The total pressure derived in Chapter IX is the pressure corresponding to the median frequency of the sodium atoms that send out light to the exterior—it may be regarded as the average pressure for the visible sodium. The total pressure derived from the line width, on the other hand, is the pressure at the bottom of the layer of visible sodium, and might therefore be expected slightly to exceed the average pressure for the visible sodium atoms. The difference encountered, partial electron pressure, the total pressure should be nearer to for the average pressure, and partial electron pressure, the total pressure should be nearer to for the total absorption pressure, is in the direction that would be anticipated, although it is larger than might have been expected. Neither value is, however, of very high accuracy, and probably the agreement can be regarded as quite satisfactory. If the same formula be applied to the hydrogen lines, which may have a width[75] of the order of 5Å, high values for the partial pressure of hydrogen are obtained. The behavior of hydrogen in the spectra of the cooler stars,[76] and the abnormally high abundance[77] derived for it in Chapter XIII, suggest that here, again, a definite abnormality of the behavior of hydrogen is involved. (d) Flash Spectrum.—It was pointed out by Russell and Stewart[78] that the density in the region that gives the flash spectrum must be exceedingly low. If this were not the case, the intensity of the scattered sunlight would be great enough, as compared to the flash itself, to register on the plate as continuous background in the time required to photograph the flash. The pressure thus estimated, from the minimum amount of material required to give scattered sunlight strong enough to be registered, is less than . (e) Radiative Equilibrium of the Outer Layers.—At the edge of a star, where radiation pressure and gravitation no longer balance, and in consequence the existence of temperature and pressure gradients, [Pg 41] such as we observe in the reversing layer, becomes possible, the equations given by Eddington[79] for the equilibrium of the interior no longer hold. The outer layers fall off more steeply than the equations predict, and in consequence it is not possible to use the equations in deriving values for the pressure or density corresponding to a layer near the boundary at a given temperature. It is certain, however, that the density deduced from the equations will be far too high, and so the predicted density at a given temperature may be used to indicate that the pressures at the boundary of a giant star are indeed very low.