Structure of the Atom. 265 



ti revolving electron is 



„ Ae 2 



i± t e(or= — g +>n(ti"r, 



with the limitation d = 7r/2. This determines w as a function 

 of >'. The previous condition v :: 1/r 2 could be satisfied if 



H^ = Bftj, — = (B^ — m)(o 2 , 



but, to attain this, other terms must be added to H t , say 

 terms due to surface distributions of electricity. We shall 

 presume these to be so arranged as to give shells of small 

 thickness within which stable circulation of an electron is 

 possible. In all other regions the resultant force upon an 

 electron is outwards. The resultant electric force acting 

 upon it may always be outwards, the electrodynamic force 

 alone being inwards. 



An electron entering the atom with a moment of momen- 

 tum opposed to that of the shells determining the field is 

 then necessarily ejected. Ejection is then also the fate of 

 any electron whose path is inclined at more than a very 

 small angle to the equatorial plane or the atom. Even when 

 this condition is satisfied, the angular momentum of the 

 electron must not deviate much from that appropriate to 

 one of the shells within which equilibrium is possible. 



Let us presume, for the sake of simplicity, that the regions 

 in which the electricity constituting the atom is in rotation 

 round a common axis are very thin shells. Regarding one 

 of these, of radius r M as being effectively a surface dis- 

 tribution of density a^, the radial component of the magnetic 

 force on the shell of radius r n is 



*-- ■ 8 r n ~ l ( r \ 3 m ~i 



H r =-7rcos6M % .awA — ) -f 2 .«vVV » 

 o L i \r n / «+i J 



where m is the total number of shells. The sign of the 

 quantity in brackets determines the stability of the shell if 

 it be free to alter the direction of its axis. 



The magnetic moment of a shell is -§7rVW. If this be an 

 absolute constant, or a small integral multiple of an absolute 

 constant, we have therein a physical basis for the magneton. 

 And if different stable arrangements with direct or reverse 

 alignment of the shells be possible, we have a condition 

 under which fundamental changes in spectra may take place. 

 If the internal field be sufficiently powerful, and it must in 

 general be so regarded since the most powerful external 

 helds at our disposal are effects of ihe same action 



