Vol. 6, 1920 
PHYSICS: DUANE AND PATTERSON 
519 
each chemical element would seem to indicate the existence of at least 
three distinct groups of lines. 
The researches of D. L. Webster and Harry Clark^ on the voltages 
required to produce the various lines in the L series of platinum and on 
the way in which their intensities increase with 'increasing voltage con- 
firm this, and prove further that the lines r], /3i, 71 and probably 72 belong 
to the second group. 
The modern theory of line spectra, also, seems to indicate the splitting 
up of the L series into groups. The differences in frequency between 
certain lines in the first group and corresponding lines in the second group 
are very nearly equal to each other. These pairs of lines with nearly 
the same frequency interval are ry-l, /3i-a2, 71-^2 and 72-/35. Sommer- 
feld^ explains this division of the L series into groups with a constant 
frequency difference on the assumption that one group of lines is due to 
electrons falling into an L orbit that is circular, and that the other group 
is produced by electrons falling into an L orbit that is elliptic. The 
equation he derives from his theory for the magnitude of the frequency 
difference fits the facts with considerable precision. 
The following facts indicate that the critical absoprtion Lai belongs 
to the first group of lines, and that the critical absorption La2 belongs 
to the second group of lines. Firstly, the wave-length of the critical 
absorption Lai lies not far from that of the line of shortest wave-length 
in the first group, and the wave-length of Lao lies close to that of the line 
of shortest wave-length in the second group. Secondly, as the authors 
have shown, ^ the square root of the frequency of Lai for the different 
elements is almost a linear function of the atomic number, while that of 
La2 departs from the linear law in the same way as do those of the second 
group of lines in Siegbahn and Friman's graphs. Thirdly, the frequency 
difference between La2 and Lai equals to a high degree of precision that 
between the pairs of lines rj-l, /3i-a2 and y2~^b which were all measured 
by the authors^ under the same experimental conditions for the tungsten 
spectrum. Fourthly, the frequency differences between La2 and Lai for 
the various chemical elements from tungsten to uranium^ agree very well 
with Sommerfeld's formula. Fifthly, the values of the critical voltages 
of two of the groups of lines in the L series of platinum measured by 
Webster and Clark^ (namely, 13.20 kilovolts and 11.45 kilovolts) agree 
very well with the values of the same quantities calculated by the quantum 
equation from our critical absorption wave-lengths (namely 13.26 kilo- 
volts and 11.54 kilovolts). 
Relative Position of Lines. — It has been shown by Duane and Hu^ that 
the critical absorption wave-length associated with the K series of Rhodium 
is about one-third of a per cent shorter than that of the shortest line (the 
7 line) in that K series. Further, Duane and Stenstrom^ have found 
that the difference between the wave-length of the critical absorption in 
