the Jlile Ha'ui/s Theories of Crystallography. 223 



the secondary forms. A crystalline edifice is therefore 

 raised by means of the integrant particles. What are the 

 laws of this extraordinary architecture? ' By laws I mean 

 the disposition of the laminae, not the means employed by 

 nature to execute the curious structure. 



Laws must exist, 1st, For the formation of the, primitive; 

 and, 2dly, For the construction of the secondary form. The 

 primitives are either similar to their integrant particles, or 

 they are not. If they are, their forms must be paralleiopi- 

 pedons, and their laws of formation very simple ; for there 

 will be the same number of integrant particles in each row, 

 as there are rows in each lamina, as there are laminae in the 

 primitive form. It is easy to conceive that all the joints 

 perfectly coincide with each other and form continued 

 planes ; neither will there be any vacuity left between the 

 particles. If the primitive be not similar to the integrant 

 particle, then the simplicity of the former case disappears. 

 I have already stated that there are three forms of integrant 

 particles; the tetraedron, the triangular prism, and the 

 parallelopipedon. There are also six primitive forms ; the 

 parallelopipedon, the octaedron, the tetraedron, the re- 

 gular hexaedral prism, the dodecaedron bounded by 

 rhombs all equal and similar, and the dodecaedron with 

 triangular sides and formed by two right pyramids united 

 base to base. Of these six primitive forms there are only 

 the parallelopipedon and the regular hexaedral prism that 

 can exactly fill up a space without leaving any vacuity. The 

 integrant particles of the former are paralleiopipedons; of 

 the latter, triangular prisms. As to the other four primitive 

 forms, their integrant particles are tetraedrons. The do- 

 decaedron bounded by rhombs is produced by twenty-four 

 similar tetraedrons without any vacuity between them; 

 the octaedron and tetraedron are formed by tetraedrons 

 leaving octaedral vacuities; and the dodecaedron bounded 

 by triangles, to be formed of tetraedrons, must implv sec- 

 tions parallel to more than six planes ; which perfectly co- 

 incides with observation. 



These vacuities, whose existence must be admitted in the 

 integrant particles, as well as between those particles when 

 forming a primitive, give rise to the following reflections : 



When the elements of a substance are chemically com- 

 bined, that substance is homogeneous. Let us suppose a 

 crystal of such a substance to be subdivided into small pa- 

 ralleiopipedons equal and similar: as the substance is homo- 

 geneous, and these little paralleiopipedons leaving no vacui- 

 ties between them, it is evident the elements that com- 

 pose 



