# 1911 Encyclopædia Britannica/Meteorology

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​METEOROLOGY (Gr. μετέωρα, and λόγος, i.e. the science of things in the air), the modern study of all the phenomena of the atmosphere of gases, vapours and dust that surrounds the earth and extends to that unknown outer surface which marks the beginning of the so-called interstellar space. These phenomena may be studied either individually or collectively. The collective study has to do with statistics and general average conditions, sometimes called normal values, and is generally known as Climatology (see Climate, where the whole subject of regional Climatology is dealt with). The study of the individual items may be either descriptive, explanatory, physical or theoretical. Physical meteorology is again subdivided according as we consider either the changes that depend upon the motions of masses of air or those that depend upon the motions of the gaseous molecules; the former belong to hydrodynamics, and the; latter are mostly comprised under thermodynamics, optics and electricity.
History.—The historical development of meteorology from the most ancient times is well presented by the quotations from classic authors compiled by Julius Ludwig Ideler (Meteorologia veterum graecorum et romanorum, Berlin, 1832). We owe to the Arabian philosophers some slight advance on the knowledge of the Greeks and Romans; especially as to the optical phenomena of the atmosphere. The Meteorologia of Aristotle (see Zeller, Phil. der Griechen) accords entirely with the Philosophica of Thomas Aquinas, the poetic songs of the troubadours, and the writings of Dante (see Kuhn’s Treatment of Nature in Dante’s Divina Commedia; London, 1897). Dante’s work completed the passage from the ancient mythological treatment of nature to the more rational recognition of one creator and lawgiver that pervades modern science. The progress of meteorology has been coincident with the progress of physics and chemistry in general, as is shown by considering the works of Alhazen (1050) on twilight, Vitellio (1250) on the rainbow, Galileo (1607) on the thermometer and on the laws of inertia, on attractions and on the weight of the air, Toricelli (1642) on the barometer, Boyle (1659) on the elastic pressure of the air in all directions, Newton (1673) on optics; Cavendish (1760), elastic pressure of aqueous vapour; Black (1752), separation of carbonic acid gas from ordinary air; Rutherford (1772), separation of nitrogen; Priestley and Scheele (1775) and Cavendish (1777), separation of oxygen; Lavoisier (1783), general establishment of the character of the atmosphere as a simple mixture of gases and vapour; De Saussure’s measurement of relative humidity by the accurate hair hygrometer (1780), Dalton’s measurement of vapour tension at various temperatures (1800), Regnault’s and Magnus’s revision of Dalton’s tension of water vapour (1840), Marvin’s and Juhlins’s measurements of tension of ice vapour (1891), and the isolation of argon by Rayleigh and Ramsay (1894).
Theoretical meteorology has been, and always must be, wholly dependent on our knowledge of thermodynamics and on mathematical methods of dealing with the forces that produce the motions within the atmosphere. Progress has been due to the most eminent mathematicians at the following approximate dates: Sir Isaac Newton (1670), Leonhard Euler (1736), Pierre Simon Laplace (1780), Jean Baptiste Joseph Fourier (1785), Simon Denis Poisson (1815), Sir George Gabriel Stokes (1851), Hermann von Helmholtz (1857), Lord Kelvin (1860), C. A. Bjerknes (1868), V. Bjerknes (1906), and to their many distinguished followers.
The earliest systematic daily record of local weather phenomena that has survived is that kept by William Merle, rector of Driby, during seven years 1331–1338: the manuscript is preserved in the Digby MS., Merton College, Oxford, and ​ was published in facsimile by George G. Symons in 1891. Doubtless many similar monastic diaries have been lost to us. In 1653 Ferdinand II. of Tuscany organized a local system of stations and daily records which extended over and beyond northern Italy. This was the first fairly complete meteorological system in Europe. The records kept during the years 1655–1670 at the Cloister Angelus near Florence (were reduced by Libri, professor of mathematics at Pisa, and published in 1830.
The history of meteorology is marked by the production of comprehensive treatises embodying the current state of our knowledge. Such were Louis Cotte’s Traité de météorologie (Paris, 1774) and his Mémoires sur la météorologie, supplement au traité (1788); Ludwig Kämtz’s Lehrbuch der Meteorologie (Halle, 1831–1836) and his Vorlesungen (1840; French 1842, English 1845); Sir John Herschel’s Meteorology (London, 1840); the splendid series of memoirs by H. W. Brandes in Gehler’s Physikalisches Wörterbuch (Leipzig, 1820–1840); E. E. F. W. Schmid’s Grundriss der Meteorologie (Leipzig, 1862); Ferrel’s Recent Advances in Meteorology (Washington, 1885); the great works of Julius Hann, as summarized in his Handbuch der Klimatologie (1883; 2nd ed., Stuttgart, 1897; vol. i., English 1903) and his Lehrbuch der Meteorologie (Leipzig, 1901, 2nd ed. 1906); the extensive studies of J. E. Woeikoff (Voeikof), as presented in his Klima der Erde (Russian 1883, German 1885) and his Meteorologie (Russian 1904).
The development of this science has been greatly stimulated by the regular publication of special periodicals such as the Zeitschrift of the Austrian Meteorological Society, 1866–1885, vol. 21 appearing with vol. 3 of the Meteorologische Zeitschrift of the German Meteorological Society in 1886, and since that date this journal has been jointly maintained by the two societies. The analogous journals of the Royal Meteorological Society, London, 1850 to date, the Scottish Meteorological Society, 1860 to date, the Meteorological Society of France, 1838 to date, the Italian Meteorological Society, and the American Meteorological Journal, 1885–1895, have all played important parts in the history of meteorology. On the other hand, the Annals of the Central Meteorological Office at Paris, the Archiv of the Deutsche Seewarte at Hamburg, the Annals and the Repertorium of the Central Physical Observatory at St Petersburg, the Annales of the Central Meteorological Office at Rome, Bulletin of International Simultaneous Met. Obs. and the Monthly Weather Review of the Weather Bureau at Washington, the Abhandlungen of the Royal Prussian Meteorological Institute at Berlin, the Meteorological Papers of the Meteorological Office, London, and the transactions of numerous scientific societies, have represented the important official contributions of the respective national governments to technical meteorology.
The recent international union for aerial exploration by kites and balloons has given rise to two important publications, i.e. the Veröffentlichungen of the International, Commission for Scientific Aerostatics (Strassburg, 1905, et seq.), devoted to records of observations, and the Beiträge zur Physik der freien Atmosphäre (Strassburg, 1904, et seq.), devoted to research.
The necessity of studying the atmosphere as a unit and of securing uniform accuracy in the observations has led to the formation of a permanent International Meteorological Committee (of which in 1909 the secretary was Professor Dr G. Hellmann of Berlin, and the president Dr W. N. Shaw of London). Under its directions conferences and general congresses have been held, beginning with that of 1872 at Leipzig. Its International Tables, Atlas of Clouds, Codex of Instructions, and Forms for Climatological Publications illustrate the activity and usefulness of this committee.
Modern meteorology has been developed along two lines of study, based respectively on maps of monthly and annual averages and on daily weather maps. The latter study seems to have been begun by H. W. Brandes in Leipzig, who first, about 1820, compiled maps for 1783 from the data collected in the Ephemerides mannheimensis, and subsequently published maps of the European storms of 1820 and 1821. Simultaneously with Brandes we find William C. Redheld in New York compiling a chart of the hurricane of 1821, which was published in 1831, and was the first of many memoirs by him on hurricanes that completely established their rotary and progressive motion. Soon after this Piddington and Sir William Reid began their great works on the storms of the Orient. About 1825 James Pollard Espy, in Philadelphia, began the publication of his views as to the motive power of thunderstorms and tornadoes, and in 1842 was appointed “meteorologist to the U.S. government” and assigned to work in the office of the surgeon-general of the army, where he prepared daily weather maps that were published in his four successive “Reports.” In 1848 the three American leaders united in letters to Professor Joseph Henry, secretary of the Smithsonian Institution, urging that the telegraph be used for collecting data for daily maps and weather predictions. Favourable action was taken in 1849, the Smithsonian maps began to be compiled about 1851 and were displayed in public from 1853 onwards. Meanwhile in England James Glaisher, with the help of the daily press, carried out similar work, publishing his first map in 1851 as soon as daily weather maps of sufficient extent could be promptly prepared by the help of the telegraph. The destructive storm of the 14th of November 1854, in the Crimea gave U. J. J. Le Verrier, at Paris, an opportunity to propose the proper action, and his proposals were immediately adopted by the secretary of war, Marshal Vaillant. On the 17th of February 1855 the emperor ordered the director-general of government telegraph lines to co-operate completely with Le Verrier in the organization of a bureau of telegraphic meteorology. The international daily bulletin of the Paris Observatory began to be printed in regular form on the 1st of January 1858, and the daily map of isobars was added to the text in the autumn of 1863. The further development of this bulletin, the inclusion of British and ocean reports in 1861, the addition of special storm warnings in 1863, the publication of the Atlas des mouvements généraux covering the Atlantic in 1865, the study of local thunderstorms by Hippolyte Marié-Davy, Sonrel, Fron, Peslin, in France, and the work of Fitzroy, Buys-Ballot, Buchan, Glaisher and Thomson in Great Britain, parallel the analogous works of the American students of meteorology and form the beginnings of our modern dynamic meteorology.
The details of the historical development of this subject are well given by Hugo Hildebrand-Hildebrandsson and Léon Teisserenc de Bort in their joint work, Les Bases de la météorologie dynamique (Paris, 1898–1907). The technical material has been collected by Hann in his Lehrbuch. Many of the original memoirs have been reproduced by Brillouin in his Mémoires originaux (Paris, 1900), and in Cleveland Abbe’s Mechanics of the Earth’s Atmosphere (vol. i., 1891; vol. ii., 1909).
The publication of daily weather charts and forecasts is now carried on by all civilized nations. The list of government bureaux and their publications is given in Bartholomew’s Atlas (vol. iii., London, 1899). Special establishments for the exploration of the upper atmospheric conditions are maintained at Paris, Berlin. Copenhagen, St Petersburg, Washington and Strassburg.
The general problems of climatology (1900) are best presented in the Handbook of Dr Julius Hann (2nd ed., Stuttgart, 1897). The general distribution of temperature, winds and pressure over the whole globe was first given by Buchan in charts published by the Royal Society of Edinburgh in 1868, and again greatly revised and improved in the volume of the Challenger reports devoted to meteorology. The most complete atlas of meteorology is Buchan and Herbertson’s vol. iii. of Bartholomew’s Atlas (London, 1899). Extensive works of a more special character have been published by the London Meteorological Office, and the Deutsche Seewarte for the Atlantic, Pacific and Indian Oceans. Daily charts of atmospheric conditions of the whole northern hemisphere were published by the U.S. Weather Bureau from 1875 to 1883 inclusive, with monthly charts, the latter were continued through 1889. The physical problems of meteorology were discussed in Ferrel’s Recent Advances in Meteorology (Washington, 1885). Mathematical papers on this subject will be found in the author’s collection known as The Mechanics of the Earth’s Atmosphere; the memoirs by Helmholtz and Von Bezold contained in this collection have been made the basis of a most important work by Brillouin (Paris, 1898), entitled Vents contigus et nuages. A general summary of our knowledge of the mechanics and physics of the atmosphere is contained in the Report on the International Cloud Work, by F. H. Bigelow (Washington, 1900). The extensive Lehrbuch (Leipzig, 1901; 2nd ed., 1906) by Dr Julius Hann is an authoritative work. The optical ​ 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 2 1/2% 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 e$_0$−h/6517 where h is the height expressed in metres and e and e$_0$ 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 e$_0$−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 m$_0$−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:—
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 1/1200th 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 ​ is still further diminished. In general one half of the heat received from the sun by the illuminated terrestrial hemisphere is absorbed by the clearest atmosphere, leaving the other half to reach the surface of the ground, provided there be no intercepting clouds. The thermal conditions actually observed at the immediate surface of the globe during hazy and cloudy weather are therefore of minor importance in the mechanism of the whole atmosphere, as compared with the influence of the heat retained within its mass.
The transmission of solar radiation through the earth’s atmosphere is the fundamental problem of meteorology, and has been the subject of many studies, beginning with J. H. Lambert and P. Bouguer. The pyrheliometer of C. S. M. Pouillet gave us our first idea of the thermal equivalent of solar radiation outside of our atmosphere or the so-called “solar constant,” the value of which has been variously placed at from 2 to 4 calories per sq. cm. per minute. At present the weight of the argument is in favour of 2·1, with a fair presumption that both the intensity and the quality of the solar radiation as it strikes the upper layers of our atmosphere are slightly variable. It is also likely that this “constant” does not represent the sun proper, but the remaining energy after the sunbeam has sifted through masses of matter between the sun and our upper atmosphere, so that it may thus come to have appreciable variations:
The coefficients of absorption for specific wave-lengths were first determined by L. E. Jewell, of Johns Hopkins University, for numerous vapour lines in 1892 (see W. B. Bulletin, No. 16). In 1904 C. G. Abbot published a table based on bolograph work at Washington showing the coefficient of atmospheric transmission for solar rays passing through a unit mass of air-namely, from the zenith to the ground. He showed that this coefficient increased with the wavelength; hence any change in the quality of the solar radiation will affect the general coefficient of transmission. The following table gives his averages for the respective wave-lengths, as deduced from ten clear days in 1901–1902 and nine clear days in 1903:—
Any variation in the energy that the atmosphere receives from the sun will have a corresponding influence on meteorological phenomena. Such variations were simultaneously announced in 1903 by Charles Dufour in Switzerland and H. H. Kimball in Washington (Monthly Weather Review, May 1903); the latter was then conducting a series of observations with Angström’s electric compensation pyrheliometer, and his conclusions have been confirmed by the work of L. Gorczynski at Prague (1901–1906) and C. G. Abbot at Washington. Kimball’s pyrheliometric work on this problem is still being continued; but meanwhile Abbot and Fowle from their bolometric observations at the Smithsonian Astrophysical Observatory have deduced preliminary Values of the observed total energy, or the solar constant, for numerous dates when the sky was very clear, as follows (see Smithsonian Mis. Coll., xlv. 78 and xlvii. 403, 1905):—
If the relative accuracy of these figures is 1%, as estimated by Abbot, then they demonstrate irregular fluctuations of 5%. But different observers and localities vary so much that Abbot estimates the reliability of the mean value, 2·12, to be about 10%. The causes of this variation apparently lie above our lower atmosphere and move slowly eastward from day to day, and as the variability is comparable with that of other atmospheric data, therefore conservative meteorologists at present confine their attention to the explanation of terrestrial phenomena under the assumption of a constant solar radiation. The large local changes of weather and climate are not due to changes in the sun, but to the mechanical and thermodynamic interactions of earth and ocean and atmosphere. Excellent illustrations of this principle are found in the studies of Blanford, Eliot and Walker on the monsoons of India, of Sieger (1892) on the contrasts of temperature between Europe and North America, of Hann (1904) on the anomalies of weather in Iceland, of Meinardus (1906) on periodical variations of the icedrift near Iceland.
The absorption of solar radiation by the atmosphere is apparently explained by the laws of diffuse reflection, selective diffusion and fluorescence in accordance with which each atom and molecule and particle becomes a new centre for the diffusion in all directions of the energy represented by some specific wave-length. The specific influences of carbon dioxide and water vapour are less than those of the liquid particles (and of cloud and rains) and of the great mass of oxygen and nitrogen that make up the atmosphere.
Specific Heat.–The capacity of dry air for heat varies according as the heat increases the volume of the air expanding under constant pressure, or the pressure of the air confined in constant volume. The specific heat under constant pressure is about 1·4025 times the specific heat under constant volume. The numerical value of the specific heat under constant pressure is about 0·2375—that is to say, that number of gram-calories, or units of heat, is required to change the temperature of 1 gram of air by 1° C. This coefficient holds good, strictly speaking, between the temperatures −30° and +10° C., and there is a very slight diminution for higher temperatures up to 200°. The specific heat of moist air is larger than that of dry air, and is given by the expression C$_p$″＝(0·2375 + 0·4805 x) where x is the number of kilograms of vapour associated with 1 kilogram of dry air. As x does not exceed 0·030 (or 30 grams) the value of C$_p$″ may increase up to 0·2519. The latent heat evolved in the 'condensation of this moisture is a matter of great importance in the formation of cloud and rain.
Radiating Power.—The radiating power of clean dry air is so small that it cannot be measured quantitatively, but the spectroscope and bolometer demonstrate its existence. The coefficient of radiation of the moisture diffused in the atmosphere is combined with that of the particles of dust and cloud, and is nearly equal to that of an equal surface of lamp-black. From the normal diurnal change in temperature at high and low stations, it should be possible to determine the general coefficient of atmospheric radiation for the average condition of the air in so far as this is not obscured by the influence of the winds. This was first done by J. Maurer in 1885, who obtained a result in calories that may be expressed as follows: the total radiation in twenty-four hours of a unit mass of average dusty and moist air towards an enclosure whose temperature is 1° lower is sufficient to lower the temperature of the radiating air by 3·31° C. in twenty-four hours. This very small quantity was confirmed by the studies of Trabert, published in 1892, who found that 1 gram of air at 278° absolute temperature radiates 0·1655 calories per minute toward a black surface at the absolute zero. The direct observations of C. C. Hutchins on dry dusty air, as published in 1890, gave a much larger value—evidently too large. Slight changes in Water, vapour and carbon dioxide affect the radiation greatly. The investigation of this subject prosecuted by Professor F. W. Very at the Allegheny Observatory, and published as “Bulletin G” of the U.S. Weather Bureau, shows the character and amount of the radiation of several gases, and especially the details of the process going on under normal conditions in the atmosphere.
Density.—The absolute density or mass of a cubic centimetre of dry air at the standard pressure, 760 millimetres, and temperature 0° C., is 0·001 29305 grams; that of a cubic metre is 1·29305 kilograms; that of a cubic foot is 0·08071 ℔ avoirdupois. The variations of this density with pressure, temperature, moisture and gravity are given in the Smithsonian meteorological tables, and give rise to all the movements of the atmosphere; they are, therefore, of fundamental importance to dynamic meteorology.
Expansion.—The air expands with heat, and the expansion of aqueous vapour is so nearly the same as that of dry air that the same coefficient may be used for the complex atmosphere itself. The change of volume may be expressed in centigrade degrees by the formula V＝V$_0$ (1+0·000 3665t), or in Fahrenheit degrees V＝V$_0$ (1 +0·000 237t).
Elasticity.—The air is compressed nearly in proportion to the pressure that confines it. The pressure, temperature and volume of the ideal gas are connected by the equation pv＝RT, where T is the absolute temperature or 273° plus the centigrade temperature p is the barometric pressure in millimetres and v the volume of a unit mass of gas, or the reciprocal of the density of the gas. The constant R is 29·272 for dry atmospheric air when the centimetre, ​the gram, the second and the centigrade degrees are adopted as units of measure, and differs for each gas. For aqueous vapour in a gaseous state and not near the point of condensation R has the value 47·061. For ordinary air in which x is the mass of the aqueous vapour that is mixed with the unit mass of dry air, the above equation becomes pv =(29·272 + 47·061x) T. This equation is sometimes known as the equation of condition peculiar to the gaseous state. It may also be properly called the equation of elasticity or the elastic equation for gases, as expressing the fact that the elastic pressure p depends upon the temperature and the volume. The most exact equations given by Van der Waals, Clausius, Thiesen, are not needed by us for the pressures that occur in meteorology.
Diffusion.—In comparison with the convective actions of the winds, it may be said that it is difficult for aqueous vapour to diffuse in the air. In fact, the distribution of moisture is carried on principally by the horizontal convection due to the wind and the vertical convection due to ascending and descending currents. Diffusion proper, however, comes into play in the first moments of the process of evaporation. The coefficient of diffusion for aqueous vapour from a pure water surface into the atmosphere is 0·18 according to Stefan, or 0·1980 according to Winkelmann; that is to say, for a unit surface of 1 sq. centimetre, and a unit gradient of vapour pressure of one atmosphere per centimetre, as we proceed from the water surface into the still dry air, at the standard pressure and temperature, and quantity of moisture diffused is 0·1980 grams per second. This coefficient increases with the temperature, and is 0·2827 at 49·5° C. But the gradient of vapour pressure, and therefore rate of diffusion, diminishes very rapidly at a small distance from the free surface of the water, so that the most important condition facilitating evaporation is the action of the wind.
Viscosity.—When the atmosphere is in motion each layer is a drag upon the adjacent one that moves a little faster than it does. This drag is the so-called molecular or internal friction or viscosity. The coefficient of viscosity in gases increases with the absolute temperature, and its value is given by an equation like the following; 0·000 248 (1 + 0·0003 665t) 2/3, which is the formula given by Carl Barus (Ann. Phys., 1889, xxxvi.). This expression implies that for air whose temperature is the absolute zero there is no viscosity, but that at a temperature (t) of 0° C., or 273° on the absolute scale, a force of 0·000 248 grams is required in order to push or pull a layer of air 1 centimetre square past another layer distant from it by 1 centimetre at a uniform rate of 1 centimetre per second.
Friction.—The general motions of the atmosphere are opposed by the viscosity of the air as a resisting force, but this is an exceedingly feeble resistance as compared with the obstacles encountered on the earth’s surface and the inertia of the rising and falling masses of warm and cold air. The coefficient of friction used in meteorology is deduced from the observations of the winds and results essentially not from viscosity, but from the resistances of all kinds to which the motion of the atmosphere is subjected. The greater part of these resistances consists essentially in a dissipation of the energy of the moving masses by their division into smaller masses which penetrate the quiet air in all directions. The loss of energy due to this process and the conversion of kinetic into potential energy or pressure, if it must be called friction, should perhaps be called convective friction, or, more properly, convective-resistance.
