A preliminary application of the observed maxima of absorption lines, in the formation of a stellar temperature scale, was given at the end of the preceding chapter. The temperatures were obtained on the assumption that , the partial electron pressure in the reversing layer, was constant for all lines and equal to . Striking inconsistencies appear in this preliminary table of temperatures. As Menzel[408] has remarked, the maxima of most of the metallic arc lines occur in stars cooler than the ionization theory, on the stated assumptions, would predict. The ultimate lines of the ionized atoms of calcium, strontium, and barium show especially large inconsistencies. The temperatures of the maxima for these atoms, deduced from the ionization formula on the assumption that , are about 3000° higher than the measured temperatures of the classes at which the maxima occur, as deduced from the color indices. The following suggestion has been advanced by Fowler and Milne[409] to account for the observed deviations of Ca+, Sr+, and Ba+. “For the maximum of the principal line of an ionized atom, the fraction of atoms in the required state is almost unity.... On the other hand ... at the maxima of subordinate lines the fraction of atoms in the required state is from to .... Thus atoms in the required state are to times as abundant for intense principal lines as for intense subordinate lines. It follows that principal lines must originate at much higher levels in the stellar atmosphere than subordinate lines, and consequently at much smaller pressures.” [Pg 134] It appears that the behavior of the ionized atoms of the alkaline earths can be satisfactorily explained in this way. The further suggestion was made that a similar effect might be expected for atoms of low excitation potential, such as manganese and magnesium. The possibility of varying as well as in the formula for the theoretical maximum places the investigation on a rather different footing. Any temperature (within wide limits) may now be obtained for the theoretical maximum of a line by appropriately varying the partial pressure. The stellar temperature scale cannot, in such a case, be fixed merely from a knowledge of the critical potentials and the observed maxima, without introducing other considerations. It is necessary to find a way of determining the appropriate partial pressures.