In the simple case of the Ca+ atom (neglecting the small number of atoms that are giving rise to the lines) only two states of the atom are possible: the normal state, called by Milne the state, and the excited, or state. A given atom exists alternately in these two states. If be the average time spent in the state, and the average time spent in the state, the average time spent by an atom in traversing its possible cycle of changes is . Now is connected with the probability of an emission, and with the probability of an absorption. Clearly depends at least partly upon the energy supply, but is an atomic constant measuring the readiness with which the atom recovers its normal state after an absorption. It is, in fact, the “average life” evaluated from Milne’s equations. The ratio , expressing the relative tendencies of Ca+ atoms to emit and to absorb the and lines, is the residual intensity at their centers, with respect to the adjacent continuous background. Einstein’s theory of radiation[436] is used in evaluating from the relation where is the ratio . From ordinary quantum principles, and both and may be derived by eliminating between the two equations. The only measured quantity in the formula is , and from the fact that is the “residual intensity” within an absorption line, we know that it must lie between 0 and 1. Hence a maximum value of may be derived for . On the insertion of the data given by Schwarzschild[437] for the residual intensity of the and lines, 2.6 magnitudes fainter than the continuous background, and corresponding to a value of equal to 0.11, the deduced value of is . The agreement of this value with those obtained in the laboratory for the atoms of hydrogen and mercury has been commented upon in a previous chapter.[438] FOOTNOTES: [429] H. H. Plaskett, Pub. Dom. Ap. Obs., 2, 325, 1922. [430] M. N. R. A. S., 84, 499, 1924. [431] H. C. 256, 1924. [432] H. C. 258, 1924. [433] Chapter IX, p. 133. [434] Milne, M. N. R. A. S., 84, 354, 1924. [435] Curtis and Burns, unpub. [436] Phys. Zeit., 18, 121, 1914. [437] Sitz. d. Preuss. Ac., 47, 1198, 1914. [438] Chapter I, p. 21. [Pg 161] CHAPTER XII SPECIAL PROBLEMS IN STELLAR ATMOSPHERES THE greater part of the present work has dealt with the discussion and interpretation of the normal spectral sequence, to , and the main features of the series have been satisfactorily attributed to thermal ionization at high temperatures. Such a discussion must naturally be the first step in the analysis of the stellar atmosphere. When the more general results of observation have been reduced, in some measure, to an orderly system, it becomes possible to consider special problems involving stars or groups of stars, which lie outside the system, or which, though included in the system, display definite abnormalities.