Plate II.—Optical Phenomena showing the Height of the Atmosphere.
Extent of the Atmosphere.—If the atmosphere were incompressible and had throughout the density that it has at the earth, its height would be about five miles only, but actually it is composed of gases that follow Boyle's law and vary in volume inversely as the pressure upon them. Since the pressure decreases with height in a geometrical progression, it would be halved for each three and a half miles of ascent were the temperature constant, but as the temperature also decreases with height, the successive intervals, beginning with three and a half miles, become shorter because the volume of a gas depends on its temperature as well as on the pressure upon it. The decrease of pressure with increasing height above the earth is shown by the left-hand scale of [Plate I]., already described, and the subsequent diminution of density to the limits of our measurable atmosphere is indicated on the right of [Plate II]., Optical Phenomena showing the Height of the Atmosphere. The gases composing the atmosphere probably extend to heights proportional to their density; viz. oxygen to about thirty miles and nitrogen to thirty-five miles, although water-vapour nearly disappears at twelve miles. From these considerations it is supposed that the atmosphere, as measurable by the barometer, vanishes at about thirty-eight miles, and this is about the height indicated by twilight, which is the reflected light of the sun when 18° below the horizon. After the great eruption of the volcano Krakatoa in the South Seas in 1883, the brilliant sunset glows and the longer twilight showed that the dust emitted by the eruption remained for more than a year suspended at a height of at least sixty miles. The so-called "luminous clouds" seen at night during the same period, and which were probably these same dust particles still illumined by the sun, were found by trigonometrical measurements to have about the same altitude. Although it is computed that at a height of seventy miles the air has less than one-millionth of its density at sea-level—which is about the density of the air remaining in the exhausted bulb of an incandescent electric lamp—it is there sufficiently dense to render meteors luminous by friction after they with great velocity enter our atmosphere. The height of these meteors has been found, from simultaneous trigonometrical measures at two stations, sometimes to exceed one hundred miles, and if we suppose the aurora borealis to be an electrical discharge in highly rarefied air, measures made in the same way indicate as great a height for our atmosphere. The height of the aurora varies enormously, but the average altitude of it and of the other phenomena described, with the corresponding computed density of the air, are shown in the preceding diagram, in which the depth of the ocean of air may be compared with the deepest seas and the highest mountains. While, as Professor Young says, it cannot be asserted that the atmosphere has any defined upper limit, yet the kinetic theory of gases seems to afford evidence that the molecules of oxygen and nitrogen do not escape from the earth's attraction, and therefore the hypothesis of Professor Förster is unwarranted, that interplanetary space is filled with Himmelsluft, or very thin air.
Temperature of the Atmosphere.—The warmth of the atmosphere is derived chiefly from the sun's rays which, arrested by the earth's surface, are partly reflected and partly radiated back through the atmosphere. Not more than seventy-five per cent.—Professor Langley says only sixty per cent.—of the heat of the sun, which is received vertically on the upper surface of the atmosphere, penetrates to the earth, and very much less than this when the angle of the sun is low. The reason why temperature diminishes as we ascend, is partly owing to the greater loss of heat by radiation through the thinner envelope of the upper strata, and partly owing to the greater absorption of the heat given off from the earth by the lower and denser strata. In general, it may be said that there is a diminution of 1° Fahrenheit for each three hundred and thirty feet that we rise vertically, but, this rate varies greatly at different heights, places, and times. For instance, the decrease is not the same on mountains as it is in the free air, and in the northern hemisphere it is greater on the south than on the north sides of mountains; it is usually greatest near the ground, and is faster in summer than in winter. But in the average, the temperature falls as much for three hundred and thirty feet of elevation as it does for a change of seventy miles on the earth's surface north or south of the equator. When dry air rises, because it is heated and thereby is made lighter, the laws of thermo-dynamics show that, by reason of its expansion, its temperature is decreased 1° Fahrenheit for each one hundred and eighty-three feet that it ascends, and, by compression, its temperature is increased as much if it is made to descend the same distance. This is called the "adiabatic rate of change of temperature," because it is produced by an alteration in the density of the air, due to variation in pressure, without the addition or loss of heat. In the course of this book there will be occasion frequently to refer to this law of heating and cooling. The adiabatic rate of change is seldom observed on mountains because of their influence upon the currents of air in contact with their flanks, or even in balloons, on account of imperfect measurements, but, as will be explained in the closing chapter, the adiabatic change of temperature is confirmed by the observations with kites, which furnish the best method of obtaining the temperature of the free air up to moderate heights. The adiabatic cooling of rising currents of air is another reason for the rapid decrease of temperature with height up to a mile or more. The upper air alters its temperature from diurnal and seasonal causes much more slowly than the lower air, and a mile above the earth the daily change of temperature, apart from the passage of "warm and cold waves," is less than one degree. At a height of six miles above the earth a temperature much below zero constantly prevails, while, at ten miles, 80° below zero has been recorded in a balloon—this is approximately the temperature prevailing winter and summer above pole and equator. These facts are expressed graphically in [Plate III]., Temperature at Different Latitudes and Altitudes, which represents half of a section of the earth, from the north pole to the equator, with the superincumbent atmosphere.
Plate III.—Temperature at different Latitudes and Altitudes.
