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



IT . 



Special Case, «=o 



When the axes of the two atoms are perpendicular to each 

 other the resulting surface is not a surface of revolution, and 

 the section of the surface by a plane containing the axis of 

 the first atom A differs for the different positions of the inter- 

 secting plane. Such a section by a plane through the two 

 atoms, the axes of both atoms lying in the plane, is shown in 

 fig. 4 (PI. XI.). The force equations for atoms so situated are 



Falon, = + ^ ^5^ { " 12 FF'P * ( Sin X C ° S X) * 



~2 + 2m 2 2n 2 ( + 20-175sin 2 Xcos 2 \) \ . . (34) 

 p p' J 



Fperp. = + 16 K^T6 sin ^{ +8PP'£| (sin\cosA,> 2 



f + 2m 2 2rc 2 (-20 + 140sin 2 \cos 2 \) j. . . (35) 

 p p' J 



Equating each to zero, we find 



7T . _ / +20-175 sin 2 \ cos 2 \\i /on . 



*=2 W* V =( 12 sin X cos X ) ' ' <**) 



\ b sin X cos A. J v ' 



There are now loop curves of stable equilibrium ha\ing their 

 maximum points in a direction at 45° with the i and /: axes, 

 besides infinite branches of instability which approach the i 

 and k axes as asymptotes. The maximum distances of these 

 loop curves are 



— *.l Along-force JEy8»v=l a 99(TI 45° with the 



a ~~ 2 ^Perpendicular-force „ =1*937 J axes. 



If the axis of the second atom A' is reversed in direction, 

 pointing toward the left instead of to the right as shown, 

 this has the effect of reversing the positive direction of the 

 j axis, since the vector k x k' is the positive direction of this 

 axis. To keep the cyclic order of the i, j, and k axes correct 

 the i axis must be reversed, which would change the sign 

 of X, and produce the effect of rotating the loop curves into 

 the first and third quadrants instead of leaving them as they 

 are in fig. 4. An additional reversal of the axis of rotation 

 of A has the effect of restoring the loop curves to their 

 original position in the second and fourth quadrants. 



77 



