272 PHYSICS: W. DUANE Proc. N. A. S. 
TABLE 3 
K Critical Absorption Frequencies 
CHEMICAL 
ATOMIC 
FREQUENCIES DIVIDED BY RYDBERG CONSTANT, v/v Q 
ELEMENT 
NUMBER 
Calculated 
Observed 
Calculated 
Potassium 
19 
262.0 
266.0 
243.7 
Rubidium 
37 
1128. 
1120. 
1091. 
Caesium 
55 
2649. 
2648. 
2591. 
Thorium 
90 
8090. 
8075. 
7962. 
In order to make the computations for chemical elements other than 
those in table 3 it appears to be necessary to make additional assump- 
tions as to just how the elements are built up in increasing values of the 
atomic numbers. There is also some difficulty about the radii of the 
various orbits. In general, a two quantum orbit has a much smaller 
radius than a three quantum orbit. 
The formulas of this and the preceding note contain no undetermined 
constants after the distribution of the electrons has been fixed; i.e., there 
is nothing in the equations which must be obtained from X-ray measure- 
ments themselves. The formulas are functions of numbers and of x 
except in the correction term for the change of mass of an electron with 
its velocity. The correction term is the only place where measured 
quantities appear. These quantities are the electron's charge e, Planck's 
action constant h, and the velocity of light c, and they may be regarded 
as having been determined by experiments other than X-ray measure- 
ments. In spite of this fact the formulas represent the observed values 
to within a few per cent. This is fairly close, considering the influences 
that have been neglected. Among the reactions that have been neglected 
we may mention the forces due to electrons in orbits outside the one 
considered, the fact that electrons inside these orbits have been supposed 
concentrated in the nucleus, forces due to the magnetic fields of the re- 
volving electrons, the influence of electrons that may be out forming 
bonds with other chemical elements and which may not, therefore, take 
part in the energy changes, etc. 
The fact that the various distributions considered give results that 
differ from each other by only a few per cent indicates that the calcula- 
tion of the K critical absorption frequency is not a sensitive method 
of determining the exact distribution of the electrons. Further, other 
distributions than those considered may furnish more accurate values. 
The important point is that the distribution of electrons is what may be 
called the chemical distribution, and that the numbers of electrons in 
the orbits are related to their quantum numbers according to equation 
4. 
