As the temperature is further raised, the second and third ionizations set in, and presumably follow the same procedure as has been outlined for less ionized atoms. The lines of N++, C++, Si++, and Si+++ will serve as examples. The lines of the doubly ionized atoms of the metals are in general in the ultra-violet portion of the spectrum, and the corresponding elements do not therefore appear in the hotter stars, where they would otherwise be anticipated. Qualitatively the prediction of the theory of ionization is fully satisfied. The quantitative discussion involves more rigorous treatment, and is reserved for a later chapter. FOOTNOTES: [355] Stewart, Phys. Rev., 22, 324, 1923. [356] De Gramont, C. R., 171, 1106, 1920. [357] Russell, Pop. Ast., 32, 620, 1924. [358] A. Fowler, Report on Series in Line Spectra, 1922. [359] R. H. Fowler, Phil. Mag., 47, 257, 1924. [360] Proc. Roy. Soc., 99A, 135, 1921. [361] M. N. R. A. S., 83, 403, 1923; ibid., 84, 499, 1924. [362] Russell and Stewart, Ap. J., 59, 197, 1924. [363] Eder and Valenta, Atlas Typischer Spektren, 10, 1911. [364] See Chapter V, p. 69. A. Fowler, Bakerian Lecture, 1924, designates this an ultimate line. [365] See Chapter XIII, p. 185. [366] Milne, Observatory, 44, 264, 1921. [367] M. N. R. A. S., 83, 403, 1923; 84, 499, 1924. [368] Sommerfeld, Atombau und Spektrallinien, 457, 1922. [369] Meggers, Kiess, and Walters, Journ. Op. Soc. Am., 9, 355, 1924. [Pg 105] CHAPTER VII CRITICAL DISCUSSION OF IONIZATION THEORY THE theory of thermal ionization, of which the preceding chapter contains an illustrative discussion, may be treated from two points of view—the sufficiency of the analytical treatment, and the nature of the underlying physical assumptions. Actually the two questions are merely two different ways of regarding the validity of the theory, but they divide the discussion conveniently into a section dealing with the analytical treatment and a section dealing with the physical assumptions. The original treatment by Saha[370] was based on the Law of Mass Action, and the application to stellar atmospheres raised questions of a physical rather than of an analytical nature. These questions are fundamental not only to the Saha treatment, but also to the more recent development of the theory, and they will be discussed in the second half of the present chapter. The first half will be devoted to the analytical formulae. MARGINAL APPEARANCE AND MAXIMUM