﻿Cubic Crystals with Theoretical Atoms. 761 



Assemblages of Atoms. 



It may easily be demonstrated as a general proposition from 

 the force equations (23), (24), and (25) that when the 

 direction of rotation of each atom is reversed, the total 

 force of the one on the other is not changed. 



When the axes of the two atoms make other angles with 



rrr 



each other than 0, — , and ir, the equations are. not so simple, 



and the labour of calculating curves is considerably greater. 

 There are two simple arrangements that may be made with 

 atoms of two different kinds, or of the same kind, using 

 these formulae, where all the atoms and their axes of rotation 

 lie in the same plane. Fig. 5 shows such an arrangement 

 of two kinds of atoms in rows and columns, adjacent atoms 

 alternating in kind and direction of axes. The formula 

 for the case a = 0, the stable equilibrium distance being 

 Jc 2 {3kV = 2'236, applies to all vertical columns, and for a = 7r 

 and k 2 @*v= L'936 applies to all horizontal rows. It is 

 evident that each atom in the plane is rigidly held in its 

 position by the action of all the others. Along a diagonal 

 line the atoms are of the same kind alternating in direction, 

 and the formula where a = nr applies, showing that although 

 they are not at the stable equilibrium distance the force of 

 any atom upon the central atom is exactly balanced by a 

 corresponding atom on the opposite side of the central atom 

 at the same distance. 



The diagram is merely illustrative of the process of building 

 up a solid structure with atoms. Of course the force perpen- 

 dicular to the plane is shown by the formulae to be zero, but 

 they also show that for any displacement perpendicular to 

 the plane there is no restoring force, and without other planes 

 of atoms it is evidently an unstable arrangement. 



There is another important consideration to be taken into 

 account in any arrangement. There are forces which de- 

 termine the directions of the axes of rotation independent of 

 any consideration of the translational forces upon the whole 

 atom. These are the third and fourth component forces *, 

 which are magnetic components contributing nothing to the 

 translational force but giving an internal turning moment. 

 These forces acting upon one atom are parallel to the plane of 

 the equator of the second atom, the one taking the direction 

 opposite to the velocity and the other opposite to the 



* Loc. ciL p. 58. 



