132 Prof. Breithaupt on Thirteen Systems of 



First, dioptase ; and I must say at once that its primary form 

 will be found to consist of two-thirds of a rhombohedron and 

 one-third of a rhombohedron : I estimated this myself some time 

 ago, but only measured the angles of one set of polar edges. 

 Haydenite ought to have the same character. It is classed as a 

 chabasite, and so it appears to be at the first glance ; but accord- 

 ing to Levy, the inclination of its rhombohedral planes to the 

 polar edges differs by some degrees. It is very probable that it 

 is hexagonal, and that it has a rhombohedral-like "diplohedron" 

 or "triplohedron" for its primary form. The late M. Schuler 

 measured this mineral in Freiberg, and found that the polar edges 

 had three angles. Schuler wished to publish this fact, but I do 

 not believe that he did so. 



Perhaps other chabasites are asymmetrical and have two 

 optical axes. It is very probable that an asymmetrical arrange- 

 ment of the primary pyramidal planes exists in magnetic pyrites. 

 I have no other ground for believing this, than the fact of its 

 magnetic character. 



The Museum at Freiberg is indebted to M. Muller for a 

 large crystal of magnetic pyrites from Norway ; it is a prism 

 more than an inch long, and has a basal plane an inch broad. 

 This crystal has a most distinct magnetic axis, which does not, as 

 I expected, run parallel to the principal axis, but is nearly or 

 quite horizontal, and is indeed perpendicular, or nearly so, to 

 two parallel planes of the prism. It may be proved hereafter 

 that the magnetic and crystallographical axes harmonize. When 

 we know better the optical characters of the various species into 

 which idocrase, tourmaline, apatite, titanites and other mine- 

 rals, according to my views, ought to be crystallographically 

 divided, the angles which the two optical axes form will assist 

 in determining and arranging them. Of the apatites which I 

 have been able to measure exactly, Pollachites galacticus and 

 Pollachites haplotypicus differ greatly. 



Tesseral minerals also show particular laws. It is known that 

 I found quite constant deviations in melanite, sp. gr. = 3*777 

 (Granatus melanites, B. M., p. 637), and in almandine (Grana- 

 tus almandinus, B. M., p. 644), sp. gr. = 4*119; so that the 

 icositetrahedron (the leucite form) is not a simple figure, but a 

 combination of an obtuse tetragonal and an acute ditetragonal py- 

 ramid. According to the measurements, the inclination of sixteen 

 principal edges gave the same angle = 131° 48' ; the same edges, 

 reckoned according to the formula \ J, would give 131° 48' 36'''; 

 but the eight remaining edges, on two angles composed of four 

 edges, lying diametrically opposite to each other, and, again, equal 

 among themselves, gave the angle = 131° 54', or a deviation of 6 

 minutes. The tetragonal pyramid is thus much more obtuse 



