Atoms and Molecules. 899 



law as regards each other. The inverse second and fourth 

 power coefficients in the development of the force as a series 

 of powers of r cancel when the atoms are neutral, leaving the 

 principal term of the series the inverse sixth power, which 

 has a negative coefficient meaning a repulsive force between 

 the two neutral groups. Examples of this are given in earlier 

 papers *, bat it is again illustrated here by the use of two of 

 the model hydrogen atoms similar to that described. 



Let the two atoms be placed at a distance apart, eacli 

 having a common axis of: rotation, as in fig. 4, which shows 

 merely the locations of the centres of the charges, ABC being 

 one atom and abc the other. A and B, also a and b, are 

 negative electrons of charge —e, while and c are positive 

 charges of plus 2e each. The rotations of the charges on 

 their axes are to be neglected in this preliminary discussion. 

 Denote the distance Cc by r, and the distances AC = CB 

 = ac = cb by b. The sum of the repulsive forces between 

 the pairs Cc, Ah, and Bcz, each at distance r, is according to 

 the inverse square law, 



F=!(-6)r-3 (!) 



There are two other repulsive forces, that of A for a, and 

 of B for h, which give respectively 



F=J(-lXr + »)-», .... (2) 

 and 



p = J(_l)(r-»)-» (3) 



There are also four attractive pairs which partly balance 

 the above, that of A for c and of C for a at a distance r + b, 

 and that of C for b and of B for c at distance r—b, which 

 give respectively when added 



F=i 2 (4)(V+5)-3 (4) 



and 



F»J(4)(r-*)-» (5) 



The expansion of these quantities in series gives 



(r + 2b)- 2 + {r-2b)- 2 = 2r- 2 + 2±b 2 r-* + 160b 4 r- 6 ..., (6) 



( r + b)- 2 + (r-b)- 2 = 2r- 2 + 6^ 2 r- 4 +10^ 4 /'- 6 ... . (7) 



* Phil. Mag. July 1913, pp. 39, 66, 71 ; and June 1915, pp. 755, 764. 



3 M2 



