and the Spectrum of Helium. 



93 



both necessary for further progress. The first hypothesis is 

 required, even for the Balmer series. 



The Lithium Atom. 



The conclusion of the preceding paper, that it is not possible 

 for three electrons and a nucleus to form a lithium atom with 

 a unit valency, after the manner of Bohr's model, was arrived 

 at without the second hypothesis. The electrons were regarded 

 as repelling each other under the law of inverse square. We 

 may now consider the possible laws of force between electrons 

 which can admit such a configuration, in which two electrons 

 form an inner ring, with one outside, while each electron has 

 a constant angular momentum. We shall not require to 

 consider whether the angular momenta of the electrons are 

 equal, or what may be the relation between their angular 

 velocities. 



Let/(r) be the law of force between two bound electrons 

 at distance r apart, and consider the three electrons at the 

 instant when they are at the corners of a triangle ABC. 

 Since the nucleus is very heavy, they are practically 

 describing orbits about it, whose radii at the instant may be 

 called (t\, r 2 , r 3 ). 



If AG, BO meet the opposite sides in L and M, we can at 



once find CL, CM. For the forces on the electron A are 

 /(b) and /(c) in the lines CA, BA, due to the other electrons, 

 and the force along OA from the nucleus. The angular 

 momentum of A does not change if the components of f(J>) 

 and f(c) perpendicular to AO counterbalance, or 



m 



M 



sinBAO 



BL 

 LC 



Thus 



an< 



sin CAO 



BL :LC::cf(b):bf(c), 



p Tj _ ab A c ) 



Similarly 



CM = 



ahf(c) 



