24 CALIFORNIA ACADEMY OF SCIENCES. 



In the following table are contained the angles for each form, 

 from which the inclination of any two faces on a colemanite 

 crystal may be calculated. I have taken as the basis for these 

 calculations the axial elements already given, viz: 



a : b : c = 0.774843 : 1 : 0.540998 

 ft = 69° 50' 45" 



In all the positive hemi-pyramids (those lying over the acute 

 angle ft), let — 



X, represent the iuclination of the face of the pyramid to the 

 plane of the vertical and clino axes (inclination to the plane of 

 symmetry. 



Y, represent the inclination of the face of the pyramid to the 

 plane of the vertical and ortho axes (inclination to the ortho- 

 diagonal section). 



Z, represent the inclination of the face of the pyramid to the 

 plane of the lateral axes (inclination to the basal section). 



fA, represent the iuclination of the clino-diagonal polar edge to 

 the vertical axis. 



v, represent the inclination of the same edge to the clino-axis. 



p, represent the inclination of the ortho diagonal polar edge to 

 the vertical axis. 



a, represent the inclination of the middle edge to the clino-axis. 



The angles of the negative hemi-pyramids (those lying over the 

 obtuse angles of the morphological axes) are represented by the 

 same characters; only where the angles differ in value from the 

 corresponding angles of the positive form, an accent is added. 

 We thus get for the negative hemi-pyramids : X',Y', Z', // and v' . 



For the positive hemi-pyramids: 



X = 63 10' 33" fx = 69° 24' 57" 



Y= 71 43 14 v= 40 44 17 



Z = 47 27 18 o- = 52 13 48 



p=61 35 12 



