266 
PHYSICS: W. DUANE 
Proc. N. A. S. 
Table 1 contains the calculated and the observed values of the ratio 
vjv\. The observed values I have taken from table 2 of the report on 
Data Relating to X-Ray Spectra which I compiled for the National Re- 
search Council. Column 4 in the table contains the observed values, 
and column 3 the values calculated according to the following scheme: 
m = 2, n 2 = 4, n z = 4, n 4 = 9, n b = 9, n 6 = 16, 
T 1 = 1, T~2 — 2, T3 = 2, T4 = 3, T5 = 3, Tq = 4. 
TABLE 1 
K Critical Absorption Frequencies 
CHEMICAL 
ELEMENT 
ATOMIC 
NUMBER 
FREQUENCIES DIVIDED BY RYDBERG CONSTANT v/vo 
Calculated 
Observed 
Calculated 
Magnesium 
12 
103.2 
95.8 
92.5 
Sulphur 
16 
187.4 
181.8 
173.3 
Calcium 
20 
297.7 
297.5 
279.7 
Iron 
26 
521.0 
523.8 
494.9 
Selenium 
34 
923.3 
930.8 
888.7 
Molybdenum 
42 
1454.0 
1474.0 
1411.0 
Tin 
50 
2125.0 
2148.0 
2063.0 
Cerium 
58 
2918.0 
2970.0 
2860.0 
Dysprosium 
66 
3896.0 
3948.0 
3820.0 
Tungsten 
74 
5043.0 
5118.0 
4954.0 
Lead 
82 
6404.0 
6463.0 
6270.0 
Uranium 
92 
8468.0 
8477.0 
8345.0 
It appears that, except in the case of the elements magnesium and sul- 
phur, the calculated values in column three do not differ from the observed 
values by as much as two per cent. Considering the fact that the equa- 
tions contain no undetermined constants after the distribution law has 
been fixed and considering the fact that various influences have been 
neglected, such as magnetic forces, forces due to electrons in outer orbits, 
the possible influence of electrons which may be forming bonds with other 
atoms, etc., the close agreement between the calculated and observed 
values appears extraordinary. 
I have also calculated the absorption frequencies, assuming a distri- 
bution according to the scheme 
n\ = 2, n% = 8, n z — 18, w 4 = 32, 
Tl =1, t 2 — 2, r 3 = 3, r 4 = 4, 
The calculated values based on this scheme do not differ very much 
from those contained in column 3 of the table. It appears, therefore, 
that the calculation of the K critical absorption frequencies does not 
furnish a very sensitive method of determining exactly what the dis- 
tribution of electrons is. It is important to note, however, that two 
electrons have a quantum number of one, sixteen electrons have a quantum 