The coefficient of resistance for the free air was determined by Mohn and Ferrel by the following considerations. When the winds, temperatures and barometric pressures are steady for a considerable time, as in the trade winds, monsoons and stationary Cyclones, it is the barometric gradient that overcomes the resistances, while the resulting wind is deflected to the right (in the northern hemisphere) by the influence of the centrifugal force of the diurnal rotation (ω) of the earth. The wind, therefore, makes a constant angle (α) with the direction of the gradient (G). There is also a slight centrifugal force to be considered if the winds are circulating with velocity v and radius (r) about a storm centre, but neglecting this we have approximately for the latitude
G sin α＝2ωv sin φ, G cos α＝ κv,
where (κ) is the coefficient connecting the wind-velocity (v) with the component of the gradient pressure in the direction of the wind. These relations give κ＝2ω sin φ/ tan α. The values of α and v as read off from the map of winds and isotherms at sea level give us the data for computing the coefficients for oceanic and continental surfaces respectively, expressed in the same units as those used for G and v. The extreme values of this coefficient of friction were found by Guldberg and Mohn to be 0·00002 for the free ocean and 0·00012 for the irregular surface of the land. For Norwegian land stations Mohn found φ＝61° α＝56·5° κ＝0·0000845. For the interior of North America Elias Loomis found φ＝37·5° α＝42·2° κ＝0·0000803.
Gravity.—The weight of the atmosphere depends primarily upon the action of gravity, which gives a downward pressure to every particle. Owing to the elastic compressibility of the air, this downward pressure is converted at once into an elastic pressure in all directions. The force of gravity varies with the latitude and the altitude, and in any exact work its variations must be taken into account. Its value is well represented by the formula due to Helmert, g＝980·6 (1 − 0·0026 cos 2φ) × (1 − fh), where φ represents the latitude of the station and h the altitude. The coefficient f is small and has a different value according as the station is raised above the earth’s surface by a continent, as, for instance, on a mountain top, or by the ocean, as on a ship sailing over the sea, or in the free air, as in a balloon. Its different values are sufficiently well known for meteorological needs, and are utilized most discreetly in the elaborate discussion of the hypsometric formula published by Angot in 1899 in the memoirs of the Central Meteorological Bureau of France.
Temperature at Sea-Level.—The temperature of the air at the surfaces of the earth and ocean and throughout the atmosphere is the fundamental element of dynamic meteorology. It is best exhibited by means of isotherms or lines of equal temperature drawn on charts of the globe for a series of level surfaces at or above sea-level. It can also be expressed analytically by spherical harmonic functions, as was first done by Schoch. The normal distribution of atmospheric temperature for each month of the year over the whole globe was first given by Buchan in his charts of 1868 and of 1888 (see also the U.S. Weather Bureau “Bulletin A,” of 1893, and Buchan’s edition of Bartholomew’s Physical Atlas, London, 1899). The temperatures, as thus charted, have been corrected so as to represent a. uniform special set of years and the conditions at sea-level, in order to constitute a homogeneous system. The actual temperature near the ground at any altitude on a continent or island may be obtained from these charts by subtracting 0·5°C. for each 100 metres of elevation of the ground above sea-level, or 1° F. for 350 ft. This reduction, however, applies specifically to temperatures observed near the surface of the ground, and cannot be used with any confidence to determine the temperature of points in the free air at any distance above the land or ocean. On all such charts the reader will notice the high temperatures near the ground in the interior of each of the continents in the summer season and the low temperatures in the winter season. In February the average temperatures in the northern hemisphere are not lowest near the North Pole, but in the interiors of Siberia and North America; in the southern hemisphere they are at the same time highest in Australia, and Africa and South America. In August the average temperatures are unexpectedly high in the interior of Asia and North America, but low in Australia and Africa.
Temperature at Upper Levels.—The vertical distribution of temperature and moisture in the free air must be studied in detail in order to understand both the general and the special systems of circulation that characterize the earth’s atmosphere. Many observations on mountains and in balloons were made during the 19th century in order to ascertain the facts with regard to the decrease of temperature as we ascend in the atmosphere; but it is now recognized that these observations were largely affected by local influences due to the insufficient ventilation of the thermometers and the nearness of the ground and the balloon. Strenuous efforts are being directed to the elimination of these disturbing elements, and to the continuous recording of the temperature of the free air by means of delicate thermographs carried up to great heights by small free “sounding balloons,” and to lesser heights by means of kites. Many international balloon ascents have been made since 1890, and a large amount of information has been secured.
The development of kite-work in the United States began in October 1893, at the World’s Columbian Congress at Chicago, when Professor M. W. Harrington ordered Professor C. F. Marvin of the Weather Bureau to take up the development of the Hargrave or box kite for meteorological work. At that time W. A. Eddy of Bayonne, New Jersey, was applying his “Malay” kite to raising and displaying heavy objects, and in August 1894 (at the suggestion of Professor Cleveland Abbe) he visited the private observatory of A. L. Rotch at Blue Hill and demonstrated the value of his Malay kite for aerial research. The first work done at this observatory with crude apparatus was rapidly improved upon, while at the same time Professor Marvin at Washington was developing the Hargrave kite and auxiliary apparatus, which he brought up to the point of maximum efficiency and trustworthiness. When he reported his apparatus as ready to be used by the Weather Bureau on a large scale, Professor Willis L. Moore, as the successor of Professor Harrington, ordered its actual use at seventeen kite stations in July 1898. This, was the first attempt to prepare isotherms for a special hour over a large area at some high level, such as 1 m., in the free air. Daily meteorological charts were prepared for the region covered by these observations; but it became necessary to discontinue them, and nothing more was done by the Weather Bureau in this line of work until the inauguration of kite work at Mount Weather in 1906. Meanwhile a special method for the reduction and study of such observations was devised by Bjerknes and Sandstrom, and was published in the Trans. American Philosophical Society (Philadelphia, 1906). The general average results as to temperature gradients were compiled by Dr H. C. Frankenfield and published in the United States Weather Bureau “Bulletin F.” from these ​ were deduced the following tables, published in the Monthly Weather Review:—
Mean Temperature Gradients in degrees Fahrenheit per 1000 ft. from the ground up to the respective altitudes.
In this table the second column gives the altitude of the ground at the reel on which the kite wire was wound. The third column shows the average gradient in degrees Fahrenheit per 1000 ft. between the reel at the respective stations, and a uniform altitude 5280 ft. above sea-level. The fourth column shows the total reduction to be applied to the temperature at the reel in order to obtain the temperature at the 1 m. level above sea. These gradients and reductions are based upon observations made only during the six warm months from May to October 1898.
The kite-work at the Blue Hill Observatory has been published in full in the successive Annals of the Harvard College Observatory, beginning with 1897, vol. xlii. It has been discussed especially by H. H. Clayton with reference to special meteorological phenomena, such as areas of high and low pressure, fair and cloudy weather, the winds and their velocities at different elevations, insolation, radiation, &c., and has served as a stimulus and model for European meteorologists. Kite-work has also been successfully prosecuted at Trappes, Hamburg, Berlin, St Petersburg, and many other European stations. The highest flights that have been attained have been about 8000 metres.
The great work of L. Teisserenc de Bort began with 1897, when he founded his private observatory at Trappes near Paris devoted to the problems of dynamic meteorology. His results are published in full in the Memoirs of the Central Meteorological Bureau of France for 1897 and subsequent years. Beginning with the sounding balloons devised by Hermite, he subsequently added kite work as supplementary to these. In the Comptes rendus (1904), he gives the mean temperatures as they result from five years of work, 1899–1903, at Trappes. Out of 581 ascensions of sounding balloons there were 141 that attained 14 km. or more, and the following table gives the average temperatures recorded in these ascensions. It will be seen that there is a slow decrease in temperate up to 2 km.; a rapid decrease thence up to 10 km., and a slow decrease, almost a stationary temperature, between 11 and 14 km.; this is the “thermal zone” as discovered and so called by him.
It is evident that the annual average vertical gradient of temperature over Paris is between 4° and 6° C. per 1000 metres of ascent in the free air, agreeing closely with the value 5° per 1000 metres, which has come into extensive use since the year 1890, on the recommendation and authority of Hann, for the reduction of land observations to sea-level. The winter gradients are less than those for summer, possibly owing to the influence of the condensation into cloud and rain during the winter season in France; the same value may not result from observations in the United States, where the clouds and precipitation of winter do not so greatly exceed those of summer. The work at Trappes is therefore not necessarily representative of the general average of the northern hemisphere, but belongs to a coastal region in which during the summer time, at great heights, the air is cooler than in the winter time, since during the latter season there is an extensive flow of warm south winds from the ocean over the cold east winds from the land. Sounding balloons have also been used elsewhere with great success. The greatest heights attained by them have been 25,989 metres at Uccle, Belgium, on the 5th of September 1907, and 25,800 metres at Strassburg, August 1905.
The most extensive meteorological explorations of the free atmosphere have been those accomplished in Germany by Richard Assmann and Arthur Berson, beginning (1887) in co-operation with the German Verein for the Promotion of Aeronautics and the Aeronautic Section of the German Army, afterwards under the auspices of the Prussian Meteorological Office, but later as a wholly independent institution at Lindenberg. All the details of the work during 1887–1889 and the scientific results of seventy balloon voyages were published in three large volumes, Wissenschaftliche Luftschiffahrten (Berlin, 1900). The work done at Tegel at the Aeronautical Observatory of the Berlin Meteorological Office, the 1st of October 1899 to April 1905, was published in three volumes of Ergebnisse. But the location at Tegel had to be given up and a new independent establishment, the “Royal Prussian Aeronautic Observatory,” was founded at Lindenberg, under the direction of Dr Assmann, who has published the results of his work in annual volumes of the Ergebnisse of that institution, considering it as a continuation of the work done at Berlin and Tegel. In addition to these elaborate official publications various summaries have been published, the most instructive of which is the chart embodying daily observations with corresponding isotherms at all attainable altitudes, published monthly since January 1903 in Das Wetter. The growth of this aerial work and the reliability of the results may be inferred from a statement of the number of ascensions made each year: 1899, 6; 1900, 39; 1901, 169; 1902, 261; 1903, 481; 1905, 513. This large number, combined with 581 voyages of Teisserenc de Bort at Trappes and many others made in England, ​ Holland and Russia, amounting in all to over 2000, enabled Assmann to compute the monthly and annual means of temperature and wind velocity for each altitude; the German results are given in table at foot of page 269.
The results of these numerous ascents, during these six years, have also been grouped into monthly means that have a reliability proportionate to the number of days on which observations were obtained at a given level, and we are now able to speak of the annual and even of the diurnal periodicity of temperature at different altitudes in the free air with considerable confidence. Some of the most important conclusions to be drawn from the best recent work were published by Hann either in special memoirs or in his Lehrbuch, from which we take the following table. The actual temperatures given in this table have only local importance, but the differences or the vertical gradients doubtless hold good over a large portion of Europe if not of the world.
Temperature in Free Air over Europe 1899–1904.
The differences of temperature between any layer and those above it and below it, or the vertical gradients at each level go through annual periodical changes quite analogous to those derived from mountain observations; the most rapid falls of temperature, or the largest vertical gradients in the free air occur on the Following dates over Europe.—
The values above given as deduced from 141 high ascensions at Trappes show that between 11 and 14 km. there was no appreciable diminution of temperature, in other words, the air is warmer than could be expected and therefore has a higher potential temperature. This fact was first confirmed by the Berlin ascensions, and is now recognized as wellnigh universal. The altitude of the base of this warm stratum is about 12 km. in areas of high pressure and I0 km. in areas of low pressure. It is higher as we approach the tropics and above ordinary balloon work near the equator if indeed it exists there. At first this unexpected warmth was considered as possibly a matter of error in the meteorographs, but this idea is now abandoned. Assmann suggested that the altitude is that of the highest cirrus, from which Cleveland Abbe inferred that it had something to do with the absorption of the solar and terrestrial heat by dissolving cirri. But the most plausible explanation is that published simultaneously in September 1908 by W. J. Humphreys of Washington, and Ernest Gold of London.
The daily diagrams in Das Wetter show that both the irregular and the periodic and the geographic variations of temperature in the upper strata are unexpectedly large, almost as large as at the earth's surface, so that the uniform temperature of space that was formerly supposed to prevail in the upper air must be looked for, if at all, far above the level to which sounding balloons have as yet attained. It is evident that both horizontal and vertical convection currents of great importance really occur at these great altitudes. These upper currents cannot be due to any very local influence at the earth's surface, but only to the interchange of the air over the oceans and continents or between the polar and equatorial regions. They constitute the important feature of the so-called general circulation of the atmosphere, which we have hitherto mistakenly thought of as confined to lower levels; their general direction is from west to east over all parts of the globe as far as yet known, showing that they are controlled by the rotation of the earth. It is likely that masses of air having special temperature conditions or clouds of vapour dust such as came from Krakatoa, may be carried in these high currents around the globe perhaps several times before being dissipated.
The average eastward movement or the west wind at 3 km. above Germany is 10.7 m. per sec. or 1° of longitude (at 45° latitude) in 42.4 minutes, or such as to describe the whole circumference of this small circle in 10.5 days. At the equator above the calm belt the velocity westward or the east wind as given by Krakatoa volcanic-dust phenomena was 34.5 m per sec., on 30° of a great circle daily, or around the equator in 12.5 days, while its poleward movement was only, 1° per day or 1.3 metre per second. The average motion of the storm centres moving westward in northern tropical and equatorial regions but eastward in the north temperate zone is at the rate of one circumference or a small circle at latitude 45° in 19 days. Observations of the cloud movements gave Professor Bigelow the following results for the United States:—
Evidently, therefore, the great west wind (that James H. Coffin deduced from his work on the winds of the northern hemisphere and that William Ferrel deduced from his theoretical studies) represents with its gentle movement poleward a factor of fundamental importance. We must consider all our meteorological phenomena except at the equator as existing beneath and controlled, if not ​caused, by this general deep swift upper current of air that began as an ascending east wind above the calm equatorial air but speedily overflowed as west wind settling down to the sea-level in the temperate and polar regions as great areas of high pressure and dry clear cool weather containing air on its return passage to the equator. The upper air is thrown easily into great billows, and wherever it rises the warm equatorial wind flows in beneath it, but when it descends we have blizzards and dry clear weather. It is a covering for the lower strata of air, it flows over them in standing waves and sometimes mixes with them at the surface of contact. It receives daily accessions from below and gives out corresponding accessions to the lower strata, by a process of overturning such as has been studied theoretically by Margules and Bigelow. At the fifth conference of the International Committee on Scientific Aeronautics (Milan, October 1906) Rykatchef presented the results of kite-work during 1904 and 1905 at Pavlosk, near St Petersburg, from which we select the results for these two years given in table at foot of page 270.
Many inversions occur during January below 1000 metres. The decrease is more rapid in summer than in winter and in clear weather than in cloudy, but of course these observations did not extend above the upper level of the cumulus cloud layer. A general survey of the existing state of knowledge of the upper atmosphere is given in the Report of the British Association for 1910.
Distribution of Aqueous Vapour.—The distribution of aqueous vapour is best shown by lines of equal dew-point or vapour tension, though for some purposes lines of equal relative humidity are convenient. The dew-point lines are not usually shown on charts, partly because the lines of vapour pressure are approximately parallel to the lines of mean temperature of the air, and partly because the observations are of very unequal accuracy in different portions of the globe. In general we may consider any isotherm as agreeing with the dew-point line for dew-points a few degrees. lower than the temperature of the air. The distribution of moisture is quite irregular both in a horizontal and in a vertical direction. On charts of the world we may draw lines based on actual observations to represent equal degrees of relative humidity, or equal dew-points and vapour pressures; but as regards the distribution of moisture in a vertical direction we are, in the absence of specific observations, generally forced to assume that the vapour pressure at any altitude h follows the average law first deduced from a limited number of observations by Hann, and expressed by the logarithmic equation, $\displaystyle \log e=\log e_{0}-h/6517$, which is quite analogous to the elementary hypsometric formula, $\displaystyle \log p=\log p_{0}-h/18400$. Therefore, in general, the ratio between the pressure of the vapour and the pressure of the atmosphere at any altitude is represented by the approximate formula, $\displaystyle \log e/p=\log e_{0}/p_{0}-h/10091$. Of course these relations can only represent average or normal conditions, which may. be departed from very widely at any moment; they have, however, been found to agree remarkably with all observations which have as yet been published. The average results are given in the following table, which is abbreviated from one published by Hann, but with the addition of the work done by the U.S. Weather Bureau, as reduced by Dr Frankenfield in 1899. The vapour constituent of the atmosphere is not distributed according to the law of gaseous diffusion, but, like temperature and the ratio between oxygen and nitrogen, is controlled by other laws prescribed by the winds and currents, namely—convection.
Diminution of the Relative Vapour Pressure with Altitude.
| Authority. | 1500 ft. | 2000 ft. | 3000 ft. | 4000 ft. | 5000 ft. | 6000 ft. | 7000 ft. | 8000 ft. | No. Obs. |
| Kites. | 0.82 | 0.78 | 0.70 | 0.61 | 0.52 | 0.49 | 0.39 | 0.44 | 1123 |
| (U.S.W.B.) | 0.82 | 0.78 | 0.70 | 0.61 | 0.52 | 0.49 | 0.39 | 0.44 | 1123 |
| Balloons. | 0.97 | 0.96 | 0.87 | 0.68 | 0.44 | 0.59 | — | — | 4 |
| (Hammon.) | 0.97 | 0.96 | 0.87 | 0.68 | 0.44 | 0.59 | — | — | 4 |
| Balloons. | 0.89 | 0.83 | 0.80 | 0.78 | 0.67 | 0.46 | 0.44 | — | 2 |
| (Hazen.) | 0.89 | 0.83 | 0.80 | 0.78 | 0.67 | 0.46 | 0.44 | — | 2 |
| Balloons. | 0.84 | 0.80 | 0.66 | 0.61 | 0.50 | 0.54 | 0.41 | 0.37 | 15 |
| (Hann.) | 0.84 | 0.80 | 0.66 | 0.61 | 0.50 | 0.54 | 0.41 | 0.37 | 15 |
| Mountains | 0.83 | 0.81 | 0.80 | 0.66 | 0.61 | 0.58 | 0.55 | 0.47 | 6 |
| (Hann.) | 0.83 | 0.81 | 0.80 | 0.66 | 0.61 | 0.58 | 0.55 | 0.47 | 6 |
| Computed | 0.85 | 0.81 | 0.72 | 0.65 | 0.58 | 0.52 | 0.47 | 0.42 | — |
| by Hann. | 0.85 | 0.81 | 0.72 | 0.65 | 0.58 | 0.52 | 0.47 | 0.42 | — |
Note.—The vapour pressure at any altitude is supposed to be expressed as a fraction of that observed at the ground. When the altitudes are given in ft. Hann’s formula becomes log e/e$_0$＝h/29539.
From 78 high balloon voyages in Germany, 1887–1899, Süring deduced the average vapour pressure in millimetres as found in the first line of the table at foot of this page (see Wissenschaftliche Luftffahrten, Bd. III., and Hann, Lehrbuch, 1906, p. 169). The observations on mountains gave Hann the pressures in the second line. Süring’s figures result from the use of Assmann’s ventilated psychrometer and are therefore very reliable.
The vapour pressure in mm. in free air over Europe is best given by Süring’s formula
$\log e_{h}=\log e_{0}={\frac {h}{6}}\left(1+{\frac {h}{20}}\right)$
where the altitude is to be expressed in kilometres. From this formula we derive the “specific moisture” or the mass of vapour contained in a kilogram of moist air as given in the following table whose numbers do not appreciably differ from “the mixing ratio” or quantity of moisture associated with a kilogram of dry air. The relative humidities vary irregularly depending on convection currents, but in clear weather when descending currents prevail they have been observed in America and over Berlin as shown in the third and fourth columns of the following table:—
Observed Specific Moisture and Relative Humidity.
| Alt. | Specific Moisture | Relative Humidity. | Relative Humidity. |
| Alt. | Specific Moisture | U.S.A. | Berlin. |
| Km. | | % | % |
| 0.0 | 1.00 | — | 77 |
| 0.5 | — | 65 | 71 |
| 1.0 | 0.76 | 65 | 71 |
| 1.5 | 0.65 | 59 | 62 |
| 2.0 | 0.55 | 59 | 57 |
| 2.5 | 0.47 | 45 | 58 |
| 3.0 | 0.39 | — | 55 |
| 3.5 | — | — | 49 |
| 4.0 | 0.26 | — | 53 |
| 4.5 | — | — | 54 |
| 5.0 | 0.17 | — | — |
| 5.6 | 0.11 | — | — |
| 5.7 | 0.17 | — | — |
| 5.8 | 0.04 | — | — |
The total amount of vapour in the atmosphere, according to Hann’s formula, is between one-fourth and one-fifth of the amount required by Dalton’s hypothesis, as is illustrated by the following table taken from an article by Cleveland Abbe in the Smithsonian Report for 1888, p. 410:—
Total Vapour in a Vertical Column that is saturated at its base.
| Altitude. Feet. | Relative Tension = e/e$_0$ | Actual Weight Gr. per Cubic Foot. | Actual Weight Gr. per Cubic Foot. | Actual Weight Gr. per Cubic Foot. | Actual Weight Gr. per Cubic Foot. | Actual Weight Gr. per Cubic Foot. | Total Vapour in the Columns expressed as Inches of Rain. | Total Vapour in the Columns expressed as Inches of Rain. | Total Vapour in the Columns expressed as Inches of Rain. | Total Vapour in the Columns expressed as Inches of Rain. |
| 0 | 1.000 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 80° F. | 70° F. | 60° F. | 50° F. | 80° F. | 70° F. | 60° F. | 50° F. |
| 0 | 1.000 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | 10.95 | 7.99 | 5.76 | 4.09 | 0.0 | 0.0 | 0.0 | 0.0 |
| 6000 | 0.524 | | 5.75 | 4.19 | 3.02 | 2.14 | 1.3 | 1.0 | 0.7 | 0.5 |
| 12,000 | 0.275 | | 3.01 | 2.20 | 1.58 | 1.12 | 2.1 | 1.5 | 1.1 | 0.8 |
| 18,000 | 0.144 | | 1.58 | 1.15 | 0.83 | 0.59 | 2.5 | 1.8 | 1.3 | 0.9 |
| 24,000 | 0.075 | | 0.82 | 0.62 | 0.43 | 0.31 | 2.7 | 2.0 | 1.4 | 1.0 |
| 30,000 | 0.040 | | 0.43 | 0.32 | 0.23 | 0.16 | 2.8 | 2.1 | 1.5 | 1.1 |
A heavy rainfall results from the precipitation of only a small percentage of the water contained in the fresh supplies of air brought by the wind; if all moisture were abstracted from the atmosphere it could only affect the barometer throughout the equatorial regions by 2·8/13·6 inches, or about two-tenths of an inch, while at the polar regions the diminution would be much less than one-tenth. Evidently, therefore, it is idle to argue that the fall of pressure in an extensive storm is to be considered as the simple result of the condensation of the vapour into rain.
