It should be noted that any tendency to extensive ionization will increase the concentration of free electrons and tend to encourage [Pg 142] recombination, thus counteracting the effect of low surface gravity. The effect of an increased concentration of free electrons will not, however, attain the magnitude of the surface gravity effect, since even for the hottest stars examined, three electrons appear to be the largest number that can be thermally removed under reversing layer conditions. The theoretical effect of lowering the pressure has been discussed by Stewart,[416] who, after alluding to the importance of the surface gravity, suggested that the ultimate lines of neutral atoms easier to ionize than the average should be weakened by low pressure, and that the corresponding enhanced lines should be strengthened. For atoms harder to ionize than the average the reverse should be the case for the two classes of lines. From this standpoint he showed that the absolute magnitude effects might be qualitatively accounted for. The “average ionization potential” was the average for the lines used in the estimates; Stewart adopted the value of six volts for Classes to . EFFECT OF TEMPERATURE AND DENSITY GRADIENTS UPON THE SPECTRUM OF A STAR There is another respect, recently analyzed by Stewart,[417] in which the spectrum of a giant may be expected to differ from that of the corresponding dwarf. He points out that “in a giant, owing to the small density, there is more material overlying the photosphere than in a dwarf having the same effective temperature; while at the same time the density in the photospheric region is less in the giant, owing to the low gravity.” These conditions furnish an interpretation of the increased blackness and sharpness of the lines in giant stars, as compared with the corresponding dwarfs. The absorption lines in giants are blacker because there is more matter above the photosphere than in dwarfs; they are sharper because the effective level at which the lines originate is at a lower pressure in the giant than in the dwarf, owing to the smaller pressure gradient in the giant [Pg 143] star, and to its lower surface gravity. The difference in line quality between a giant and a dwarf is at once obvious from the spectra, and this effect renders direct comparisons of estimated line-intensities a matter of extreme difficulty. It is an effect that must be taken into account in examining the agreement between the observations and the theory.