270 PHYSICS: W. DUANE Proc. N. A. S. 
TABLE 2 
K Critical Absorption Frequencies 
CHEMICAL 
ELEMENT 
ATOMIC NUMBER 
FREQUENCIES DIVIDED BY R YD BERG CONSTANT, p/vo 
Calculated 
Observed 
Calculated 
Magnesium 
12 
103.3 
95.8 
92.6 
Sulphur 
16 
181.1 
181.8 
167.0 
90 
290.0 
297.5 
272.0 
Iron 
26 
510.1 
523.8 
484.0 
Selenium 
34 
918.4 
930.8 
873.8 
Molybdenum 
42 
1431. 
1474. 
1388. 
Tin 
50 
2056. 
2148. 
1994. 
Cerium 
58 
2854. 
2970. 
2796. 
Dysprosium 
66 
3853. 
3948. 
3777. 
Tungsten 
74 
4990. 
5118. 
4901. 
Lead 
82 
6362. 
6463. 
6228. 
Thorium 
90 
7891. 
8075. 
7774. 
Uranium 
92 
8313. 
8477. 
8190. 
It appears from a comparison of table 2 with table 1 of the previous 
note that the values computed according to the integral equations are 
somewhat smaller than those computed by the rough formulas. They 
differ, therefore, from the observed values more than do the rough cal- 
culations. The formula, however, gives the right order of magnitude 
for the K critical absorption frequencies. 
In making the computations by the formulas of this and of the preceding 
note no account has been taken of the influence of electrons in orbits 
larger than that containing the electron under discussion at A. It is 
quite possible that the forces due to the electrons in these orbits would 
push the electron at A further from the meridian plane of the atom. 
This would reduce the value of the angle a, reduce the value of the cor- 
rection term that is subtracted from the main term in the expression for 
v/vot and therefore increase the calculated value of v/v Q . This might 
bring the computed values closer to the observed. An accurate estimate 
of the correction, however, would be extremely difficult to obtain. 
If we calculate the radius of an orbit from the above equations, we 
find that it contains as a factor the square of the quantum number of the 
orbit, as well as other quantities. This means that the orbits having 
the same quantum number do not differ very much in radii, but that when 
the quantum number changes there is a considerable difference in radii. 
In the above distribution of electrons four orbits have quantum numbers 
of two, and four have quantum numbers of three. The radii of the two 
quantum orbits do not differ very much from each other, and the radii 
of the three quantum orbits do not differ very much from each other, but 
the latter are much larger than the former. It follows from this that the 
