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



to the sixth power of v when the radii of the orbits are each 

 equal to m in a* units, 



r .a,on g =+]^| { -«- 2 + m 2 (l-r)(3-4-5X>-* + m\l-F)2(-7-5 + 37-5X* 



-32-S125X 4 )tr 6 ], . (44) 

 F 2 ai„n g =-/3 2 rF lalong , (45) 



*W= + lS^ sin2X { l #5 »»'( 1 - r )»" 4 +m 4 (l-r) 2 (-7-5 + 13-125X ! )»- 6 ) , 



. . . (46) 

 F Vrp . = -/3 2rl V P . ( 47 > 



Here T denotes cos y, and 7 is the phase difference between 

 the instantaneous positions of the two electrons being con- 

 sidered, and is constant for synchronous rotation. When 

 we add the forces of the two electrons, one in each atom, 

 upon each other, the electrons on the opposite positive 

 charges and the positive on the positive, the force of one 

 hydrogen atom upon another with axes parallel and when 7 

 is zero degrees is 



F aloIlg =^^p';+~^J« 4 + (-16 + 24X 2 ) [ , 2 + m 2 (20-100XH87-5X*)| 



. . . (48) 



F pe r p.=r6KS 6Sin2x {~ 8! ' 2+Wi2(20 - 35X2) ) < 49 > 



Stable Equilibrium for Translational Forces in the 

 Hydrogen Alolecule. 



Equating the along force to zero we find 



/^=[l-5-2-25X*+(-l-5 + 2-25X 2 );p. . (50) 



The plot of this curve is shown in fig. 13. Equating the 

 perpendicular force (49) to zero gives sin 2\ = 0, denoting 

 the vertical and horizontal axes on the chart. Since the 

 brace in this equation contains no j3 term there is no curve 

 equating this factor to zero. The values of v obtained from 

 this are very small and have no meaning, since the equations 

 only hold for large values. The series from which it is 

 derived is not convergent for small values. The arrows 

 indicate the directions of the two component forces at various 

 locations on the chart, and show that there is a stable position 

 of! equilibrium for the two positions on the axis, one above 

 and the other below the central atom. 



