Atoms and Molecules. 907 



where 

 C + A' = 0, 



E + C'=-606 4 + 60 / oa 2 6 2 -15 / o 2 a 4 =-15(2/> 2 - / 9a 2 ) 2 , 



G+E' = -42066+ UlQpaW-^paW- 630/> 2 a 4 6 2 + 3 ^po 2 a 6 > 



I + G'=-2268^ 8 + 15624pa 2 f !> 6 -6615 i oa 4 6 4 + 315 / oa 6 /> 2 



- 15120 / o2 a ^4 + 5670/oW 2 - ~j p 2 a 8 . (25) 



The coefficient of the r~ 4 term, therefore, vanishes for the 

 non-spherical electrons just as it did in the preceding example 

 for the case of point charges. In the former example the 

 r~ 6 term gave a strong repulsion for the electrostatic force 

 between the two atoms, but now the r~ 6 coefficient, E + O', 

 depends upon the relative values of b and a, that is, depends 

 entirely upon the shape of the electron. It was pointed out 

 above that the large coefficient of the r~ 6 term in the point- 

 charge example prevented further progress^ because there 

 cannot possibly be a force due to the motion of charges 

 great enough to neutralize this repulsion and give an equi- 

 librium distance. In order that the r~ 6 term of (25) shall 

 vanish it must be true that 



2 



2b 2 = pa 2 or 



i-0 » 



Let us examine this relation in some detail because it 

 reveals the limits between which the eccentricity of the 

 ellipse representing the meridian section of the electron 

 lies. It may be shown that p is equal to the square of the 

 eccentricity of the ellipse, for by definition /o = E 2 /<?, and 

 on account of the assumption of uniform density the 

 two charges E 2 and e are proportional to their volumes. 

 Hence we have 



Vol. ellipsoid _ %ira^b _ a 2 __ e e 1 



Vol. inscribed sphere ~ ^irW "~ W ~~ E[ ~~ e — E 2 "~ I— />' 



. . . (27) 

 whence 2 



p = a -^L =e *, (28) 



the square of the eccentricity. Hence the relation to be 

 studied (26) becomes 



a\b = s/2je (29) 