Barometric Pressure.—The horizontal distribution of barometric pressure over the earth’s surface is shown by the isobars, or lines of equal pressure at sea-level; it can also be expressed by a system of complex spherical harmonics. As the indications of the mercurial barometer must vary with the variation of apparent gravity, whereas those of the aneroid barometer do not, it has been agreed by the International Meteorological Conventions that for scientific purposes all atmospheric pressures, when expressed as barometric readings, must be reduced to one standard value of gravity, namely, its value at sea-level and at 45° of latitude. In this locality its value is such as to give in one second an acceleration of 980·8 centimetres, or 32·2 English ft. per second. The effect of the variation of apparent gravity with latitude is therefore to make the mercurial barometer read too high, between 45° and the equator, and too low, between 45 and the pole. The gravity-correction to be applied to any mercurial barometric-reading at or near sea-level, in order to get the atmospheric pressure in ​ standard units, should be given on the edge of a meteorological chart, unless the isobars shown thereon already contain this correction. On such charts it will be perceived that the barometric pressure at sea-level is by no means uniform over the earth’s surface, and daily weather charts show very great fluctuations in this respect, the lowest pressures being storm centres and the highest pressures areas of clear cool dry weather. But even the normal average charts show high pressures over the continents in the winter and low pressures over the oceans, these conditions being reversed in the summer time; moreover, Schouff (Pogg. Ann., 1832) first demonstrated that the average pressure in the neighbourhood of the equator is slightly less than under either tropic, and that there is a still more remarkable diminution of pressure from either tropic towards its pole. The exact statement of these variations of pressure with latitude was subsequently worked out very precisely by Ferrel, and forms the basis of his explanation of the general circulation of the earth’s atmosphere and its influence on the barometer. The series of monthly charts for the whole globe, compiled by Buchan and published by the Royal Society of Edinburgh in 1868, as well as Buchan’s later and more perfect charts in the meteorology of the “Challenger” Expedition, Edinburgh, 1889, and in Bartholomew’s Atlas, first revealed clearly the fact that the distinct areas of high and low pressure which are located over the continents and the oceans vary during the year in a fairly regular manner, so that the pressure is higher over the continents in the winter season and lower in the summer season, the amount of the change depending principally upon the size of the continent. A part of this annual variation in pressure is undoubtedly introduced by the methods of reduction to sea-level; indeed, if the data of the lower stations are reduced up to the level of 10,000 or 15,000 ft., we sometimes find the barometric conditions quite reversed. These annual changes are intimately connected as cause and effect with the annual changes of temperature, moisture and wind; it is quite erroneous to say that the observed charted pressures control the winds; there is a reaction going on between the wind and the barometric gradient, the resistance and rotation of the earth’s surface, such that the true relation between these factors is a complex but fundamental problem in the mechanics of the atmosphere.
The vertical distribution of pressure as deduced from observation shows a rate of diminution with increasing altitude very closely but not entirely accordant with the laws of static equilibrium, as first elaborated by Laplace in his hypsometric formula. The departures from this law of static equilibrium are sufficient to show that, if our atmosphere is really in a state of equilibrium, it must be a matter of dynamics and not of statics. The general average relation of the density of the air to the altitude and temperature, and the total pressure of the superincumbent atmosphere, are shown in the accompanying diagram (fig. 1), which is taken from a memoir on the equations of motion by Joseph Cottier, published in the U.S. Monthly Weather Review for July 1897. The diminution of pressure with altitude, as shown in this diagram for average conditions, but not for the temporary conditions that continually occur, follows a logarithmic law, and can undoubtedly be extended upwards for the normal atmosphere only to a height of 20 or 30 m., owing to our uncertainty as to the actual conditions in the upper portions of the atmosphere. This diagram is based upon the assumption that the atmosphere is in a state of convective equilibrium such that the ascending and descending masses expand and cool as they ascend, or contract and warm up as they descend, nearly but not quite in accordance with the adiabatic law of the change of temperature in pure gases.
The departure of atmospheric temperatures from the strictly adiabatic law, as shown by Cottier, is undoubtedly due largely to the heat absorbed by and radiated from moist or hazy or dusty air. In 1890, Abbe showed that a very moderate rate of radiation from the atmosphere suffices to explain the coolness of slowly descending air. The absorption by the atmosphere of radiations from the earth and sun, or the balance between warming by absorption and cooling by radiation, is the basis of the arguments of W. J. Humphreys (Astrophysics, Jan. 1909), and E. Gold (Proc. Roy. Soc., 1908, lxxxii., 45 A.), explaining the existence of the “thermal layer.”
The direct evaluation of this radiation and absorption has been attempted by many. The genuine law a(q−p) is adopted by Gold as closely representing nature, whence it follows that (1) the adiabatic rate of cooling in convection currents must cease at a height corresponding to one-half of the barometric pressure at sea-level; (2) an isothermal layer must exist at the level where the absorption of solar radiation equals that of the terrestrial and atmospheric radiation; (3) within this thermal layer convection is difficult or impossible; (4) above this region the vertical temperature gradient must depend essentially on radiation and is less than that needed for convective equilibrium; (5) below this level the atmospheric radiation exceeds the atmospheric absorption and vertical currents can only be kept up by the convection of heat or aqueous vapour from the earth’s surface to the adjacent layer of air.
Limit of the Atmosphere.—The limiting height of the atmosphere must be at some unknown elevation above 20 m. where the temperature falls to absolute zero. But the uncertainty of the various hypotheses as to the physical properties of the upper atmosphere forbids us to entertain any positive ideas on this subject at the present time. If we define the outer limit of the atmosphere as that point at which the diffusion of gases inwards just balances the diffusion outwards, then this limit must be determined not by the hypsometric formula, but by the properties of gases at low temperatures and pressures under conditions as yet uninvestigated by physicists.
Cloudiness.—It is evident that the clouds (q.v.) are formed from clear transparent air by the condensation of the invisible moisture Fig. 1 therein into numerous minute particles of water, ice or snow. Notwithstanding their transparency, these individual globules and crystals, when collected in large masses, disperse the solar rays by reflection to such an extent that direct light from the sun is unable to penetrate fog or cloud, and partial darkness results. In a general survey of the atmosphere the geographical distribution of the amount of cloudy sky is important. When the solar heat falls upon the surface of the cloud it is so absorbed and reflected that, on the one hand, scarcely any penetrates to the ground beneath, while on the other hand the upper surface of the cloud becomes unduly heated. Even if this upper surface is completely evaporated, it may continually be renewed from below, and, moreover, the evaporated moisture mixing with the air renders it very much lighter specifically than it would otherwise be. Hence the upper surface of the cloud replaces the surface of the ground and of the ocean; the air in contact with it acquires a higher temperature and greater buoyancy, while the ground and air beneath it remain colder than they would be in sunshine. The average cloudiness over the globe is therefore intimately related to the density and circulation of the atmosphere; it was first charted in general terms by L. Teisserenc de Bort of Paris, about 1886. The manifold modifications of the clouds impress one with the conviction that, when properly understood and interpreted, they will reveal to us the most important features. of the processes going on in the atmosphere. If the farmer and sailor can correctly judge of the weather several hours in advance by a casual glance at the clouds, what may not the professional meteorologist hope to do by a more careful study? Acting on, this idea, in 1868 Abbe asked from all of his correspondent observers full details as to the quantity, kind and direction of motion of each layer of clouds; these were telegraphed daily for publication in the Weather Bulletin of the Cincinnati Observatory, and for use in the weather predictions made at that time. Since January 1872 similar data have been regularly telegraphed for the use of the U.S. Weather Bureau in preparing forecasts, although the special cloud maps that were compiled thrice daily have not been published, owing to the expense. These data were also published in full in the Bulletin of the International Simultaneous Meteorological Observations for the whole northern hemisphere during the years 1875–1884. Abbe’s work on the U.S. Eclipse Expedition to the West Coast of Africa in 1889–1890 was wholly devoted to the determination of the height and motions of the clouds by the use of his special form of the marine nephoscope. The use of such a nephoscope is to be strongly recommended, as it gives the navigator a means of determining the bearing of a storm centre at sea by studying the lower clouds, better than he can possibly do by the observation of the winds alone. The importance of cloud study has been especially emphasized by the International Meteorological Committee, which arranged for a complete year of systematic cloud-work by national weather bureaus and individual observatories throughout the world from May 1896 to June 1897. In this connexion H. H. Clayton of Blue Hill Observatory published a very comprehensive report on cloud forms in 1906. The complete report by Professor F. H. Bigelow on the work done by the U.S. Weather Bureau forms a part of the annual report for 1899, and constitutes a remarkable addition to our knowledge of the subject. Some preliminary account of this work was published in the American Journal of Science for December 1899.
Although all the international cloud-work of 1896–1897 has now been published in full by the individual institutions, as in the case of the International Polar Research Work of 1883, yet a comprehensive study of the results still remains to be made. Some of these have, however, been brought together in Mohn’s discussion of the observations by Nansen during the voyage of the “Fram” and also in Hann’s Lehrbuch and in Bigelow’s Report on Cloud-work. The mean
The annual average velocity of hourly movement in metres per second without regard to direction may be summarized as follows:—
The movements of the upper clouds are more rapid in winter than in summer at these northern stations, but among the median and lower clouds a retardation takes place apparently due to the ascending currents that form rain and snow. Above 8000 metres at Upsala the average velocity in winter exceeds 30 metres per second, whereas in summer it is 20; at Toronto and Blue Hill the absolute velocities are larger but in the same ratio. In the United States the maximum velocities from the west attain 100 metres per second and over 80 or 70 metres per second are not rare, but in Europe the corresponding figures are 70, 60, 50. (See also Cloud.)
II.—Meteorological Apparatus and Methods
The observational basis of meteorology is the frequent and, if possible, continuous record of the temperature, moisture and barometric pressure at different altitudes in the free atmosphere, the direction and velocity of the wind, the rain and snow-fall, and the kind, amount and motion of the clouds. For Europe these data have been furnished with more or less accuracy and continuity by thousands of observers ever since 1653, when Ferdinand II., grand duke of Tuscany, organized a system of daily observations in Italy under the general supervision of Luigi Antinori. During the 19th century great efforts were made to obtain equally full records from all parts of the land and ocean, and thousands of navigators were added to the great corps of observers. Other matters have also been investigated, the most important being the intensity of radiation from the earth at night-time and from the sun by day-time, the optical phenomena of the sky, the amount of dust in the air, the electrical condition and the chemical constitution of the atmosphere. Although all the instruments used belong to the category of physical apparatus, yet certain points must be considered as peculiar to their use in connexion with meteorology.
Thermometer.—In using the thermometer to determine, the temperature of the free air it is necessary to consider not merely its intrinsic accuracy as compared with the standard gas thermometer of the, International Bureau of Weights and Measures at Paris, but especially its sluggishness, the influence of noxious radiations, the gradual change of its zero point with time, and the influence of atmospheric pressure.
Sensitiveness.—The thermometer indicates the temperature of the outside surface of its own bulb only when the whole mass of the instrument has a uniform temperature. Assuming that by appropriate convection we can keep the surface of the thermometer at the temperature of the air, we have still to remember that ordinarily this itself is perpetually changing both in rapid oscillations of several degrees and in diurnal periods of many degrees, while the thermometer, on account of its own mass or thermal inertia, always lags behind the changes in the temperature of its own surface. On the other hand, radiant heat passes easily through the air, strikes the thermometer, and raises its temperature quite independently of the influence of the air whose temperature we wish to measure. The internal sluggishness or the sensitiveness of the thermometer is usually different for rising and for falling temperatures, and is measured by a coefficient which must be determined experimentally for each instrument by observing the rate at which its indications change when it is plunged into a well-stirred bath of water whose temperature is either higher or lower than its own. This coefficient indicates the rate per minute at which the readings change when the temperature of the surface of the bulb is one degree warmer or colder than the temperature of the bath. Such coefficients usually vary between 1/20th of a degree centigrade for sluggish thermometers, and one or two degrees for very sensitive thermometers; Suppose, for instance, that the coefficient is one-half degree, then when the rate of change in the temperature of the air is one degree per minute this is exactly the same as the rate of change which the thermometer itself undergoes when its own temperature is two degrees different from that of the air; consequently, the thermometer will lag behind the air temperature to that extent and by the corresponding amount of time, assuming that the air itself flows fast enough to keep the surface of the bulb at the air temperature. When the air temperature ceases to rise or fall, and begins to change at the same rate in the opposite direction, the thermometer will fail to record the true maximum or minimum temperature by an appreciable error depending upon the rapidity of the change, and will follow the new temperature changes with the same lag. For example, in the case just quoted, if a rising temperature suddenly changes to a falling temperature, the error of the thermometer at the maximum temperature will be two degrees, and yet the thermometer may be absolutely correct as compared with the standard when it is allowed five or ten minutes time to overcome the sluggishness. It is very difficult to obtain the temperature of the free air at any moment within 1/10th of a degree Centigrade, owing to the sluggishness of all ordinary thermometers and the perpetual variations in the temperatures of the atmospheric currents.
Radiation.—When a thermometer bulb is immersed in a bath of liquid all radiant heat is cut off, but when hung in the open air it is subject to a perpetual interchange of radiations between itself and all its surroundings; consequently its own temperature has only an indirect connexion with that of the air adjacent to it. One of the most difficult problems of meteorology is so to expose a thermometer as to cut off noxious radiations and get the true temperature of the atmosphere at a specific place and time. The following are a few of the many methods that have been adopted to secure this end: Melloni put the naked glass bulbs within open sheltering caps of perforated silver paper. Flaugergues used a protection consisting of a simple vertical cylinder of two sheets of silver paper enclosing a thin layer of non-conducting substance, like cotton or wool. The influence of radiation upon a thermometer depends upon the radiating and absorbing powers of its own surface; a roughened surface of lamp-black radiates and absorbs perfectly; one of chalk powder does nearly as well; glass much more imperfectly; while a polished silver surface reflects with ease, but radiates and absorbs with the greatest difficulty. Fourier proposed to use two thermometers side by side, one of plain glass and the other of blackened glass; the difference of these would indicate the effect of radiation at any moment; but instead of plain glass he should have used polished silver. His method was quite independently devised and used by Abbe in 1865 and 1866 at Poulkova, where the thermometers were placed within a very light shelter of oiled paper. In order to use this method successfully, both the black and the silvered thermometers should be whirled side by side inside the thermometer shelters (see Bulletin of the Philosophical Society of Washington for 1883). Various forms of open lattice-work and louvre screens have been devised and used by Glaisher, Kupffer, Stevenson, Stowe, Dove, Renou, Joseph Henry and others, in all of which the wind is supposed to blow freely through the screens, while the latter cut off the greater part of the direct sunshine and other obnoxious radiations by day, and also prevent obnoxious radiation from the thermometer to the sky by night. The Italian physicist Belli first proposed a special artificial ventilation drawing the fresh air from the outside and making it flow rapidly over the thermometer. Even before his day de Saussure, Espy, Arago and Bravais whirled the thermometer rapidly either by a small whirling machine, or by attaching it to a string and swivel and whirling it like a sling. When this whirling is done in a shady place excellent results are obtained. Renou and Craig placed the thermometer in a thin metallic enclosure or shelter, and whirled the latter. Wild established the thermometer ​ in a fixed louvre shelter, but by means of a Ventilating apparatus drew currents of fresh air from below into the shelter, where they circulated rapidly and passed out. In Germany, since 1885, Dr Assmann has developed the apparatus known as the ventilated psychrometer, in which the dry-bulb thermometer is placed within a double shelter of thin metallic tubing, and the air is drawn in rapidly by means of a small ventilating fan. In the observations made by Abbe on the cruise of the “Pensacola” to the West Coast of Africa, the dry- and wet-bulb thermometers were enclosed within bamboo tubes and rapidly whirled. The inside of the wet-bulb tube was kept wet, so that its surface, being cooled by evaporation, could not radiate injuriously to the thermometer. In the system of exposure adopted by the U.S. Weather Bureau the dry and wet bulbs are whirled by a special apparatus fixed within the louvred shelter, which is about 31/2 ft. cube, and is placed far enough above the ground or building to ensure free exposure to the wind. In using the whirling and Ventilating methods it is customary to take a reading after whirling one minute, and a second reading at the end of the second minute, and so on until no appreciable changes are shown in the thermometer. Of course in perfectly calm weather these methods can only give the temperature of the air for the exact locality of the thermometer. On the other hand, when a strong wind is blowing the indicated temperature is an average that represents the long narrow stream of air that has blown past the thermometer during the few minutes that are necessary in order that its bulb may obtain approximately the temperature of the air.
Change of Zero.—All thermometers having glass bulbs, especially those of cylindrical shape, are sensitive to changes of atmospheric pressure. The freezing-point, determined under a barometric pressure of 30 in., or at sea-level, stands higher on the glass tube than if it had been determined under a lower pressure on a mountain top. Therefore delicate thermometers, when transported to great heights, or even during the very low pressure of a storm centre, read too low and need a correction for pressure. The zero-point also changes with time and with the method of treatment that the bulb has received as to temperature. Owing to the slow adjustment of the molecules of the glass bulb to the state of stable equilibrium, their relations among themselves are disturbed whenever the bulb is freshly heated. At this time the freezing-point is temporarily depressed to an amount nearly proportional to the heating. The normal method of treatment consists in first determining the boiling-point of the thermometer, and, after a few minutes, the freezing-point. If this method is uniformly followed the two fiducial points will stay in permanent relation to each other. A thermometer that has been used for many years by a faithful meteorological observer has almost inevitably been going through a steady series of changes; in the course of ten years its freezing-point may have risen by 2° or 3° F., and, moreover, it changes by Fully a tenth of a degree between summer and winter. The only way completely to eliminate this source of error from meteorological work is to discard the mercurial thermometer altogether; but instead of adopting that course, the use is generally recommended of thermometers whose bulbs are made of a special glass, upon which heating and cooling have comparatively very little influence. Any argument as to secular changes in the temperature of the atmosphere is likely to be greatly weakened by the unknown influence of this source of error, as well as by changes in the methods of exposure and in the hours of observation.
Barometer.—The barometer (q.v.) indicates the elastic pressure prevailing in gas or liquid at the surface of the mercury in the open tube or cistern, provided that the fluid at that point is in a state of quiet relative to the mercury.
Any motion of the air will have an influence upon the reading quite independently of the prevailing elastic pressure. The pressure within a mass of gas at any point is the summation of the effects due to the motions of the myriad molecules of the gas at that point; it is the kinetic energy of the molecules striking against each other and the sides of the enclosure, which in this case is the surface of the mercury in the cistern of the instrument. If the barometer moves with respect to the general mass of the gas there is a change in the pressure on the mercurial surface, although there may be none in the general mass of the free gas, and a barometer giving correctly the pressure of the air at rest within a room will give a different indication if the instrument or the air is set in rapid motion so that the air strikes violently against it. If the barometer moves with the air it will indicate the elastic pressure within the air. When the wind blows against an obstacle the air pressure is increased slightly on the windward side and diminished on the leeward side. It is thus obvious that in determining the pressure within the free atmosphere the exposure of the barometer must be carefully considered. The influence of a gale of wind is to raise the elastic pressure within a room whose window faces to the windward, but to lower the pressure if the window faces to the leeward. The influence of the draught up chimney, produced by the wind blowing over its summit, is to lower the pressure within the room. The maximum effect of the wind in raising the pressure is given by the formula. P−P$_0$＝0.000 038 3 × V$^2$, where the pressure is given in inches and the velocity in miles per hour. This amounts to about one-tenth of an inch in a 50-m. wind, and to nearly four-tenths in a 100-m. wind. The diminution by a leeward window or a draught up .chimney is usually less than this amount. This alteration in pressure, due to the local effect of wind, does not belong to the free atmosphere but to the method of exposure of the barometer, and can be eliminated only by methods first described by Abbe in 1882: it is a very different matter from the general diminution of pressure in the atmosphere produced by the movement of the wind over a rotating earth and by the centrifugal force within a vortex. The latter is an atmospheric phenomenon, independent of instruments and locality, which in hurricanes and tornadoes may amount to several inches of the mercurial column. It is, however, quite common to find in the continuous records of pressure during a hurricane evidence of the fact that the low pressure due to the hurricane and the special diminution due to the exposure of the barometer are combined together, so that when the calm centre of a hurricane passes over a station the pressure temporarily rises by the amount due to the sudden stoppage of the wind and the local exposure effect.
The other sources of error that give rise to discrepancies in meteorological work relate to the temperature of the instrument, the sluggishness of the movement of the mercury, and the inevitable large secular changes in the correction for capillarity, due principally to the changes in the condition of the surfaces of the glass and the mercury, especially those that are exposed to the open air. The international comparisons of barometers show that discrepancies exist between the best normals or standards, and that ordinary barometers must always be compared with such standards at the temperatures and pressures for which they are to be used.
