Prof. W. H. Miller on Quarts, Ice, and Karstenite. 125 



published in the Abhandlungen der Senckenbergischen Naturfor- 

 schenden Gesellschaft, Frankfurt a. M. vol. viii. 



Let the symbols 10 0, 010 denote faces normal to the lines 

 bisecting the obtuse and acute angles between the optic axes, 

 01a face parallel to the plane of the optic axes, and 110 the 

 face which, according to the observations of Hessenberg, makes 

 with 100 an angle of 48° 15', the angle between two planes 

 being measured by the angle between normals to them drawn 

 from any point in the interior of the crystal. 



The crystals from Liineburg exhibited faces of the forms 

 100, 010, 110, 210, 310, 5 10, 5 40, 3 2 0, 410, 4 3 0, 

 15 0, 5 2 0, 5 3 0, of which the 4th .. . 9th were first observed 

 by Hessenberg. The last four appear to be new. The faces of 

 all these forms give very indistinct reflections, with a single ex- 

 ception : in one of the crystals a .face of the form 110 was 

 very perfect ; the observed values of the angles it made with 

 the cleavage 100 were:— 131°, 45', 44'*2, 44'*55, 44'*5, 44'*7; 

 mean 131° 44'-6. Hence 100, 1 1 =48° 15'*4. The angles 

 between the different faces and the face 100, taking Hessen- 

 berg' s value of the angle 100, 110, are : — 



010, 001 . 



. 90 



100, 010 . 



. 90 



100, 001 . 



. 90 



100, 5 10 . . 



. 12 38 



100, 410 . 



. 15 39 



100, 310 . 



. 20 29 



100, 520 . 



. 24 8 



100, 210 . 



. 29 15 



100, 530 . 



. 33 55 



100, 320 . 



. 36 45 



100, 430 . 



. 40 2 



100, 540 . 



. 41 52 



100, 110 . 



. 48 15 



100, 150 . 



. 79 53 



When light is refracted through the prism bounded by the 

 planes 10 0, 110, the least-refracted ray is polarized in a plane 

 parallel to 1. The indices of the light in this plane are :— 



Extreme red 1*569 



Brightest part of spectrum . . . 1*577 



Boundary of green and blue . . 1*580 



Extreme violet 1*589 



In water one optic axis seen through the faces 110, 110. 



321T4 



