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PHYSICS: H. S. UHLER 
1 Hardy, G. H., and Littlewood, J. E., these Proceedings, 2, 1916, (583-586). 
2 Berwick, W. E. H., Mess. Math., Cambridge, 45, 1916, (154-160); Fowler, R. H., London, 
Proc. Math. Soc, (Ser. 2), 14, 1915, (189-207); Kakeya, S., Tdhoku Sci. Rep. Imp. Univ., 
2, 1913, (33-54) and Ibid., 4, 1915, (105-109). 
3Weyl, H., Math. Ann., Leipzig, 77, 1916, (313-352); see also Gdliingen Nachr. Ges. 
Wiss., 1914, (234-244). 
" Borel, E.; Palermo, Rend. Circ. Mat., 27, 1909, (247-271); see also notes to Borel, E., 
LeQons sur la theorie des fonctions, 2d. ed., Paris. 
6 Faber, G., Math. Ann., Leipzig, 69, 1910, (372-443), especially p. 400. 
« Hobson, E. W., London, Proc. Math. Soc, (Ser. 2), 12, 1912, (297-308). 
7 Fatou, P., Acta Math., Stockholm, 30, 1906, (335-400), especially p. 349. 
ON MOSELEY'S LAW FOR X-RAY SPECTRA 
By Horace Scudder Uhler 
SLOANE PHYSICAL LABORATORY, YALE UNIVERSITY 
G>mmu.iicated by B. B. Boltwood, December 23, 1916 
While engaged in making interpolations, by the method of least 
squares, of unknown from known wave-lengths of high frequency spectra 
I noticed certain systematic deviations from Moseley's law which led 
me to investigate three interesting questions that have not been pre- 
viously discussed, probably because the older data did not seem to be 
sufficiently accurate to justify close mathematical analysis. These 
questions are: (i) How accurately does Moseley's law reproduce the 
observed wave-lengths? (ii) What empirical formula will represent 
the numerical data within the limits of experimental error? and (iii) 
What is the order of magnitude of the high frequency radiations of ele- 
ments having small atomic numbers and of which the spectra have not 
yet been obtained? In the following paragraphs definite answers 
will be given to questions (i) and (ii), while a tentative solution of the 
third problem is necessitated by the fact that it involves extrapolation. 
The wave-lengths used in the computations were taken from the recent 
papers by M. Siegbahn, W. Stenstrom, and E. Friman. These data 
were chosen because they are the latest, they were all obtained in the 
same laboratory with the same spectrometers, and they constitute the 
most extensive, accurate and consistent set available. 
Moseley's law is that, for any one series {a, /8, y, etc.), the square- 
root of the frequency of the lines is a linear function of the atomic num- 
bers of the radiating elements. In symbols -k/v^ = a b N, where 
= frequency, N = atomic number, a and b are constants for one 
series. When a and b are calculated by the method of least squares, 
from the 48 known wave-lengths of the L-ai series, extending from zinc 
(N = 30, X = 12.346 A) to uranium {N = 92, X = 0.911 A), the values 