Anemometer.—The wind is measured either by means of its pressure against any obstacle or by revolving apparatus that gives some idea of the velocity of its movement. The pressure is supposed to interest the engineer and navigator, but the velocity is the fundamental meteorological datum; in fact, the pressure of the wind varies with the nature of the obstacle, the method of exposure, the density of the air, and even the mass of rain carried along with it.
Pressure anemometers date from the pendulous tablet devised by Sir Christopher Wren about 1667, and such pressure plates continue to be used in an improved form by Russian observers. Normal pressure plates are used at a few English and Continental stations. The windmill anemometers devised by Schober and Woltmann were modified by Combes and Casella so as to make an exceedingly delicate instrument for laboratory use; another modification by Richard is extensively used by French observers. In the early part of the 19th century Edgeworth devised and Robinson perfected a windmill system in which hemispherical cups revolved around a vertical axis, and these have come into general use in both Europe and America. Many studies have been made of the exact ratio between the velocity of the wind and the rotations of the Robinson anemometer. The factor 3 is usually adopted and incorporated into the mechanism of the apparatus, but in ordinary circumstances this factor is entirely too large, and the recorded velocities are therefore too large. The whirling cups do not revolve with any simple relation to the velocity of the wind, even when this is perfectly steady. The relation varies with the dimensions of the cups and arms and the speed of the wind, but especially with the steadiness or gustiness of the wind. The exact ratio must always be determined experimentally for each specific type of instrument; in most instruments in actual use the factor for steady wind varies between 2·4 and 2·6. When the wind is gusty the moment of inertia of the moving parts of the instrument necessitates an appreciable correction; thus, when the gust is at its height the revolving parts receive an impetus that lasts after the gust has gone down, so that the actual velocity of the cups is too high. For this reason, also, comparisons and studies of anemometers made in the irregular natural winds of a free air are unsatisfactory. For the average natural and gusty winds at Washington, D.C., and on Mount Washington, N.H., and the small type of Robinson's anemometer used in the U.S. Weather Bureau Service, Professor C. F. Marvin deduced the table (see p. 275) for reduction from recorded to true velocity. This table involves the moment of inertia of the revolving parts of the instrument and the gustiness of the winds at Washington, and will therefore, of course, not apply strictly to other types of instruments or winds, for which special studies must be made.
About 1842 a committee of the American Academy of Arts and Sciences experimentally determined, for a large variety of chimney caps, or cowls, or hoods, the amount of suction that produces the draught up a chimney, and shortly afterwards a similar committee made a similar investigation at Philadelphia (see Proc. Amer. Acad. i. 307, and Journal of Franklin Institute, iv. 101). These investigations showed that the open end of the chimney, acting as an obstacle in the wind, is covered by a layer of air moving more rapidly than the free air at a little distance, and that therefore between this layer and the aperture of the chimney there is a space ​ within which barometric pressure is less than in the neighbouring free air. The draught up the chimney is due to the pressure of the air at the lower end or fireplace pushing up the flue into this region of low pressure, quite as much as it is due to the buoyancy of the heated air within the flue. From such experiments as these there has been developed the vertical suction-tube anemometer, as devised by Fletcher in 1867, re-invented by Hagemann in 1876, and introduced into England by Dines.
Marvin’s Table for the Reduction of Velocities, given by the small- sized Robinson’s Anemometer in gusty winds.
In his Meteorological Apparatus and Methods (Washington, 1887) Abbe gives the theory of this class of anemometers and develops the following additional forms: Two vertical tubes, whose apertures are respectively directed to the windward and the leeward, and within which are two independent barometers, give the means of determining the barometric pressure plus the wind pressure and minus the wind pressure respectively, so that both the velocity of the wind and the true barometric pressure can be determined. If instead of a simple opening at the top of the tube we place there horizontally the contracted Venturi’s tube, we obtain a maximum wind effect, which gives an accurate measure of the wind velocity, and is the form recommended by Bourdon as an improvement on that of Arson. In all anemometers of this class the inertia of the moving parts is reduced to a minimum, and the measurement of rapid changes in velocity and of the maximum intensity of gusts becomes feasible. On the other hand, these researches have shown how to expose a barometer so that it shall be free from the dynamic or wind effect even in a gale. It has only to be placed within a room or box that is connected with the free air by a tube that ends in a pair of parallel plane plates. When the wind blows past the end of this tube it flows between these plates in steady linear motion, and can produce no disturbance of pressure at the mouth of the tube if the plates are at a suitable distance apart. This condition of stable flow, as contrasted with permanent flow, was first defined by Sir William Thomson (Lord Kelvin) (see Phil. Mag., Sept. 1887). Such a pair of small circular plates can easily be applied to a tube screwed into the air-hole at the back of any aneroid barometer, and thus render it independent of the influence of the wind. As to the exposure of the anemometer, no uniform rules have as yet been adopted. Since the wind is subject to exceedingly great disturbances by the obstacles near the ground, an observer who estimates the force of the wind by noticing all that goes on over a large region about him has some advantage over an instrument that can only record the wind prevailing at one spot. The practice of the U.S. Weather Bureau has been to insist upon the perfectly free exposure of all anemometers as high as can possibly be attained above buildings, trees and hills; but, of course, in such cases they give records for an elevated point and not for the ground. These are therefore not precisely appropriate for use in local climatological studies, but are those needed for general dynamic meteorology, and proper for comparison with the isobars and the movements of the clouds shown on the daily weather map.
Hygrometer.—Moisture floats in the atmosphere either as invisible vapour or as visible haze, mist and cloud. The presence of the latter generally assures us that the air is fully saturated. The total amount of both visible and invisible vapour contained in a unit volume of cloud or mist is directly determined by the Schwackhofer or Svenson hygrometer, or it may be ascertained by warming a definite portion of the air and fog and measuring the tension of the vapour by Edelmann’s apparatus. Both these methods, however, are in practice open to many sources of error. If only invisible aqueous vapour is present we may determine its amount by several methods: (a) the chemical method, by absorbing and weighing it; (b) the dewpoint method, by cooling the air down to the temperature where condensation begins; (c) Edelmann’s method, by absorbing the moisture chemically and measuring the change in vapour tension; (d) by adding vapour until the air is saturated, and measuring either the increased tension or the quantity of evaporation; (e) the psychometric method, by determining the temperature of evaporation.
The wet-bulb thermometer, which is the essential feature of the last method, was used by Baumé in 1758 and de Saussure in 1787, but merely as giving an index of the dryness of the air. The correct theory of its action was elaborated by many early investigators: Ivory, 1822; August, 1825; Apjohn, 1834; Belli, 1838; Regnault, 1845. From the last date until recent years no important progress was made in our knowledge of the subject, and it was supposed that the psychrometer was necessarily crude and unsatisfactory; but in its modern form it has become an instrument of much greater precision, probably quite as trustworthy as the dew-point apparatus or other method of determining atmospheric moisture. In order to secure this accuracy the two bulbs must be of the same size, style and sensitiveness; the wet bulb must be covered with thin muslin saturated with pure water; both thermometers must be whirled or ventilated rapidly, but at the definite prearranged rate for which the tables of reduction have been computed; and, finally, both thermometers must be carefully sheltered against obnoxious radiations. In order to attain these conditions European observers tend to adopt Assmann’s ventilated psychrometer, but American observers adopt Arago’s whirled psychrometer, set up within an ordinary thermometer shelter. By either method the dew-point should be determined with an accuracy of one-tenth degree C. or two-tenths F. As a crude approximation, we may assume that the temperature of the dew-point is below the temperature of the wet bulb as far as that is below the dry bulb. A greater accuracy can be attained by the use of Ferrel’s or Marvin’s psychometric tables or Grossman’s formula. But the vapour tension over ice and over water as measured by Marvin and by Juhlin must be carefully distinguished and allowed for. The Smithsonian Meteorological Tables (ed. of 1908) and the new psychrometer tables by Ejerkeland for temperatures below freezing (Christiania, 1907) represent the present condition of our knowledge of this subject. Glaisher deduced empirically from a large mass of observations certain factors for computing the dew-point, but these do not represent the accuracy that can be attained with the whirled psychrometer, nor are they thoroughly satisfactory when used with Regnault’s tables and the stationary psychrometer. Especially should their use be discarded when the wet bulb is greatly depressed below the dry bulb and the atmosphere correspondingly dry. For occasional use at stations, and especially for daily use by travellers and explorers, nothing can exceed the convenience and accuracy of the sling psychrometer, especially if the bulbs are protected from radiation by a slight covering of non-conducting material, or even metal, as was done by Craig in 1866–1869 for the stations of the U.S. Army Surgeon-General. The hair hygrometer gives directly the relative humidity or the ratio between the moisture in the air and that which it would contain if saturated. The very best forms perform very well for a time, and are strongly recommended by Pernter, and must be used in self-recording apparatus for balloons and kites; they are standardized by comparison with the ventilated psychrometer, which itself must be dependent on the standard dew-point apparatus.
Rain and Snow Gauge.—The simple instrument for catching and measuring the quantity of rain, snow or hail that falls upon a definite horizontal area consists essentially of a vertical cylinder and the measuring apparatus. The receiving mouth of the cylinder is usually terminated by a cone or funnel, so that the water running down through the funnel and stored in the cylinder is protected from evaporation or other loss. The cylinder is firmly attached to the ground or building, so that the mouth is held permanently at a definite altitude.
The sources of error in its use are the spattering into it from the ground or neighbouring objects, and the loss due to the fact that when the wind blows against the side of the cylinder it produces eddies and currents that carry away drops that would otherwise fall into the mouth, and even carries out of the cylinder drops that have fallen into it. As a consequence all the ordinary rain-gauges catch and measure too little rainfall. The deficit increases with the strength of the wind and the smallness or lightness of the raindrops and snowflakes. If we assume that the correct rainfall is given by a gauge whose mouth is flush with the level of the ground and is surrounded by a trench wide enough to prevent any spatter, then, on the average of many years and numerous observations with ordinary rain-gauges in western Europe, and for the average character of the rain in that region and the average strength of the attending winds, the deficit of rain caught by a rain-gauge whose mouth is 1 metre above the ground is 6% of the proper amount; if its elevation is 1 ft. above ground, the deficit will be 31/2%. This deficit increases as the gauges are higher above the ground in proportion approximately to the square root of the altitude, provided that they are fully exposed to the increase of wind that prevails at those altitudes. It is evident that even for ​ altitudes of 5 or 10 ft. the records become appreciably discrepant from those obtained at the surface of the ground. The following table shows in the last column the observed ratio between the catches of gauges at various altitudes and those of the respective standards at the level of the ground. Unfortunately, there are no records of the force of the wind to go with these measurements; but we know that in general, and on the average of many years, corresponding with those here tabulated, the velocity of the wind increases very nearly as the square root of the altitude. Although this deficit with increasing altitude has been fully recognized for a century, yet no effort has been made until recent years to make a proper correction or to eliminate this influence of the wind at the mouth of the gauge. Professor Joseph Henry, about 1850, recommended to the observers of the Smithsonian Institution the use of the “pit-gauge.” About 1858 he recommended a so-called shielded gauge, namely—a simple cylindrical gauge 2 in. in diameter, having a wide horizontal sheet of metal like the rim of an inverted hat soldered to it. This would undoubtedly diminish the obnoxious currents of air around the mouth of the gauge, but the suggestion seems to have been overlooked by meteorologists In 1878 Prof. F. E. Nipher of St Louis, Missouri, constructed a much more efficient shield, consisting of an umbelliform screen of wire-cloth having about sixty-four meshes to the square inch. This shield seems to have completely annulled the splashing, and to have broken up the eddies and currents of wind. With Nipher’s shielded gauges at different altitudes, or in different situations at the same altitude, the rain catch becomes very nearly uniform; but the shield is not especially good for snow, which piles up on the wire screen. Since 1885 numerous comparative observations have been made in Europe with the Nipher gauge, and with the “protected gauge” devised by Boernstein, who sought to prevent injurious eddies about the mouth of the gauge by erecting around it at a distance of 2 or 3 ft. an open board fence with its top a little higher than the mouth of the gauge. The boards or slats are not close together, but apparently afford as good a protection as the shield of Professor Nipher, and give good results with both snow and rain.
Altitude and Relative Catch of Rain. :
| Situation and Size of Gauge. | Years of Record | Years of Record | Altitude. | Altitude. | Relative Catch. |
| | | | Metres. | Metres. | % |
| | | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 0 | 100 |
| Calne, 5-in. and 8-in. | 4 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 1 | 90 |
| Castleton, 5-in. and 8-in. | 3 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 2 | 88 |
| Rotherham, 5-in. | 8 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 3 | 86 |
| St Petersburg: Central Physical | | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 4 | 85 |
| Observatory, 10-in. | 10 | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 5 | 85 |
| | | | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | 6 | 84 |
| London: Westminster Abbey | 1 | | | 9·1 | 77 |
| Emden | 2 | | | 11 | 72 |
| St Petersburg: Central Physical | | | | | |
| Observatory | 1 | | | 13 | 68 |
| York: Museum | 3 | | | 13 | 80 |
| Calcutta: Alipore Observatory | 7 | | | 15 | 87 |
| Woodside: Walton-on-Thames | 1 | | | 15 | 73 |
| Philadelphia: Frankford Arsenal | 3 | | | 16 | 95 |
| Sheerness: Waterworks | 3 | | | 21 | 52 |
| Whitehaven: St James’s Church | 10 | | | 24 | 66 |
| St Petersburg: Central Physical | | | | | |
| Observatory | 10 | | | 25 | 59 |
| Paris: Astronomical Observatory | 40 | | | 27 | 81 |
| Dublin: Monkstown | 6 | | | 27 | 64 |
| Oxford: Radcliffe Observatory | 8 | | | 34 | 59 |
| Copenhagen: Observatory | 4 | | | 36 | 67 |
| London: Westminster Abbey | 1 | | | 46 | 52 |
| Chester: Leadworks | 2 | | | 49 | 61 |
| Wolverhampton: Waterworks | 3 | | | 55 | 69 |
| York Minster | 3 | | | 65 | 60 |
| Boston: St Botolph’s Church | 2 | | | 79 | 47 |
In general it is now conceded by several high authorities that the measured rainfall must be corrected for the influence of the wind at the gauge, if the latter is not annulled by Nipher’s or Boernstein’s methods. A practicable method of measuring and allowing for the influence of the wind, without introducing any very hazardous hypothesis, was explained by Abbe in 1888 (see Symons’s Meteorological Magazine for 1889, or the U.S Monthly Weather Review for 1899). This method consists simply in establishing near each other several similar gauges at different heights above the ground. but in otherwise similar circumstances. On the assumption that for small elevations the diminution of the wind, like that of the rainfall, is very nearly in proportion to the square root of the altitude, the difference between the records for two different altitudes may be made the basis of a calculation which gives the correction to be applied to the record of the lower gauge, in order to obtain the rainfall that would have been caught if there were no wind. It is only when the catch of the gauge has been properly corrected for the effect of the wind on the gauge that we obtain numbers that are proper to serve for the purpose of determining the variation of the rainfall with altitude and locality, the influence of forests and the periodical changes of climate. Methods of measuring dew, frost, hail, sleet, glatteis and other forms of precipitation still remain to be devised; each of these has its thermodynamic importance and must eventually enter into our calculations.
It has been common to consider that the rain-gauge cannot be properly used on ships at sea, owing to the rolling and pitching of the vessel and the interference of masts and rigging; but if gauges are mounted on gimbals, so as to be as steady as the ordinary mariner’s compass, their records will be of great importance. Experimental work of this sort was done by Mohn, and afterwards in 1882 by Professor Frank Waldo; but the most extensive inquiry has been that of Mr W. G. Black (see Journal Manchester Geographical Society, 1898, vol. xiv.), which satisfactorily demonstrates the practicability and importance of the marine rain-gauge.
Evaporometer.—The moisture in the atmosphere comes from the surface of the earth or ocean by evaporation, a process which goes on continually, replacing the moisture that is precipitated as rain, hail, snow and dew, and maintaining the total quantity of the moisture in the atmosphere at a very uniform figure. The rate of evaporation depends on the temperature, the dryness, and the velocity of the wind. It is not so important to meteorologists to know where the moisture comes from as to know its amount in the atmosphere, and in fact no method has yet been devised for determining how much moisture is given up by any specific portion of the earth, or ocean, or forest. Our evaporometers measure the quantity of moisture given off by a specific surface of water, but it is so difficult to maintain this water under conditions the same as obtain in nature that no conclusions can be safely deduced as to the actual evaporation from natural surfaces. The proper meteorological use of these evaporometers is, as integrating hygrometers, to give the average humidity of the air, the psychrometer giving the conditions prevailing at any moment.
Among the many forms of evaporometer the most convenient is that devised by Piche, which may be so constructed as to be exceedingly accurate. The Piche evaporometer consists essentially of a glass tube, whose upper end is closed hermetically, whereas the lower end is covered by a horizontal disk of bibulous paper, which is kept wet by absorption from the water in the tube. As the water evaporates its descent in the tube is observed, whence the volume evaporated in a unit of time becomes known. So long as the paper remains clean, and the water is pure, the records of the instrument depend entirely upon the evaporating surface, the dryness of the air, and the velocity of the wind. Careful comparisons between the Piche and the various forms of absolute evaporometers were made by Professor Thomas Russell, and the results were published in the U.S. Monthly Weather Review for September 1888, pp. 235–239. By placing the Piche apparatus upon a large whirling machine he was able to show the effect of the wind upon the amount of evaporation. This important datum enabled him to explain the great differences recorded by the apparatus established at eighteen Weather Bureau stations; based upon these results, he prepared a table of relative evaporation within thermometer shelters at all stations. The actual evaporation’s from ground and water in the sunshine may run parallel to these, but cannot be accurately computed. It is probable that Professor Russell’s computations are smaller than the evaporation’s from shallow bodies of water in the sunshine, but larger than for deep bodies, like the great lakes, and for running rivers. Recent elaborate studies of evaporation have been undertaken in Egypt and in South Africa—but perhaps the most interesting case occurs in southern California. Here the Colorado river, having broken through its bounds, emptied itself into a great natural depression and formed the so-called “Salton Sea,” about 80 m. long, 20 wide and 100 ft. deep, before it could be brought under control. This sea is now isolated, and will, it is hoped, dry up in eight or ten years. Meanwhile the U.S. Weather Bureau has established a large number of evaporation stations in and around it, and has begun the study not only of the relation between evaporation, wind and temperature, but of the eventual disposition of this evaporation throughout the atmosphere in the neighbourhood of the sea (see the Reports of Professor F. H. Bigelow in U.S. Monthly Weather Review, 1907–1909, as also the elaborate bibliography of evaporation in the same volumes). Although the influence of the evaporation on local climate is scarcely appreciable to our hygrometric apparatus, yet it is said to be so in the development and ripening and drying of the dates raised on the U.S. government experimental "date farm” a few miles north-east of the Salton Sea.
​ Nephoscope.—The direction and apparent velocity of the motion of a cloud are best observed by means of the nephoscope, which has now become a necessary item in the outfit of any first-class meteorological station. Among the various forms of this instrument are the nephodoscope of Fornioni, the marine nephoscope of Fineman, the simple mirror with attachments used by Clayton, the cloud camera of Vettin, and the alt-azimuths of Mohn and Lettry. The most perfect form for use on land is that devised by Professor Marvin in 1896 for the U.S. Weather Bureau stations (see fig. 2); while the most convenient for use at sea is that devised and used in 1889 by Professor Abbe on the cruise of the U.S. ship “Pensacola” to the west coast of Africa, but first described in the report of the International Meteorological Congress held at Chicago in August 1893.
Fig. 2.—Marvin’s Nephoscope.
The construction of this instrument is shown in figs. 3, 4, 5. In using it the observer looks down upon a horizontal mirror and observes the reflection of the cloud. By moving his eye he brings any cloudy point into coincidence with, the reflection of a small fixed spherical knob K above the mirror, and keeps the images of the knob and the cloud coincident as they pass from the centre of the mirror to its edge. This line of motion shows the azimuth of the horizontal component of the cloud’s motion. The course of the vessel is shown by the compass card and lubber line AF seen below the mirror. The apparent angular velocity of the cloud, as it would be if the cloud started from the zenith, is obtained by counting the seconds that elapse between its passage from the centre to the edge, or to a small circle inscribed within the edge. With Marvin’s nephoscope two observers a short distance apart may easily determine the apparent altitude, and azimuth, and motion of any cloud, whence its true altitude and velocity may be computed. But when the observer uses Abbe’s marine nephoscope on a vessel which is itself in motion he observes the resultant of his own motion and that of the cloud. If his vessel is under his control, so that he may change its velocity or direction at will, he easily determines this resultant for two different courses, and obtains data by which he is enabled to calculate the real altitude and velocity of the cloud in terms of his own velocity. As the marine nephoscope can be used on a wagon moving rapidly over a smooth road, or in a small boat on a smooth pond, almost as well as on a larger sea-going vessel, it becomes an instrument of universal application for cloud study. It is also equally convenient for observing the positions of auroras, halos, meteors, and other special phenomena. For the international work undertaken during the year 1898 the photographic camera established upon an alt-azimuth mounting, or the so-called photogram-meter, was especially developed. In this apparatus photographs of the clouds are taken simultaneously at two or more stations, and in each case the centre of the photographic plate has its altitude and azimuth determined. From this centre one can measure on the plate the additional angles required in order to fix the altitude and azimuth of any point that is photographed, and thus the dimensions of the whole visible cloud and its internal or differential motions can be determined, as well as its general motion. During the years 1896–1898 about twenty stations were occupied throughout the world for the purpose of determining accurately the altitudes and motions of every layer of cloud.
