﻿Cubic Crystals ivith Theoretical Atoms. 755 



Practically the only special cases we have to study are, 

 therefore, where the two atoms are of the same kind, and 

 where they must have rings with one or two electrons. 

 Hydrogen on hydrogen, containing a single electron in the 

 atom, is one of these exceptions and it has been treated as 

 a special case, the equilibrium position of two hydrogen 

 atoms forming a molecule of hydrogen having been found, 

 as given in a subsequent section. 



The general equations for the mechanical force of the 

 second atom A' upon the first atom A, with the exceptions 

 noted, are as follows: — 



F i = + ^ T -r+^Sm 2 a)SnVr+3Xcosa + -75Zsina-3-75XY 2 cosa 



-3-75X 2 Zsin*-3-75X 3 cos«l ir 4 -2m 2 2 n 2 r+9-375X 



J p p L 



+ 7-5Zsin«cosa + 13'125Xcos 2 a-13-125(X 3 + 5XY 2 + 2XZ 2 sin 2 « 



+ 5X 3 COS 2 a + 7X 2 Z sin a cos a -f- Y 2 Z sin a cos a + XY 2 COS 2 a) 



+ 59-0625( + X 3 Z 2 sin 2 a + X 3 Y 2 H-X 5 cos 2 a + XY 2 Z 2 sin 2 « + XY 4 



+ X 3 Y 2 cos 2 «+2X 4 Zsinacos«+2X 2 Y 2 Zsin«cosa)lv- 6 "|i, . (23) 



F = + T ^i+ a ^Sm 2 a>2^Vr + 3Ycosa-3-75Y 3 cos a -3-75XYZsina 

 y XaJ L 6 p P' L 



-3-75X 2 Ycos*~V 4 - 2m 2 Sn 2 r + 20-625Y4-l-875Ycos 2 a 

 J p p' L 



-13-125(2X 2 Y + 6Y 3 + 2YZ 2 sin 2 a + 4X 2 Ycos 2 « + 6XYZsinacos«) 



+ 59-0625( + X 2 YZ 2 sin 2 a + X 2 Y 3 + X 4 Ycos 2 «+Y 3 Z 2 sin 2 a + Y 5 + X 2 Y 3 cos^ 



+ 2X 3 YZsinacosa + 2XY 3 Zsinacosa)lv- 6 T;, .... (24) 



jL=+* -r + 542m 8 «2nVr + l-5Zcos* + -75Xsin«--3-75Y 2 Zcosa 

 KaJ L c p p' L 



~3-75XZ 2 sina-3-75X 2 Zcos«l^- 4 -Sm 2 2n 2 r + 5-625Z 



J p p' L 



+ 3'75Zsin 2 a + 7'5Xsinacosa + l-875Zcos 2 a-13-125(-fX 2 Z 

 + 4Y 2 Z + Z 3 sin 2 a + 3X 2 Zcos 2 a + 4XZ 2 sinacosa+X 2 Zsin 2 a 

 + X 3 sinacosa + Y 2 Zsin 2 a + XY 2 sin«cos«)+59-0625( + X 2 Z 3 siir« 

 + X 2 Y 2 Z + X 4 Zcos 2 « + Y X2 Z 3 sin 2 a + Y 4 Z + X 2 Y 2 Zcos 2 a 



+ 2X 3 Z 2 sinacosa + 2XY 2 Z 2 smacosa)]tT 6 }# (25) 



3C2 



