560 Prof. 0. W. Richardson on a Theory of the 



equilibrium position gives rise to no external force, so that 

 the electrostatic effect of its motion will be equivalent to the 

 creation of an equal and opposite charge at the equilibrium 

 position. Thus when the negative electron has moved a 

 distance f we shall have an electric doublet of moment — eg. 

 Let the coordinates of the undisturbed position of the vibrating 

 electron at A be x y' and those of the displaced position 

 x' + f , y' (see fig. 1) . The doublet at A will give rise to 



Fig. 1. 



IA + 



■r'+£y' 



electric force at B in the plane of the figure. Let xy be the 

 coordinates of the equilibrium position of an electron belonging 

 to an atom which happens to be situated at B. Under the 

 influence of the force in question this electron will move to a 

 point in the plane of the figure whose coordinates may be 

 denoted by x + a^ , y + a 2 £. An expression for a ± and a 2 may 

 easily be found. Since 



and 



iY=(.v-x'?+(y-y'Y i 



(4) 



the potential V XJ at xy can be calculated. From equation (3) 

 we have 



-f-^ ^ ^ =X ^f 



(5) 



if e is kept positive, the displacements being those of the 

 negative electrons. As is a coefficient similar to Ai of equa- 

 tion (3), the suffix denoting that it is the sth. electron which 



