512 Sir J. J. Thomson on the Structure of 



force must become attractive when the electron is displaced 

 from this position away from the centre and repulsive when 

 it is displaced towards it. 



If there are two electrons A and B in the atom, these must 

 be situated so that the centre of the positive charge is mid- 

 way between A and B ; the distance AB is determined by the 

 condition that the repulsion between A and B is equal to the 

 attraction exerted by the positive charge on either of these 

 electrons ; three electrons will arrange themselves at the 

 corners of an equilateral triangle, four at the corners of a 

 regular tetrahedron and so on ; the electrons are on the surface 

 of a sphere concentric with the positive charge. When there 

 are any number of electrons, the conditions for equilibrium 

 are that the electrons should be so symmetrically placed that 

 the force exerted on any electron by the other electrons should 

 be along the radius, and that the magnitude of this radial 

 force should be the same for all the electrons. 



It can be shown without difficulty (J. J. Thomson, Phil. 

 Mag. ser. 6, vol. vii. p. 237) that the radial force on an 

 electron P due to the other electrons Q, R. S . . . is equal to 

 e 2 S k /4tt?- 2 , where ?* = OP, being the positive charge, e is 

 the charge on an electron, and 



« 1 1.1. 



siniPOQ siniPOR ' sin^POS ' 

 or if we take to denote one of the angles JPOQ . . . 



Sji=2 - — hj 

 sin 6 



where X denotes that the sum is to be taken for all the angles. 

 Hence if we can find a distance r so that the attractive force 

 •exerted by a positive charge on a electron at this distance is 

 equal to <? 2 S„/l7rr 2 , and if the electrons are so symmetrically 

 arranged that S« is the same for each electron, the electrons 

 will be in equilibrium under the central force. 



This equilibrium, however, will be unstable unless another 

 condition is satisfied, and it is the limitation imposed by this 

 condition that in my opinion determines the structure both 

 of the atom and the molecule. 



A simple illustration will show the stringency of this 

 condition. Suppose that the electron P is displaced along 

 OP from its position of equilibrium by a small distance 6>, 

 all the other electrons remaining fixed, then it can be shown 

 that in consequence of this displacement of P the repulsion 



