632 



BELL SYSTEM TECHNICAL JOURNAL 



electron both revolve about their common centre of mass in ellipses 

 — we will think, as before, only of circles (Figure 1). The radii a and .1 

 of the circular orbits of the nucleus and the electron, being the respect- 

 ive distances of the particles from their centre of mass, stand in the 

 reciprocal ratio of the masses M of the nucleus and m of the electron; 

 and as they describe their orbits in the same period (since the centre 



Fig. 1 — Diagram to illustrate how the electron and the nucleus rt\ol 

 coiiiinon centre of mass in synchronous orbits 



\c arounil 



of gra\ity is at rest and always between them) their speeds :■ and 1' 

 stand in the same ratio: 



a/ A =vlV=Mim. 



I introduce tiie symb:)l ix to denote the eciual c|uaiuities 



M _ a _ f 

 jr^tra+A~v-\-V' 



(8) 



(9) 



The potential energy of the atom, reckoned as always from the state 

 in which the nucleus and the electron are infinitely far apart, is obvi- 

 ously — e-J{a-\-A) = —e^n/a. The kinetic energy of the atom is the 

 sum of the portion \ mv- belonging to the electron and the portion 

 J MV', belonging to the nucleus. I point out that the "centrifugal 

 force" acting upon the electron is mv'/a, and that acting upon the 

 nucleus is M]^/A, and each of these separately must be equal to the 

 reciprocal attraction e-/{a+A)- of nucleus and electron; and I leave 

 it to the reader to show by means of these equalities that the kinetic 

 energy amounts to J eV/a. The total energy of the atom is there- 



