724 Sir J. J. Thomson on the Application of the 



three electrons to each of these cells. This would corre- 

 spond to a trivalent element and would possess cubical 

 symmetry. The disposition of the atoms round the dodeca- 

 hedron is as follows : — 



Let us call the corners where four edges meet the octa- 

 hedral points, as these points are at the corners of a regular 

 octahedron, and let us take the axes of the octahedron as the 

 axes of %, y, and z. Each of these octahedral points, e. g. P 

 the one whose coordinates are (0, 0, d), has four atoms round 

 it, in a plane through P at right angles to the line joining 

 the point P to the centre ; the lines joining P to these 

 atoms are parallel to the two axes of the octahedron which 

 are at right angles to OP, and the distance of each of these 

 atoms from P is equal to d the distance of P from the centre. 

 In addition to these atoms there is one at the centre of each 

 dodecahedron. It will be seen that this arrangement of the 

 atoms is equivalent to that of a system of face-centred 

 cubes, the centres of the cubes being at the octahedral points 

 of the dodecahedra and the sides of the cubes parallel to the 

 octahedral axes. 



The Cubo-octahedi 



*on. 



This has twenty-four corners, and when the cells are packed 

 together so as to fill space each of the corners forms a part 

 of four cells ; there will be thus on the average six electrons 

 to each cell, so that this gives a symmetrical arrangement 

 for the arrangement of the electrons in a hexavalent solid. 

 (Fig. 2.) 



Pig- 2. 



The disposition of the atoms may be represented as 

 follows : — Take the centre of one of the cells as origin and 

 the perpendiculars to the three square faces as the axes of 

 coordinates, then the atoms are represented by two lattices; 

 in (1) the coordinates of a point on the lattice are represented 

 by pdj qd, rd, where p, q, r are even positive or negative 

 integers and d is the distance of one of the plane faces from 

 the centre of the cell ; in (2) the coordinates are represented 



