268 
PHYSICS: W. DUANE 
Proc. N. A. S. 
in the orbit to A, and half at the furthest point in the orbit from A. In 
the computations presented in this note I assume that the forces are the 
same as if the electricity of the electrons in the orbit BC were uniformly 
distributed along the orbit. As in the previous note, I neglect the forces 
acting on an electron at A, due to the electrons in the orbits that are larger 
than the orbits A B C D, and assume that the forces due to the electrons 
in the orbits smaller than A B C D are the same as if these electrons were 
concentrated at the nucleus of the atom. 
The terms in the expression for the ratio of the critical absorption 
frequency to the Rydberg constant, v/v Q , due to the two innermost 
electrons, are the same as in the previous case (expressions 6 and 12 of 
the previous note). To get the correction term due to the electrons in 
the orbits outside of the inner orbit we proceed as follows: Equating to 
zero the horizontal components of the forces acting on an electron at A 
due to the nucleus and to the electrons inside and in the orbits A B C D } 
we get the equation 
IT 
at/ <$ n de 
N'cos*a = T f — 
Zw ° (1 + tan 2 a sin 2 6) h 
where 0 is half the angle made by the radius of the orbit BC drawn to 
any point in the orbit with the vertical. 
Similarly, equating the centripetal acceleration of the electron at A 
to the centripetal force acting on it, due to the nucleus, to the electrons 
inside the orbits A B C D and to the electricity of the orbit BC, and re- 
ducing, we get the equation 
mv 2 a = N'sin 3 a — nB — s nt (14) 
, ^ tan z a £ sin 2 0dd 
where B = — f 2 - ^ (15) 
Zw ° (1 +tan 2 asin 2 d) 1 
and where s n is given by equation 9 of the previous note. 
Combining equation 14 with equation 2 of the previous note, represent- 
ing the angular momentum law, we get an expression similar to equation 
10 for the kinetic energy of the electron at A. Taking the sum of these 
expressions for all the electrons with one of the electrons of the inner 
orbit removed and with it in place, and substituting in formula 3, repre- 
senting the frequency law, we get the equation for v/v Q 
~ = 2{N- .25) 2 (1 + 72 £ 2 + Vs /3 4 +.0 ~N 2 (l + 'A £' 2 + 7s 0 l4 + • . ) 
2n 
+ 2 T 2 [iVWa - nB " S «Y 
