phenomena of the atmosphere are well treated by E. Mascart in his Traité d’optique (Paris, 1891–1898), and by J. M. Penter, Meteorologische Optik (1904–1907). Of minor treatises especially adapted to collegiate courses of study we may mention those by Sprung (Berlin, 1885); W. Ferrel (New York, 1890); Angot (Paris, 1898); W. M. Davis, (Boston, 1893); Waldo (New York, 1898); Van Bebber (Stuttgart, 1890); Moore (London, 1893); T. Russell (New York), 1895. The brilliant volume by Svante Arrhenius, Kosmische Physik (Leipzig, 1900) contains a section by Sändstrom on meteorology, in which the new hydrodynamic methods of Bjerknes are developed.
I.—Fundamental Physical Data
There can be no proper study of meteorology without a consideration of the various physical properties of the atmospheric gases and vapours, each of which plays an independent part, and yet also reacts upon its neighbours.
Atmospheric air is a mixture of nitrogen, oxygen, aqueous vapour, carbonic acid gas (carbon dioxide), ammonia, argon, neon, helium, with slight traces of free hydrogen and hydro-carbons. The proportions in which these gases are present are quite constant, except that the percentage of aqueous vapour is subject to large variations. In an atmosphere that is saturated at the temperature of 90° F., as may occur in such a climate as that of Calcutta, the water may be 212% of the whole weight of any given volume of air. When this aqueous vapour is entirely abstracted, the remaining dry gas is found to have a very uniform constitution in all regions and at all altitudes where examination has been carried out. In this so-called dry atmosphere the relative weights are about as follows: Oxygen, 23·16; nitrogen and argon, 76·77; carbonic acid, 0·04; ammonia and all other gases, less than 0·01 in the lower half of the atmosphere but probably in larger percentages at great altitudes. Of still greater rarity are the highly volatile gases, argon (q.v.), neon, krypton and helium (q.v.).
Outer Limit.—These exceedingly volatile components of the atmosphere cannot apparently be held down to the earth by the attraction of gravitation, but are continually diffusing through the atmosphere outwards into interstellar space, and possibly also from that region back into the atmosphere. There are doubtless other volatile gases filling interstellar space and occasionally entering into the atmosphere of the various planets as well as of the sun itself; possibly the hydrogen and hydro-carbons that escape from the earth into the lower atmosphere ascend to regions inaccessible to man and slowly diffuse into the outer space. The laws of diffusion show that for each gas there is an altitude at which as many molecules diffuse inwards as outwards in a unit of time. This condition defines the outer limit of each particular gaseous atmosphere, so that we must not imagine the atmosphere of the earth to have any general boundary. The only intimation we have as to the presence of gases far above the surface of the globe come from the phenomena of the Aurora, the refraction of light, the morning and evening twilight, and especially from the shooting stars which suddenly become luminous when they pass into what we call our atmosphere. (See C. C. Trowbridge, “On Luminous Meteor Trains” and “On Movements of the Atmosphere at Very Great Heights,” Monthly Weather Review, Sept. 1907.)
Such observations are supposed to show that there is an appreciable quantity of gas at the height of 100 m., where it may have a density of a millionth part of that which prevails at the earth’s surface. Such matter is not a gas in the ordinary use of that term, but is a collection of particles moving independently of each other under those influences that emanate from sun and earth, which we call radiant energy. According to Störmer this radiant energy is that of electrons from the sun, and their movements in the magnetic field surrounding the earth give rise to our auroral phenomena.
According to Professor E. W. Morley, of Cleveland, Ohio, the relative proportions of oxygen and nitrogen vary slightly at the surface of the earth according as the areas of high pressure and low pressure alternately pass over the point of observation; his remarkably exact work seems to show a possible variation of a small fraction of 1%, and he suggests that the air descending within the areas of high pressure is probably slightly poorer in oxygen. The proportion of carbonic acid gas varies appreciably with the exposure of the region to the wind, increasing in proportion to the amount of the shelter; it is greater over the land than over the sea, and it also slightly increases by night-time as compared with day, and in the summer and winter as compared with the spring and autumn months. During the year 1896 Professor S. Arrhenius in the Phil. Mag., and in 1899 Professor T. C. Chamberlin in the Amer. Geol. Jour., published memoirs in which they argued that a variation of several per cent. in the proportion of carbonic; acid gas is quite consistent with the existence of animal and vegetable life and may explain the variations of climate during geological periods. But the specific absorption of this gas for solar radiations is too small (C. G. Abbot, 1903) to support this argument. The question whether free ozone exists in the atmosphere is still debated, but there seems to be no satisfactory evidence of its presence, except possibly for a few minutes in the neighbourhood of, and immediately after, a discharge of lightning. The general proportions, of the principal gases up to considerable altitudes can be calculated with close approximation by assuming a quiescent atmosphere and the ordinary laws of diffusion and elastic pressure; on the other hand, actual observations show that the rapid convection going on in the atmosphere changes these proportions and brings about a fairly uniform percentage of oxygen, nitrogen and carbonic acid gas up to a height of 10 m.
