Mat 21, 1920] 



SCIENCE 



507 



electrons in outer rings is slightly greater 

 than would be the case, if it were actually in 

 the nucleus itself. The theory, applied to 

 cases where more than one electron revolve 

 about the nucleus, does not appear as yet to 

 be thoroughly satisfactory. 



Bohr's theory has been applied to the 

 characteristic X-ray spectra with some suc- 

 cess in particular cases. For instance, Som- 

 merfeld's calculation of the frequency differ- 

 ence between the lines in the Ka group by 

 means of elliptic orbits, etc., seems to repre- 

 sent the facts to a considerable degree of 

 precision. 



In general the theory does not indicate the 

 distribution of the electrons among the va- 

 rious orbits, and this distribution must be 

 determined by other considerations, or else it 

 must be chosen to fit ".ho X-ray data. The 

 latter procedure has been followed by Debye, 

 Kroo, Wiggard and Sommerfeld. The calcu- 

 lation of the frequency of the a^ line in the K 

 series by Sommerfeld seems to agree with the 

 facts to a remarkable degree of accuracy. 

 None of the formulas, however, appear to 

 give the frequencies of all the lines in the 

 X-ray spectra. 



It might be interesting to calculate the 

 frequencies of the critical absorption asso- 

 ciated with the K series, using a distribution 

 of electrons similar to that adopted by Lewis 

 and Langmuir in their theory of a static 

 atom. In this theory the inner shell contains 

 two electrons, the second shell contains two 

 layers of 8 electrons each, the third, two 

 layers of 18 each, etc. Translating this dis- 

 tribution from the static atom over into the 

 dynamic atom I shall assume that the inner 

 orbit of one quantum (t = 1) contains 2 

 electrons; that outside this are two orbits of 

 two quanta (t = 2), one just outside the other 

 and each containing 8 electrons etc. 



K ABSORPTION PREQUENCIIS 



The table contains the data. Two columns 

 of calculated values are given, one corrected 

 for the mutual influence of neighboring rings 

 of electrons on each other and one un- 

 corrected. The observed values represent our 



measurements of the critical absorption fre- 

 quencies,^ which are the highest X-ray fre- 

 quencies known to be characteristic of the 

 chemical elements. Except for aluminium 

 the observed values differ from the calculated 

 values by less than the correction for the 

 influence of the rings on each other. Con- 

 sidering that none of the quantities used in 

 the calculations have been taken from X-ray 

 data, the agreement may be regarded as good, 

 especially for the chemical elements of high 

 atomic number. 



The above distribution of electrons does 

 not give the proper values for the frequencies 

 of the emission lines of chemical elements of 

 low atomic numbers, so that the problem can. 

 not be said to have been solved. 



- = 2(.V - J - 0.)(1 -I- W + i^i' + • • •) 



-|- S — (jV — m — «2 



S - (iV - m - i 



■s,.-4,+ l)K 



ch 



(.V-*). 



ni = 2, 712 =8, m = 8, m = 9, ns = 9. • ■ ■ 



Tl = 2, T2 = 2, T3 = 3, r4 = 3, ■ ' • . 



vc = Rydberg Fundamental Frequency 



D. The Origin of Radiation, by A. W. Hull, 



of the Research Laboratory of the General 



Electric Co. 



The rapidity with which our theories of 

 atomic structure have advanced during the 

 last ten years has left the impression that 

 each new contribution was a new theory, and 

 that one must choose between these appar- 



2 Physical Beview, December, 1919. 



