132 
THE QUANTUM [i X . 5 
results given in the table. It may be pointed out that the method 
would also lead to unsymmetrical configurations which would 
yield different values for the characteristic constants. 
It is of interest to note that from a study of the secondary 
spectrum of hydrogen at higher pressures, Sandeman * has isolated 
a band, showing a P, Q, and R combination having a moment 
of inertia agreeing within the errors of measurement with that 
found for this static model of triatomic hydrogen. 
5. A Static Model for Helium 
For the positively charged helium atom,f consisting of a 
positively charged nucleus (charge + 2e) and a single negative 
electron (charge — e), there is a position of stable equilibrium 
determined by r — \a n . The work that must be done to remove 
the electron from this position to a position of rest at an infinite 
distance from the nucleus is four times the corresponding amount 
in the case of the hydrogen atom, exactly as in Bohr’s original 
theory. It is assumed that there is repulsion between nucleus 
and electron due to the quantum force, of amount e 2 a n /r 3 . 
For a neutral helium atom, consisting of a positive nucleus 
and two electrons, a number of configurations are theoretically 
possible. We consider first symmetrical configurations in which 
the nucleus is at the middle point of the line joining the electrons. 
The table below gives the results for two possible models, A and 
B. A refers to a model in which no quantum force acts between 
the electrons, and B to a model in which such a force is included. 
Data for Helium Atom 
r (A.U.) 
W t (volts) 
Ionized helium atom, C . 
0-265 
54-ïo 
Neutral helium atom, A . 
0-303 
82-84 
Neutral helium atom, B . 
0-265 
94-67 
Change from A to C 
— 
2874 
Change from B to C 
— 
4°'57 
These values of W for the neutral atom are not in agreement 
with the experimental results, which yield the value 78-6 volts. 
If, however, we assume with Bohr that a neutral atom is formed 
by the successive binding of electrons by the atomic nucleus, it 
may be that the symmetrical arrangement assumed is never 
* Sandeman, Proc. Roy. Soc., voi. 108, p. 607, 1925. 
t H. S. Allen, Proc. Roy. Soc. Edin., voi. 44, p. 116, 1924.