﻿Cubic Crystals with Theoretical Atoms. 769 



Stable Equilibrium for the Phase Difference in the 

 Hydrogen Molecule. 



It remains to be shown that when the phase angle 7 is 

 zero the two electrons are in stable equilibrium as to phase 

 for small displacements along the orbit. It is, first, evident 

 by considering the instantaneous forces when 7 is exactly 

 zero that there is no force to accelerate or to retard the 

 second electron. The static force due to the positive charge 

 of the opposite atom on the electron may be resolved into 

 two, the one perpendicular to the plane of the orbit and the 

 other along the radius of the orbit, neither of which gives 

 any tangential force along the orbit for any position of the 

 electron. The only other force is that due to the second 

 electron upon the first. The instantaneous values of the 

 four components of this force when resolved along the 

 tangent to the orbit is given by equations (53) to (56) 

 of the former paper. These all vanish when 7 = and 

 #3=0, as it does when the atom is on the axis, which 

 completes the proof of phase equilibrium of the electrons 

 when 7 = 0. 



That the equilibrium is stable may be shown by slightly 

 displacing the second electron along its orbit. The effect of 

 the positive charge gives no force along the orbit as before. 

 We need only consider electron on electron. For small 

 displacement a small component of force is obtained along 

 the tangent for the first, second, and third components of 

 the instantaneous force, but not for the fourth. (See 

 equations (1), (2), (3), and (4) of former paper.) The fourth 

 component depends upon the rate of change of the distance 

 R between the electrons which is zero. The first and second 

 components give respectively 



e 2 

 F i = KR 3 ^ d% ^ 51 ) 



e 2 S 2 

 F 2 =-^taA% (52) 



where A7 is the small displacement angle, a* the radius of 

 the orbit, and R the distance between electrons, also between 

 atoms. The second force is negligible in comparison with 

 the first because ft % is a small quantity. These two com- 

 ponents alone show instability because they tend to increase 

 Phil. Mag. S. 6. Vol. 29. No. 174. June 1915. 3 D 



