(b) Sharpness of lines.—The occurrence, as sharp distinct lines in the spectra of the stellar atmosphere, of lines that are diffuse in the laboratory at atmospheric pressure, and only become sharp when the pressure is very much reduced, indicates that the pressure in the reversing layer must be extremely low. The mere existence of distinct hydrogen lines points to a pressure of less than half an atmosphere, as was shown by Evershed,[65] and the lines 4111, 4097, 3912 of chromium,[66] 3421, 3183 of barium,[67] and 4355, 4108, 3972 of calcium,[68] which are sharp and distinct in the solar spectrum, but which only lose their diffuseness in the laboratory under vacuum conditions, indicates pressures probably far lower than 0.1 atmospheres. The lines of doubly ionized nitrogen, which are seen as sharp clear absorption lines in the early stars and the cooler stars,[69] are also somewhat hazy under even the finest laboratory conditions,[70] and probably arise in regions of very low pressure in the stellar atmosphere. (c) Widths of lines.—The width of an absorption line, produced by “Rayleigh Scattering” close to resonance conditions, is given by Stewart[71] as where is the observed width of the line, the wave-length expressed in the same units, and the number of molecules per square centimeter column in the line of sight. It is unfortunate that the widths of Fraunhofer lines are hard to measure and difficult to interpret. Results obtained from objective prism spectra will probably differ from those derived with the aid of a slit spectrograph, and moreover, in estimating a line with wings it is hard to judge what should be regarded as the “true” line width. Russell and Stewart[72] estimate for the lines in the solar spectrum. Then, on the assumption that the reversing layer has a thickness of a hundred kilometers, the partial pressure of neutral sodium in the reversing layer, as derived by Russell and Stewart from the formula just quoted, is of the order . At the solar temperature, 5600°, about 99 per cent of the sodium present is in the ionized condition,[73] and thus the total partial pressure of sodium atoms may be of the order . If it be assumed that sodium constitutes about 5 per cent of the total material present, the total pressure thus derived is of the order . [Pg 40] The lines are of course the ultimate lines of neutral sodium. It will be shown[74] in Chapter IX that the partial electron pressure in the region from which ultimate lines originate is probably between at maximum. When 99 per cent of the atoms are ionized, the pressure rises by a factor of about 100, and the corresponding partial electron pressure becomes between . As the total pressure is probably, at the solar temperature, about twice the partial electron pressure, the total pressure should be nearer to .