VII.] CRYSTALLIZATION. 77 



are equal, the optical elasticity is the same in all direc- 

 tions, and no polarisation takes place. Such is the case in Cubic 



, . , , crystals. 



cubic crystals. 



When two of the axes of elasticity are equal, and the 

 third either greater or less, the ellipsoid is a spheroid of 

 rotation, having the axis that is unequal to the others as 

 its geometrical axis ; the geometrical axis is the only axis 

 the sections at right angles to which are circles, and con- 

 sequently is the axis of no polarisation, or optic axis : a 

 ray passing in any other direction is polarised. Crystals Uniaxial 

 with these optical properties are called uniaxial. 



When all the three axes of elasticity are unequal, the 

 ellipsoid is not a spheroid of rotation : there are two 

 diameters, at right angles to which the sections are circles, 

 and which consequently are optic axes : these are not 

 coincident with any of the axes of elasticity, but are 

 in the same plane with the axes of greatest and least 

 elasticity. Crystals with these optical properties are called Biaxial 



, . . 1 crystals. 



biaxial. 



It is necessary to bear in mind, that the axes of elasticity 

 and the optic axes are not lines, but directions ; and that 

 the ellipsoid by which the optical structure of a crystal 

 is represented, though a true representation of facts, is 

 imaginary. 



After this brief account of the geometrical and 

 optical properties of crystals, it is time to give some 

 account of their classification. Tlie classes, or systems, of Systems of 

 crystals are distinguished from each other by' the incli- '^'^^^ 

 nation of their axes, the equality or inequality of their 

 parameters, and their optical properties. 



In the cubic system, the axes are at right angles and Cubic . 

 the parameters equal : the optical elasticity is equal in all ^•'^^ *^™" 

 directions, and is represented by a sphere ; they have, 

 consequently, no polarising structure. 



In the square prismatic system, the axes are at right Square 

 angles ; two of the parameters are equal, but the third is system. ^*^ 

 unequal to the other two. The axis of unequal parameter 

 is called the vertical axis; it is an axis of symmetry 

 for the crystal, — that is to say, the edges and angles 