Sunshine Recorder.—The ordinary meteorological record specifies the proportion of sky that appears to be covered with cloud, or the so-called cloudiness, usually expressed in tenths. The observer generally confines his attention to that portion of the sky within sixty degrees of the zenith, and ignores the lower zone, since the clouds that are found therein are often at so great a distance from him that their record is not supposed to belong to his locality. As the cloudiness—or its reciprocal, the sunshine—is supposed to be the most important item in agricultural climatology, and is certainly very important for dynamic meteorology, it is usually considered desirable to obtain more complete records than are given by only one or two specified hours of observation. To this end apparatus for recording sunshine, or, rather, the effect of cloudiness, is widely adopted. At least three forms are worth describing as being extensively used.
The Jordan photographic sunshine recorder consists of a cylinder enclosing a sheet of sensitive paper; the sun’s rays penetrate through a small aperture, and describe a path from sunrise to sunset, which appears on this sheet after it has been properly washed with the fixing solution. Any interruption in this path, due to cloudiness or haze, is of course clearly shown, and gives at once the means of estimating what percentage of the day was clear and what cloudy. The modified form of the instrument devised by Professor Marvin has been used for many years at about forty Weather Bureau stations, but the original construction is still employed by other observers throughout the world. The Stokes-Campbell recorder consists of a globe of glass acting as a burning-glass. A sheet of pasteboard or a block of wood at the rear receives the record, and the extent of the charring gives a crude measure of the percentage of full or strong sunshine. Many of these instruments are used at stations in Great Britain and the British colonies. The Marvin thermometric sunshine recorder consists of a thermometer tube, having a black bulb at the lower end and a bright bulb at the other. The excess of temperature in the black bulb causes a thread of mercury to move upwards, and for a certain standard difference of temperature of about 5° F., such as would be produced by the sun shining through a very thin cloud or haze, a record is made by an electric current on a revolving drum, and simply shows when during the day sunshine of a certain intensity prevailed, or was prevented by cloudiness, D. T. Maring, in the U.S. Monthly Weather Review for 1897, described an ingenious combination of the thermometer and the photographic register of cloudiness which is worthy of further development. It gives both the quantity of cloudiness and intensity of the sunshine on some arbitrary relative scale.
The intensity of the sunshine, as sometimes employed in general agricultural studies, is crudely shown by Violle’s conjugate bulbs, which are thin copper balls about 3 in. in diameter, one of them being blackened on the outside and the other gilded. When exposed to the sunshine the difference in temperature of the two bulbs increases with the intensity of the sunshine, but as the difference is dependent to a considerable extent on the wind, the Violle bulbs have not found wide application. The Arago-Davy actinometer, or bright and black bulbs in vacuo, constitutes a decided improvement upon the Violle bulbs, in that the vacuous space surrounding the thermometers diminishes the effect of the wind. The physical theory involved in the use of the Arago-Davy actinometer was fully developed by Ferrel, and he was able to determine the coefficient of absorption of the earth’s atmosphere and other data, thereby showing that this apparatus has considerable pretensions to accuracy. In using it as contemplated by Arago and Davy and by Professor Ferrel, we read simply the stationary temperature attained by the bright and black thermometers at any moment, whereas the best method in actinometry consists in alternately shading and exposing any appropriate apparatus so as to determine the total effect of the solar radiation in one minute, or some shorter unit of time; this method of using the Arago-Davy actinometer was earnestly recommended by Abbe in 1883, and in fact tried at that time; but the apparatus and records were unfortunately burned up. This so-called dynamic, as distinguished from the static, method was first applied by Pouillet in 1838 in using his pyrheliometer, which was the first apparatus and method that gave approximate measures of the radiant heat received from the sun. In order to improve upon Pouillet’s work more delicate apparatus has been constructed, but the fundamental methods remain the same. Thus Ångström has applied both Langley’s bolometer and his own still more sensitive thermoelectric couple and balance method; Violle uses his absolute actinometer, consisting of a most delicate thermometer within a polished metal sphere, whose temperature is kept uniform by the flow of water; while Crova, with a thermometer within an enclosure; of uniform temperature, claims to have attained an accuracy of one part in a thousand. Chwolson has reviewed the whole subject, of actinometry, and has shown the greater delicacy of his own apparatus, consisting of two thin plates alternately exposed to and shielded from sunshine, whose differences of temperature are measured by electric methods.
As none of the absolute methods for determining the solar radiation in units of heat lend themselves to continuous registration, it is important to call attention to the possibility of accomplishing this by chemical methods. The best of these appears to be that devised by Marchand, by the use of a device which he calls the Phot-antitupimeter. In this the action, of the sunlight upon a solution of ferric-oxalate and chloride of iron liberates carbonic acid ​ gas, the amount of which can be measured either continuously or every hour; but in its present form the apparatus is affected by several serious sources of error.
Fig. 3.—Abbe’s Marine Nephoscope. Horizontal Projection of Mirror.
The electric compensation pyrheliometer, as invented by Knut Angström (Ann. Phys., 1899), offers a simple method of determining accurately the quantity of radiant energy. He employs two blackened platinum surfaces, one of which receives the radiations to be measured, while the other is heated by an electric current.
Fig. 4.—Abbe’s Marine Nephoscope. Horizontal Projection of Compass.
The difference of temperature between the two disks is determined by a thermocouple, and they are supposed to receive and lose the same amount of energy when their temperatures are the same. A Hefner lamp is used as an intermediate standard source of radiation, and alternate observations on any other source of radiant heat give the means of determining their relation to each other.
Fig. 5.—Abbe’s Marine Nephoscope. Vertical Section.
By means of two such instruments Angström secured simultaneous observations on the intensity of the solar radiation at two points, respectively, 360 and 3352 metres above sea-level, and determined the amount of heat absorbed by the intermediate atmosphere. An accuracy of 1–1000 appears to be attainable, and this apparatus is now being widely used. The records of 1901–1905 have already given rise to the belief that there is a variation in our insolation that may eventually be traced back to the sun’s atmosphere.
Meteorograph.—The numerous forms of apparatus designed to keep frequent or continuous register of the prevailing pressure, temperature, moisture, wind, rainfall, sunshine, evaporation, and other phenomena are instruments that belong peculiarly to meteorology as distinguished from laboratory physics. Such apparatus may be broadly divided into several classes according as the records are obtained by the help of photography, or electricity, or by direct mechanical action. The prevailing tendency at present is in favour of apparatus in which the work of the recording pen is done by a falling weight, whose action is timed and limited by the making and breaking of electric currents by the meteorological apparatus proper. The most serious defect in such instruments, even when kept in good working order, is a want of sensitiveness commensurate with the desired openness of scale. It is very important that a fraction of a minute of time should be as recognizable as one-tenth of a degree of temperature; one thousandth of an inch of barometric pressure, and velocities of one hundred miles per hour, as well as rapid changes in all these elements, must be measurable. But instruments whose scales are large enough to record all these quantities are usually so sluggish as regards time that the comparison of the records is very unsatisfactory. In order to study the relationships between temporary and fleeting phenomena, it is necessary that all instruments should record upon the same sheet of paper, so that the same time-scale will answer for all.
The instruments that respond most nearly to the general needs of meteorology are the various forms of meteorographs devised by Wild for use at St Petersburg, by Sprung and Fuess for use at Hamburg and Berlin, and by Marvin for Washington. The photographic systems for pressure and temperature introduced many years ago at stations in Great Britain and the British colonies are not quite adequate to present needs. The portable apparatus manufactured by Richard Frères at Paris is in use at a very large number of land stations and on the ocean, and by giving special care to regular control-observations of time, pressure and temperature, important results may be obtained; but in general the timescales are too small, and the unknown sources of error too uncertain, to warrant implicit reliance upon the records.
Polarimeter.—The brightness and blueness of the sky light, and especially its polarization, have been observed with increasing interest, as it seems possible from these elements to ascertain something with regard to the condition and amount of the moisture of the air. With a simple Nicol’s prism held in the hand and turned slowly about the axis of vision one can quickly recognize the fact that the sky light is polarized, and that the polarization is largely due to the air or dust lying between us and the clouds in the distant horizon. Arago, with a more delicate form of polariscope, determined the existence of a socalled neutral region near the sun. Babinet located a neutral point or zone about as far from the anti-sun as was Arago’s from the sun itself. Brewster discovered a neutral point near the sun and horizon, disappearing when the sun is more than 15° above the horizon. Finally, Brewster explored the sky sufficiently to draw lines of equal polarization, which he published in Johnston’s Physical Atlas, and which were confirmed by Zantedeschi in 1849. Since those days far more delicate work has been done—first by Bosanquet of Oxford, afterwards Prof. E. C. Pickering of Harvard University and Prof. A. W. Wright of Yale University. A later contribution to the subject is by Jensen (see Met. Zeit. for Oct.–Dec. 1899), who has observed the brightness as well as the polarization, and thus completed the data necessary for testing the various physical theories that have been proposed for the explanation of this phenomenon. We owe to Tyndall the discovery that when a beam of white light penetrates a mass of fine aqueous mist the latter sends off at right angles a delicate blue light, which is almost wholly polarized in a plane at right angles to the plane ​ of reflection. As the particles of mist grow larger, the blue light becomes whiter and the polarization disappears. The original vapour particles are undoubtedly so small as to be comparable in size with a fraction of the wave-length of ordinary light, and Rayleigh was able to show that molecular as well as minute particles must have a power of selection, and that the diffused sky light comes to us by selective reflection. On this basis we should expect that in the driest air at great heights, where the temperature is low and condensation has but just begun, and the dust particles are rare, there would occur the smallest aqueous particles reflecting light of the feeblest intensity but the largest percentage of polarization. Rayleigh has shown that it is quite possible that the molecules of oxygen and nitrogen constituting the atmosphere may also exercise a diffuse selective reflection, and contribute to the brightness and polarization that are mainly due to aqueous vapours. (See Sky.)
We thus see the theoretical importance of adding photometry and polarimetry to the work of a meteorological observatory. The apparatus to be used in this Connexion will vary somewhat with the exact character of the observations to be made. The most extensive researches that have yet been carried out in this line with a meteorological application in view are those of Jensen, Crova, Cornu, Pickering, Kimball, Nichols, and especially Rubenson, who in fact recommended that polarimetry and photometry should go hand in hand. In order to measure the position of the plane of polarization the Arago polariscope may be used, but, in order to measure the percentage of polarized light, Mascart’s modification of the Savart is better. In order to measure the general brightness of a spot in the sky, Jensen has used a slight modification of the Weber photometer, and in fact Weber himself has applied the same method to the measurement of the daylight. The complete work of Jensen was published in the Schriften of the Scientific Association of Schleswig-Holstein in 1899, and, like the memoir published by Rubenson in 1863, it gives the meteorological conditions in full as a basis for the investigation of the Connexion between sky light and the moisture in the atmosphere. In his work during 1906–1909 with Ångström’s pyrheliometer Mr A. H. Kimball of Washington has advantageously used the Pickering polarimeter, and has shown that the transparency of the air and the polarization of light go hand in hand.
Cyanometer.—The cyanometer devised by Arago to measure the blueness of the sky consisted of an arbitrary scale of blues on a strip of porcelain, with which one could compare the blue of the sky. This comparison, however, is open to many subjective errors. A more satisfactory apparatus is Zollner’s photometer, or some equivalent, in which a patch of white surface is illuminated by any particular tint or combination that may be desired. In fact, Maxwell’s colour-box admits of ready application to the analysis of sky light, and reveals at once the proportions of red, yellow, and blue that may be contained therein.
Dust-counter.—The importance of observing the dustiness of the atmosphere has been especially realized since the invention and use of various forms of apparatus for counting the number of particles of dust in a small volume of air. These inventions are due to Mr John Aitken, of Edinburgh.
The latest form of his apparatus is the very convenient “pocket dust-counter.” In this the air contained in a small receiver is rendered dustless by repeated expansions; the cooling due to expansion forces the vapour to condense upon the dust, which, becoming heavy, falls to the bottom, so that in a short time all is removed. A small stop-cock is now turned, so as to allow a definite small quantity of air to enter and mix with the dustless air in the receiver. The dusty and the dustless airs are now thoroughly mixed, and again the whole quantity within the receiver is expanded, and the dust nuclei fall down by the condensation of vapour upon them. Assuming that every particle of dust is represented by a minute droplet of water, we have but to count the latter; this is easily done by causing all the drops to fall upon a polished plate of black glass, which is divided into small squares by fine lines ruled with a diamond point. Usually each of these squares represents a small fraction of a cubic centimetre of air; thus in one case the number of fog particles averaged 2·6 per square millimetre of the glass plate, and, as the multiplying factor was 100, this corresponded to 260 particles of dust in a cubic centimetre of air. The cleanest air has been found in the West Highlands of Scotland, where 16 particles per cubic centimetre was once recorded as the minimum, while 7600 was the maximum. On the Rigi Kulm, in Switzerland, the cleanest air gave 210, and the dustiest 16,500. On comparing the records of the dust-counter with the record of the apparent state of the air, Mr Aitken found that 500 particles per cubic centimetre corresponded to clear air, and 1900 to a thick haze in which distant mountain tops were hidden. In the cities the particles of soot and effluvia of all kinds act as dust, and both in London and Paris the numbers ran as high as 80, 116, 150 and 210 thousand per cubic centimetre.
Electrical Apparatus.—The electrical phenomena of the atmosphere undoubtedly belong to meteorology, and yet the methods of observation have been so unsatisfactory and the difficulty of interpreting the results has been so baffling that regular observations in electricity are only carried out at a very few meteorological institutions. A general summary of our knowledge of the subject was prepared by J. Elster and H. Geitel for the International Congress held at Chicago in 1893, but since that date the methods and apparatus of observation have received important modifications.
In general the water-dropping collector of Lord Kelvin, arranged for continuous record by Mascart, continues to be the best apparatus for continuous observation at any locality, and a portable form of this same apparatus is used by explorers and in special series of local observations. In order to explore the upper air the kite continues to be used, as was done by A. J. McAdie for the Weather Bureau in 1885 and by Weber at Kiel in 1889. The difference of potential between the upper and lower end of a long vertical wire hanging from a balloon has been measured up to considerable altitudes by Elster and Tuma. In general it is known that negative electricity must be present in the upper strata just as it is in the earth, while the intervening layer of air is positively electrified. The explanation of the origin of this condition of affairs is given in the recent researches of Sir J. J. Thomson (Phil. Mag., Dec. 1899), and his interpretation is almost identical with that now recognized by Elster (see Terrestrial Magnetism, Jan. 1900, iv. 213).
Fig. 6.—Marvin-Hargrave Kite, with Meteorograph in position.
According to these results, if positive and negative ions exist in the upper strata and are carried up with the ascending masses of moist air, then the condensation of the moisture must begin first on the negative ions, which are brought down eventually to the earth’s surface; thus the earth receives its negative charge from the atmosphere, leaving a positive charge or an excess of positive ions in the middle air. (See G. C. Simpson, “Atmospheric Electricity,” Monthly Weather Review, Jan. 1906, p. 16.)
The observations of atmospheric electricity consist essentially in determining the amount and character of the difference of potential between two points not very far distant from each other, as, for instance, the end of the pipe from which the water-drops are discharged, and the nearest point of the earth or buildings resting on the earth. The record may have only an extremely local value, thus the investigations of Professor John Trowbridge of Harvard University, made in conjunction with the U.S. Weather Bureau in 1882–1885, show that the differences vary so much with the winds, the time of day, and the situation of the water-dropper that the mere comparison of records gives no correct idea of the general electrical relationships. It has been suggested that possibly daily telegrams of electric conditions and daily maps of equipotential curves over the North American continent would be of help in the forecasting of storms, but it is shown to be useless to attempt any such system until some uniform normal exposure can be devised. Indeed it has not yet been shown that atmospheric electricity is of importance in dynamic meteorology. (See Atmospheric Electricity.)
Aerial Research.—The exploration of the upper atmosphere is to be regarded as the most important field of research at the present time; the kite and the balloon enable observers and apparatus to be carried to considerable heights, though by no means so far as is desirable. The kite was first used in meteorological work by Alexander Wilson Kites. at or near Glasgow in 1749, and has since then been frequently used by English observers. It was used in 1867 by Abbe in studying the winds under a thundercloud, and in 1877 in ​ studying the depth of the ocean breeze on the coast of New Jersey, but the later revival of interest in the subject Fig.7.—Marvin Kite Reel for hand power. dates from the work done in England in 1882 by E. D. Archibald, who used the kite to carry up anemometers to very considerable heights, and thereby determined the relative movement of the air in the free atmosphere. In 1883 Alexander McAdie used the kite in his studies of atmospheric electricity, Professor Cleveland Abbe proposed to use it for a complete exploration as to temperature, moisture and wind, but W. A. Eddy of New York first forced its varied capabilities upon public attention, and accepted the suggestion of Professor Cleveland Abbe to employ it for meteorological work. Having flown his kites at the Blue Hill Observatory, and having carried up with them the self-registering apparatus devised by Mr Ferguson, Eddy left the further prosecution of this work to Mr Rotch, who has made this a prominent feature of the work at his observatory, having carried up meteorographs to the height of 15,000 feet by means of a series of kites flying in tandem. The officials of the U.S. Weather Bureau have developed the admirable cellular kite, invented by Hargrave of Australia, and Professor Marvin’s works on the theory and construction this form are well known.
The general appearance of the Marvin or Weather Bureau kite, his reel and other apparatus that go with it, and his meteorograph, are shown in Figs. 6, 7, 8. The size ordinarily used carries about 68 sq. ft. of supporting surface of muslin tightly stretched on a light wooden frame. The line, made of the best steel piano-wire, is wound and unwound from a reel which keeps an automatic record
Fig. 8.—Marvin Kite Meteorograph.
of the intensity and direction of the pull. The reeling in and out may be done by hand, but ordinarily demands a small gas-engine. The observer at the reel makes frequent records of the temperature, pressure and wind, the apparent angular elevation of the kite, and the length of wire that is played out. At the kite itself the Marvin meteorograph keeps a continuous record of the pressure, tempera ture, humidity and velocity of the wind. The meteorograph, with its aluminium case, weighs about two pounds, and is so securely lashed behind the front cell of the kite that no accident has ever happened to one, although the kites sometimes break loose and settle to the ground in a broken country many miles away from the reel. On four occasions the line has been completely destroyed by slight discharges of lightning; but in no case has the kite, the observer, or the reel been injured thereby. Of course, such lightning is preceded by numerous rapidly increasing sparks of electricity from the lower end of the wire, which warn the observer of danger. During the six months from May to October 1898, seventeen kite stations were maintained by the U.S. Weather Bureau in the region of the lakes, the Upper Mississippi and the Lower Missouri valleys, in order to obtain data for the more thorough study of atmospheric conditions over this particular part of the country. During these months 1217 ascents were made, and as no great height was attempted they were mostly under 7000 or 8000 feet. There was thus obtained a large amount of information relating to the air within a mile of the earth’s surface. The general gradients of temperature, which were promptly deduced and published by H. C. Frankenfield in 1899 in a bulletin of the Weather Bureau, gave for the first time in the history of meteorology trustworthy observations of air temperatures in the free atmosphere in numbers sufficient to indicate the normal condition of the air.
The kite and meteorograph have now been adopted for use by all meteorologists. The highest flight seems to be that of the 3rd of October 1907, at Mt Weather in Virginia, when 23,110 ft. above sea-level or 21,385 ft. above the reel was attained by the use of 37,300 ft. of wire and 8 kites tandem.
The balloon was used for the scientific exploration of the atmosphere quite freely during the 19th century. The first important voyages were those of Gay-Lussac and Biot at Paris in August and September of 1804. The next important ascent was that of Bixio and Barral in 1850 at Paris. The most remarkable high ascents have been Balloon. those of James Glaisher, 2nd of September 1862, and Berson at Berlin in 1889; on both of these occasions the aeronauts attained altitudes of from 30,000 to 35,000 feet. Systematic ascents at many points in Europe simultaneously on pre-arranged dates were made during the years 1895–1899, and led to the development of a general international system of ascension on pre-arranged days of the year that is now a very important feature in the study of the atmosphere.
Fig. 9.—Chart of Isotherms in Free Air above Trappes.
This diagram shows the height at which the isotherms of 0°, −25°, −40°, −50° C. were encountered on the respective dates. Below the ground-line are given both the dates and the temperatures of the air observed at the ground when the balloon started on each ascent. The isotherms of −40° and −50° are not given for certain ascents, because in these the balloon did not rise high, enough to encounter those temperatures.
Owing to the great risk of human life in these high ascents and especially to the fact that we desire records from still greater heights, efforts have been made to devise self-recording apparatus that may be sent up alone to the greatest heights attainable by free hydrogen balloons carrying the least possible amount of ballast. The pioneer in this new field of work was Léon Teisserenc de Bort of Paris. As these ascensions are made with great velocity, and therefore as nearly vertical as possible, he called them “soundings,” because of their analogy to the mariner’s usage at sea, and his balloon is called a “sounding balloon.” The balloons of silk collapse, those of india-rubber explode, and descend about as rapidly as they ascended, ​ Such balloon soundings have been made not only individually, but, by pre-arranged system, simultaneously in combination with the ascent of free-manned balloons above referred to; and at some places kites have been simultaneously used in order to obtain records for the lower atmosphere. The first experiments in simultaneous work were made in 1896 and 1897, when ascents were made at eight or more points in France, Germany and Russia. These experiments and the discussions to which they gave rise have emphasized the importance of increasing the sensitiveness of the self-recording apparatus, and as far as practicable the rapidity of the ventilation of the thermometers, and of providing more perfect protection against radiation from the sun or to the sky. It is believed that accurate records may be attained up to at least 30,000 metres, but as yet only 26,000 has been attained, and the records brought back are still under considerable criticism on account of instrumental defects. In general the wind that supports a kite also furnishes sufficient ventilation for the thermometer; but in the case of the sounding balloon, which as soon as its rapid rate of ascent diminishes floats along horizontally in the full sunshine, a strong artificial ventilation must be provided. Moreover, the sluggishness of the best thermometers is such that during the rapid rise the records of temperature that are being made at any moment really belong to some altitude considerably below the balloon, and a most critical interpretation of the records is required. Notwithstanding all criticisms, however, the balloon work in all localities agrees in showing the existence of a region above the 10,000-metre level, where temperatures cease to diminish rapidly, and may even become stationary.
