100 ; (3) the 
twins of staurolite on 032 and 130, and of aragonite on 110 ; (4) twin of 
scheelite (IV Uc) on the faces of the prisms of the first and second 
order ; (5) the supplementary twin of pyrite on faces of the rhombic 
dodecahedron. 
3 Be (in III Be, C Be) : 3 BcPL, twin axes of (a) twins of calcite and 
chabazite, on the basal plane, and (b) twins of spinel and fluor on the 
octahedron. 
ix. Lines with co-linear and contra-directional cyclic number 2 or 6. 
As the plane of twinning is here a plane of symmetry (§5, v.), there 
cannot be plane twinning, and line and point twinning are equivalent, 
(§12, iii.). The twin plane is contra-directional, and the twin axis 
co-directional. 
2 TJk (in II Uk, III Bu ) : 2 UlcLI , twin axes at right angles to the planes 
of symmetry in the twins of pyrargyrite referred to under 3 Bui. 
6Uk (in VI Uk): 6 UkLI. 
2Bk (in II Bu, IV Bk, IV Bu, VI Bk, VI Bu, CBu ): 2 BkLI, the 
normals to the rhombic dodecahedron in twins of eulytine with point 
twinning. 
QBk ( in VI Bk): QBkLI . 
x. Other twin axes with even co-linear cyclic number are lines of 
symmetry of the untwinned structure and cannot be axes of line twinning. 
Plane and point twinning are equivalent (§12, ii.). The twin plane is 
co-directional, and this is also the case with the twin axis, except where its 
directions are unlike in the untwinned structure. 
4t77c (in IV Uk) : kUkPI. 
