ISOMI.TKH SYSTKM 





any OIK- form on the triangle will depend upon the; value of the 

 variable. As the pole of any of the variable forms approaches 

 the angle of the triangle, both variables approach their limits; and 

 upon reaching their limits the pole assumes the position of one of 

 the a\f> of symmetry, and as there is only one point in the angle 

 of the triangle, therefore there is only one possible form of the 

 hexahedron, rhombic dodecahedron, or octahedron, and they are 

 known as the fixed, or limiting forms. All substances crystallix- 

 ing in these forms must have the same angle. 



In each type there are always seven possible forms. The most 

 general form is represented by the area of the triangle; and as the 

 number of points which the pole of the face may occupy is unlimited, 

 there are therefore innumerable individuals forming a series. The 

 three sides of the triangle each represents a series of variable forms, 

 as here also there is a large number of points on each side between 

 the angles, each of which may be occupied by the pole in turn. 

 The three angles of the triangle represent the three fixed forms, 

 as there is only one point in each of the three angles. The 

 seven forms possible in each type are represented by the seven 

 elements of the triangle, of which the three angles represent the 

 three fixed forms, and the three sides and area represent the 

 variable forms. 



Combination of Forms 



Crystals may present one form only, when the number of faces 

 is very limited ; more often they are combinations of two, three, or 

 even all seven of the possible forms in the type, and in addition 

 forms of the same series ; in such cases the number of faces possible 



Fio. 84. 



FIG. 85. 



on a crystal is very large and their relation complex. Such com- 

 plex crystals are rare in nature, for by far the larger number are 



