The theory outlined in the preceding chapters was used in determining the astrophysical behavior of lines corresponding to known series relations. When the validity of the theory has been established, it is possible, as was pointed out by the writer,[430] by Fowler and Milne,[431] and by Menzel,[432] to deduce the ionization potentials of lines of unknown series relations from their astrophysical behavior. The ionization potentials were estimated in this way for the table in Chapter I. In general the observations show that the higher the ionization [Pg 157] potential, the higher the temperature at which the corresponding lines attain maximum. This is in strict accordance with theory. It is not possible to predict the exact form of the relation between temperature of maximum and ionization potential. For the observed cases in which (the ultimate lines), . It would appear that should approach zero as approaches zero. But in this case (the negative energy of the excited state, which must always be less than ) also approaches zero, and the relation becomes indeterminate. The form of the curve as approaches zero has merely a theoretical interest, as no known element has an ionization potential of less than four volts. In the present application the relation will be treated as an empirical one. The curves given by the writer and by Menzel for the relation between ionization potential and display a good general regularity, and the deviations, as was pointed out in a previous chapter,[433] probably arise from differences of effective level. Owing to this source of irregularity, great accuracy is not to be anticipated in the deduced ionization potentials. The effective level is at the greatest height for lines of low excitation potential. The excitation potentials corresponding to the astrophysically important lines of the once, twice, and thrice ionized atoms in the hotter stars are in all known cases highland thus the error introduced by neglecting to correct for effective level is small. The error introduced by an excitation potential of the wrong order is, moreover, a constant and not a percentage error, and thus becomes less serious in estimating high ionization potentials. Accordingly the deduced ionization potentials will probably be of the right order. The relation connecting ionization potential and may, for our purposes, be treated as an empirical relation between ionization potential and spectral class. This mode of regarding the question has the advantage of being quite independent of the adopted temperature scale. We merely assume that the sequence of spectral classes is a temperature sequence. The ionization potentials corresponding to lines [Pg 158] of known maximum may then be deduced by interpolation. TABLE XXV Element Ionization Potential Authority C++ 45 Payne N+ 24 Ibid. N++ 45? Ibid. O+ 32 Ibid. O++ 45 Fowler and Milne Si 8.5 Menzel, Payne S+ 20 Payne S++ 32 Ibid. Sc+ 12.5 Menzel Ti+ 12.5 Ibid. Fe 7.5 Ibid.