PASSAGE OF ONE FORM IXTO ANOTHER. 



49 



The idea here intended to be expressed will become more intelli- 

 gible by a reference to the annexed figures. Fig. 116 represents a 

 regular hexagonal Prism, with its terminal edges replaced by tan- 

 gent planes, the new planes being but slightly produced. Fig. 117, 

 the same, in which the new planes ure still farther extended ; and 

 Fig. 118, in which the hexagonal summits have given place to mere 

 points, and the sides of the prism entirely disappeared, the original 

 solid having become a Dodecahedron with triangular faces. 

 Fig. 116. Fig. 117. Fig. 118. 



The foregoing instance may serve to explain what is understood 

 in crystallography, when it is said one form passes into another. 

 The latter solid is said to be derived from the first. 



It is requisite that the student should be made acquainted with 

 some of those forms, which may thus be derived from others accord- 

 ing to the laws of symmetry, since these derivations will explain 

 that multiplicity of forms under which the crystals of the same spe- 

 cies sometimes occur. (. 30.) 



It has been seen that, in the regular Tetrahedron, the Cube, and 

 the regular Octahedron, all the faces in each are equal and similarly 

 situated ; and that the same is true as respects their solid angles and 

 edges. A similar identity has been ascribed to the faces and edges 

 of the rhombic Dodecahedron, and, also, to its six solid angles form- 

 ed from the meeting of four plane angles, and to its eight solid angles 

 of three plane angles. 



The similar parts of one of these solids would be modified in a sim- 

 ilar manner, if we suppose that its similar edges or similar solid an- 

 gles are replaced by tangent planes; and if we suppose the second- 

 ary planes to be so extended as to extinguish those of the primary, 

 it is obvious a new polyhedral solid must appear, contained under 

 faces amounting in number to the edges or angles replaced in the 

 original form. 



If now we collect the number of similar parts, which are similar- 

 ly situated, as respects the centre in each of the above mentioned 

 forms, we have the following result. 

 5 



