﻿and its Relation to the Quantum Theory. 855 



equations for R and Z are 



e 2 2e 2 R 



mH ~ mR<j>* = 41| - j^j^jm > • • ( 4 ) 



m (R 2 -fZ 2 p W 



If we eliminate <£ by means of the relation (3), equation (4) 

 becomes 



** — J.--D3 "• A D2 * /U2 i ^72X3/2' * * ' \ D / 



2<? 2 R 

 4^R* T 4 R 2 ~ (R 2 + Z 2 p * 



It will be found convenient to use certain reduced units 

 expressing the fact that the scale of the model is arbitrary. 

 Let 



R2 2e ' 2 R y Z n_ P 2 , / 71 



mA 3 A A time' A 



where A is a constant depending on the size of the model. 

 The equations of motion then take the form 



JJ2 == \- J 'T~W r 7 ? ,2 i £2\3/2> .... (o) 



B- (r' + f 2 ) 372 " 



. (9) 



Development of Solution as Perturbations from 

 Circular Orbits. 



Let 



77= \/l — zc-cos 2 Bf, S = w^cosB^, 



where 10 is a positive constant less than unity. If we neglect 

 the term ^r in equation (8), which is due to the force of 

 repulsion between the negative electrons, r=rj, f=S will be 

 an exact solution of the dynamical problem provided the 

 constants p, A, and 10 satisfy the relation = 1 — w. The two 

 electrons then revolve about the nucleus in the familiar 

 circular orbits found in the problem of two bodies. The 

 intersection of the planes of the two orbits is a nodal line 

 perpendicular to the axis of symmetry, w* is the sine of the 

 angle between the plane of one of the orbits and the plane 

 normal to the axis of symmetry. 



To obtain a solution of the complete equations of motion 

 let us write 



