Electron Theory of Chemistry to Solids. 725 



by pd, qd, rd, where p, q, r are positive or negative integers,, 

 two of these must be odd and one even. These two lattices 

 are again equivalent to a system of face-centred cubes. 



The preceding results may be summed up in the following- 

 table, where the first column gives the valency of the atom, 

 the second the possible shapes of the cells formed by its 

 electrons, and the third the nature of the symmetry of the 

 arrangement. 



Valency. Shape of Cell. Symmetry. 



1 . Cube with electrons at the corners cubical. 



2. Hexagonal prisms hexagonal. 



Cubes with electrons at the centres of one set of 



parallel faces tetragonal. 



3. Hexagonal prisms with an electron at the centre 



of each end hexagonal. 



Cubes with electrons at the centres of two sets 



of parallel faces . . , tetragonal. 



Rhombic dodecahedron - , . . cubical. 



4. Face-centred cube cubical. 



Hexagonal prism with two electrons along the 



axis at equal distances from the centre hexagonal. 



5. Hexagonal prisms with electrons at the centres 



of the side faces hexagonal. 



Electrons ac the corners of cubes with a regular 



tetrahedron of electrons inside cubical. 



6. Hexagonal prisms with electrons at the centres 



of all faces hexagon. 



Cubo-octahedron , cubical. 



Face-centred cube with two electrons inside .... tetragonal. 



7. Electrons at the corners of a cube with six 



electrons inside at the corners of a regular 



hexahedron cubical. 



Electrons at the corners and centres of side faces 

 of a hexagonal prism with, two electrons 

 inside, on the axis, at equal distances from 

 the centre hexagonal. 



Though the table is not complete it will be seen that for 

 most of the valencies more than one arrangement of the 

 electrons is possible, indicating that for such elements there 

 might be allotropic modifications with different crystalline 

 forms. 



Hitherto we have supposed that the cells in which the 

 electrons may be arranged are regular solids, that the 

 parallelepipeda are cubes, the hexagonal prisms regular, 

 and so on; it is evident, however, that such an assemblage 

 of regular cells with the atoms at their centres will, if it be 



