262 
PHYSICS: W. DUANE 
Proc. N. A. S. 
electrons, sixteen in each orbit. Of course, for atoms containing less 
than ninety-two electrons the outer groups are incomplete, or missing 
altogether. 
To each pair of orbits belongs a certain quantum number, r. For 
the inner orbit r = 1, for the second group r = 2, for the third group 
r = 2, for the fourth and fifth r = 3, and for the sixth group r = 4. 
According to this distribution the number of electrons in an orbit (except 
the innermost) equals the square of the orbit's quantum number. 
The fundamental laws of the theory may be expressed by the following 
equations : 
Acceleration Law mv 2 /a= Centripetal Force (1) 
Angular Momentum Law mm = h/2w (2) 
Frequency Law hv = Wi — W 2 (3) 
Distribution Law n = t 2 (4) 
where m is the mass of an electron, v, its velocity, a, the radius of its 
orbit, and W\ and Wi are the total amounts of energy possessed by the 
atom in the two states of dynamic equilibrium. 
In computing vibration frequencies we first calculate the velocity 
of each electron from equations 1 and 2, and then find the total energy 
of all the electrons, including both the potential and kinetic energies. 
Taking into account the change of mass of an electron with its velocity, 
the total energy may be represented by 
where /3 = v/c, c being the velocity of light. If the velocity of the electron 
is small, as compared with the velocity of light, this expression reduces to 
To compute the K critical absorption frequency (according to equation 
3) we must calculate the value of W for the atom, when one electron 
is missing from the inner orbit, and subtract from it the value of W, 
when this electron is in its proper place. The difference between these 
two terms equals h multiplied by the critical absorption frequency, v. 
Each of the terms in the expressions obtained for W contains the quan- 
tity 
W = 2 m 0 c 2 (Vl-/3 2 -1), 
W = -sy 2 m 0 v\ 
2Tr 2 e 4 m 0 
(5) 
as a factor. This is the Rydberg fundamental constant. It simplifies 
the equations to calculate the ratio of the absorption frequency to this 
fundamental constant, i.e., v/v 0 . 
