T. L. Walker — Examination of Triclinic Minerals. 177 



a hemimorphic axis there can be no equivalence — the basal 

 planes 0001 and 0001 in the hemimorphic tourmaline being 

 crystallographically different ought to give different etching 

 figures. This mineral is a representative of a large class of 

 substances whose crystals have no crystallographic center and 

 whose parallel planes are equivalent only when this is required 

 by other elements of symmetry — lines or planes. Thus in the 

 case of calamine, or hemimorphite, which is devoid of a cen- 

 ter of symmetry, we should expect the basal planes 001 and 

 001 to give different corrosion pits, but pairs of parallel pris- 

 matic faces should give similar etching figures. This is required 

 by the presence of two planes of symmetry (100)_and (010) 

 and may be proved as follows : the prismatic faces 110 and 110 

 are symmetrical about the symmetry plane (010), therefore 

 these faces are equivalent and the etching figures on them 

 must also be similar ; but the faces 110 and 110 are symmetrical 

 with regard to the symmetry plane (100), therefore the faces 

 are equivalent and the etching figures must be similar. But 

 since the faces 110 arid 110 are both equivalent to the face 110, 

 therefore they are equivalent to one another and will give simi- 

 lar etching figures, though the crystal possesses no centre of 

 symmetry. In the same way it may be shown that all four 

 prismatic faces are equivalent. 



Yery few experiments have been made with etching figures 

 to determine the equivalence of pairs of parallel faces. I first 

 made a few experiments to prove that parallel faces give simi- 

 lar figures when they belong to the same crystal form and dif- 

 ferent figures when they belong to different crystal forms, and 

 then proceeded to examine some of the triclinic minerals with 

 a view to determine which of them have equivalent parallel 

 faces and which different. There are two recognized divisions 

 in the triclinic system : first, crystals having surfaces in pairs 

 which are crystallographically equivalent and give similar etch- 

 ing figures, and second, crystals whose surfaces are not always 

 present in parallel pairs, and when they are, do not give similar 

 corrosion figures and are not crystallographically equivalent. 

 The first group are holohedral triclinic, and since they possess 

 a centre of symmetry, Zirkel and others refer to them as 

 centro-symmetric. The second group is often referred to as 

 hemihedral triclinic or tetartohedral monoclinic, but as the 

 crystals possess no element of symmetry, whether of line, 

 plane or point, they are appropriately spoken of as asymmetric. 

 Up to the present time no mineral representative of this latter 

 group is known. A small number of complete artificial chem- 

 ical salts crystallize in asymmetric forms. 



Am. Jour. Sci. — Fourth Series, Vol. V, No. 27.— March, 1898. 

 12 



