Vol. 7, 1921 
PHYSICS: W. DUANE 
261 
cular, that they occurred in pairs and that the two orbits in a pair lay 
opposite to each other in parallel planes equi-distant from the nucleus, 
as represented in the figure. This gives a volume distribution of electrons. 
The mutual repulsion of the electrons for each other keep the orbits apart. 
It is necessary, however, to suppose that the electrons in the two orbits of 
a pair revolve in opposite directions. Otherwise they would be pulled 
together to form a single orbit in a plane through the nucleus (at least 
for elements of high atomic numbers). The revolution in opposite di- 
rections has the advantage, among others, of reducing the magnetic 
field due to the electrons for points at a distance from the atom to a very 
small value. 
The theory contains three fundamental laws. The acceleration law, 
the angular momentum law and the frequency law. The acceleration 
law states that the centripetal acceleration of each electron revolving 
in its orbit equals the centripetal force acting on it, due to the attraction 
and repulsion of all the electrical charges in the atom acting according 
to Coulomb's inverse square law. The angular momentum law states 
that the angular momentum of each electron equals a whole number 
(called the quantum number), r, multiplied by Planck's action constant, 
h, and divided by 2ir. According to the frequency law, the product of h 
into the frequency of vibration, v, of the radiation emitted during a shift 
of the electrons from one position of dynamic equilibrium to another 
equals the difference in the amounts of energy in the atom before and 
after the shift. 
The first two laws cannot be true at every instant of time. One or 
both of them must represent average values. In the modern develop- 
ment of the theory a definite integral of certain generalized coordinates 
is equated to a multiple of h. 
The theory does not determine the numbers of electrons in the various 
orbits. In making calculations, however, we must know how the electrons 
are distributed. Several authors have calculated X-ray frequencies 
by choosing distributions of electrons in the orbits that best fit the X-ray 
data themselves. I have taken a distribution suggested by the intervals 
between the inert gases in the sequence of chemical elements. It has 
long been supposed that these intervals correspond to groups of electrons 
in the atom that are completely filled up. From this point of view we 
get as the numbers of electrons in the various groups the following: the 
inner orbit contains two electrons. The next group consists of a pair 
of parallel orbits containing in all eight electrons, four in each orbit. 
The third group contains eight electrons, four in each of the two parallel 
orbits. The next group contains eighteen electrons in all, nine in each 
of the two parallel orbits. The fifth group also contains eighteen, nine 
in each orbit. The outside pair of parallel orbits contains thirty-two 
