For ultimate lines, where the excitation potential is equal to zero, and accordingly reduces to unity, the value of should be equal to the constant product predicted in a previous [Pg 137] paragraph. Fowler and Milne suggested a partial electron pressure of to for Ca+ on the basis of a maximum at , assumed temperature 4500°. This is the effective temperature of the class, deduced spectrophotometrically, and “the reversing layer should be at a lower temperature—its average temperature should be in the neighborhood of, or somewhat lower than, the Schwarzschild boundary temperature,[iv] which is some 15-20 per cent lower than the effective temperature.” The value 4000° is therefore adopted here for . For this value becomes for Ca+; for Sr+ (, 35000°), , and for Ba+ (Ma? 3000°), . The maximum for Sr+ is the best determined of the three, as the Ca+ lines are too strong and too far into the violet for an accurate estimate among the cooler stars, and the Ba+ line is rather faint, and is heavily blended. The constant product may then be expected to be of the order of . The prediction is examined in the table that follows. The temperature of the class at which the lines attain maximum is assumed from spectrophotometric data, and is expressed to the nearest five hundred degrees. TABLE XX Atom Ionization Potential Excitation Potential Max. Sum Mg+ 14.97 8.83 9000° 5.32 Ca 6.09 1.88 3000 3.64 Ti 6.5 0.84 3500 2.7 Cr 6.75 0.94 3000 2.39 Mn 7.41 2.16 3500 3.77 Zn 9.35 4.01 5600 3.0 Ca+ 11.82 0.00 4000 0.00 Sr+ 10.98 0.00 3500 0.00 Ba+ 9.96 0.00 ? 3000 0.00 Mg 7.61 2.67 ? 4000 3.25 [iv: The Schwarzschild approximation to the boundary temperature is given by the expression [Pg 138] where is the effective temperature and the boundary temperature.] Successive columns give the atom, the critical potentials in volts, the spectral class at which maximum occurs, the assumed , calculated from the theory, , and the sum of the quantities in the two preceding columns. The only quantity that is not fixed by the laboratory data is , which is derived from the data presented in Chapter II. It will be seen that the quantity entered in the last column is sensibly constant, and equal to about -10, in accordance with prediction. All available maxima have been used. It appears that the foregoing evidence constitutes a fair and satisfactory test of the Fowler-Milne equations, and that, in the region in which the test can be applied, the agreement with theory is as close as can be expected from the material. It also appears that the “serious and undoubtedly real” discordance of theory and observation, quoted by Menzel in the discussion of the maxima observed by him, is removed by introducing these considerations of level.