134 Prof. Breithaupt on Thirteen Systems of 



ively to the three planes mutually at right angles to each other, in 

 which lie the twenty-four edges of the crystals before mentioned ; 

 and I found that one optical axis was plainly visible, in a direc- 

 tion perpendicular to a hexahedral plane. The cutting of the 

 crystal was not quite perfect, and therefore the point of inter- 

 section was not very clear; but the double refraction was un- 

 questionable. I am now having a similar cube cut out of a cry- 

 stal of almandine. 



It has long been known that I discovered a particular law in 

 the crystallization of iron pyrites and cobalt-glance, by which 

 the pentagonal dodecahedron may be disjoined and formed into 

 a combination of two rhombohedrons, while the hexahedron and 

 octahedron retain their peculiarities. Naturally all forms with 

 two- and threefold edges must behave in the same way, and be 

 capable of being disjoined and formed into figures with one axis. 

 I never found even two of those truncations, which are placed 

 obliquely on the edges of the cube, to have a like inclination to 

 the hexahedral planes. 



The crystals of iron pyrites used in these investigations were 

 from Kongsberg in Norway (with calc-spar), from Traversella, 

 from Schemnitz in Hungary (in druses with galena, and blende), 

 and from Mautern in Styria. The difference in the inclination 

 of the planes of a supposed pentagonal dodecahedron is only 

 4 minutes, as shown in the above-mentioned crystals j but in 

 the cobalt-glance from Skutterud in Norway, and from Tuna- 

 berg in Sweden, it is above 8 minutes. These facts have up to 

 this time been ignored in mineralogical treatises, but have never 

 been contradicted. 



M. Websky, a pupil of mine, has confirmed them ; he found 

 a difference of from 5 to 10 minutes, and presented his ob- 

 servations to me, which I take this opportunity of acknow- 

 ledging. 



The behaviour of the last-named minerals so far resembles the 

 garnets, that if you place the crystal so as to have the axis of an 

 acute rhombohedron perpendicular, it will be exactly represented 



by the formula ^r-, while the obtuse rhombohedron is still more 



obtuse than it would be if represented by this formula. These 

 pyrites have also one of the four hexagonal axes as the principal 

 axis. The hexahedron will remain as the general primary form 

 of this genus, which I call Marcasites, and to which all the 

 pyrites belong which crystallize in the tesseral form. But the 

 obtuse rhombohedron designated for the future as B, will be an 

 especial primary form for those species which do not possess a 

 pentagonal dodecahedron, but which are formed by the combina- 

 tion of two rhombohedrons. 



