The case of the ultimate lines of the ionized atoms is of especial interest. At their maximum, if the Fowler-Milne theory is correct, ionization is almost complete, and more than 99 per cent of the element is giving the ionized ultimate lines. At a temperature higher than that required for maximum, lowered pressure can “increase” the ionization only by the removal of the second electron. By this process the intensity of the ionized ultimate lines is decreased, since the number of singly ionized atoms is thereby reduced. The fall from maximum towards the hotter stars, which is displayed by the ionized lines of Ca+, Sr+, and Ba+ can be due only to the progress of second ionization, and there seems to be no escape from the conclusion that [Pg 145] the ultimate lines of the ionized atom should theoretically decrease in strength, with lowered pressure, for stars hotter than those required to bring the lines to maximum. The point is made increasingly clear when it is recalled that, at the maximum, all of the substance is presumably at work giving the lines in question. It is not therefore possible to increase the number of active atoms by any process whatever that involves merely a change in pressure. For ionized subordinate lines the theoretical effect should be the same as for the ultimate lines, for the fall after maximum is here again caused by the increase in the number of doubly ionized atoms, and the consequent decrease in the number of those singly ionized. Thus, although the subordinate lines are not already using all the available atoms at maximum, so that increased intensity with lowered pressure is possible, it would still appear that they should be weakened at temperatures higher than that corresponding to maximum intensity in the spectral sequence. The pure pressure effects just discussed will be superposed upon the Stewart effect, which depends upon the photospheric depth. The latter will cause a general increase in the strength of all lines from dwarf to giant, as a result of the greater amount of matter lying above the photosphere in the giant. The two effects are observed together when direct intensity measures are employed, such as the estimates embodied in Chapter VIII, while the pressure effect is given almost purely when differential estimates of intensity for the same spectrum are used, as in most investigations of spectroscopic parallax. The observational evidence from both sources will now be put forward, in order to examine the sufficiency of the theories that have been advanced to account for the absolute magnitude effects.