138 On New Systems of Crystallization in the Mineral Kingdom. 



In each of these four groups the determining forms are con- 

 tinued as before. 



In the first, the cube, octahedron (with the tetrahedron) and 

 the rhombic dodecahedron. 



In the second, the basal pinacoid and the two prisms differ- 

 ing 30° from each other. 



In the fourth, the pinacoids of the base and of the macro- and 

 brachy-diagonals. 



Moreover, I take each base as being horizontal and each 

 prism as vertical. 



The asymmetrical forms are arranged according to the length 

 of their various axes. 



Other circumstances, which are well enough understood, must 

 be taken into account for the further division of one-axed forms. 



All this and much more will shortly appear in a forthcoming 

 work. 



Especial notice will be taken of the analogy between the cry- 

 stallographical, optical, electrical, and magnetic phenomena ; and 

 Councillor Reich has kindly promised a valuable paper on the 

 last-mentioned subject. 



Six new systems of crystallization ft. e. the sections B of the 

 first three groups) are thus to be added to those already known ; 

 and by this means all the systems are brought nearer to each 

 other. No doubtful conclusions have been formed, for they are 

 all founded on ascertained facts. A person must have some 

 self-confidence who has used scientific means for assisting him 

 in his researches for more than forty years, and who during that 

 period has measured between 12,000 and 13,000 angles with the 

 reflective goniometer, and has also determined the specific gra- 

 vity in more than 4000 instances, and who has often had to deal 

 with inferior specimens. 



These new systems will perhaps have to contend with a good 

 deal of opposition; but I am convinced that their correctness 

 will be established by investigation. 



Feb. 16th, 1860. 

 I have been enabled this day to examine a plate of dioptase 

 one millimetre thick, cut from a transparent crystal perpendicular 

 to the principal axis, with Amici's polarizing microscope, which 

 has already been productive of so much benefit ; and to my great 

 satisfaction the plate showed two optical axes in a beautiful 

 manner. I estimate the angle formed by the two optical axes 

 at 4°. Thus the rhombohedron cannot be the primary form 

 of dioptase ; it must be either a rhombohedron-like diplohedron, 

 or triplohedron. I hope by measurements to determine this 

 satisfactorily. 



