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 [Pg 141] gravitation at the surface of the star.”[415] The relation between the surface gravity and the pressure is given by where is the “homogeneous depth.” The pressure is then directly proportional to the surface gravity. INFLUENCE OF PRESSURE ON THE SPECTRUM Lowered pressure increases the degree of ionization. The tendency of the atoms to lose electrons by thermal ionization should depend solely on their energy supply, and should thus be independent of the pressure. The total absorbing power of the gas will, however, depend on the number of suitable atoms that it contains, not upon their rate of formation. The number of suitable ionized atoms present at any moment in the atmosphere is a function not only of the rate at which ionization proceeds, but also of the rate of recombination. The more readily recombination takes place, the larger is the number of effective neutral atoms, and the smaller the number of effective ionized atoms, when a steady state is attained. The rate of recombination, which depends upon the probability of a suitable encounter between an ionized atom and a free electron, will increase with the pressure—more accurately, with the partial pressure of free electrons. The higher the pressure, therefore, the greater the number of neutral atoms, and the smaller the number of ionized atoms. This argument explains at once the strength of the neutral (arc) lines in the spectra of stars of low luminosity (high surface gravity), and the predominance of ionized (spark) lines for absolutely bright stars (low surface gravity, resulting chiefly from large radius). Low surface gravity, then, increases the number of ionized atoms present by discouraging recombination.