The following table is adapted from the one given by Eddington for the relation between distance, , from the center, density , and temperature , for a typical giant star of Class , effective temperature 6500°. The distance from the center is expressed in terms of the solar radius, the density in grams per cubic centimeter, and the temperature in absolute units. The last entry in the first column represents the total radius of the star. 0 0.1085 6,590,000° 4 0.0010 1,380,000° 1 0.0678 5,640,000 5 0.00015 730,000 2 0.0215 3,840,000 6 0.0000093 290,000 3 0.0050 2,370,000 6.9 0.000000 ...... At a depth where the temperature is 290,000°, ten times the temperature in the reversing layer of any known star, the density given is about . An atmosphere a hundred kilometers in thickness (the supposed approximate depth of the reversing layer) and of this density would contain only a hundred grams per square centimeter of surface. In order to bring the density into harmony with the densities derived for the reversing layer it is necessary to suppose that the value[80] of falls to 0.4 per cent of its value at 290,000° as the temperature falls, from [Pg 42] 290,000° to 29,000°, to 10 per cent of its value. The fall of density displayed in the table appears to be rapid enough to warrant this supposition; and in any case, as was pointed out earlier, the actual fall is probably greater than the formula predicts. The general theory of stellar equilibrium is, then, consistent with very low pressures in the reversing layer. More than this cannot be said, as the formulae are not directly applicable. (f) Observed Limit of the Balmer Series.—The earlier members of the Balmer series of hydrogen are produced by the transfer of electrons from 2-quantum orbits to 3-quantum orbits (), 4-quantum orbits (), and so forth. The later members of the series are associated with orbits of higher and higher quantum numbers. The major axis of the orbit varies as the square of the quantum number, and therefore a hydrogen atom which is producing, say, , is effectively much larger than one which is giving rise to . As was early suggested by Bohr,[81] the production of the higher members of the series must depend upon the possibility of existence of the corresponding outer orbits. As a preliminary assumption it appears probable that the existence of the larger orbits will depend on the proximity of neighboring atoms, and hence on the pressure.