742 Sii* J. J. Thomson on the Application of the 



the square o£ the distance is, for N atoms and N electrons, 



e 2 



-N.l-77^ 



a 



It follows, as on p. 735, that the bulk modulus will be 

 given by 



where N is the number of atoms per unit volume. 



Since N = ^ an 



, 1 /2A\ 1 /3 



■'nn 



y 



This is not much more than half the value for the previous 

 arrangement, which agreed exceedingly well with experiment. 

 Hence we conclude that the arrangement we have just been 

 discussing does not represent that of the alkali metals, while 

 the distribution with one atom at the centre of a cube of eight 

 electrons does so. 



Compressibility of a irivalent element. 



We proceed to test the theory by taking another case 

 where the distribution of electrons is of a different character 

 from either of the preceding cases. 



A trivalent element when in a solid state must have the 

 atoms and electrons arranged so that there are three electrons 

 for each atom. If the solid crystallizes in the regular system 

 this will require each atom to be surrounded by a rhombic 

 dodecahedron of electrons. When these dodecahedra are 

 packed together so as to fill space, the arrangement can be 

 seen to be equivalent to any one of the following : — 



1. A system of cubical cells with the atoms at the corners 

 of the cube and also at the centre of its faces. The electrons 

 are arranged (a) at the middle points of the edges or the cube, 

 (b) at the centre of the eight cubes into which the larger cube 

 is divided by planes bisecting its edges at right angles, (c) an 

 electron at the centre of the large cube. This arrangement 

 gives the equivalent of four atoms per cell : the electrons at 

 the middle points of the edges are equivalent to 3, those at 

 the centre of the little cubes 8 ; these with the one at the 

 centre of the large cube make 12 — three times the number 

 of atoms. 



