﻿Cubic Crystals with Theoretical Atoms. 759 



exerted by the central atom upon the second atom at the 

 position of the arrow. They show that the loop curves above 

 and below the equator are stable positions of equilibrium for 

 small displacements, the force tending to restore the atom to 

 the curve for both the along- and perpendicular-forces. The 

 infinite branches approaching the asymptotes shown by dotted 

 lines are positions of unstable equilibrium for the along-force, 

 the along- force being a repulsion throughout all the shaded 

 region on the chart, and an attraction in the clear regions. 



If the loop curve of the along-force intersected that of the 

 perpendicular-force at any point, this point of intersection 

 would be a position of stable equilibrium for all displacements 

 in the t, k plane; but there is no such intersection, and hence 

 no position where only two such general atoms unite to form 

 a molecule when the axes are parallel. This statement doss 

 not apply to the special cases above noted where there are 

 one or two electrons only in some of the rings. 



Special Case, ol — it. 



When the axes of the two atoms are parallel but in 

 opposite directions, we obtain equations which differ from 

 (27) and (28) only in the sign of the/SJt' 2 term. This might 

 have been foreseen, by observing that the part of the force 

 arising from the first or electrostatic component is not 

 altered by changing the direction of rotation, but that the 

 magnetic or second component is changed in sign. This case 

 gives instead of (29) and (30) 



a =tt hP*v=i 8-12X 2 )> • • C 32 ) 



k 2 /3*v = i(- 40 + 7 'OX 2 )* (33) 



The resulting chart in fig. 3 has a very different appearance, 

 due to this change in sign, giving loop curves for both the 

 along and perpendicular components along the equatorial 

 direction instead of along the direction of the axis. 



The distances to the maximum points of the loops are in 

 the two cases, 



_q ( distance for along-force, k 2 fS*v = V5 =2*236 ) direction of 

 \ „ „ perp.-force, „ = vTO = 3*162 j axis. 



, ,, along-force, „ = V3'75 = 1*936 1 direction of 

 , „ perp.-force, „ = s/Vh =2*739 ) equator. 



« = 7T ) 