III.—Physical and Theoretical Meteorology
The ultimate aim of those who are devoted to any branch of science is to penetrate beyond the phenomena observed on the surface to their ultimate causes, and to reduce the whole complex of observations and empirical rules based upon limited experiences to a simple deductive system of mechanics in which the phenomena observed shall be shown to flow naturally from the few simple laws that underlie the structure of the universe. A correct “theoria” or physical and logical argumentation deducing from primary laws all the phenomena constitutes the noblest achievement of man in science. It is by such works that Newton and Laplace distinguished themselves in astronomy. The development of the true physical and mechanical theories of atmospheric phenomena has made great progress, but is still inferior in completeness to astronomical work, owing to the great complexity of the meteorological problems. The optical and the thermal phenomena have been very satisfactorily elucidated, the electrical phenomena promise to become clear, but the phenomena of motion or aerodynamics have only been elucidated to a limited extent. We must, however, introduce the reader to some of the works that have been published on the subject, in the hope that thereby he will himself be persuaded to further study and stimulated to contribute to our knowledge.
Between the years 1853 and 1861 Professor William Ferrel published in Gould’s Astronomical Journal, Runkle’s Mathematical Monthly, and the American Journal of Science several treatises on the motions of solids and fluids relative to the earth’s surface. His work resulted in the elucidation of the problems of the atmosphere, and in ingenious ways, applicable approximately to such complex cases, and analytically equivalent to the arithmetical method of quadratures or the graphic methods of geometry, he deduced important relations between the density of the air, the barometric pressure, and the attending winds. His essays seemed to show that it might be possible to treat the complex problems of meteorology logically and deductively by analytical, numerical and graphic processes, and his memoirs were the first in which observed average meteorological conditions were properly co-ordinated with the fundamental formulae of mechanics. A beautiful memoir on the steady motions of the atmosphere was published in 1868 in the Astronomische Nachrichten by Professor Adolph Erman, and is now reprinted in vol. ii. of Abbe’s Mechanics of the Earth’s Atmosphere. Espy’s, Coffin’s, Henry’s and Ferrel’s ideas were made the basis of the system of daily weather predictions published by the present writer in 1869 in the Daily Weather Bulletin, of the Cincinnati Observatory. Subsequently this work was taken up by the (government, and greatly enlarged during 1871–1891 by the chief signal officers of the army, and after 1891 by the chiefs of the U.S. Weather Bureau. Ferrel’s writings first attracted the attention of European meteorologists in consequence of reviews published by Hann in the Zeitschrift of the Austrian Meteorological Society in January 1875, but especially after they had been reprinted in a convenient form by the U.S. Signal Office as “Bulletin No. VIII.” In 1881 Ferrel, after finishing his works on the tides for the U.S. Coast and Geodetic Survey, began a new and extensive series of meteorological contributions, three of which were published by the U.S. Coast Survey and the rest by the Signal Office. Stimulated by the urgent needs of the modern weather bureaus throughout the world, and by the beauty of the mathematical problems presented, numerous mathematicians have lately taken up the study of the earth’s atmosphere, so that the literature of the subject is now far more extensive than is generally supposed, including memoirs by Helmholtz, Kelvin, Bjerknes and other famous men.
In addition to the purely mechanical problems, the numerous physical problems have also been carefully treated, both experimentally and mathematically. The problems of radiation have been elucidated by Langley, Hutchins, Angström, Paschen, Violle, Maurer, Crova, Chwolson, Very, Homin, Tamura, Trabort and Coblendz. The thermodynamic problems have been especially developed by Kelvin, Hertz, von Bezold, Ferrel, Brillouin, Neuhoff, Bigelow and Margules. The physical problems involved in the formation of rain-drops have been studied by an optical method by Carl Barus, and with brilliant success, from an electrical point of, view, by C. T. R. Wilson and Sir J. J. Thomson at the Cavendish Laboratory, Cambridge, England.
In a complete study of the mechanics of the earth’s atmosphere we naturally begin by expressing in simple analytic formulae all the various conditions and laws according to which every particle of the air must move. Some of these conditions are local, depending upon the resistances at various points of the earth’s surface; others are of the nature of discontinuous functions, as, for instance, when the ascent of moist air above a certain level suddenly gives rise to condensation and clouds, to the evolution of latent heat, to the precipitation of rain, to the shading of the air and the ground below the clouds, and to the sudden interception of all the solar heat at the upper surface of the cloud. It seems, therefore, incredible that the problems of the atmosphere can ever be resolved by purely analytical methods; there must be devised combinations of numerical and graphical, and possibly even mechanical methods to reproduce the conditions and give us special solutions adapted to particular cases. But even these special methods can only be perfected in proportion as we attain approximate solutions of the simpler problems, and it is in this preliminary work that a good beginning has already been made.
The present state of theoretical physical and mechanical meteorology cannot be fully presented in non-technical English text. It is necessary to employ algebraic formulae, or numerical tables, or graphic diagrams, the former being certainly the least cumbersome and the most generally available. The uniform system of notation devised by Professor F. H. Bigelow, and a very complete summary of the formulae of physical meteorology expressing the results of many recent students will be found in chapters x. and xi. of his Report on the International Cloud Observations, published as vol. ii. of the annual report of the chief of the U.S. Weather Bureau for 1898–1899. The fundamental laws to which the atmosphere is subject are as follows:—
A. The Equation of Elastic Pressure.—The pressure shown and measured by the barometer is an elastic pressure acting in all directions equally at the point where it is measured. By virtue of this elastic pressure a unit volume of air will expand in all directions if not rigidly enclosed, but will cool in so doing. On the other hand, if forcibly compressed within smaller dimensions, it will become warmer. For a given temperature and pressure a unit volume of air of a prescribed chemical constitution will have a prescribed definite weight. The general relations between absolute temperature, pressure and volume are expressed by the formula
| pv＝RT | (1) |
where T expresses the absolute temperature, p the elastic pressure, v the volume, and R is a constant which differs for each gas, being 29·2713 for ordinary pure dry air and 47·060 for pure aqueous vapour, if we use as Fundamental units the kilogram, metre and centigrade degree. This equation is sometimes called the law of Boyle and Charles, or of Gay-Lussac and Marriotte, and it is also known as the equation of condition for true gases, meaning thereby that it expresses the fact that the ideal gas would change its volume directly in proportion to its absolute temperature and inversely in proportion to its elastic pressure. All gases depart from this law; in proportion as they approach the vaporous condition on the one hand, which is brought about by great pressure and low temperature, or the ultra-gaseous condition on the other hand, which obtains under high temperatures and low pressures. The more accurate law of Van der Waals would complicate our problems too much. In place of the absolute temperature T we may substitute the expression 273° C. × (1 + α t), where α is the coefficient of volumetric expansion of the gas for a unit degree of temperature ＝0·00367 and t is the temperature expressed on the centigrade scale.
B. Hypsometric Conditions.—The pressure of the atmosphere at any place depends primarily on the weight of the superincumbent mass of air, and therefore diminishes as we ascend to greater heights. If the air is in motion, that and other considerations come in to affect the pressure; but if the air is quiet relative to the earth’s ​ surface, then the pressure at any altitude is expressed by the so-called barometric or hypsometric formula
| $p=\int _{ho}^{h}-\sigma gdh$ | (2) |
where σ is the density and g the apparent gravity for each layer of air whose vertical thickness is dh. The integral of this formula depends upon the vertical distribution of temperature, and moisture, and gravity; but under the simplest possible assumptions as to these vertical gradients, the following formula was deduced by Laplace and is generally known as his hypsometric formula:—
| $h-h_{0}=18400\left(1+0\!\cdot \!00367t\right)\left(1+0\!\cdot \!378{\frac {e}{p}}\right)\left(1+0\!\cdot \!0026\cos 2\phi \right)$ | (2a) |
$\left(1+{\frac {h+k}{6370191}}\right)\left(1+0\!\cdot \!00157\right)\log {\frac {p_{0}}{p}}$.
In this formula t is the average temperature, e the average vapour tension of the layer of air, p the barometric pressure at the top of the layer, p$_0$, the pressure at the bottom, φ the latitude of the station, h the elevation above sea-level of the lower limit of the stratum, and h$_0$, that of the upper limit. The modifications which this formula needs in order to adapt it to other hypotheses representing more nearly the actual distribution of temperature, moisture and gravity, have been elaborately investigated by Angot in a memoir published in 1899 in Part I. of the Memoirs of the Central Meteorological Bureau of France for the year 1896. Angot, Hergesell and Rykatcheff have also shown that for hypsometric work of any pretensions to accuracy it is simplest and best to use Laplace’s formula for successive thin strata of air, and add together the individual results, rather than attempt a more complex single formula for the whole stratum; yet the latter seems to be essential for work in aerodynamics.
C. Thermodynamic Relations.—The temperature of the air is due to the quantity of molecular energy that is present in the form of heat, but usually there is also present a quantity of molecular energy that is spoken of as latent heat. This latent heat is said to do internal work, such as melting ice or boiling water, while the sensible heat does external work, such as expanding and pushing in all directions. These molecular energies can be transformed into each other over and over again without appreciable loss, and this power of transformation is expressed by the various equations of thermodynamics, of which the fundamental one for our purpose is
| $d\mathrm {Q} =\mathrm {C} _{v}dt+Apdv=\mathrm {C} _{v}dt+\mathrm {ART} dv/v$. | (3) |
This equation expresses the fact that when a quantity of heat measured in calories, dQ, is added to or taken from a mass of dry air, there may result both a change of temperature, dt, corresponding to one portion of the heat, C$_v$dt, and a quantity of external work corresponding to the remaining portion of the heat (Apdv). It usually happens that the quantity of heat in a given mass of air does not remain the same for any length of time; it is diminished by radiation or is increased by absorption, and a certain quantity is lost when rain, snow or hail drops down from the air, while quantity is added to the atmosphere when moisture evaporates and mixes with the dry air as invisible vapour, even the passage of rain-drops down through a lower layer alters the thermal conditions appreciably. The changes due to increase and diminution of moisture are usually small as compared with the great gain due to absorption and convection of solar heat or with the loss by radiation. If these losses and gains are to be taken account of, then the quantity dQ in the above equation is finite and important. On the other hand, in some cases atmospheric processes go on so rapidly or under such peculiar circumstances—for instance, in the interior of a cloud—that the change in the quantity of heat may be considered as temporarily negligible. In these cases dQ is zero; the changes in temperature balance the changes in external work, and the thermal process is said to be adiabatic.
D. The Condition of Continuity.—When a mass of liquid or gas goes through several motions and changes without being disrupted or otherwise broken into smaller portions, and without the formation of either local condensations into solid or liquid masses or of bubbles and vacuous spaces in its interior, and when all the changes that go on proceed by gradual continuous processes as to time, then the mass of the fluid, is subject to the law of continuity as to mass, and the motion of the fluid is continuous as to velocity. These conditions are assumed in elementary hydrodynamics, and are implied in the process of integration, and in the equation of continuity
| ${\frac {\partial \rho }{\partial i}}+{\frac {\partial \left(\rho u\right)}{\partial x}}+{\frac {\partial \left(\rho v\right)}{\partial y}}+{\frac {\partial \left(\rho w\right)}{\partial z}}=0$ | (4) |
where ρ is the density, t is the time and ∂ the ordinary symbol for partial differentiation. But the fact is that meteorologists have to deal entirely with discontinuous external forces such as insolation ceasing at sunset and renewed daily; radiations of heat changing abruptly with land and ocean and cloudiness and snow covering; discontinuous boundary conditions and resistances at the earth’s surface altering at every change from mountains to plains; discontinuous masses changing with additions and abstractions of moisture, rain and snow—all which lead to discontinuous vortex motions and overturnings and rearrangements of the atmospheric strata. The only factors that are continuous for any length of time or extent of area are the rotation of the earth and the attraction of gravitation. In the presence of such difficulties as these we must at present confine ourselves to the solution. of very special local definite problems or to the general statistical problems of our atmosphere.
E. Conditions as to Energy and Motion.—When the total quantity of heat, both latent and sensible, remains constant or changes in a continuous manner, and when the motions are continuous, the mechanical and thermal processes are expressible by ordinary differentials and integrals. Motions of fluids involve both energy and inertia, and are subject to conditions expressed by the following equations of hydrodynamics:—
a. Equations of energy. Let the kinetic energy be T, the potential energy V, the intrinsic energy W: l, m, n, be cosines of the angle between the pressure p, and S the inwardly directed normal to the boundary surface. Then will
| ${\frac {\partial \left(\mathrm {T+V+W} \right)}{\partial t}}=\int \int p\left(lu+mv+nv\right)d\mathrm {S}$. | (5) |
b. Equations of acceleration and inertia. Let P be the potential of the external forces acting on a unit mass of the atmosphere; $\mu$, be the coefficient of viscosity or internal friction. Then will
| $-{\frac {\partial \mathrm {P} }{\partial x}}-{\frac {1}{\rho }}{\frac {\partial p}{\partial x}}={\frac {\partial u}{\partial t}}+u.{\frac {\partial u}{\partial x}}+v.{\frac {\partial u}{\partial y}}+w.{\frac {\partial u}{\partial z}}$ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | (6) |
| $-\mu \left[{\frac {\partial ^{2}u}{\partial x^{2}}}+{\frac {\partial ^{2}u}{\partial y^{2}}}+{\frac {\partial ^{2}u}{\partial z^{2}}}\right]$ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | (6) |
| $-{\frac {\partial \mathrm {P} }{\partial y}}-{\frac {1}{\rho }}{\frac {\partial p}{\partial y}}={\frac {\partial v}{\partial t}}+u.{\frac {\partial v}{\partial x}}+v.{\frac {\partial v}{\partial y}}+w.{\frac {\partial w}{\partial z}}$ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | (6) |
| $-\mu \left[{\frac {\partial ^{2}v}{\partial x^{2}}}+{\frac {\partial ^{2}v}{\partial y^{2}}}+{\frac {\partial ^{2}v}{\partial z^{2}}}\right]$ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | (6) |
| $-{\frac {\partial \mathrm {P} }{\partial z}}-{\frac {1}{\rho }}{\frac {\partial p}{\partial z}}={\frac {\partial w}{\partial t}}+u.{\frac {\partial w}{\partial x}}+v.{\frac {\partial w}{\partial y}}+w.{\frac {\partial w}{\partial z}}$ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | (6) |
| $\mu -\left[{\frac {\partial ^{2}w}{\partial x^{2}}}+{\frac {\partial ^{2}w}{\partial y^{2}}}+{\frac {\partial ^{2}w}{\partial z^{2}}}\right]$ | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | (6) |
Approximate Assumptions and Solutions.—After introducing into the preceding system of fundamental equations (1–6) the actual conditions as accurately as they are known relative to gravity, solar radiation, the rotation of the earth, the viscosity of the air, its mass or inertia, its absorption and radiation of heat, its variable content of moisture, the precipitation of rain and cloud, the mutual inter-conversions of latent and sensible heat, a special difficulty occurs when we attempt to integrate these equations, because we have still to express analytically the initial conditions of the atmosphere as to pressure and temperature, and its boundary conditions as between the rough earth surface on its lower side and the unknown outward surface on its upper side. As the true earth’s surface cannot be represented by any simple algebraic formula, it is customary to assume that it is a uniform sphere, neglecting at least partially, if not wholly, the spheroidal shape. We may first assume that there is no friction between the earth and the air, but must afterwards make allowance for its influence. Thirdly, we assume that the action of the earth’s surface to heat the air and to throw moisture by evaporation into the atmosphere is perfectly uniform. Finally, in many cases we go so far as to assume that the atmosphere is an incompressible rare liquid having a uniform density and a uniform depth of about 8000 metres, corresponding to the average standard density of dry air under a pressure of 760 millimetres and a temperature of 0° C. Even under these simplifications the analytic difficulties have been too great to admit of rigorous solutions, except in a few of the simplest cases.
The treatment of atmospheric problems by Ferrel was followed by an equally ingenious mathematical treatment by Professors Guldberg and Mohn, of Christiana, in two papers published by them in 1876 and 1880 respectively. These authors, like Ferrel, treat isolated portions of the atmosphere and obtain special solutions, which, however, have not the generality that must eventually be demanded in a rigorous and general discussion of the atmosphere movements. Elegant mathematical solutions of our problems were first given in 1882 by Oberbeck, of the university of Halle, in the Ann. Phys. xvii. 128. But even Oberbeck’s solutions are obtained under various simplifying assumptions that restrict their satisfactory application to the daily weather conditions. Oberbeck’s first memoir treats of the mechanics of stationary cyclonic movements. Assuming that the isobars are concentric circles, and that in the outer portion of a cyclone the air has only horizontal movements, while in the inner portion it has only vertical movements, he solves his system of equations for the inner and outer regions of the cyclone separately. He shows that in general the pressure increases on all sides outwards from the centre; the gradient also increases from the centre outwards to the limit of the inner region, whence it diminishes in the outer region and at a great distance becomes inappreciable. In both regions the paths of the wind are curved lines, logarithmic spirals, which cut the isobars or the radial gradient everywhere at the same angle; therefore the movement of the air can be considered as a spiral inflow from all sides towards the centre. But the angle between the wind and the gradient follows different laws in the outer and inner regions, depending in the former on the rotation of the ​ earth and the friction, but in the latter also on the intensity of the ascending current of air. In passing from the outer to the inner surface the wind experiences a sudden change of angle, so that the directions of the winds are not continuous, although the movement and the barometric pressures are assumed to be continuous. This latter peculiarity does not occur in nature, and is undoubtedly an analytical result peculiar to Oberbeck’s method of treating the fundamental equations.
An improvement in the mathematical analysis was introduced by Dr F. Pockels of Göttingen in a memoir published in the Met. Zeit., 1893, pp. 9–19. He deduces equations showing the continuous changes of temperature, pressure, gradient, wind direction, and velocity from the centre of the cyclone to the outer edge of the anticyclone, or, more properly, the peri-cyclone; these, therefore, may reasonably be supposed to have their counterparts in nature. Such mathematical solutions, however, are based upon the assumption that we are dealing with a comparatively small portion of the earth’s surface, which may be considered as a plane having a uniform diurnal rotation and a uniform coefficient of friction. Moreover, the movements in the cyclones and anti-cyclones are assumed to be steady and permanent by reason of the perfect balance of all the forces involved therein. Of course these conditions are not exactly fulfilled, but in general Pockels shows that his theoretical results agree fairly well with the observed conditions as to wind and pressure. He computes the actual distribution of these elements under the assumption that the centre of the anti-cyclone is at latitude 55·5, and that the coefficient of friction is 0·00008, whereas viscosity proper would require only 0·0002. An elegant mathematical presentation of these studies in cyclonic motion is given by W. Wien, Lehrbuch der Hydrodynamik (Leipzig, 1900).
Notwithstanding the fact that these difficult mathematical investigations still lead us to unsatisfactory results, they are yet eminently instructive as showing the methods of interaction of the various forces involved in the motions of the atmosphere. We must therefore mention the interesting attack made by Oberbeck upon the problem of the general circulation of the atmosphere. His memoir on this subject was published in the Sitzungsberichte of the Academy of Sciences at Berlin in 1888. The fundamental assumption in this memoir implies that there is a general and simple system of circulation between the equatorial and the polar regions, but the eventual solution of the problem leads Oberbeck to two independent systems of winds, an upper and a lower, without any well-defined connexion at the polar and equatorial ends of these two currents, so that after all they are not rigorously re-entrant. Among the hypotheses introduced in the course of his mathematical work, the most important, and perhaps the one most open to objection, is that the distribution of temperature throughout the atmosphere in both the upper and lower strata can be represented by the equation T＝A + B (1−3 cos$^2$ θ). Undoubtedly this equation represents observations in the lower strata near the surface of the earth, but the constants that enter into it, if not the form itself, must be changed for the upper strata. The solution arrived at by Oberbeck gives the following equations representing the components of the movement of the atmosphere toward the zenith V, toward the north N, and toward the east O:—
* V＝C(1−3 cos$^2$ θ) 𝑓σ
* N＝−6 C cos θ sin θ φ σ
* O＝D[sin θ(1 − 3 cos$^2$θ)𝑔σ + 6 cos$^2$θγσ].
In accordance with these equations he deduces the general circulation of the atmosphere as follows: In the lower current the air flows from the polar regions eastward until it reaches the parallel of 30° or 40°; it then turns directly towards the equator, and eventually westward, until at the equator it becomes a strong east wind (or a so-called west current). In the upper layer the movement begins as an east wind, turns rapidly to the north at latitude 20° or 30°, and then becomes a south-west wind (or north-eastern current) in the northern hemisphere, but a north-west wind (and south-eastern current) in the southern hemisphere. Of course in the higher strata of air the currents must diminish in strength. In a second paper in the same year, 1888, Oberbeck determines the distribution of pressure over the earth’s surface as far as it is consistent with his system of temperatures and winds. His general equation shows that as we depart from the equator the pressure must depend upon the square and the fourth power of the cosine of the polar distance or the sine of the latitude, and in this respect harmonizes with Ferrel’s work of 1859, although more general in its bearings. By comparing his formulae with the observed mean pressure in different latitudes, Oberbeck obtains the general angular velocity of the air relative to the earth, i.e. 0·0292 (sin$^2$φ−0·0836), which is quite small and is a maximum (4·6 metres per second) at latitude S. 56° 27′. H. Hildebrandsson (1906) showed that observations do reveal an east wind prevailing above the equatorial belt of calms.
