﻿Cubic Crystals with Theoretical Atoms. Ihl 



to any two atoms. It should be noted that there are no terms 

 in the coefficient of v~ 4 which do not contain the factor /3 J , 

 whereas there are many such terms in the coefficient of v~*. 

 In fact, the terms containing ySJ in this coefficient are added 

 to the terms without /3J: and since /3| is a very small 

 quantity, all these /3* terms have been omitted from the 

 coefficient of v~ 6 as they do not affect the value of F in a 

 perceptible degree. 



The study of these equations is by no means completed. 

 When the three component forces are resolved along the 

 radius vector joining the centres of the atoms to get the total 

 attraction or repulsion between them, and equated to zero, 

 the result gives the locus of all points where there is no force 

 between the atoms along the radius vector. For any given 

 angle a between the axes of the two atoms we obtain a 

 surface in space surrounding the atom which varies in shape 

 continuously with a change in a. It seems likely that these 

 surfaces possess important mathematical properties, and may 

 prove to be of considerable interest to the mathematician. 

 Only a few of the sections of these surfaces by a plane through 

 the origin have as yet been worked out, but they have proved 

 to be of considerable interest because it has been possible by 

 means of them to demonstrate the complete stability of a 

 simple crystal on the cubic system, such as rock-salt or 

 potassium chloride. 



When using the numerical values of (3 ^ and the dimen- 

 sions of the positive electron given in my theory of the atom, 

 I obtain dimensions for a crystal which agree within the 

 limits of error with the experimental work of Bragg and 

 others and confirm his opinion that there is but a single atom 

 at each corner of the cube in the crystals mentioned. Fig. 1 

 shows a portion of such a crystal and indicates tl.-e direction 

 that the axis of rotation of each atom must assume to produce 

 a stable equilibrium structure. Each axis takes the direction 

 of the long diagonal of some cube in a manner to be described 

 in a subsequent section. 



Special Case, u — 0. 



When the axes of rotation are parallel in the same direction, 

 and a = 0, the equations are much simplified. The axes of 

 reference may then be chosen so that the two atoms lie in 

 the i, k or the x, z plane and v/ = 0, also Y — 0. Since Y is a 

 factor of F ?/ , this force vanishes, showing that the total force 

 lies in the ?', a: plane. The forces may then be resolved along 



