126 Prof. W. H. Miller on Quartz, Ice. and Karstenite. 



and the other seen through the faces 1 1 0, 110, appeared to 

 make with one another an angle of 36° 22'. Hence the direc- 

 tion of either optic axis within the crystal makes an angle of 

 22° 1' with a normal to the face 010. 



In crystals from Berchtesgaden, Hessenberg searched in vain 

 for a face of the form 101, for the existence of which I consi- 

 dered that I had had satisfactory evidence. I therefore reex- 

 amined the crystal in which I supposed it to be visible. Using 

 a spot of sunlight reflected from a plane mirror as the bright 

 signal, the crystal being adjusted so that the intersection of the 

 faces 111, 111 was parallel to the axis of the instrument, an 

 image of the spot of sunlight was seen as if reflected from a face 

 making equal angles with the faces 111, 111; but on ma- 

 king the crystal revolve round the axis of the branch of the 

 holder parallel to the plane of the circle, the spot remained im- 

 movable. Hence it is evident that the spot of light seen was not 

 due to a single reflection, but to a reflection at each of two sepa- 

 rations in the interior of the crystal parallel to the faces 01 

 and 100. 



In several of the fragments of crystals from Berchtesgaden 

 faint separations indicative of cleavages were observed, which, 

 on measuring the angles they made with the face 10 with a 

 position- micrometer, were found to be parallel to the faces of the 

 form 110. It was not found possible to separate the crystal 

 in the direction of this cleavage, on account of the superior faci- 

 lity of the other cleavages. 



Some colourless crystals from Stassfurth, given me by M. 

 Pisani, of Paris, had the faces of many of the simple forms 

 striated to such an extent that it was extremely difficult to mea- 

 sure the angles they made with one another. By using for the 

 bright signal a large beam of sunlight reflected from the mirror 

 of a heliostat, I think I have ascertained the existence of the fol- 

 lowing forms, the last two being the least certain : — 



100, 010, 001, 110, 210, 310, 320, 430, 5 10, 



10 2, 2 3. 



001, 102 . . ' . 26 33 

 001, 203 ... 33 40 



