of certain Crystals, ^f^ 



the tangents of these angles 1414, to 493 : : 2,87 : 1, which 

 also expresses the ratio of the axis of the sphere to that of 

 the spheroid, or the proportional diameters of the generating 

 ellipse. 



Hexagonal Prisms. 



If our elementary spheroid be on the contrary oblong, in- 

 stead of oblate, it is evident that by mutual attraction, their 

 centres will approach nearest to each other when their axes 

 are parallel, and their shortest diameters in the same plane 

 (fig. 13.) The manifest consequence of this structure would 

 be, that a solid so formed would be liable to split into plates 

 at right angles to the axes, and the plates would divide into 

 prisms of three or six sides with all their angles equal, as 

 occurs in phosphate of lime, beryl, &c. 



It may further be observed, that the proportion of the 

 height to the base of such a prism must depend on the ratio 

 between the axes of the elementary spheroid. 



The Cube. 



Although I could not expect that the sole supposition of 

 spherical or spheroidical particles would explain the origin of 

 all the forms observable among the more complicated crys- 

 tals, still the hypothesis would have appeared defective, if it 

 did not include some view of the mode in which so simple a 

 form as the cube may originate. 



A cube may evidently be put together of spherical particles 

 arranged four and four above each other, but we have already 

 seen that this is not the form w^hich simple spheres are natu- 

 rally disposed to assume, and consequently this hypothesis 



l3 



