CKYSTAI.i.nCKAlMiy 



supplement of the inter-facial angle r'ac; for details of measure- 

 incut see page 149. 



Symmetry. All natuiv in its building follows rules of sym- 

 metry : worms possess many segments, one of which is a repeti- 

 tion of the conditions found in that adjacent. The leaves of 

 plants are placed on the stem following definite rules of repetition ; 

 and in vertebrates the right side is a mirror image of the left, 

 following a bilateral plan. These rules in organic nature are only 

 partially adhered to and are not followed with that mathematical 

 exactness which the constancy of the interfacial angles in crystals 

 demands. Symmetry may be defined as the repetition of condi- 

 tion following definite rules. The rules of symmetry in crystals 

 apply not only to the repetition of faces, which determine the 

 outward form, but to the internal molecular arrangement and all 

 the physical properties as well. 



In crystals the three rules of symmetry are : (1) symmetry in 

 regard to a plane; (2) symmetry in regard to an axis; (3) sym- 

 metry in regard to a center. 



A solid is said to possess a plane of symmetry when that plane 

 divides the solid in two halves, in such a manner that all the con- 

 ditions on one side are faithfully 

 repeated on the other side of the 

 plane, as in a mirror image ; or if 

 from any point c, Fig. 13, on one 

 side of the plane ab, a perpen- 

 dicular be drawn to the plane and 

 extended in a straight line an 

 equal distance on the opposite 

 side of the plane, if the plane is 

 a plane of symmetry, there will 

 be a point c at its extremity, the 

 conditions surrounding which will 

 be exactly the same as the con- 

 ditions surrounding the original 

 point, and the solid is said to be 

 symmetrical in respect to a plane. 

 A plane mirror is the best ex- 

 ample of a plane of symmetry, as on looking in the mirror every 

 object in front is apparently repeated in the mirror. Symmetry 

 in regard to a plane is the symmetry of reflection. 



If the similar parts of a solid are repeated more than once in 



FIG. 13. Plane of Symmetry. 



