xu INTRODUCTION. 



1. Of the Physical Characters of Minerals. 

 External Form and Strvcture, 



Crystallography, or a knowledge of the crystalline forms of minerals, is of 

 the highest importance. It is true minerals frequently occur in an amor- 

 phous state ; in which case, the particles of which they are composed are 

 arranged according to no definite law ; but they very often are crystallized, 

 i. e. assume certain regular and determinate forms called crystals. 



To one ignorant of the subject the shapes of these seem to be Innumer- 

 able ; but on closer examination such does not prove to be the case. On 

 the contrary, it is found that all these numerous and sometimes complex 

 varieties of crystals may be reduced to some five or six simple types, of 

 which the others are only modifications or variations — and even that the 

 complicated forms of crystals may be sometimes actually converted into the 

 typical form by the mechanical process of cleavage. 



This simple or elementary form to which each particular crystal is capable 

 of being ultimately reduced, has been called, therefore, its primary form. 



Various systems of crystallography have been proposed by different 

 authors. The classification adopted here is nearly the same as that employed 

 by Brooke and Miller in their admirable edition of Phillips's Manual, and is 

 a modification of the systems of varfous other crystallographers. These 

 systems, six in number, are called respectively, the Cubical., Pyramidal, 

 Rhomhic, Oblique., Anorthic, and Hexagonal or Rhombohedral.* 



1. The Cubical System — has three equal axes, intersecting one another at 

 at right angles. 



Thus, in the cube, the regular octahedron and the rhombic dodecahedron, 

 which belong to this system, the height, and the length, and the breadth of 

 the axes are all equal, and are at right angles to each other. In the cube 

 the axes are drawn from the centres of opposite faces ; in the regular octa- 

 hedron they connect the opposite solid angles ; and similarly in the rhombic 

 dodecahedron. 



2. Pyramidal System. — In the pyramidal system there are, also, three 

 axes intersectinfj each other at right angles ; but one of these, called the 

 vertical axis, differs in length from the other two, or lateral axes, which are 

 equal. 



The right square prism, and the octahedron with a square base, belong to 

 this system. 



In the first the axes connect the centres of opposite faces, and are at right 

 angles to one another. 



In the octahedron with a square base, which bears the same relation to 

 the right square prism as the regular octahedron does to the cube, the axes 

 connect the opposite solid angles. 



3. Rhombic System. — In this system there are three unequal axes Inter- 

 secting one another at right angles. It includes the right rectangular prism, 

 the right rhombic prism, and the octahedron with a rhombic base. 



* These corrpspond respectively with the following systems employed in Dana's Manual of 

 Mineralogy, 4th edition :—l. Monometric, or Tesseral. 2. Dimetric. 3. Trimetric. 4. Mono- 

 clinic. 5. Triclinic. 6. Hexagonal. 



