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PHYSICS: H. S. UHLER
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Hardy, G. H., and Littlewood, J. E., these PROCEEDINGS, 2, 1916, (583-586). 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., Tohoku Sci. Rep. Imp. Univ., 2, 1913, (33-54) and Ibid., 4, 1915, (105-109). Weyl, H., Math. Ann., Leipzig, 77, 1916, (313-352); see also G1ttingen Nachr. Ges. Wiss., 1914, (234-244). 4 Borel, E., Palermo, Rend. Circ. Mat., 27, 1909, (247-271); see also notes to Borel, E., Leons sur la theorie des fqnctions, 2d. ed., Paris. * Faber, G., Math. Ann., Leipzig. 69, 1910, (372-443), especially p. 400. 6 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. 1
ON MOSELEY'S LAW FOR X-RAY SPECTRA By Horace Scudder Uhler SLOANE PHYSICAL LABORATORY. YALE UNIVERSITY Commuaicated by B. B. Boltwood, December 23, 1916
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 previously 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 elements 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 extrapol