Aqueous Vapours.—The distribution of aqueous vapour is controlled by temperature quite as much as by convection and has very little to do with diffusion; the law of its distribution in altitude has been well expressed by Hann by the simple formula: log e＝log e0−h/6517 where h is the height expressed in metres and e and e0 are the vapour pressures at the upper station and sea-level respectively. Hann’s formula applies especially to observations made on mountains, but R. J. Süring, Wissenschaftliche Luftfahrten, III. (Berlin, 1900) has deduced from balloon observations the following formula for the free air over Europe—
log e＝log e0−h(1 +h/20000)/6000.
He has also computed the specific moisture of the atmosphere or the mixing ratio, or the number of grams of moisture mixed with 1 kilogram of dry air for which he finds the formula
log m＝log m0−h(1 +3h/40)/9000.
The relative humidity varies with altitude so irregularly that it cannot be expressed by any simple formula. The computed values of e and m are as given in the following table:—
| Altitude Metres. h. |
Relative Vapour Pressure. e/e0. |
Relative Specific Moisture. m/m0. |
| 0 | 1000 | 1000 |
| 1000 | 655 | 759 |
| 2000 | 431 | 555 |
| 3000 | 266 | 391 |
| 4000 | 158 | 264 |
| 5000 | 91 | 172 |
| 6000 | 50 | 108 |
| 7000 | 27 | 65 |
| 8000 | 14 | 38 |
In addition to the gases and vapours in the atmosphere, the motes of dust and the aqueous particles that constitute cloud, fog and haze are also important. As all these float in the air, slowly descending, but resisted by the viscosity of the atmosphere, their whole weight is added to the atmosphere and becomes a part of the barometric record. When the air is cooled to the dew-point and condensation of the vapour begins, it takes place first upon the atoms of dust as nuclei; consequently, air that is free from dust is scarcely to be found except within a mass of cloud or fog.
Mass.—According to a calculation published in the U.S. Monthly Weather Review for February 1899, the total mass of the atmosphere is 1/1,125,000 of the mass of the earth itself but, according to Professor R. S. Woodward (see Science for Jan. 1900), celestial dynamics shows that there may possibly be a gaseous envelope whose weight is not felt at the earth’s surface, since it is held in dynamic equilibrium above the atmosphere; the mass of this outer atmosphere cannot exceed 11200th of the mass of the earth, and is probably far less, if indeed it be at all appreciable.
Conductivity.—Dry air is a poor conductor of heat, its coefficient of conduction being expressed by the formula: 0·000 0568 (1 +0·00190 t) where the temperature (t) is expressed in centigrade degrees. This formula states the fact that a plate of air 1 centimetre thick can conduct through its substance for every square centimetre of its area, in one second of time, when the difference of temperature between two faces of the plate is 1° C., enough heat to warm 1 gram of water 0·000 0568° C., or 1 gram of air 0·000 239° C., or a cubic centimetre of air 0·1850°·C., if that air is at the standard density for 760 millimetres of pressure and 0° C. The figure 0·1850° C. is the thermometric coefficient as distinguished from the first or calorimetric coefficient (0·000 0568° C.), and shows what great effect on the air itself its poor conductivity may have.
Diathermancy.—Dry air is extremely diathermanous or transparent to the transmission of radiant heat. For the whole moist atmosphere the general coefficient of transmission increases as the waves become longer: and for a zenithal sun it is about 0·4 at the violet end of the spectrum and about 0·8 at the red. By specific absorption many specific wave-lengths are entirely cut off by the vapours and gases, so that in general the atmosphere may appear to be more transparent to the short wave-lengths or violet end of the spectrum, but this is not really so. When the zenithal sun’s rays fall upon a station whose barometric pressure is 760 mm., then only from 50 to 80% of the total heat reaches the earth’s surface, and, thus the general coefficient of transmission for the thickness of one atmosphere is usually estimated at about 60%. Of course when the rays are more oblique, or when haze, dust or cloud interfere, the transmission
