306 



On the Intimate Structure of Crystals. 



the primitive octahedron in that direction. As a consequence the 

 atoms of fluorine must be as widely divergent from each as possible, 

 and since no gyrality has been detected in any of the numerous forms 

 of fluorspar, it may be concluded that they are disposed in holohedral 

 symmetry ; this cannot be that of case 2, for this would not permit of 

 contact between the fluorine atoms of adjacent primitive octahedra, 



FIG. 11. 



and thus would not be compatible with stability ; we are thus led to 

 attribute to fluorspar the structure of case 1. Calculating from these 

 premises it is found that the diameter of the atom of fluorine is 

 measured by the quantity 1-573 ; from this it follows that the gross 

 volume is 3 - 892, a result in accordance with what knowledge we 

 possess of the gross volume of fluorine in other compounds. It will be 

 observed that this number is smaller than that previously assigned to 

 the diameter of an atom of hydrogen. 



The hardness and cleavage of fluorspar stand in direct connection 

 with its structure ; its perfect octahedral cleavage may be correlated 

 with the vacant spaces which remain in the crystal as a consequence 

 of the symmetrical disposition of the complex octahedral groups ; its 

 hardness both with this and the arrangement of the atoms within the 

 octahedral groups. The difference in the hardness in different direc- 

 tions has been very carefully explored ; on the faces of the cube its 

 maximum lies parallel to the tetragonal axes, its minimum to the 

 digonal axes, and it is in these directions that the atoms are respec- 

 tively in closest proximity and the reverse ; on the octahedral faces 

 the maxima lie parallel to the trigonal axes, and the minima to the 

 digonal axes, which again are directions of greater and less proximity 

 of the atoms. 



In concluding this part of the subject I desire to express my cordial 

 thanks to Professor Miers for much friendly criticism and useful 

 advice. 



