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



the radius vector joining the atoms and perpendicular to this 

 vector, giving the simplified equations* 



u = +2m 2 2>i 2 (-40 + 200X 2 -175X 4 )")>. . (27) 

 p p' J 



F ^- = + 16 K^e sin 2 *{ + ^/3%v 2 



+ 2™ 2 2n 2 (-40 + 70X 2 )V .... (28) 

 p p' J 



where ?v is the angle of latitude that the line joining centres 

 of atoms makes with the plane of the equator, and X = cos\. 

 If the force in (27) comes out positive it denotes an attraction 

 between the atoms, a repulsion if negative. If the force in 

 (28) comes out positive it indicates that the second atom is 

 forced in a direction toward the positive pole of the first 

 atom. Equating each force to zero and solving for v, we find 



a = 10 /40-200X 2 + 175XV 



**■»-( S-12X 2 > ' ■ * ^ 



and £ 2 /3*r = i(40-70X 2 A (30) 



where & 2 =(PP'~2m 2 2<)^ (31) 



p p' 



The equations (29) and (30) are plotted as curves in fig. 2 in 

 terms of k 2 &*v as radius vector; and since k 2 /3* is constant 

 for a given pair of atoms these radii are proportional to the 

 actual distance between the atoms. In this case the complete 

 equilibrium surface in space is obtained by revolving all the 

 curves about the axis of the atom A, the k axis, giving a 

 surface of revolution. A surface of revolution is obtained 

 only when the axes of the two atoms are parallel in the same 

 or opposite directions. 



The factor sin 2\ in (28) shows that in addition to the points 

 on the curved surface obtained from (30), the perpendicular 

 component force is also zero at all points on the k axis or on 

 the equator, that is in the i, j plane. The arrows in the figure 

 indicate the directions of the along- and perpendicular-forces 



* These identical equations have also been obtained from the 

 instantaneous values of the force when integrated for synchronous 

 rotation, which shows that they are true for either synchronous or 

 non-synchronous rotation. 



