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.
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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.