Contemporary with Oberbeck’s admirable memoirs are those by Professor Diro Kitao, of the university of Tōkyō, who, as a student of mathematics in Germany, had become an expert in the modern treatment of hydrodynamic problems. In three memoirs published by the Agricultural College of the university of Tōkyō in the German language in the years 1887, 1889 and 1895, he develops with great patience many of the minutiae of the movement of the earth’s atmosphere and cyclonic storms. The assumptions under which he conducts his investigations do not depart from nature quite so far as those adopted by other mathematicians. Like Ferrel, he adheres as closely as possible to the results of physical and meteorological observations; and although, like all pure mathematicians, he considers Ferrel as having departed too far from rigorous mathematical methods, yet he also unites with them in acknowledging that the results attained by Ferrel harmonize with the meteorology of the earth.
The fact is that the solution of the hydrodynamic equations is not single, but multiplex. Every system of initial and boundary conditions must give a solution appropriate and peculiar to itself. The actual atmosphere presents us with the solution or solutions peculiar to the conditions that prevail on the earth. Entirely different conditions prevail on Jupiter and Saturn, Venus and Mars, and even on the earth in January and July, and therefore a wholly new series of solutions belongs to each case and to each planet of the solar system. It matters not whether we attempt to resolve our equations by introducing terrestrial conditions expressed by means of analytical algebraic formulae, and integrate the equations that result, or whether we adopt a graphic process for the representation of observed atmospheric conditions and integrate by arithmetical, geometrical or mechanical processes. In all cases we must come to the same result, namely, our resulting expressions for the distribution of pressure and wind will agree with observations just as closely as our original equations represented the actual temperatures, resistances and other attending conditions. In the last portion of Kitao’s third memoir he gives some attention to the interaction of two cyclonic systems upon each other when they are not too far apart in the atmosphere, and shows how the influence of one system can be expressed by the addition of a certain linear function to the equations representing the motions of the other. He even gives the basis for the further study of the extension of cyclonic storms into higher latitudes where conditions are so different from those within the tropics. Finally, he suggests in general terms how the resistances of the earth’s surface, in connexion with the internal friction or viscosity of the air, are to be taken into consideration, and shows under what conditions the assumptions that underlie his own solutions may, and in fact must, very closely represent the actual atmosphere.
The General Circulation of the Atmosphere.—If the meteorologist had a sufficient number of observations of the motions of the air to represent both the upper and lower currents, he would long since have been able to present a satisfactory scheme showing the average movement of the atmosphere at every point of its course, and the paths of the particles of air as they flow from the poles to the equator and return, but hitherto we have been somewhat misled by being forced to rely mainly on the observed movements of clouds. This motion has been called the general circulation of the atmosphere; it would be a complex matter even if the surface of the earth were homogeneous and without special elevations, but the actual problem is far different. Something like this general circulation is ordinarily said to be shown by the monthly and annual charts of pressure, winds and temperature, such as were first prepared and published by Buchan in 1868, and afterwards in Bartholomew’s Physical Atlas of 1899. We must not, however, imagine that such charts of averages can possibly give us the true path of any small unit mass of air. The real path is a complex curve, not re-entrant, never described twice over, and would not be so even if we had an ideal atmosphere and globe. It is a compound of vertical and undulatory movements in three dimensions of space, variable as to time, which cannot properly be combined into one average.
The average temperatures, winds and pressures presented on these charts suggest hypothetical problems to the student’s mind quite different from the real problems in the mechanics of the atmosphere—problems that may, in fact, be impossible of solution, whereas those of the actual atmosphere are certainly solvable. The momentary condition presented on any chart of simultaneous observations constitutes the real, natural and important problems of meteorology. The efforts of mathematicians and physicists have been devoted to the ideal conditions because of their apparent simplicity, whereas the practical problems offered by the daily weather chart are now so easily accessible that attention must be turned towards them. The most extensive system of homogeneous observations appropriate to the study of the dynamics of the atmosphere is that shown in the Daily Bulletin of International Simultaneous Observations, published by the U.S. Signal Service in the years 1875–1384, with monthly and annual summaries, and a general summary in “Bulletin A,” published by the U.S. Weather Bureau in 1893. The study of these daily charts for ten years shows how the general circulation of the atmosphere differs from the simple problems presented in the idealized solutions based on monthly and annual averages. The presence of a great and a small continent, and a great and small ocean, and especially of the moisture, with its consequent cloud and rain, must enter into the study of the problem of the general circulation. The most prominent features of the general circulation of the atmosphere are the system of trade winds, north-easterly in the northern tropics and south-easterly in the southern tropics, the system of westerly winds beyond the trade-wind region, namely, north-westerly in the north temperate and south-westerly in the south temperate zone, and again the system ​ of upper winds shown by the higher clouds, namely, south-westerly in the northern hemisphere and north-westerly in the southern.
Halley in 1680, and Hadley in 1735, gave erroneous or imperfect explanations of the mechanical principles that bring about these winds. As some errors in regard to this subject are still current, it is necessary to say that it is erroneous to teach that atmospheric air weighs less on being heated, or by reason of the infusion of more moisture, and that therefore the barometer falls. The addition of more moisture must increase its weight as a whole; heat, being imponderable, cannot directly affect its weight either way. We are liable to disseminate error by the careless use of the world “lighter,” since it means both a diminution in absolute weight and a diminution in relative weight or specific gravity. Heat and moisture may diminish the specific gravity of a given mass of air by increasing its volume, or of a given volume by diminishing its mass, but neither of them can of themselves affect the pressure shown by the barometer so far as that is due to the weight of the atmosphere. It is not proper to say that by warming the air, thereby diminishing its specific gravity and causing it to rise, so that colder air flows in to take its place, we thereby diminish the barometric pressure. It is easily seen that in the expression p＝RT/v, which, as we have before said, is the law of elasticity, T and v may so vary as to counterbalance each other, and allow the pressure p to remain the same. Within any given room or other enclosure hot air may rise on one side, flow over to the opposite, cool and return, and the circulation be kept up indefinitely without any necessary change in pressure. The problem of the relation between wind and pressure in the free atmosphere is more complex than this, and involves the consideration of the inertia of the masses of air that are in motion with the earth around its axis. The air is so extremely mobile that it moves quickly in response to slight differences in pressure that cannot be detected by ordinary barometric measurement. The gradients or differences of pressure that are shown on meteorological charts are not directly, but only very indirectly, due to buoyancy, as caused by heat and moisture. The pressure gradients, so-called, are not merely the prime causes of the winds, but are equally and essentially the results of the winds. They are primarily due to the fact that the atmosphere is rapidly revolving with the surface of the earth around the earth’s axis, while at the same time it may be circulating about a storm centre. Inappreciable differences of pressure start the winds in motion, and the air moves towards the region of low pressure, just as in the pneumatic despatch tubes the flow of air towards the low pressure carries the packages along. But in the free air, where there are less important resistances to be overcome, the freedom of motion is greater than in these pneumatic tubes. No sooner is the atmosphere thus set in motion by pressure from all sides towards the central low pressure than it rapidly acquires a spiral circulation, and thereby there is superimposed (in the northern hemisphere) a decided diminution of pressure on the left hand side of the wind, and an equally rapid increase on the right hand side. The gradient of pressure in the direction of the wind overcomes resistances, but the gradient of pressure, perpendicular to the direction of the wind, is far greater than that in the direction of the wind, and is that which produces the areas of decided low pressures that appear as storm centres on the daily weather map. Therefore, in general, the wind cuts across the charted isobars in oblique directions and at angles which are nearly 90° for the feeble winds far removed from the centres, but which are almost zero for the most violent winds near the low centre. The winds acquire this spiral circulation for two reasons—(a) all straight line, gusts or jets in fluids, subject to any form of resistance, necessarily break up into rotating spirals whenever the velocity exceeds a certain limit, because the resistances deprive some particles of the fluid of a little more of their original velocity and energy than the other particles near by them, and thus the whole series is drawn away from linear into curvilinear paths; (b) in addition to their rectilinear motions the particles of air have a rapid circular motion in common with the whole atmosphere diurnally around the earth’s axis. Therefore every particle of moving air comes under the influence of a set of forces depending on its own rate of motion relative to the earth’s surface and its position relative thereto. If the particles are moving eastward, viz. in the same direction as the earth’s diurnal rotation, then the result is as though the atmosphere were rotating more rapidly than does the earth at present; consequently the particles of wind push toward the equator as though the atmosphere were trying to adopt a more flattened spheroidal figure corresponding to its greater velocity of rotation. If the particles are moving westward, on the other hand, it is as though the atmosphere were revolving less rapidly than the earth, and as though the flattened spheroid of revolution due to the present rate of rotation were more decidedly flattened than need be; consequently the particles of air push towards the poles. If the winds blow toward either pole, then their initial moment of inertia about the earth’s axis, due to the initial radius and the eastward movement of the air, must be retained; consequently, as the air advances into higher latitudes and to smaller circles of diurnal rotation its velocity must increase, and must carry the particles to the east of their initial meridians. If the wind blow towards the equator its initial moment of inertia must be applied to a larger radius, and its velocity correspondingly diminished so that it is left behind or falls away somewhat to the west. “The reasoning of those who in attempting to explain the trade winds assume that the atmosphere in moving toward) or from the equator has a tendency to retain the same original linear velocity is erroneous” (Ferrel’s Movements of Fluids, 1859). In general the winds tend to retain their moments of inertia, and in the northern hemisphere must necessarily always be deflected continuously toward the right hand. The exact amount of this deflection was first distinctly stated by Poisson, as applied to the movements of projectiles; it was also announced by Tracy of New Haven in 1843, but was first applied to the atmosphere by Ferrel, who deduced its meteorological consequences. This law is not to be confounded with that of Buys Ballot, who in 1861 deduced from his observations in Holland the rule that the gradient of pressure between two stations for any day would be followed in twenty-four hours by a wind perpendicular to that gradient, and having the lower pressure on the left hand. Buys Ballot’s law was in the nature of a rule for prediction, and was modified by Buchan 1868, who enunciated the following: “The wind blows towards the regions of low pressure, but is inclined to the gradient at an angle which is less than 90°.” In this form Buchan’s law was an improvement upon the laws current among cyclonologists, who had assumed that, in a rough way, the wind blew in circles around the low centre, and was therefore sensibly at right angles to the gradient. It ought, however, to be said that Redfield throughout the whole course of his studies, from 1831 to 1857, never gave adherence to this view, and in fact for the severer portions of hurricanes determined the average inclination of the movements of the lower clouds at, New York City to be about 7° inwards as compared with the truly circular theory. Now Ferrel’s law explains mechanically the reason why the winds do not blow either radially or circularly, and gives the means for determining their inclination to the isobars in all portions of the cyclone and for various degrees of resistance by the earth’s surface. The general proposition that the barometric gradients on the weather map are not those that cause the wind, but are, properly speaking, the result of the combined action of the wind, the rotation of the earth, and the resistances at the earth’s surface, as first explained by Ferrel, seems to have been neglected by meteorologists until brought to their attention repeatedly by Professor Abbe between 1869 and 1875, and especially by Professor Hann in a review of Ferrel’s work (see Met. Zeit. 1874). The independent investigations of Sprung, Koeppen, Finger, and especially Guldberg and Mohn, confirm in general the correctness of Ferrel’s law.
It is quite erroneous to imagine that the low pressures in storm areas and in the polar regions, and especially the belt of low pressure at the equator are due simply to the diminution of the density and weight of the air by the action of its warmth or its moisture, or to the abundant rainfall as relieving the atmosphere of the weight of water. It has been clearly shown that none of these operations can directly affect the barometric pressure to any appreciable extent, but that high and low pressure areas, as we see them on the weather map, owe their existence entirely to the mechanical interaction of the diurnal rotation of the earth and the motions of the atmosphere. The demonstration of this point by Ferrel in 1857 is considered to have opened the way for modern progress in theoretical meteorology.
Both Espy and Hann have abundantly shown that the formation and downfall of rain do not produce any low barometric pressure unless they produce a whirling action of the wind—that, in fact, the latent heat evolved by the condensation of vapour into rain may so warm up the cloud as to produce a temporary rise in pressure even at the surface of the ground, due to the outward push produced by the sudden expansion of the cloud. [The details of the thermodynamics of, this operation have been elucidated by Wm. von Bezold.] The force with which the wind presses to the right or tends to be deflected in that direction is 2nv sin φ, while the curvature of the path of the wind is measured by its radius of curvature, which is v/2n sin φ, where v is the velocity of the wind, n is the equatorial velocity of the earth’s rotation, and φ is the latitude. It will be seen from this that there is no deflection at the equator; therefore, as Ferrel stated, there is no tendency to the formation of great whirlwinds at the equator, hence hurricanes and typhoons are rarely found within 10° of the equator.
Ferrel frequently speaks of an anti-cyclone, whereby he means the area of high pressure just outside of a strong cyclonic whirl; the expression peri-cyclone would have been more appropriate and is sometimes substituted. The term anti-cyclone, as first introduced by Galton in 1863 is applied to a system of winds blowing out from a central area of high pressure, and this is the common usage of the term in modern meteorology. The term cyclone among meteorologists and throughout English literature, except only a few cases in the United States, is equivalent to the older usage of whirlwind, and it is unfortunate that misunderstandings often arise because local usages in America apply the word cyclone to what has for centuries been called a tornado. The mechanical principles discussed by Ferrel led him to an algebraic relation between the barometric gradient G, the wind velocity v, the radius of curvature of the isobar r, and the inclination i between the wind and the isobar, which is ​ expressed by the following formula for the pressures that prevail at sea-level:—
G＝[(2n sin φ + cos iv/r )v sec i ] / [83,000,000].
A popular exposition of this and other results of Ferrel’s work is given by Archibald in Nature (May 4, 1882), and still better in Ferrel’s Treatise on the Winds (New York, 1889, and later editions).
The charts of mean annual pressure, temperature and wind above referred to show certain broad features that embrace the whole system of atmospheric circulation, viz. the low pressures at the equator and the poles, the high pressures under the tropics, the trade winds below and the anti-trades above, with comparative calms under the belts of equatorial low pressure and tropical high pressure. The first effort of the mathematician was to explain how these mean average conditions depend upon each other, and to devise a system of general circulation of the wind consistent with the pressures, resistances and densities. But, as we have already said, such a system may be very far from that presented by the real atmosphere, and little by little we are being led to a different view of the question of the general circulation. The earlier students of storms generally accepted one of two views as to the cause of whirlwinds. They were either (1) formed mechanically between two principal currents of air flowing past each other, the so-called polar and equatorial currents; or (2) they were due to the ascent of buoyant air while the heavier air flowed in beneath, the whirling motion being communicated by the influence of the rotation of the earth, or by the greater resistances on one side than on the other. In order to explain why hurricanes and typhoons exist continuously for many days, or even weeks, it is necessary that there should be a source of energy to maintain a continued buoyancy and rising current at the centre, and this was supposed to be fully provided for by Espy’s proof of the liberation of latent heat consequent on the formation of cloud and rain. To this latter consideration Abbe in 1871 added the important influence of the sun’s heat intercepted at the upper surface of the cloud. At this stage of the investigation the whirlwind is but an incident in the general circulation of the atmosphere, but further consideration shows that it ought rather to be regarded as an essential portion of that circulation, and that when temperature gradients and density gradients exceed a certain limit the formation of great whirlwinds is inevitable. Therefore an atmosphere containing several whirlwinds is just as truly a system of general circulation in the one case as an atmosphere without a whirlwind is in the other. The formation of rain, the evolution of latent heat, and even the absorption of heat at the upper surface of the cloud really constitute a normal general circulation in this special case. We may therefore consider a system of vortices, which is a system of discontinuous motions, as the most natural solution of the equations of motion—but the mathematical treatment of this form of motion has not yet been sufficiently well developed, for the discontinuity relates not only to the motion but to the thermal conditions and the interchange of vapour and water.
In 1890 Professor Hann published a careful analysis of the actual temperature conditions prevailing over an extensive area of high pressure in Europe, and showed that the temperatures of the upper strata in both high and low areas, namely, in anti-cyclones and cyclones are often directly contrary to those supposed to prevail by Espy and Ferrel. This study necessitated a more careful examination into the radiation of heat from the dust and moisture of the atmosphere, and Professor Abbe seems to have shown that in areas of high pressure and clear weather a very slow descending movement throughout each horizontal layer gives time for a radiation of heat that explains the anomalies of temperature, but the dynamic phenomena still remained unexplained. On the other hand, von Helmholtz in several memoirs of 1888–1891 showed that waves or billows may be formed in the atmosphere of great extent at the dividing surface between upper and lower strata moving in different directions and with different velocities. Under specific conditions these billows may become like the breakers and caps of waves of the ocean when driven by the wind. The hypothesis that these aerial breakers correspond to our troughs of low pressure and the storms experienced in the lower atmosphere seemed very plausible. As these billows are formed between upper and lower air currents of great extent, which themselves represent a large portion of the horizontal circulation between the poles and the equator, it results that if von Helmholtz’s suggestion and Hann’s hypothesis are correct then all general storms must be considered as essentially a part of the general circulation rather than as caused by the vertical circulation over any locality. It must occur to everyone to adopt the intermediate view that, on the one hand, the local vertical circulation, with its clouds, rain, hail and snow, and evolution of latent heat, and, on the other hand the waves and whirls in the general circulation, mutually contribute toward our storms and fair weather. It only remains to allot to each its proper importance in any special case.
Undoubtedly aerial billows, and the clouds that must frequently accompany them, exist everywhere in the earth’s atmosphere. Perhaps their extent and importance are not properly appreciated. A voyage around the Atlantic Ocean in 1889–1890, made by Professor Abbe, specifically to study cloud phenomena, revealed many remarkable cases, such as the cumulus rolls that, extend in a remarkably symmetrical series from the island of Ascension westwards for 100 m. in the south-easterly trades, or the delicate fields of cirro-cumuli that extend from the islands of Santa Lucia. and Barbados for 200 m. eastwards under favourable conditions. The mixtures and vorticose motions going on within aerial billows to form these clouds have been interpreted by Brillouin. In the further elucidation of the mechanism of storms Hann showed that every study of observational material confirms the conclusion that the descent of denser cool dry air is as important as the ascent of warm moist air, and that although the evolution of latent heat within the clouds of a storm may explain the local cloud phenomena, yet it will not explain the storm as a whole. The first “norther or blizzard” that was charted at Washington in November 1871 was at once seen to be a case of the underflow of a thin layer of cold dry air descending from high altitudes above Canada on the eastern slope of the Rocky Mountains, but driven southward by an excess of centrifugal energy added to a moderate barometric gradient. It was seen that in such grand overturnings the descent of masses implies energy communicated by the action of gravity, but the whole mechanics of this process was not clear until the publication by Margules of his memoir Über die Energie der Stürme (Vienna, 1905), which will be referred to hereafter.
Mathematics have, almost without exception, assumed a so-called steady condition in the motion of the atmosphere in order to achieve a successful integration of the general equations of motion. The restrictions within which Helmholtz and others have worked, and the limits within which their results are to be accepted, have been analysed by Dr E. Herrmann in a memoir of which a translation is published in the bulletin of the American Mathematical Society for June 1896. Of course Herrmann’s own investigation is also based upon certain simplifying hypotheses, such as the absence of outside disturbing forces and of viscosity and friction, a homogeneous ellipsoidal surface, and a uniform initial temperature and rate of revolution corresponding to an initial state of equilibrium. If now the initial static equilibrium be disturbed by introducing a different distribution of temperature, viz. one that varies with altitude and latitude, but is uniform in longitude along any circle of latitude, then the first question is whether the atmosphere can settle down to a new state of static equilibrium. Herrmann shows that in general it cannot do so, but that the new state and the future states can only be those of motion and dynamic equilibrium. If, however, there be no external forces acting on the atmosphere, then in one case static equilibrium relative to the earth can occur, namely, when the new temperatures are so distributed in the atmosphere as to satisfy the equation
$\int$ ρ r $^2$ w d V＝M,
in addition to the ordinary equations of elasticity, inertia and continuity previously given, and to those representing the boundary conditions, M being the total amount of inertia of the atmosphere relative to the axis of rotation. In general, the movements in the atmosphere must consist not only of an interchange between the poles and the equator, but also of east and west motions, and there must therefore be a different rate of diurnal rotation for each stratum. The second step in this inquiry is, Can these movements become perfectly steady with this unvarying or steady distribution of temperature? In other words, Can the temperature and the movements be so adjusted to each other that each shall remain invariable within any given zone of latitude? The reply to this is, that if they are to become thus adjusted they must satisfy a certain differential equation, which itself shows that steady motions and stationary temperatures cannot exist if there be any north or south component. Apart from the fact that Herrmann assumes no friction, it would seem that he has proved that steady motions and stationary pressures cannot exist in the atmosphere over a homogeneous spherical surface, and presumably the same result would follow of a rotating globe for the irregular surface of the actual globe. The motions of the real atmosphere must therefore consist of irregular and periodic oscillations and discontinuous whirls and rolls superimposed upon more uniform, regular progressions, but never repeating themselves. Consequently, the conclusions deduced by those who have assumed that steady conditions are possible must depart more or less from meteorological observations. There is a general impression that the belt of low pressure at the equator and the low areas at the poles and the high pressures under the tropics are pseudo-stationary, and really represent what would be steady conditions if we had an ideal smooth globe; but Herrmann’s researches show that the unsteadiness observed to attach to these areas under existing conditions would also attach to them under ideal conditions. They really have and must have irregular motions, and we, by taking annual averages, obtain an ideal annual distribution of pressure, temperature and wind that does not represent any specific dynamic problem. The averages represent what is considered proper in climatology, but are quite, improper and misleading from a dynamic point of view, and have no logical mechanical connexion with each other.
