92 



MINEEALOGT. 



It will be seen that, in the formation of these two different 

 dodecahedrons on the same primary form, the cube, if the 

 molecules, as they doubtless are, be all of the same cubic 

 form, they must be very differently arranged in the two cases ; 

 for in the rhombic dodecahedron, fig. 24, the faces are all 

 equal, and inclined on the faces of the cube at the same 

 angle ; while in the pentagonal dodecahedron, the faces of 

 the pyramid are only equal two and two, a and , 5 and , 

 and are inclined on the planes of the cube at different angles. 

 From measurements by the goniometer, and calculations care- 

 fully made, for the purpose of determining the mode of aggre- 

 gation of atoms of the same shape, requisite to produce these 

 different forms, it has been ascertained that the pyramids of 

 the rhombic dodecahedron, fig. 24, must be composed of suc- 

 cessive layers of molecules, each layer being of the thickness 

 of one molecule, and each successive layer diminishing by 

 the breadth of one molecule on each side ; but that in the 

 case of the pentagonal dodecahedron, fig. 29, the layers com- 

 posing its pyramids must be of the thickness of two mole- 

 cules, and must diminish in breadth unequally on the two 

 sides; that is, on the side of the quad- 

 rangular plane a, they must diminish 

 two molecules in breadth, for one in 

 height ; and on the side of the trian- 

 gular plane b, they must diminish one 

 molecule in breadth, for two in height, 

 thus (fig. 30). 



Hence, it is inferred that external 

 form depends, as might be supposed, 

 on internal structure, and is deter- 

 mined by the combination of minute 

 particles of regular shape. 



We will now submit a list of the primary forms, which, on 

 the authority of Mr. Brookes, are supposed to be in number 

 fifteen: 



1. The cube, contained within six square prisms (fig. 31). 



2. The regular tetrahedron, contained within four equila- 

 teral triangular planes (fig. 32). 



3. The regular octohedron, resembling two four-sided 

 pyramids, set base to base. The planes are equilateral 

 triangles ; and the common base of the two pyramids, which 



FIG. SO. 



