﻿764 Dr. A. C. Crehore on the Construction of 



opposite parallel edges of a cube. This plane is always per- 

 pendicular to one face of the cube and makes angles of 45° 

 with each of the other faces. 



Equilibrium for Translational Forces. 



As far as the translational force upon the atom is con- 

 cerned, its value for all adjacent atoms along any edge may 

 be found by substituting in the general formulae (23), (2-4), 



and (25) the one set of values Y = 0, X= - _^L 6 , Z = + ^1 

 I 3 6 



cos a= -, a = 70° 31 ''7, which gives the forces 

 o 



Fx= + K^" {PP'£J ( -1*089) ir 4 + 2m 2 2rc 2 ( + 3-517) tr* j i, (38) 



COS a = 1 



R= + ^- JPP'/3J ( + '19245)tr 4 + Sm 2 S^( + l"686)u- 6 ] A. (39) 



Multiplying F x by X and F y by Z, and taking the sum to 

 rind the total force along the line joining the atoms, we find 



F -= + jAt ( PP'/3 Jir 4 + 2m 2 2* 2 (-l-90>- 6 ) . (40) 



cos a=5 



Whence, equating to zero we find the distance for stable 

 equilibrium to be 



& 2 /3*t-=l-378 (41) 



for the value of k 2 see (31) above. 



This result includes both cases where the ax^s point as in 

 fig. 8 and as in fig. 11, since we have shown above that a 

 reversal of both axes of rotation does not change the force. 

 The same remark applies to figs. 9 and 10, and includes all 

 adjacent atoms along edges throughout the whole structure. 

 This result proves that for a small displacement of any given 

 atom in any direction there is a strong force brought to bear 

 upon it to restore it to this position due to the six face- 

 centred atoms above and below, to the ri^ht and left, and to 

 the front and back of it. 



This statement does not apply to the other surrounding 

 atoms. They produce a zero resultant translational force, 

 but neither a restoring force nor the opposite for small dis- 

 placements. It is seen that any pair of atoms adjacent to 

 the given central atom along a diagonal line either of a face 

 or of a cube has axes parallel to each other. The general 



