670 DELL SYSTEM TECItXlC.lL JOURNAL 



I hope it will he aiipreciated that the foregoing statements about the 

 orbits are fatally incomplete, except in the first case. Nothing could 

 be done unless it were possil)le to know, not merely the general shape 

 of each t\pe of orbit, but the exact mathematical expression for it, 

 and for the energy-\'alue of each orbit of each type. In some cases 

 this knowledge is available; in others, it is not. For the cases desig- 

 nated here by J3, J4 and J 5, it is a\'ailable; wherefore it is possible 

 to go about the process of seeking the distinctive features of orbits 

 possessing the preassigned energy-\alues, or inversely the energy- 

 values of orbits distinguished by certain features. 



K. FlKTIlliR l.NTICKI'KHT.VnoN OK TlIK SPKI TK.\ OK HVDROC.K.V .\ND 



loMzi:i) HK:i.irM 



Continuing for the moment to accept the energy-\alues of the 

 stationary states of the hydrogen atom as gi\en by 



Wi=-Rh, Wi=-Rli 4, ]V,= -Rh <) 



and continuing to acceiH the atom-uKidei consisting of a nucleus 

 and a revolving electron; let us consider what are the properties of the 

 elliptical orbits, in which if the electron re\ol\ed, the atom-model 

 would possess one or another of the recjuired energy-values. 



According to equation (40), the energ\- of the atom-model, when 

 the electron is rexoKing in an cllii)se <it wliich \hv nuijdr axis is '2(i, 

 is given b>' 



H'= -eE/2a 



irrespective of the eccentricity of the ellipse. In this, as in all fol- 

 lowing equations, E is ecjual to e for h>drogen and to '2e for ioni/ed 

 helium. If we set this expression ecjual to one of llie ri'(|uire<l tiiergy- 

 \alues, for instance to Wi, we ha\e 



2ai=-eE, IT, =(/i Rli. (.50) 



The atom-model therefore has ihi' proper energy-value I^i for the 

 normal state of the hydrogen atom, it ilie electron is re\oK-ing in 

 any ellipse for wliicli ilie major axis is cE Rh. The circle of diameter 

 eE Rh of whi( li \\t' li.i\ e heretofore been thinking is only one of these 

 ellipses, it is the one for which the major .uul tiie minor axes are 

 identical and t = (); there is an inrmilN' of oiiu-rs. 



Should we then di\est the circular orbits of the prominence which 

 has been accorded to them, and a.ssimie for instance that when the 

 atom is in its normal stale the electron is moving in an\- one of the 

 infinity of ellipses of which the major axis is eE, Rh' This might be 



