Vol. 6, 1920 PHYSICS: DUANE AND PATTERSON 
527 
applied to the X-ray tube. This was 22,750 volts. The applied voltage 
lies so far above the critical voltages, however, that the effect due to 
variations in the latter do not amount to as much as three per cent. 
Figure 2 in the paper referred to above*^ contains curves representing 
the four strongest (3 lines. The heights of the peaks corresponding to 
^2, 1^3 and ^4 are proportional respectively to the numbers 100, 55, 16 
and 9; the voltage applied to the tube in this experiment being 24,800 
volts. 
The ratio of intensities of the two a emission lines possesses special 
theoretical interest. Sommerfeld'' has developed a theory which predicts 
the relative intensity of certain lines in the spectrum. By applying the 
quantum theory to electron orbits that do not lie in the same plane he 
finds that the number of postitions which the plane of an orbit can occupy 
is greater by unity than the quantum number associated with the elec- 
tron's angular coordinate. According to a line of reasoning due to Bohr^^ 
one of these positions is in a certain sense dynamically impossible, which 
reduces the number of possible positions the plane of the orbit can occupy 
by unity. According to Sommerfeld's theory all the possible positions 
of the orbit's plane are equally probably, and hence the intensity of the 
line is proportional to the number of possible positions. 
In the case of the a lines in the K series this theory agrees very well 
with the facts. ^ The a lines in the L series, however, do not have the 
relative intensity predicted by the theory. The elctrons producing these 
a lines fall from M orbits into the same Li orbit. Those producing the 
ai line fall from the first. Mi, orbit, which has three quanta associated 
with the angular coordinates, while those producing the 0:2 line come 
from the orbit M2, which has only two quanta associated with the angular 
coordinates. According to Sommerfeld, therefore, the relative intensities 
should be in the ratio of 4 to 3. As a matter of fact, the ratio is very much 
larger than this. The curve in figure 3 represents the two a lines in the 
L series of tungsten. The ratio of the heights of the two peaks is about 
10 to 1. According to Bohr's "analogue principle" the transfer from 
M2 to Li could not take place, unless the atom were in a field of force. 
This may account for the weakness of the a2 line. 
1 Siegbahn and Friman, Phil. Mag., London, April, 1916 (403); and Nov. 1916 (497). 
2 de Broglie, /. Physique, Paris, May-June, 1916 (161). 
2 Duane and Patterson, Proc. Nat. Acad Sci., Washington, Sept. 1920. 
4 Webster and Clark, Ihid., March, 1916; and Webster, Ihid., Jan., 1920. 
^ Sommerfeld, Atombau und Spektrallinien. 
^ Duane and Patterson, Physic. Rev., Ithaca, 1920. 
' Duane and Hu, Ihid., Oct., 1919 (369). 
8 Duane and Stenstrom, Ibid., April, 1920 (329); and Proc. Nat. Acad. Sci. Wash- 
ington, Aug., 1920. 
9 Overn, Physic. Rev., Aug., 1919 (137). 
10 Siegbahn, Phil. Mag., Nov., 1919 (639). 
Bohr, Copenhagen Academy, 1918. 
