6 MINERALOGY 



as representing the sphere of action, or the sphere of vibration, or 

 oscillation, of each molecule. 



While the number of elementary point-systems is limited to 14, 

 the number of complex point-systems must be much extended in 

 order to reach a satisfactory explanation of the symmetry of those 

 crystalline types in each system lower than the normal. These 

 lower types of symmetry may be produced by a combination of 

 the elementary point-systems: 1. As if one were pushed within 

 the other, there will be, in such a case, two sets of molecules, one 

 occupying a position in respect to the other, as if translated along 

 a definite direction. 2. By the rotation of one in regard to the 

 other. 3. By both rotation and translation. The number of 

 point-systems made possible by these methods will reach 230. 

 It still remains true, however, that in regard to their symmetry 

 they will all be included in the 32 possible types of crystals. 



Definition of a crystal. A crystal is a homogeneous chemical 

 compound bounded by plane faces, and its physical properties 

 are alike along parallel directions. 



Crystal growth. If growth is considered to be an increase of 

 size only, then crystals may be said to grow. This crystalline 

 growth must not be confounded with organic growth, which is a 

 development. The tissues in an organism increase in complexity ; 

 the unit in organic growth is the cell, which increases by division. 

 One cell producing two, these in turn increase in size by an assimi- 

 lation of material within the cell wall. Organic growth takes 

 place from within, while crystalline growth goes forward by the 

 attachment of crystalline molecules from without the point- 

 system, extending the individual crystal laterally in every direc- 

 tion by .the thickness of each molecular sheet added. One crystal 

 therefore cannot be an embryo of another, as when a sufficient 

 number of molecules have collected to form a unit of the point- 

 system, and are fixed in the required position, they will possess 

 all the crystalline characters. Microscopic crystals, however 

 small, are just as perfect in regard to their chemical and physical 

 properties as a crystal a foot in diameter, the difference being a 

 mere matter of mass or bulk. 



Crystallization. It has been shown that in the crystalline state 

 of matter each molecule has a definite and fixed position relative 

 to those surrounding it. In the liquid, gaseous, and dissolved 

 states, every molecule is free to move, and in any direction, leav- 

 ing out of account the so-called liquid crystals; and until their 



