will be justified for the cooler stars, within the limits of accuracy permitted by the data, and will be extended by simple extrapolation to the formation of a temperature scale for the hotter stars, where the temperatures cannot be safely estimated from the color indices.
The salient point is that complete absorption will occur for any line at a depth that is inversely proportional to the abundance of the corresponding state of the atom. No light in this wave-length reaches the exterior from any lower level, and the deepest level from which the line originates therefore forms a lower boundary to the effective portion of the atom in question. The “effective level” from which a line comes is probably best regarded as the level at which the effective atoms above the “lower boundary” have their median frequency. Clearly the partial pressure will differ at different effective levels, and thus abundance has a direct influence on the appropriate value of the partial pressure.
The theory with which we have so far been concerned deals with the excited fraction of the total amount of the element which is present. A knowledge of this quantity suffices for specifying the variation of intensity for the lines of any one element. But the absolute abundance of a given atomic state varies jointly with the fractional concentration of the appropriate state and the total amount of the element present. Now, for the first time, the absolute abundance of different atomic species becomes of possible importance, as a factor affecting the depth from which radiation corresponding to the given atom will penetrate. Fowler and Milne[410] rightly claimed that their method of maxima eliminated questions of relative abundance, “if
can be regarded as known ... [and constant]. The proper value of
must be a function of the abundance of the atom in question relative to free electrons.”
The question of relative abundances of elements in the reversing layer is discussed[411] in [Chapter XIII]. It may be mentioned that the abundances there deduced depend upon estimates of marginal appearance. Probably all lines are unsaturated at marginal appearance, that is, there are not enough suitable atoms present completely to absorb all the incident light of the appropriate wave-length. Hence all suitable atoms present, as far down as the photosphere, where general opacity begins to render the gas hazy, are actually contributing to the line. At marginal appearance, then, all the intensity phenomena are probably due to pure abundance, and considerations of level are eliminated. The deduced abundances are therefore independent of effects such as are discussed in the present chapter, and the results of [Chapter XIII] may be cited as giving evidence that the stellar abundances, for all the atoms here to be considered except barium, have a range with only a factor of ten, which is negligible in comparison with the quantities to be discussed. The relative abundance of different atomic species will therefore be neglected in what follows, although, with more accurate data than are now available, it should become a factor of importance.
Fractional concentrations, as derived from the ionization formula, govern the effective level at which absorption takes place. Fowler and Milne, as was pointed out earlier, suggested that the higher the fractional concentration at maximum, the higher the level and the lower the partial pressure from which the line originates. They suggested that the pressure for a principal line at maximum is from