36 



STRICTURE OF MINERALS. 



2. Half the similar parts of a crystal, alternate in position, 

 are modified independently of the other half. 



In the cube, octahedron, or dodecahedron, if one edge is 

 replaced, all the other edges will be replaced, and by the 

 same planes. If there are two planes on one edge, (fig. 32) 

 there will be two on every other edge ; and the two on each 

 will have the same inclinations. If there are three planes 

 on one angle, (fig. 33) there will, in the same manner, be 

 three on the other seven angles. Perfect symmetry is thus 

 preserved, however numerous the added planes. The fol- 

 lowing figures illustrate this principle, that all the edges, and 

 all the angles are modified alike. 



32 33 34 35 



This symmetry is well seen in the solids which the secon- 

 dary planes, in the above figures, produce, if enlarged till 

 .he primary planes are obliterated. Thus from figure 32, 

 comes the form in figure 36, the planes e' being enlarged till 

 the planes P are obliterated ; from 33, comes the form in 

 fig. 37 ; from 34, the" form in 38 ; and from 35, the form in 

 39. The form in figure 37 has 24 faces, and is called a 

 trapezohedron. It is common in garnet and leucite. 

 36 37 38 39 



In figure 35, there are six planes on each angle, and as there 

 are eight angles in the cube, the solid represented in figure 

 39 has forty-eight faces. Both 38 and 39 are forms of the 

 diamond. 



In connection with the law above given, it is stated that 

 half the similar parts may be modified independently of 

 the other half. The parts thus modified are alternate with 

 one another and still produce symmetrical solids. Thus the 



What second law is mentioned ? Explain the first law ty examples. 



