AEPINUS ATOMIZED. 



839 



brought a little nearer, the equilibrium becomes unstable; and we may 

 infer that both electrions jump to the right, E' to settle at a point 

 within the atom A on the left hand side of its centre; and Z^outside A', 

 to settle at a point still within A. If, lastly, we bring the centres closer 

 and closer together till they coïncide, E cornes again within A' , and the 



two electrions settle, as shown in fig. 3 

 at distances on the two sides of the com- 

 rnon centre, each equal to 



2 



1 



which for the case a! 



Fig. 3. 



E'C= CE = '622 



1 r 



2 " V 



2.27 



28 



3ûi is 



= '622 *. 



§10. Mutual action ofthiskind might 



probably be presented in such binary combinations as 0 2 ,N 2 ,H 2 ,C1 2 



X' 



i 



■ .-J' 



x — x'y \ ' 



Each of thèse being equated to zéro for equilibrium gives us two équations 

 which are not easily dealt with by frontal attack for the détermination of two 

 unknown quantities ce, a?'; but which may be solved by a method of successive 

 approximations, as follows : — Let a? 0 , . . .x^ x' 0 , x f 11 ....x' i: be successive 

 approximations to the values of x and x\ and take 



3 "T" /3 

 |3J « 



where D 2 i = (^f+^i — x\y. As an example, take a — 1, «' = 3. To find solutions 

 for graduai approach between centres, take successively ^ = 2'9, 2'8, 2*7, 2*6. 

 Begin with x 0 =0, x' 0 = 0, we find a? 4 = '01243, x\ = '0297, and the same 

 values for cc 5 , and œ' 5 . Take next £ = 2*8, * 0 = '01243, == -0297 ; we find 

 x u = x 5 = '0269, x\ = x\ = "0702. Thus we have the solution for the second 

 distance batween centres. Next take £ = '2'7, x 0 = '0269, a?' 0 = "0702 ; we find 

 x 6 = x n = '0462, x' G — x\ = "1458. Working similarly for £ = 2-6, we do not 

 find convergence, and we infer that a position of unstable equilibrium is reached 

 by the electrions for some value of Ç between 2*7 and 2*6, 



