Sd.Mi: (().V//.A//'(»A'. lA') .l/U./.\(/s l.\ rilVSli \ l.\ (i7.< 



f><t> of the electron in its sarioiis cirriil.ir orliils is p<}> = tih '2w. wliirli 

 may be written 



/ (}^ ii<p = uh (54) 



tile inteyr.il liiinji t.ikiii .ironnd .1 lonipU'Ic re\ nliilinn, .1 fornuihi- 

 tion in wliiili the soniewh.il distressing I'.iilor 1 '2k CDrn eniently 

 vanishes. Correspond injj to this integral we ha\e .nioliur 



fp<>dr = mf'l;^d4. (55) 



also to he taken aroinul a complete revolution, therefore from r„i„,= 

 a(l— f) to r„^^,=a{\-\-i) and back again. The materials for per- 

 forming this integration are furnished in equation (35); if the reader 

 can perform it he will arrive at the value. 



/Vrf. = 2./>,[— i^.^-l] 



(56) 



and if the eccentricity of the ellipse conforms to equation (o3), so 

 that the integral of the angular momentum of the electron is kh, 

 then Uie integral of the radial momentum is 



\ .\I,(lr={>t-k]li. (57) 



t )ur position may now be described in the following words. We 

 have accepted the values —Rh n" (h = 1,2,3 . . . ) for the successive 

 stationan,- states of the hydrogen atom; we have accepted an atom- 

 mo Jel consisting of a nucleus and a revolving electron; we have 

 traced the orbits which would entail these various energy-values, 

 and we have found that for each of these energy-values there are 

 infinitely many elliptical orbits which would entail it, — to wit, for 

 the Hth stationan,- state, all the infinitely many ellipses of which 

 the major a.xis is given by 



2a„ = n-h"-'2w-meE. (58) 



Furthermore we have sought for distinctive features which might 

 discriminate these ellipses from all the others which entail "wrong" 

 energy-values, i.e., energ>-\alues which are not included in the list 

 — Rh. —Rh A, —Rh !».... One such we found in the integral 

 \2Kdl of the kinetic energy of the electron around the ellipse; this 

 integral assumes the value nh for each ellipse which entails the energy- 

 value — Rlin-, so that we could define the permitted orbits as those 



