Voi,. 7, 1921 
PHYSICS: W. DUANE 
267 
number of two, thirty-six electrons have a quantum number of three, etc. 
On examining the data closely we find a systematic deviation of the 
calculated from the observed values. This deviation becomes most 
marked in the elements of low atomic number. It lies in the same direction 
as the well-known difference between the observed and calculated io- 
nizing potentials of helium. 
In order to see whether a better representation of facts can be obtained 
by supposing that the two inner electrons revolve in opposite directions 
in separate orbits, I have made the calculations on that basis. The 
only difference in formula 11 occurs in the terms representing the inner- 
most orbit. The first two terms of equation 11 must be replaced by 
the single term. 
(tf-l)*(l + 74/8' , + 7»/»' 4 +.-.) (12) 
Column 5 of the table contains the results of the computations. It 
appears from the data of column 5 that the observed and calculated 
values differ from each other by amounts up to 4y 2 %. A systematic 
variation exists which increases as the atomic weight decreases, and which 
lies in the opposite direction to that represented by the data of column 3. 
1 Science, May 21, 1920. 
2 Fall Meeting of the National Academy of Sciences, 1920; Physic. Rev., March, 
1921, p. 431. 
3 This can be proved easily for the particular case in question. For a proof of the 
theorem in a more general form see A. Sommerfeld, Atombau und Spektrallinien, Ap- 
pendix 5. 
ON THE CALCULATION OF THE X-RAY ABSORPTION FRE- 
QUENCIES OF THE CHEMICAL ELEMENTS (SECOND NOTE) 
By William Duane 
Jefferson Physical Laboratory, Harvard University 
Communicated July 25, 1921 
In a note presented to the National Academy of Sciences 1 I have given 
some computations of the K critical absorption frequencies of the chemical 
elements based on the Rutherford-Bohr theory of the structure of atoms 
and the mechanism of radiation. In these computations I have assumed 
that the electrons were distributed in circular orbits, which did not lie 
in planes passing through the nucleus of the atom. 
In order to estimate roughly the forces exerted on a,n electron in one 
orbit (A in the figure of the previous note) due to the electrons in the 
parallel orbit, I assumed that they were the same as if the charges of the 
electrons in the orbit BC were concentrated, half at the nearest point 
