514 
PHYSICS: DUANE AND PATTERSON Proc. N. A. S. 
the average values of the differences in their neighborhoods by more than 
the estimated errors, except in one or two cases. In other words, the 
V I /X may be represented as a function of the atomic number by a smooth 
curve, from which the individual values do not differ by more than the 
experimental errors. In the case of the absorption band, Lai, this curve 
differs a small amount from a straight line. In the cases of the bands 
La2 and Las, however, the departures from the straight line law appear 
to be much greater. A very much more pronounced variation from 
the linear law has been noted in the case of the critical absorption fre- 
quencies associated with the K series of X-rays.^ These departures 
from the straight line law have been ascribed to the relativity change of 
mass with velocity of the electrons connected with the production of the 
X-rays. 
The fact that the values of V ] /X do not differ from a smooth curve 
law by more than the indicated errors of measurement shows that our 
estimates of accuracy are substantially correct. 
The Relation between the Emission and Absorption Frequencies. — It has 
been found by experiment that the difference between the critical ab- 
sorption wave-number of the K series and one of the critical absorption 
wave-numbers of the L series equals the wave-number of one of the a 
lines in the K series to within the limits of error. ^ The experiments were 
performed with the X-ray spectrum of tungsten. As the emission wave- 
lengths in the K series have not been measured for chemical elements of 
higher atomic numbers than that of tungsten, we cannot test this law 
between the K and L series for the heavier elements. We can test the 
law, however, in the case of the L and M series of thorium and uranium, 
for here all the ncessary data is available. The tables of Siegbahn and 
Friman^ contain the emission wave-lengths in the L series, and Sten- 
strom^ has measured three absorption wave-lengths in the M series for 
each of these two elements. Using our values of the L absorption wave- 
lengths we have compiled the following table of wave-numbers (Table 3) : 
TABLE 3 
Relation Between Absorption and Emission Wave-Numbers 
L and M Series 
u 
Th 
U 
Th 
u 
Th 
Absorption 
Lai 
-Mai 
1 
099 
1 
.047 
Lar 
-Ma^ 
1 
085 
1 
.034 
Lai- 
-Maz 
1 
.038 
0 
.988 
Emission 
Lai 
1 
098 
1 
.045 
Lai 
1 
085 
1 
.032 
Absorption 
Lai- 
-Mai 
1 
403 
1 
.322 
La2- 
-Mai 
1 
389 
1 
.309 
Lor 
-Maz 
1 
342 
1 
.263 
Emission 
L^z 
1 
408 
1 
319 
L&i 
1 
389 
1 
305 
Absorption 
Laz- 
~Mai 
1 
472 
1 
385 
Laz- 
-Mai 
1 
458 
1 
372 
Las- 
-Maz 
1 
411 
1 
.326 
Emission 
Lfiz 
1 
408 
1 
319 
It appears from this table that the wave-numbers of the emission lines 
Lai Lai and L^i agree very well with the differences between the absorp- 
tion wave-numbers Lai-Mai, Lai-Mai and Lai-Ma^, respectively. 
