The density gradient is thus eliminated. The optical depth is furthermore related to the pressure by the relations where is the value of gravity at the point in question, and whence In considering the stellar atmosphere we are dealing with a layer so near the surface that the value of g involved is effectively the “surface gravity” for the star. If is constant, a condition [Pg 36] probably approximately fulfilled,[60] the pressure at constant optical depth is then directly proportional to the surface gravity, which varies as the product of the mean density and the radius of the star. Some idea of the range in pressure with which we shall be concerned in the stellar atmosphere can therefore be obtained from stars of known mean density and radius. The data for eight such stars, all of the second type, are contained in Table X, which is adapted from tabulations given by Shapley.[61] Successive columns contain the name of the star, the spectral class, the mean densities of the two components in terms of the solar density, the hypothetical radii of the two components (on the assumption of solar mass) in terms of the sun’s radius, and the product of mean density and radius for each component. TABLE X Star Class Mean density Radius Product SX Cas 0.0004 0.0002 15.3 18.6 0.006 0.004 RX Cas 0.0005 0.0004 14.3 14.3 0.007 0.006 RZ Oph 0.001 0.00003 10.1 33.5 0.010 0.001 RT Lac 0.0013 0.010 4.6 4.6 0.059 0.046 W Cru 0.00002 0.000025 94 36 0.00019 0.0009 U Peg 0.83 0.67 1.2 1.2 1.0 0.8 W G 1.8 1.8 0.9 0.9 1.6 1.6 Sun 1.0 1.0 1.0 In mean density these stars display a range of , while the range in surface gravity is , illustrating the significant fact that the mean density varies far more widely than the surface gravity. The latter quantity is the important one in determining the pressure that may be assumed to exist in the reversing layer. If the masses of the very luminous stars of low mean density, such as W Crucis, exceed the solar mass, as they most probably do, the hypothetical radii are [Pg 37] increased, and the range in surface gravity becomes even smaller than before. The data for stars of known mean density and radius permit the estimation of the range in surface gravity, and hence of the range in pressure, encountered in the reversing layer. In the absence of knowledge of the appropriate optical depth, however, the actual pressure cannot be deduced from such considerations, and recourse must be made to more indirect methods. The present view is based upon a number of considerations, none of which would alone be of great weight. All of the conclusions, taken together, however, indicate that the upper limit of the pressure for the region in which the Fraunhofer lines originate is of the order of .