THE increase of the volume of atmospheric air, under Constant pressure, being directly proportional to the increment of temperature, while the coefficient of expansion is 0.00203 for 1° of Fahrenheit, it will be seen that a temperature of 3,272,000° Fah. communicated to the terrestrial atmosphere would reduce its density to 1/6643 of the existing density. Accordingly, if we assume that the height of our atmosphere is only 42 miles, the elevation of temperature mentioned would cause an expansion increasing its height to 6643 × 42 = 279,006 miles. This calculation, it should be observed, takes no cognizance of the diminution of the earth's attraction at great altitudes, which, if taken into account, would considerably increase the estimated height. Let us now suppose the atmosphere of the sun to be replaced by a mediuni similar to the terrestrial atmosphere raised to the temperature of 3,272,000°, and containing the same quantity of matter as the terrestrial atmosphere for corresponding area. Evidently the attraction of the sun's mass would under these conditions augment the density and weight of the supposed atmosphere nearly in the ratio of 27.9 I; hence its height would be reduced to 279,006/27.9=10,000 miles. But if the atmosphere thus increased in density by the sun's superior attraction consisted of a compound gas principally hydrogen, say 1.4 times heavier than pure hydrogen, the height would be 14.7 × 10,000 = 100,000 miles. The pressure exerted by this supposed atmosphere at the surface of the photosphere would obviously be 14.7 × 27.9 = 410 pounds per square inch, nearly. Unless, therefore, the depth greatly exceeds 100,000 miles, and unless it can be shown that the mean temperature is less than 3,272,000° Fah., the important conclusion must be accepted that the solar atmosphere contains so small a quantity of matter that notwithstanding the great depth it will offer only an insignificant resistance to the passage of the solar rays. Now, the assumed mean temperature, 3,272,000°, so far from being too high, will be found to be considerably underrated. It will be recollected that the temperature at the surface of the photosphere, determined by the ascertained intensity of solar radiation at the boundary of the earth's atmosphere, somewhat exceeds 4,035,000°. Consequently, as the diminution of intensity caused by the dispersion of the rays, will be inversely as the convex areas of the photosphere and the sphere formed by the boundary of the solar envelope, viz., 1.52: 1, the temperature at the said boundary will be 4,035,000°/1.52 = 2,654,600° The true mean, therefore, will be 3,344,800°, instead of 3,272,000° Fah., a difference which leads irresistibly to the inference that, either the solar atmosphere is more than 100,000 miles in depth, or it contains less matter than the terrcstrial atmosphere, for corresponding area. It will be demonstrated hereafter that the retardation of the rays projected from the border of the photosphere consequent on the increased depth of the solar atmosphere (supposed to be the main cause of the observed diminution of energy near the sun'S limb), cannot appreciably diminish the intensity of the radiant heat, The ratio of diminution of the density of the gases composing the solar atmosphere at succeeding altitudes, is represented by Fig. 5, in which the length of the ordinates of the curve a d b shows the degree of tenuity at definite points above the photosphere. This curve has been constructed agreeably to the theory that the densities at different altitudes, or what amounts tothe same, the weight of the masses incumbent at succeeding points, decreases in geometrical progression as the height above the base increases in arithmetrical progression. The vertical line a c has been divided into 42 equal parts, in order to facilitate comparisons with the terrestrial atmosphere, the relative density of which, at corresponding heights, is obviously as correctly represented by this diagram as that of the solar atmosphere. It is true that, owing to the greater height of the latter compared with the attractive force of the sun's mass, the upper strata of the terrestrial atmosphere will be relatively more powerfully attracted than the upper strata of the vastly deeper solar atmosphere. The ordinates of the curve a d b will therefore not represent the density quite correctly in both cases. The discrepancy, however, resulting from the relatively inferior attraction of the sun's mass at the boundary of its atmosphere, will be very nearly neutralised by the increased density towards that boundary, consequent on the great reduction of temperature — fully 1,380,000° Fah.— caused by the dispersion of the solar rays before entering space. It may be well to add that, in representing the relative height and pressure of the terrestrial atmosphere, a c in our diagram indicates forty-two miles, while b c indicates a pressure of 14.7 pounds per square inch; and that in representing the solar atmosphere, a c indicates 100,000 miles and b C 410 pounds per square inch. Bearing in mind the high temperature and small specific gravity, the extreme tenuity in the higher regions of the solar atmosphere will be comprehended by mere inspection of our diagram. Already midway towards the assumed boundary, the density of the solar atmosphere is so far reduced that it contains only 1/152000 of the quantity of matter contained in an equal volume of atmosphere at the surface of the earth.
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ERICSSON, J. The Temperature of the Sun . Nature 4, 449–452 (1871). https://doi.org/10.1038/004449a0