Atoms and Molecules. 905 



the same as (19) in all the even powers of ?% while the 

 signs of the odd powers are reversed. The attractive forces 

 are those between the positive charges and the electrons. 

 Equation (16) gives the force between a ring and a point 

 charge, and the positive charge may still be regarded as a 

 point because of its very small dimensions, 10~ 16 cm., as 

 compared with that of the electron, 10~ 18 cm. By changing 

 Ei in (16) to positive 2e, which changes the sign of the 

 expression, we have the force between the ring of the 

 electron and the positive charge. To this must be added 

 the force of E x , the inscribed sphere, upon the positive 

 charge, each being a point charge, giving at the distance r : 



F = ~ hr- 2 -3pa 2 r-± + 



ectron * I 



!5 4„,-e 35 



electron K I 4 O 



+ir/>«v- 10 -}- . . (20) 



To obtain from this the force of the most distant electron a 

 on the positive charge C, change r in (20) into r-\-b, giving 



F = ^{Ar- 2 + Br- 3 +C^-HD^- 5 + Er- 6 4-Fr- 7 



a on C n 



orCona. + Gr" 8 + Hr~*+ If-" 10 * .. .}, 



where 



A=2; B=-46; C = 6b 2 -2>pa 2 ; D= -Sb d + I2pa 2 b ; 



15 4 5 



E = 10M-30^& 2 + ^a 4 5 V=-12b'» + 60pa 2 b*-^pa*b ; 



G=Ub & -105paW+?f pa*b 2 -~ pa« ; 

 H=-166 7 + lG$pa 2 b 5 -210pa*b*+35pa*b ; 



QAK 31^ 9.K 



l = 1 $ b *-2b2pa%* + ^paW-^pa*b 2 +^pa*. . (21) 



The force of the nearer electron, b, upon the positive 

 charge is the same as (21) except that the signs of the 

 odd powers of r are reversed. Hence the electrostatic force 

 of the whole atom (ABC) upon the distant electron, a, of 

 the other atom is the sum of A on a (19), B on a (18), and 

 C on a (21), giving 



F = ~{AV- 4 +BV- 5 +CV- 6 +DV" 7 +EV- 8 



atom ABC & 



+ FV-9+ GV- 10 ...}, 



