The most important factor involved in the theory is , the partial pressure of electrons in the reversing layer. By assuming constant at about , and treating as the unknown, a temperature scale which agrees substantially with those derived from measurements of radiation may be deduced from the observed positions of the maxima. The first discussion of the data then available was made by Fowler and Milne in their original paper.[379] Subsequent investigations of the positions of maxima have been published by Menzel[380] and by the writer.[381] These observations, and the scale derived from them, will be discussed in the two following chapters. The value of has been recently shown by several kinds of investigation to be at least as low as was assumed by Fowler and Milne, so that their assumption that a uniform mean pressure can be used, as a first approximation, in deriving a temperature scale from their formula appears to be justified. Milne[382] points out that “on whatever specific assumptions” the theory rests, “the mean pressure for a maximum of intensity in an absorption line is found to depend on the absolute value of the absorption coefficient. In fact ... it is clear [Pg 110] that the greater the absorbing power of the atoms in question, the more opaque is the stellar atmosphere in the frequency concerned, and so the greater the height and the smaller the pressure at which the line originates.” That the absorption coefficient in the stellar atmosphere is very high is suggested by the reorganization times (“lives”) of such atoms as have been investigated,[383] and Milne’s discussion of the life of the excited calcium atom from astrophysical data lends weight to the suggestion. A high absorption coefficient leads at once to low pressures in the reversing layer, and theory has gone far towards indicating that pressures of the order of are to be expected on a priori grounds.[384] The observational evidence bearing on pressures in the reversing layer will be found[385] in Chapter III. The case appears to be a strong one, resting on evidence of many different kinds—notably pressure shifts, line sharpness, and series limits. Russell and Stewart,[386] in their exhaustive discussion of the question, conclude that “all lines of evidence agree with the conclusion that the total pressure of the photospheric gases is less than 0.01 atmosphere, and that the average pressure in the reversing layer is not greater than 0.0001 atmosphere.” The observational evidence gives the total pressure, but the partial electron pressure will not differ greatly from this. Although even in the hottest stars three ionizations is the greatest number observed, most of the elements that constitute the stellar atmosphere are appreciably ionized at temperatures greater than 4000°, so that the partial electron pressure is at least half the total pressure. PHYSICAL ASSUMPTIONS