74 HABIT AND INTELLIGENCE. [cHAP. 



Secondary truncated by cubic faces, and cubes with edges truncated 

 by dodecabedral faces ; and other instances of the occur- 

 rence of secondary planes on the angles or edges of the 

 Transi- primary forms. Gradations between two of the primary 

 fornfs forms of the same species, as for instance between the 

 cube and the octahedron, are possible through these com- 

 bined forms. But gradation between the angles of any 

 two faces on each other is not possible : for, as already 

 stated, the intercept of any face on any axis stands in a 

 simple ratio to the parameter of that axis ; and were there 

 indefinite gradation, they would have to pass through 

 complex ratios. 

 Analogy The existence of different forms within the limits of 

 m-ganisms. ^^^^ same crystalline species may perhaps be remotely 

 compared to the existence of those different forms within 

 the limits of the same organic species which are related 

 to each other as male and female, as larva and perfect 

 form, and in other ways of which I cannot now speak 

 particularly. 

 Law of In normally formed crystals, every face has a similar 



symme ry. ^^^^ opposite to it ; and not only opposite to it, but in 

 every position where a face is possible that is similarly 

 situated with respect to similar axes. Similar faces, in 

 crystallography, are those which are similar in relation to 

 similar axes, though they may not be similar in size or 

 form : and similar axes are those which are inclined to the 

 other axes at equal angles, and the parameters measured 

 on which are equal. 



Crystals that present all the faces required by the law 

 of symmetry just stated are called holohedral crystals. 

 But in many cases only half the faces of a holohedral 

 form, or half of some particular set of similar faces, are 

 presented, the alternate ones being left out. Such forms 

 Hemi- ^^^ Called hemihedral ; the tetrahedron, for instance, is 

 hedrism. the hemihedral form of the octahedron. There is no 



instance of anything like heniihedrism among organisms. 

 V Another way in which crystals deviate from typical 



„ . symmetry is by the production of hemimorphic forms, 

 morpliism. In these the two extremities of the crystal are of different 



