994 Dr. Dorothy Wrinch on the 



on this view, be governed by the formulse of classical 

 dynamics. 



For these reasons the results o£ this paper should have 

 some bearing on the conditions under which an electron 

 originally moving in any way in the neighbourhood of an 

 atom may be captured and retained. But in default of a 

 more precise development of atomic theory, we have set out 

 the results as solutions of a formal general dynamical 

 problem in the theory of orbits, for the need for such 

 a scheme of solution is recognized here as well as in 

 electrical theory. 



A doublet consisting of two equal and opposite charges — 

 of electrical or other type — subject to the inverse square law 

 of attraction admits a potential 



Y=— yLtcos 0/r 2 



at all external points. This involves both a radial force E, 

 and a transverse force T on any unit particle in the field of 

 the doublet. R is measured along r increasing, and T in 

 the direction increasing. The values are given by 



R=— 4^ = -2/xcos0/r 3 , 



QT 



T = -dV/rd0= -^ sin 0/r 8 . 



The equations of the orbit of the particle are of the well- 

 known form 



r-rd* =R, 



l/rd/dt(r 2 0) = T. 



Denoting r 2 by h — so that mh is the angular momentum 

 when the particle has mass m, — we can show that 



h 2 = ( - R - T du/udO ) lh 2 {u + d 2 ujd0 2 ) 



= fi (sin du/dO + 2u cos 0) / (u + d 2 u/d0 2 ) ; . (1) 

 and also dh 2 ld0 = 2r 3 T = -2fi sin (2) 



These are obtained by the usual procedure of eliminating 

 the time. The field of the doublet is symmetrical about the 

 axis = 0, and we shall find it convenient to consider only 

 those motions which begin on the side of the plane defined 

 by 



for it is clear that other possible motions will merely be 

 reflexions of these in the axis; their separate discussion 

 is therefore unnecessary. 



