Stewart’s argument also suggests the answer to an important question raised by Pannekoek[418] in the course of his discussion of the absolute magnitude effect. The latter remarks that “the general decrease of luminosity with advancing type for the same value of relative line-intensity, which is shown ... by most reduction curves ... corresponds to the decrease in , as for the same and smaller smaller surface brightness means smaller luminosity. If we take account, however, of the direct influence of temperature on ionization, which acts much more strongly in the opposite direction, we must expect equal ionization in the more advanced types for much smaller g and higher luminosities, contrary to the empirical reduction curves. It looks as if this effect is compensated by some other direct influence of temperature on the spectrum.”[419] The influence suspected by Pannekoek may be found, at least in part, in the “theoretical decrease with increasing temperature and density in the quantity of material overlying the photosphere. Thus the contrast between line and continuous background tends to become less along the giant series (since, furthermore, for the same abundance of active material, a given line is formed always at the same depth).”[420] This suggestion was advanced by Stewart to account for the observed displacement, towards cooler classes, of the maxima of absorption lines discussed in Chapter X. It is certain that some such factor will be operative in the reversing layer, but it is believed that the burden of the shift of maxima should be borne by the effective level, which has been discussed in more detail in the [Pg 144] preceding chapter. It would be of interest to compare the two effects quantitatively, but the effect of temperature gradient has not yet formed the basis of numerical predictions. PREDICTED EFFECTS ON INDIVIDUAL LINES The discussion involving the average ionization potential appears to permit of more rigorous treatment. Suppose the “average ionization potential” of Stewart’s discussion to be replaced by the ionization potential corresponding to the atoms whose lines are at maximum for the class in question. It then follows directly from theory that the effects of lowered pressure on the different classes of lines will be as below: Atom Line Effect of lowered pressure Hotter than class Cooler than class for maximum for maximum Neutral Ultimate Weakened .... Neutral Subordinate Weakened Weakened Ionized Ultimate Weakened Strengthened Ionized Subordinate Weakened Strengthened It is especially to be noted that all lines should theoretically be weakened in passing from dwarf to giant, excepting the lines of an ionized atom at temperatures lower than those required to bring them to maximum. This leaves out of account the effect of photospheric depth, which will be introduced later as a correcting factor.