the Hydrogen Molecule. 1029 



charges C and c. The displacement of the centre of the 

 electron A from the centre of C is the sum of the two minor 

 axes of these spheroids, but since the minor axis of the 

 positive charge C is very small in comparison the whole 

 displacement is practically equal to the minor axis of the 

 negative electron, or numerically, 1*065 X 10~ 13 cm. 



The forces according to the above equation must then be 

 written down for each pair of charges, one from each atom, 

 with due regard to their actual distances, since the small dis- 

 placement, b, is not negligible. This fact makes the process 

 quite laborious, and we must content ourselves with giving 

 the final result only, namely the whole force of the second 

 atom upon the first. So far as the electrostatic part of the 

 force is concerned the coefficients of the r~ 2 and r~ 4 terms 

 of the series are zero, and only even terms appear thereafter. 

 The gravitational equation (57) of the first paper above 

 mentioned contributes, however, something to the r~ 2 term, 

 and in the following result the term thus obtained is included. 

 The force of the second atom upon the first may be written 



I* m =T X {>- (Z)A 



H " atom ' +y(6 2 -^a 2 )V,, 2 8(Z>-s 



+ f A 6 * 2 - £ A 8 ]/^ (Z)'- 10 • • } • ( 17 > 



A similar expression answers for the z-component when 

 X is changed to Z before the brace, and ^-functions are 

 substituted for .r-functions, as for example, /z, 28 (Z) instead 

 or/ I>28 (Z). These functions follow. 



/ r>26 (Z) = l + 3Z 2 , (18) 



/ I>28 (Z) = -3(1-14Z 2 + 21Z 4 ), • ■ • (19) 



/ Ii30 (Z) = 5-135Z 2 +495Z 4 -429Z«, (20) 



/,' 32 (Z) = 5(7-308Z 2 + 2002Z*-4004Ze + 2431Z 8 ), . (21) 



A*(Z)=-1 + 3Z«, (22) 



./;, 28 (Z) = -15 + 70Z 2 -63Z 4 , (23) 



/, )30 (Z) = 35-315Z 2 + 693Z 1 -429Z«, (24) 



/•,, 3 2(Z) = 315-4620Z 2 + 18018Z*-25740Z« + 12155Z 8 . (25) 