Perhaps it should be explained, that whereas the curvature of the earth with respect to the height of the atmosphere in the previous diagram was not exaggerated, in the present diagram the height of the atmosphere over the radius of the earth is enormously increased. At the north pole the mean annual temperature is about 0° Fahrenheit, and at the equator it is about 80°. It is seen that the atmospheric layer having a temperature of 50° (here represented in section by a line) touches the earth at 45° latitude, but is about two miles above the equator. In the same way the line of freezing (32°) leaves the earth's surface at 58° latitude and rises to about three and a half miles over the equator; the line of 0° rises from the pole to about seven miles at the equator. This is familiarly illustrated by the fact that only the highest mountains in the tropics are snow-capped, while within the Arctic circle the snow-line descends nearly to sea-level. The lines in the diagram show the mean annual temperatures, but the isothermal surfaces rise in summer and sink in winter, the change of altitude being greatest in northern regions and near the ground. Frequently there is an inversion of temperature, that is to say, it is warmer above than below. Notably, in Siberia, where the winter temperature is 60° below zero, there can be no immediate decrease of temperature with height, and it is probable that there is a warmer layer of air interposed between the very cold earth and the still colder upper air, so that the temperature first rises rapidly with elevation and then falls slowly to the limits of the atmosphere. In temperate latitudes it often happens, with a high barometric pressure, in winter that the mountain stations enjoy a long period of still and relatively warm weather, as compared to that experienced in the valleys. But the subject of inversions of temperature will be discussed at length in considering the results of the balloon and kite observations.
The observations from balloons at great heights are neither sufficiently numerous nor accurate to enable us to form an opinion as to what is the temperature of interplanetary space, which the kinetic theory of gases places at 460° Fahrenheit below zero. This temperature is called "the absolute zero," and is calculated from the fact that air under a constant pressure contracts 1⁄490 of its volume for each degree Fahrenheit it is cooled below the temperature of freezing water, and consequently under no pressure it should have an infinite volume and a temperature of about 490° below freezing, or 458° below zero. There are other hypotheses regarding the temperature of space, but since it can never be measured directly, it will probably remain a matter of speculation. It is certain, however, that if the earth were deprived of its atmosphere, the temperature would fall very low, and even with our atmosphere as a blanket our earth would be uninhabitable were it not for the aqueous vapour which controls the selective absorption of the solar rays, transforming them into obscure rays so that they cannot escape from the atmosphere. Water-vapour, then, is a very important factor in the physics of the atmosphere, but it can only be considered briefly here.
Moisture of the Atmosphere.—The air is constantly absorbing moisture from the water on the earth, but the tension of this aqueous vapour decreases with elevation much faster than does the atmospheric pressure. At the height of about a mile and a quarter half the quantity of water-vapour is below, while we must rise about three and a half miles to reduce the quantity of air one-half, as may be seen in [Plate I]. The relative humidity, or the percentage of moisture in the air, as compared to the amount which it could contain at that temperature, is nearly the reverse at low and at high levels. It is found from the kite-observations at Blue Hill, that up to the height of a mile or two the air is drier during winter and at night, and damper during summer and in the day-time than it is near the ground. At great heights probably the air is always very dry. The condensation of the invisible vapour into a visible form is considered in the next chapter on clouds.
It is apparent that our observational knowledge of the atmosphere is gained by two general methods of exploring it, viz. observations made from the earth upon clouds and optical phenomena at a distance, and observations made directly in the air itself. Although it was realized at the beginning of this century that meteorological observations were almost all conducted at the very bottom of our atmosphere—"in the shoals and shallows of the ocean of air," von Humboldt said—yet only within the past thirty years was it thought necessary to replace the occasional observations on mountains by systematic and long-continued ones, comparable to those so generally carried on at low levels. It is an evidence of the zeal in America to advance the young science of meteorology, that the first mountain-top station in the world was established in 1871 upon Mount Washington, and that both this exposed post of observation, 6300 feet above the sea, and the one more than twice as high on Pike's Peak, which was for a long time the highest in the world, were maintained for many years by the United States Signal Service. The present highest station in the world is maintained by the Harvard Observatory upon El Misti in Peru, where, at a height exceeding 19,000 feet, a combination of self-recording instruments was constructed by my assistant, Mr. Fergusson, to operate during three months without attention. It must be admitted, however, that the addition to our knowledge of the physics of the atmosphere afforded by the American stations has been slight and incommensurate with the expense incurred. More has been gained from the mountain stations in Europe, notably from those in the Austrian Alps, which have furnished data for Dr. Hann's splendid discussions of the thermo-dynamics of the atmosphere. While mountain stations present the only means of obtaining continuous observations at a considerable and constant height, still they have serious drawbacks. Not only is the distribution of mountains over our globe irregular, but since they form part of the earth's crust, terrestrial influences affect all observations made upon them. In the case of plateaux this was at once admitted, but by placing the stations on the summits of high and isolated peaks, it was hoped to approximate to the conditions of the free air. It is now recognized that the equilibrium of the atmosphere is so delicate that for its dynamical study exact and minute measurements of temperature, moisture, and currents are required, and the methods which will be described are intended to give the values of these elements free from terrestrial disturbances.