Electron Theory of Chemistry to Solids. 743 



2. Another equivalent arrangement is a system of cubical 

 cells with electrons at the corners and the centres of the faces 

 and at the centres of each of the eight cubes into which the 

 larger cube is divided : the atoms are at the middle points of 

 the edges of the large cube, and one is at the centre of the 

 large cube. The electrons at the corners of the cube in this 

 arrangement correspond to the octahedral electrons. 



3. An arrangement with the electrons at the corners, 

 the centres of the edges and the centre of a cube, and at the 

 centres of half the eight small cubes into which the larger 

 cube is divided : the atoms are placed at the centres of the 

 four little cubes not occupied by the electrons. The centres 

 are chosen so that both the electrons and atoms are at the 

 corners of regular tetrahedra — the electrons on the outside 

 of the cube with this arrangement corresponding to the 

 cubical electrons on the dodecahedron. 



To calculate the compressibility we proceed, as before, by 



e. e 

 .calculating 2-^- for each type of atom and electron. 



Starting with the positive atom, the arrangement 1 affords 



the easiest means of calculating E2-, where E is the 



r 



charge on a positive atom and r the distance of the charge e 



e 2 

 from E. Putting E = 3<?, I find this sum is equal to — -^-432, 



where d is a side of the large cube. 



For an octahedral electron, using the arrangement 2 for 



e 2 

 calculation, I find the corresponding quantity to be — -j . 1. 



For a cubical electron, using arrangement 3 for calcu- 



e 2 

 lation, the corresponding quantity is — -= . 7*2. 



Each atom is associated with one octahedral electron and 

 two cubical ones, so that the value for N atoms with their 

 associated electrons is 



2 2 * 



-4N^(43-2 + -l + 14-4)=-N|(28-8). 



If N is the number of atoms per unit volume, M the mass 

 of an atom, ^^ __ A 



where A is the density of the substance. 



Since there are four atoms in each cube whose side is d y 



AT 4 1 / A V 3 



N= ^ or d=\m) ■ 



