As Professor Kramers kindly informs me, he too has obtained most of the results derived in 3. (To be published shortly.)

a_{i} is then the integral of the absorption coefficient over all frequencies, considering the absorption curve as approaching zero on both sides of the natural frequency. In reality the absorption coefficient at large frequencies approaches a small positive value corresponding to the scattering of a free charge. This part of the absorption coefficient has to be subtracted.

N. Bohr, Zs. f. Phys. 13, p. 161; 1923.

H. A. Kramers, Nature, 113, p. 673; 114, p. 310, 1924; H. A. Kramers and W. Heisenberg, Zs. f. Phys., 31, p. 681; 1925. See also M. Born, Zs. f. Phys., 26, p. 379; 1924 and J. H. van Vleck, Phys. Rev., 24, p. 344; 1924.

This is identical with a formula obtained previously by R. Ladenburg, Zs. f. Phys., 4, p. 451; 1921 in a different way; see also R. Ladenburg and F. Reiche, Naturwiss., 11, p. 584; 1923.

For an elaborate mathematical discussion of the case of few atoms in a wavelength cube leading to the same conclusion the reader is referred to F. Reiche, Ann. d. Phys. 50, pp. 1 and 121, 1916.

Disregarding the different possible orientations of the orbits of the valence electrons.

These are the values customarily used in x-ray notation; their ratio is that of the statistical weights of the two states.

For a detailed discussion of the experimental evidence and references to the literature see H. A. Kramers, Phil. Mag., 46, p. 836; 1923; see also F. K. Richtmyer, Phys. Rev., 27, p. 1; 1926.

Bergen Davis and H. M. Terrill, Proc. Nat. Ac., 8, p. 537; 1922;A. H. Compton, Phil. Mag., 45, p. 1121; 1922;C. C. Hatley and Bergen Davis, Phys. Rev., 23, p. 290; 1924;Bergen Davis and R. von Nardroff, Phys. Rev., 23, p. 291; 1924; Proc. Nat. Ac., 10, p. 60, 384; 1924;C. C. Hatley, Phys. Rev., 24, p. 486; 1924;R. von Nardroff, Phys. Rev., 24, p. 143; 1924;E. Hjalmar and M. Siegbahn, Nature, 115, p. 85; 1925;A. Larsson, M. Siegbahn and T. Waller, Phys. Rev., 25, p. 235; 1925.Bergen Davis and C. M. Slack, Phys. Rev., 25, p. 881; 1925;M. Siegbahn, Journ. de Phys., 6, p. 228; 1925;Bergen Davis and C. M. Slack, Phys. Rev., 27, p. 18; 1926.A. Larson, Zs. f. Phys. 35, p. 401; 1926;I am indebted to Professor Davis and Mr. Slack for some additional unpublished material. This deals with the refraction of X-rays in silver on the long wavelength side of the K-limit. Below are given the values of δ.106. as observed and as computed from the Lorentz formula and from (9) respectively: .707 Å.U.; -5.3±.6, -5.7, -6.0; .515 Å.U.; -3.0±.4, -2.1, -3.1; .500 Å.U., -2.5±.3, -1.0, -2.9; .485 Å.U., -2.2±.3, 16.4, -2.5.

W. Kuhn, Zs. f. Phys., 33, p. 408; 1925.

W. Thomas, Naturwiss., 13, p. 627; 1925. See also F. Reiche and W. Thomas, Zs. f. Phys., 34, p. 510; 1925.

W. Heisenberg, Zs. f. Phys., 31 p. 617; 1925.

E. C. Stoner, Phil. Mag., 48, p. 719; 1924.

The shifted radiation can be considered, as far as the variation of its frequency with the angle of observation is concerned, as coming from sources moving in the direction of the incident beam with a velocity depending on the frequency of this beam (see A. H. Compton, Phys. Rev., 21, p. 483; 1923). With coherence of the shifted radiation we mean that, if by a Lorentz transformation we go to a coordinate system in which the sources are at rest, then in this system the radiation coming from them has a definite phase relation to the incident waves. The fact that one does not observe selective reflection in crystals at angles corresponding to the shifted radiation does not contradict this, as the moving sources need not start moving all at the same time so that they no longer form a lattice.

W. Bothe and H. Geiger, Zs. f. Phys., 32, p. 639; 1925.

A. H. Compton and A. W. Simon, Phys. Rev., 26, p. 289; 1925.

Bohr, Kramers and Slater, Phil. Mag., 47, p. 785, 1924; Zs. f. Phys., 24, p. 69; 1924.