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 [Pg 139] 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. TABLE XXI Atom Ionization Potential Excitation Potential Max. He+ 54.2 48.2 35000° C+ 24.3 18.0 l6000 He 24.7 21.1 10000 Si++ 31.7 4.8 18000 Si+++ 45.0 24.0 25000 The values given in the preceding table constitute the only contribution that can be made by this form of ionization theory to the formation of a stellar temperature scale. Values assigned to intermediate classes must be conjectural. From the observed changes of intensity from class to class, temperatures may be interpolated roughly, and a temperature scale, formed on these general grounds, is reproduced in Table XXII. Values not derived from observed maxima are italicized. TABLE XXII Class Temperature Class Temperature 3000° 9000° 3000 10000 3500 13500 4000 15000 5000 17000 5600 18000 7000 20000 7500 25000 8400 to 35000 FOOTNOTES: [408] H. C. 258, 1924. [409] M. N. R. A. S., 84, 499, 1924. [410] M. N. R. A. S., 84, 499, 1924. [411] Chapter XIII, p. 177. [Pg 140] CHAPTER X EFFECTS OF ABSOLUTE MAGNITUDE UPON THE SPECTRUM DIFFERENCES between the spectra of stars of the same spectral class have long been recognized. The empirical correlation of relative line intensities with absolute magnitude was made the basis for the estimation of spectroscopic parallaxes.[412] Such differences within a class were later related in a qualitative way to differences of pressure, in conjunction with the theory of thermal ionization, and have been regarded as corroborative evidence that the type of process contemplated by that theory actually represents what goes on in the atmospheres of the stars. In the present chapter the theory of the various effects will first be discussed, and later the predictions from the theory will be compared with observational data. INFLUENCE OF SURFACE GRAVITY ON THE SPECTRUM