The first theoretical discussion of the effects of absolute magnitude upon the stellar spectrum seems to have been made by Pannekoek,[413] who pointed out that “stars of the same spectral class ... will show differences depending solely on ...
,” where
is the surface gravity, and
the absorption coefficient. Pannekoek considered all stars of the same spectral class to have the same temperature, and for the purposes of his argument the differences in temperature between giants and dwarfs can be neglected, although actually they may for other reasons have a noticeable effect on the spectrum. If
be regarded as constant, a plausible assumption for various reasons,[414] “the physical quantity, directly given by the spectra used for the determination of spectroscopic parallaxes is the gravitation at the surface of the star.”[415] The relation between the surface gravity and the pressure is given by
