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The height of the atmosphere; or, the elevation to which it
extends beyond the surface of the earth.
The height of the atmosphere is considered, by many writers and lecturers on this subject, as a point fully determined, and is treated as familiarly as the height of the Andes or the Alps, or of Mount Etna or Mount Blanc. But the height of the atmosphere has never yet been fully ascertained, and, it is probable, will never be accurately determined. If, indeed, the air were of an equal density, from the surface of the earth to the top of the atmosphere, its height might be easily determined; for it is found by experiment, that the weight of a column of air extending to the top of the atmosphere, is equal to the weight of a column of water of the same base and 32 feet high. Supposing water to be 840 times heavier than air-multiply 840 by 32 feet, and the product will be 26,880 feet, or 5 miles and 160 yards for the height of the atmosphere, were its density at every elevation exactly the same as at the surface of the earth. But we know that the density of the air decreases and is more rarefied and expanded the higher we go; and, from other considerations we know that it extends far beyond the limit now stated ; so that this calculation can afford us no accurate idea of the height to which the atmosphere extends.
Another method, therefore, of determining this point was devised by philosophers, which approaches nearer to the truth. It is found by observation, that the sun is about eighteen degrees below the horizon before twilight comes to an end in the evening. Now, twilight is caused by the rays of the sun being refracted and reflected from the higher parts of the atmosphere to the earth; otherwise, we should be involved in total darkness at the moment the sun descended below the horizon. From this circumstance, the height of the highest part of the atmosphere which is capable of refracting the
rays of light may be determined.
Let F A B (fig. 5) represent the horizon of an observer at A; S D, a ray of light falling upon the atmosphere at D, and making an angle, S D B, of 18° with the horizon; the angle s D A will then be 162o. From the centre c, draw C D, and it will be perpendicular to the reflecting particles at D, and will likewise bisect the angle s D A. In the right-angled triangle C D A, the angle c D A is equal to 81°; or, if we allow for refraction, 81° 30', A C, the radius, or half-diameter of the earth, is nearly
equal to 4000 miles. Then, by the rules of trigonometry,
81° 30'.. 9.995203
As the sine of the angle CDA
3.606857 From C D, equal to the semi-diameter of the earth and atmosphere, subtract c A, or the semi-diameter of the earth, and the remainder, ED, equal to 441 miles, will be the height of the atmosphere. In this operation, the logarithms of the second and third terms of the proportion are added, and the logarithm of the first term subtracted from the sum.
The same result is produced by the following proportion :
3.602060 8.3° 10.004800
TO CD = 4011)
It appears, then, that in ordinary cases, the air, at the height of forty-four miles and a half, is capable of reflecting to us the rays of light. But, as a sensible illumination has been perceived when the sun is much further below the horizon than what has been now stated, there is some reason to conclude, that the air is sufficiently dense for reflecting a sensible degree of light at the height of nearly two hundred miles.
Various considerations, founded on meteoric phenomena, serve to prove that the atmosphere extends to a much higher elevation than fortyfour or fifty miles. In the year 1719, a remarkable luminous meteor, or fire-ball, was seen, whose altitude was computed to be seventy-three miles above the surface of the earth. On the 18th of August, 1783, a brilliant fire-ball passed over Britain and the adjacent countries; and, from various circumstances which were particularly marked by different observers, it was calculated that its elevation above the earth could not be less than ninety or a hundred miles. In passing over certain parts of England, a loud report was heard and a hissing noise.
The meteor of
1719 is said to have been attended with an explosion, which was heard over the whole island of Great Britain, occasioning a violent concussion of the atmosphere, and seeming to shake even the earth itself. Now, in these, and multitudes of similar phenomena, we have instances of fire and flame being supported, and sounds conveyed to the earth from a height of ninety or a hundred miles; and, consequently, even in these elevated regions, notwithstanding the great rarefaction of the air, it must still have the
supporting flame and propagating sound. Even although the fire-balls alluded to be supposed to consist of electrical matter—which is the general opinion—yet the difficulty is not thereby removed ; for, it is found, by some late experiments, that the electrical fire cannot penetrate a perfect vacuum. And, therefore, there is reason to conclude, that we are still ignorant of the precise extent of the atmosphere, and of the nature of the fluids which occupy its superior regions. That the meteors now referred to, however elevated, were not beyond the limits of the atmosphere, appears from this consideration, that the atmosphere revolves with the earth in its course round the sun, at the rate of 68,000 miles an hour. Now, as the meteor of 1783 moved from north to south, if it had been beyond the limits of the atmosphere, it would have been left, in the course of a minute, more than a thousand miles to the westward, by the earth