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



If electrons are placed at the centres of each of the six 

 faces of the cubes as well as at the corners, since each 

 middle point is shared by two cubes, each of the six central 

 electrons will count as one half ; the number of electrons will 

 be four times the number of cells, so that this is a possible 

 distribution for a tetravalent element. 



The atoms at the centres of these cells may either form a 

 rectangular spnce lattice of the simplest kind, or a system 

 built up of different lattices ; since a series of layers of 

 these face-centred cubes will still fit, if one layer, for 

 example, a horizontal one, is moved relatively to the layer 

 above or below it parallel to a diagonal of a horizontal face 

 of the cube and through a distance equal to one-half the 

 length of the diagonal. By moving the layers about in this 

 way we can get distributions of the atoms corresponding to 

 the distributions of the centres of the spheres in the different 

 methods of piling shot. 



If instead of placing electrons at the centres of the faces 

 we place them at the middle points of the twelve edges of 

 the cube, since each middle point is shared by four cubes, 

 these twelve electrons count as three, so that in this arrange- 

 ment, as in the previous one, the number of electrons will be 

 four times the number of cells. This arrangement would 

 be possible for a tetravalent element ; we shall see, however, 

 that it is much less stable than the previous one. 



Another symmetrical arrangement with cubical cells is one 

 where four electrons at the corners of a regular tetrahedron 

 are placed inside the cell. These are to be placed according 

 to the following plan : — Let AB be two points at the opposite 

 ends of a diagonal of one of the faces of the cube, C and D 

 the ends of the diagonal of the parallel face, CD being at 

 right angles to AB. Join 0, the centre of the cube, with 

 ABOD ; measure from equal lengths, OP, OQ, OR, OS, 

 along OA, OB, 00, OD ; then P, Q, R, S will be the corners 

 of a tetrahedron symmetrical with respec*t to the cube. If 

 there are electrons at each corner of the cube this arrange- 

 ment will give five electrons per cell. 



The preceding arrangements are all symmetrical with 

 respect to three axes at right angles to each other and so 

 would correspond to the cubical system in crystallography. 



If instead of placing electrons at the centres of all the 

 faces of the cubes we place them only on the faces at right 

 angles to the axis of a, we get a distribution which gives 

 two electrons per cell but which is not symmetrical about 

 the three axes sd, y, z, and so could not correspond to a 

 crystal belonging to the cubical system, but to one belonging 



