The maximum number of lines seen, while quite consistent for plates made with the same dispersion, is somewhat increased when the dispersion is made much greater. The number of lines seen in the spectra of various stars with strong hydrogen lines, made with a dispersion of about 40 mm. between and , varies between thirteen and twenty. The corresponding pressures, derived from Bohr’s estimate that a pressure of about 0.02 mm. would be required for the production of thirty-three Balmer lines, and on the assumption that the pressure varies as the sixth power of the quantum number, lie between and . These pressures are of course to be regarded as upper limits, for it is possible to miss several lines at the violet end of the series, and Wright, with larger dispersion, does indeed record twenty-four Balmer lines in Cygni; on the other hand it is not likely that the estimated number will exceed the actual number of lines. The pressures in the reversing layer, as derived from the observed limit of the Balmer series, are then of the same order as the pressures derived by the other methods outlined above. This is of especial interest because the method, if applicable, is a direct one, and gives results for individual stars, whereas all the other methods, excepting the one based on pressure shifts, are essentially indirect. (g) Ionization and Chemical Equilibrium.—The evidence adduced by Russell and Stewart[88] has been greatly amplified by Fowler and Milne,[89] and by the data bearing on their theory which were subsequently published by the writer[90] and by Menzel.[91] It is not intended to present the evidence from ionization theory here in support of the low pressures inferred by the other methods for [Pg 45] the reversing layer. The pressure derived in the present chapter, and considered as independently established, will be used in Chapters VII ff. to derive a stellar temperature scale, for the reversing layer, from the line-intensity data presented. SUMMARY The following tabulation contains a synopsis of the reversing layer pressures derived by the methods that have been outlined. The extreme tenuity of the stellar atmosphere appears to be unquestionably established by the data set forth above, and a maximum effective pressure of may therefore be assumed in a discussion of the spectra of reversing layers. Pressure Shifts less than Line Sharpness less than Line Width Flash Spectrum Radiative Equilibrium order of Limit of Balmer Series to (upper limit) (Ionization to ) FOOTNOTES: [58] Eddington, Zeit. f. Phys., 7, 731, 1921. [59] Pannekoek, B. A. N., 19, 1922. [60] Milne, Phil. Mag., 47, 217, 1924. [61] Ap. J., 42, 271, 1915; Princeton Contr. No. 3, 82, 1915. [62] M. N. R. A. S., 83, 403, 1923. [63] Ap. J., 59, 197, 1924. [64] St. John and Babcock, Ap. J., 60, 32, 1924. [65] M. N. R. A. S., 82, 394, 1922. [66] King, Ap. J., 41, 110, 1915. [67] King, Ap. J., 48, 32, 1918.