5i6 
PHYSICS: DUANE AND PATTERSON Proc. N. A. S. 
Mas-Lai, but no line corresponding to it has been observed. The transfer 
Ma3-La2 can occur according to Rubinowicz's theory, but not according 
to Bohr's, and there is no line to correspond with it. The other trans- 
fers, involving Laz, are not covered by the theory, for it does not in its 
present form include a third L orbit. 
Sommerf eld's L-Doublet Theory. — Sommerfeld has worked out an in- 
teresting theory of the splitting up of the L series into two distinct parts — 
the L series doublet. An account of his reasoning may be found in his 
book, Atombau und Spektrallinien, Chapter 5. According to this theory 
the difference in frequency Ai' between the two parts of the L series is due 
to the difference between the energies of electrons travelling in circular 
orbits and of electrons travelling in elliptic orbits. Some atoms are sup- 
posed to have circular L orbits, and other atoms of the same chemical 
element, elliptic L orbits. The general equation (28), in the chapter re- 
ferred to, for the difference, Av, in wave-number, reduces to 
for the L doublet, where v ^ = 109737 is Rydberg's fundamental wave- 
number, a = = .007286, b = a{N — n), N is the atomic number, 
he 
and n, a correction term due to the influence of neighboring electrons in 
the atom. Sommerfeld has tested his theory by means of the wave- 
number differences between certain emission lines in the spectra of a great 
many chemical elements, and has deduced from this data the value n = 
3.63. Although there is some difficulty in interpreting this value of 
the constant, n, we have used it to test the formula by means of our values 
of the critical absorption wave-numbers.^^ According to the theory the 
wave-number difference in the doublet should equal the difference between 
the wave-numbers of the absorption bands Lai and La2. 
TABLE 4 
The; L-Doublet Wave-Number Differences, Av X 10 
CHEMICAL 
ELEMENT 
ATOMIC 
NUMBER 
OBSERVED 
CALCULATED 
n = 3.63 
n = 3.45 
MODIFIED 
Tungsten 
74 
0. 1083^6 
0.1071 
0.1087 
0.1037 
Platinum 
78 
0.1387=^7 
0.1369 
0.1384 
0.1327 
Gold 
79 
0.1489 ±7 
0.1453 
0.1468 
0.1411 
Mercury 
80 
0.1561±8 
0.1540 
0.1558 
0.1496 
Thalium 
81 
0.1654 ±8 
0.1635 
0.1652 
0.1587 
Lead 
80 
0.1765±8 
0.1733 
0.1751 
0.1682 
Bismuth 
83 
0.1852±7 
0.1836 
0.1856 
0.1782 
Thorium 
90 
0.2744 ±13 
0.2713 
0.2739 
0.2639 
Uranium 
92 
0.3036 ±13 
0.3023 
0.3044 
0.2941 
