[iv: The Schwarzschild approximation to the boundary temperature is given by the expression 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.

When the theory has been applied and justified for the classes where the temperature scale is well determined by other methods, it may be extrapolated to fix the temperature scale for the hotter stars. As before, the fractional concentration at maximum varies but slowly with , and is determined mainly by . If now be so chosen that is always approximately equal to , the value of derived from the equations will be the appropriate one for the class in question. This value of has to be found by trial. It so happens that the temperatures thus obtained are not very different from those originally predicted without entering into considerations of effective level. The excitation potentials of the highly ionized stages of the lighter elements are invariably large, and all lead to values of of the order of . It is to be noted that values of greater than are not indicated.

The following tabulation represents the resulting temperature scale for the hotter stars. It must be remembered that is here the derived quantity, whereas in Table XX it was the known quantity used for calibration.