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



the displacement angle Ay. The third component* gives 



a force tending to restore the electron and produce stability. 

 The ratio of F 3 to F x gives 



Fo 6 2 R 2 



S— %f—«- (54) 



If this ratio exceeds unity when the distance R is that for 

 stable equilibrium of the translational forces, the moments of 

 the forces are also stable. 



The distance between the atoms at the position of equi- 

 librium is found by making X = in (50), which gives, taking 

 the negative sign, 



0J«>=3 or v=^ .... (55) 



This proves that the ratio in (54) is equal to three, and that 

 the restoring force of the third component is three times 

 greater than the electrostatic force of the first component. 

 The total restoring force for a small displacement along the 

 orbit is then 



f= ~eJ As '- • ■ • • • • (56) 



where As is the linear displacement. 



Vibration Frequencies in the Hydrogen Atom. 



We will now find the force with which one hydrogen atom 

 is restored to its original position when displaced along the 

 line joining the atoms. Let the common centre of mass of 

 the two atoms be taken as origin, a point halfway between 

 the atoms which remains fixed, and let each of the two 

 atoms be displaced to an equal distance away from the origin. 

 The force equation (48) becomes, when X = 0, 



F do n g =+g{+^^- J -^a|^ + ^aJ a -«}, (57) 



where x is the distance in centimetres from the mid-point to 

 one atom. Differentiating to find the rate of change of the 



* The factor (l4-w)~i was omitted from the text, p. 73, in giving the 

 formula (55), but it appears in the brackets in the alternative value there 



given 



