and the Spectrum of Helium. 97 



of this series is formed by the radiation, during the collection 

 o£ the atom from infinite dispersion, of an amount of energy 



W=^L/( m + -8C1181-^- 9 )l 



Now if there is any force whatever between the two 

 electrons, they can only have stationary states when they 

 are continually in a Jine with the nucleus, provided that 

 their orbits are in the same plane. This can be proved 

 immediately, on the supposition that they move with constant 

 angular momenta. When they are in this line with the 

 nucleus continually, their angular velocities must be equal ; 



■©■ 



and since their angular momenta are specified, the radii must 

 be in a constant ratio, which is one of equality if the angular 

 momenta are equal. Let the rapulsion between them, when 



at distance r apart, be — . Then their orbits are given by 



d 2 u x 



_{v_ _\ *> 1 



u l =~. 



d6 2 + ? ' 2 I r 2 2 (r, + r 2 )» J h 2 %* ? ' 2 "" r 2 ' 



In the ' Monthly Notices '* it is proved that these orbits do 

 not exist unless they are identical, under the inverse square 

 law. For other laws, we may proceed as follows. Let the 

 angular momenta mh^ and mh 2 be given by h 1 = oi 2 h i h 2 = fi 2 h, 

 a 2 and /3 2 being in a ratio of integers on Bohr's view, but 

 more generally, perhaps, in other constant ratios. Then if co 

 is the angular velocity, 



and 



= « 2 A, r 2 2 a>=£ 2 A; 



/3 a. 



ri-, u 2 =u^ 



* March 1914. 

 Phil Mag. S. 6. Vol. 28. No. 163. July 1914. H 