Closely connected, with this study of steady motions under a constant supply and steady distribution of solar heat comes the further question as to what regular variations in atmospheric pressure and wind can be produced by regular seasonal variations ​ in the heat received from the sun; for instance, what variation in the earth’s atmosphere corresponds to the periodic variations of the solar spots. The general current of Helmholtz’s investigations shows that no periodic change in the earth’s atmosphere can be maintained for any length of time by a given periodic influence outside of the atmosphere. On the other hand, it is barely possible that wave and vortex phenomena on the sun’s surface may have the same periodicities as regular phenomena in the earth’s atmosphere, so that there may be a parallelism without any direct connexion between the two.
An important paper on the application of hydrodynamics to the atmosphere is that by Professor V. Bjerknes, of Stockholm, Sweden, which was read in September 1899 at Munich, and is now published in an English translation in the U.S. Monthly Weather Review, Oct. 1900 (“On the Dynamic Principle of Circulatory Movements in the Atmosphere”). In this memoir Bjerknes applies certain fundamental theorems in fluid motion by Helmholtz, Kelvin and Silberstein, and others of his own discovery to the atmospheric circulation. He simplifies the hydrodynamic conceptions by dealing with density directly instead of temperature and pressure, and uses charts of “isosteres,” or lines of equal density, very much as was proposed by Abbe in 1889 in his Preparatory Studies, where he utilized lines of equal buoyancy or “isostaths,” and such as Elkholm published in 1891 as “isodenses” and which were called “isopyks” by Müller-Hauenfels. Bjerknes has thus made it practicable to apply hydrodynamic principles in a simple manner without the necessity of analytically integrating the equations, at least for many ordinary cases. He also gives an important criterion by which we may judge in any given case between the physical theory, according to which cyclones are perpetually renewed, and the mechanical theory, according to which they are simply carried along in the general atmospheric current. Bjerknes’s paper is illustrated by another one due to Mr Såndström, of Stockholm, who has applied these methods to a storm of September 1898 in the United States The further development of Bjerknes’s methods promises a decided advance in theoretical and practical meteorology. His profound lectures at Columbia University in New York and in Washington in December 1905 aroused such an interest that the Carnegie Institution at once assigned the funds needed to enable him to complete and publish the applications to meteorology of the methods of analysis given in detail in Bjerknes’s Vorlesungen (Leipzig, i. 1900, ii. 1902), and in his Recherche sur les champs de force hydrodynamiques (Stockholm), Acta Matematica (Oct. 1905). In his lectures of 1905 at Columbia University Bjerknes treated the atmosphere as a continuous hydrodynamic field of aerial solenoids and forces acting on them, to which vector analysis can be applied, as was done by Heaviside for electric and magnetic problems. Every material point is a small spherical mass of air free to extend or contract with pressure, temperature or moisture; free to rotate about each of three movable axes passing through its centre and to move along and revolve about three fixed axes through the centre of the earth. These numerous degrees of freedom are easily expressed in Bjerknes’s notation and by his typical equations of motion. The density at any point is recognized as the fundamental “dimension” controlling inertia and movement. The observed atmospheric condition at any moment is shown by a series of isodense surfaces intersecting potential surfaces of equal gravity and thus forming a continuous mass of unit solenoids. This field becomes either an electric, magnetic or hydrodynamic field according to the interpretation assigned to the notations—in either case the analytical processes are identical. The analogies or homologies of these three sets of phenomena are complete throughout, and those of one field elucidate or illustrate those of the two other fields. This is the outcome of the study of such analogies begun by Euler, Helmholtz, Hoppe, and extensively furthered by Maxwell and Kelvin, but especially by C. A. Bjerknes. The homologies or analogies by V. Bjerknes are given at p. 122 of his Recherche (1905), and include the following six triads:—
| I. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hydrodynamics | velocity of unit mass |
| I. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Magnetics | magnetic induction |
| I. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Electrics | electric induction |
| II. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hydrodynamics | intensity of the field |
| II. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Magnetics | intensity„ of the„ field„ |
| II. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Electrics | intensity„ of the„ field„ |
| III. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hydrodynamics | velocity of energy |
| III. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Magnetics | intrinsic magnetic polarization |
| III. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Electrics | intrinsic„ electric polarization„ |
| IV. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hydrodynamics | velocity of expansion per unit volume |
| IV. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Magnetics | density of the true magnetic mass |
| IV. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Electrics | density„ of the true „ electric tic mass„ |
| V. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hydrodynamics | density of the dynamic vortex |
| V. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Magnetics | density„ of the„ steady magnetic current |
| V. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Electrics | density„ of the„ steady„ magnetic current„ |
| VI. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Hydrodynamics | specific volume |
| VI. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Magnetics | magnetic permeability |
| VI. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$ | Electrics | dielectric constant |
which have been slightly rectified by Dr G. H. Ling, Am. Jour. Math. (1908). In the application of Bjerknes’s methods of study to the daily weather map Såndström draws special maps to represent the solenoids and the forces. Barometric pressures are reduced from the observing stations not only down to sea-level but up to other level surfaces of gravity. The differences between these level surfaces represent the work done in raising a unit mass from one level to the next (see Bjerknes and Såndström, A Treatise on Dynamic Meteorology and Hydrography, Washington, 1908).
The Diurnal and Semi-diurnal Periodicities in Barometic Pressure.—For a long time attempts were made to explain the periodic variations of the barometer by a consideration of static conditions, but it is now evident that this problem, like that of the circulation of the atmosphere, is a question of aerodynamics. A most extensive series of researches into the character of the phenomena from an observational point of view has been made by Hann, who gave a summary of our knowledge of the subject in the Met. Zeit. for 1898, translated by R. H. Scott in the Quart. Jour. Roy. Met. Soc. (Jan. 1899) (see also an important addition by Hann and Trabert in the Met. Zeit., Nov. 1899, and the summary of his results as given in his Lehrbuch, 1906). Hann has shown that at the earth’s surface three regular periodic variations are established by observation, viz. the diurnal, semi-diurnal and ter-diurnal. On the higher mountains these variations change their character with altitude. (1) At the equator the diurnal variation is represented by the formula 0·30 mm. sin (5°+x), where x is the local hour angle of the sun. In higher latitudes either north or south the coefficient A$_1$＝0·30 mm. diminishes, but the phase angle, 5°, varies greatly, generally growing larger. It is therefore evident that this diurnal oscillation depends directly on the hour angle of the sun, and probably, therefore, principally on the amount of heat and vapour received by the atmosphere from the ocean and the ground at any locality and season of the year. It is apparently but little affected by the wind, but somewhat by altitude above sea; the amplitude diminishes to zero at a certain elevation, and then reappears and increases with the opposite sign; the phase angle does not change. (2) Superimposed upon this diurnal oscillation is a larger semi-diurnal one, which goes through its maximum and minimum phases twice in the course of a civil day. The amplitude of this variation is largest in equatorial regions, and is expressed by the formula A$_2$＝(0·988 mm.–0·573 mm. sin$^2$φ) cos$^2$φ as given by Hann, or A$_2$＝(0·92 mm.–0·495 sin$^2$φ) cos$^2$φ as revised by Trabert. This amplitude also may be considered as variable along each zone of latitude having a maximum value on certain central local meridians. The times at which the semi-diurnal phases of maximum and minimum occur are subject to laws different from those for the diurnal period. Within the tropics the phase angle is 160° and at 50° N. it is 147°, and between these limits it seems to be the same over the whole globe, so that the phase does not depend clearly upon the hour angle of the sun or on the local time. The amplitudes appear to depend on the excess of land in the northern hemisphere as compared with the water and cloud of the southern hemisphere. The amplitude also varies during the year, being greatest at perihelion and least at aphelion. Hann suggests that this is an indirect effect of the sun’s heat on the earth, as the northern hemisphere is hotter when the earth is in aphelion than is the southern hemisphere when the earth is in perihelion, owing to the preponderance of land in the north and water in the south. (3) The ter-diurnal oscillation has the approximate value shown by the formula 0·04 mm. sin (355°+3x). The phase angle is sensibly the same everywhere, and the amplitude varies slightly with the latitude. Both phase and amplitude have a pronounced annual period which is as remarkable as that of the semi-diurnal oscillation; the maximum amplitude occurs in January in the northern hemisphere, and in July in the southern.
The physics of the atmosphere has not yet been explored so exhaustively as to explain fully these three systematic barometric variations, but neither have we as yet any necessity for appealing to some unknown cosmic action as a possible cause of their existence. The action of the solar heat upon the illuminated hemisphere, and the many consequences that result therefrom, may be expected to explain the barometric periods. The variations of sunshine and cloud must inevitably produce periodic variations of temperature, moisture, pressure and motion, whose exact laws we have not as yet fathomed. Among the many methods of action that have been studied or suggested in connexion with the barometric variations the most important of all is the so-called tidal wave of pressure due to temperature. Laplace applied his investigations on the tides to the gravitational tide of the ocean, and when he passed to the corresponding solar and lunar gravitational tides of the atmosphere he was able to show that they must be inappreciable, unless, indeed, certain remarkable relations existed between the circumference of the earth and the depth of the atmosphere. As these relations do not exist, it is generally conceded as certain that the gravitational tides, both diurnal and semi-diurnal, cannot exceed a few thousandths of an inch of barometric pressure. On the other hand, the same process of mathematical reasoning enables us to investigate the action of the sun’s heat in producing a wave of pressure that has been called a pressural tide, due to the expansion of the lower layer of air on the illuminated half of the globe. The laws that must govern these pressural tides have been investigated by Kelvin, Rayleigh (Phil. ​ Mag., Feb. 1890), and especially by Margules (Vienna Sitz. Ber. 1890–1893). The two latter have shown the truth of a proposition enunciated by Kelvin in 1882, without demonstration, to the effect that the free oscillation produced by a relatively small amount of tide-producing force will have an amplitude that is larger for the half-day term than for the whole-day term. They therefore explain the diurnal and semi-diurnal variations of the barometric pressure as simple pressural tides or waves of expansion, originally produced by solar heat, but magnified by the resonance between forced and free waves in an atmosphere and on a globe having the specific dimensions of our own. The analytical processes by which Laplace and Kelvin arrived at this special solution of the tidal equation were objected to by Airy and Ferrel, but the matter has been, as we think, most fully cleared up by Dr G. H. Ling, in a memoir published in the Annals of Mathematics in 1896. He seems to have shown that, although a literally correct result was attained by Laplace in his first investigation, yet his methods as presented in the Mécanique céleste were at fault from a rigorous analytical point of view. The process by which a diurnal temperature wave produces a semi-diurnal pressure oscillation, as explained by Rayleigh and Margules, may be stated as follows: The diurnal temperature wave having a twenty-four hours period is the generating force of a diurnal pressure tide, which is essentially a forced and small oscillation. The natural period of the free waves in the atmosphere agrees much more nearly with twelve than with twenty-four hours. In so far as the forced and the free waves reinforce each other, the semi-diurnal waves are reinforced far more than the other, so that a very small semi-diurnal term in the temperature oscillations will produce a pressure oscillation two or three times as large as the same term would in the diurnal period. These reinforcements, however, depend upon the elastic pressure within the atmosphere, just as does the velocity of sound. If the prevailing barometric pressures were slightly increased, the adjustment of the twelve-hours free wave of pressure to the forced wave of temperature could be so perfect that the barometric wave would increase to an indefinite extent. For the actual temperatures the periodicity of the free wave is about thirteen hours, or somewhat longer than the forced wave of temperature, so that the barometric oscillation does not become excessive. It would seem that we have here a suggestion to the effect that if in past geological ages the average temperature at any time has been about 268° C. on the absolute scale, then the pressure waves could have been so large as to produce remarkable and perhaps disastrous consequences, involving the loss of a portion of the atmosphere. A modification of this idea of resonance has been developed by Dr Jaerisch, of Hamburg (Met. Zeit., 1907), but the general truth of the Kelvin-Margules-Rayleigh theorem still abides.
The Thermodynamics of a Moist Atmosphere.—The preceding section deals with an incompressible gas, and therefore with simple, pure hydrodynamics. If now we introduce the conception of an atmosphere of compressible gas, whose density increases with altitude, so that rising and falling currents change their temperatures by reason of the expansion and compression of the masses of air, we take the first step in the combination of thermodynamic and hydrodynamic conditions. If we next introduce moisture, and take precipitation into consideration, we pass to the difficult problems of' cloud and rain that correspond more nearly to those which actually occur in meteorology. This combination has been elucidated by the works of Espy and Ferrel in America, Kelvin in England, Hann and Margules in Austria, but especially by Hertz, Helmholtz, and von Bezold in Germany, and by Brillouin in France. A general review of the subject will be found in Professor Bigelow’s report on the cloud work of the U.S. Weather Bureau and his subsequent memoirs “On the Thermodynamics of the Atmosphere” (Monthly Weather Review, 1906–1909).
The proper treatment of this subject began with the memoir of Kelvin on convective equilibrium (see Trans. Manchester Phil. Soc., 1861). The most convenient method of dealing approximately with the problems is graphic and numerical rather than analytical and in this field the pioneer work was done by Hertz, who published his diagram for adiabatic changes in the atmosphere in the Met. Zeit. in 1884. He considers the adiabatic changes of a kilogram of mixed air and aqueous vapour, the proportional weights of each being λ and μ respectively. In a subsequent elaborate treatment of the same subject by von Bezold in four memoirs published during 1889 and 1899, the formulae and methods are arranged so as to deal easily with the ordinary cases of nature which are not adiabatic; he therefore prepares diagrams and tables to illustrate the changes going on in a unit mass of dry air to which has been added a small quantity of aqueous vapour, which, of course, may vary to any extent. Both Hertz and von Bezold consider separately four stages or conditions of atmosphere: (A) The dry stage, where aqueous vapour to a limited extent only is mixed with the dry air. (B) The rain stage, where both saturated vapour and liquid particles are simultaneously present. (C) The hail stage, where saturated aqueous vapour, and water, and ice are all three present. (D) The snow stage, where ice vapour and snow itself, or crystals of ice, are present. The expressions aqueous vapour and ice vapour do not occur in Hertz’s article, but are now necessary, since Marvin, Fischer and Juhlin have been able to show that vapour from water and vapour from ice exert different elastic pressures, and must therefore represent different modifications of liquid water. According to Hertz, we may easily follow this mass of moist air as it rises in the atmosphere, if by expansion it cools adiabatically so as to go successively through the four preceding stages. For a few thousand feet it remains dry air. It then becomes cloudy and enters the second stage. Next it rises higher until the cloudy particles begin to freeze into snow, sleet or hail, which characterizes the third stage. When the water has frozen and the cloud has ascended higher, it contains only ice particles and the vapour of ice, a condition which characterizes the fourth or snow stage. If in this condition we give it plenty of time the precipitated ice or snow may settle down, and the cloudy air, becoming clear, return to the first stage; but the ordinary process in nature is a circulation by which both the cloud and the air descend together slowly, warming up as they descend, so that eventually the mixture returns to the first stage at some level lower than the clouds, though higher than the starting-point.
The exact study of the ordinary non-adiabatic process can be carried out by the help of Professor Bigelow’s tables, and especially by the very ingenious tables published by Neuhoff (Berlin, 1900), but the approximate adiabatic study is so helpful that in fig. 10 we have traced a, few lines from Hertz’s Fig. 10.—Diagram for Graphic Method of following Adiabatic Changes. diagram sufficient to illustrate its use and convenience. The reader will perceive a horizontal line at the base representing sea-level; near the middle of this line is zero centigrade; as we ascend above this base into the upper regions of the air we come under lower pressures, which are shown by the figures on the left-hand side. The scale of pressures is logarithmic, so that the corresponding altitudes would be a scale of equal parts. The temperature and pressure at any height in the atmosphere are shown by this diagram. If the air be saturated at a given temperature, then the unit volume can contain only a definite number of grams of water, and this condition is represented by a set of moisture lines, indicated by short dashes, showing the temperature and pressure under which 5, 10 or 20 grams of water may be contained in the saturated air. Let us now suppose that we are following the behaviour of a kilogram mass of air rising from near sea-level, where it has a pressure of 750 millimetres, a temperature of 27° C., and a relative humidity of 50%. A pointer pressing down upon the diagram at 750 millimetres and 27° C. will represent this initial condition. A line drawn through that point parallel to the moisture lines will show that if this air were saturated it would contain about 22 grams of water; but inasmuch as the relative humidity is only 50%, therefore it actually contains only 11 grams of water, and an auxiliary moisture line may be drawn for this amount. If now the mass rises and cools by expansion, the relation between pressure and temperature will be shown by the line α α. When this line intersects the inclined moisture line for 11 grams of water we know that the rising mass has cooled to saturation, and this occurs when the pressure is about 640 millimetres and the temperature 13·2° C. By further rise and expansion a steady condensation continues, but by reason of the latent heat evolved the rate of cooling is diminished and follows the line β β. The condensed vapour or cloud particles are here supposed to be carried up with the cooling air, but the temperature of freezing or zero degrees centigrade is soon attained—as the diagram shows—when the pressure is about 472 millimetres. At this point the special evolution of latent heat of freezing comes into play; and although the air rises higher and more moisture is condensed, the temperature does not fall because the water already converted into vapour and now becoming ice is giving out latent heat sufficient to counteract the cooling due to expansion. This illustration from Hertz’s diagram therefore shows that the curve for cooling temperature coincides with the vertical line for freezing, and is represented on the diagram by the short piece β γ. By this expansion due to ascent the volume is increased while the temperature is not changed; therefore, the quantity of aqueous vapour has increased. When the ascending mass has reached the level where the pressure is 463 millimetres it has also reached the moisture line that represents this increase in aqueous vapour. As this shows that the aqueous particles have now all been frozen, and as the air is now continuously rising, while its temperature is always below freezing-point, therefore at levels above this point the vapour that condenses from the air is supposed to pass directly over into the condition, of solid ice. Therefore from this point onwards the falling temperatures follow along the line γ γ, and continue along it indefinitely From these considerations it follows that the clouds above the altitude of freezing temperatures are essentially snow crystals, and if the air rises slowly there may be time for the water and ice to settle down towards the ground; in this case the quantity ​of snow left within the clouds must be very small, and the cloud has the delicate appearance peculiar to cirrus; Hertz’s original diagram is quite covered by these systems of α, β, γ and δ lines, and the moisture lines. The lines show the density of the moist air at any stage of the process. The improved diagram by Neuhoff, published in 1900, is reprinted in the second volume of Abbe’s Mechanics of the Earth’s Atmosphere, and its arrangements help to solve many problems suggested by the recent progress of aerial research.
In von Bezold’s treatment of this subject only illustrative diagrams are published, because the accurate figures, drawn to scale; are necessarily too large and detailed. He presents graphically the exact explanation of the cooling by expansion, the loss of both mass and heat by the rainfall and snowfall, and the warmth of the remaining air when it descends as foehn winds in Switzerland and chinook winds in Montana. Even in the neighbourhood of a storm over low lands and the ocean, the warm moist air in front, after being carried up to the rain or snow stage, flows away on the upper west wind until a corresponding portion of the latter descends drier and warmer on the opposite side of the central low pressure. In order to have a convenient term expressive of the fact that two masses of air in different portions of the atmosphere having different pressures, temperatures and moistures, would, if brought to the same pressure, also necessarily attain the same temperature, von Bezold introduced the expression “potential temperature,” and devised a simple diagram by which the potential temperature may be determined for any mass of air whose present temperature, pressure and moisture are known. In an ascending mass of air, from the beginning of the condensation onwards, the potential temperature steadily increases by reason of the loss of moisture, but in a descending mass of air it remains constant at the maximum value attained by it at the highest point of its previous path. In general the potential temperatures of the upper strata of the atmosphere are higher than those of the lower. In general the so-called vertical temperature gradient is smaller than would correspond to the adiabatic rate for the dry stage. This latter gradient is 0·993° C. per hundred metres for the dry stage, but the actual atmospheric observations give about 0·6°. Apparently this difference represents primarily the latent heat evolved by the condensation of vapour as it is carried into the upper layers, but it also denotes in part the effect of the radiant heat directly retained in the atmosphere by the action of the dust and the surfaces of the clouds. Passing from simple changes due to ascent and descent, von Bezold next investigated the results of the mixture of different masses of air, having different temperatures and humidities, or different potential temperatures. The importance of such mixtures was exaggerated by Hutton, while that of thermodynamic processes was maintained by Espy, but the relative significance of the two was first clearly shown by Hann as far as it relates to the formation of rain, and further details have been considered by von Bezold. The practical tables contained in Professor Bigelow’s report on clouds, and those of Neuhoff as arranged for the use of those who follow up von Bezold’s train of thought, complete our methods of studying this subject.
A most important application of the views of von Bezold, Hertz and Helmholtz was published by Brillouin in his memoir of 1898. Just as we have learned that the motions of the atmosphere are not due either to the general distribution of heat or to local influences exclusively, but in part to each, and just as we have learned that the temperature of the air is not due either to radiation and absorption or to dynamic processes exclusively, but to both combined, so in the phenomena of rain and cloud the precipitation is not always due to the cooling by mixture, or to the cooling by expansion, or to radiation, but is in general a complex result of all. The effect of the evaporation of cloudy particles in the production of descending cold currents has always been understood in a general way, but was first brought to prominence by Espy in 1838, and perhaps equally forcibly by Faye in 1875. Helmholtz, in his memoirs on billows in the atmosphere, showed how contiguous currents may interact on each other and mix together at their boundary surface; but Brillouin explains how these mixtures produce cloud and rain—not heavy rains, of course, but light showers, and spits of snow and possibly hail. He says: “When the layers of clear or cloudy air are contiguous, but moving with very different velocities, their motion, relative to the earth because of the rotation of our globe, assumes a much more complicated character than that which obtains when the air has no horizontal but only a vertical motion. We know in a general manner what apparent auxiliary forces must be introduced in order to take into account this rotation, and numerous meteorologists have published important works on the subject since the first memoirs by Ferrel. But their points of view have been very different from mine. The subjects that I desire to study are the surfaces of discontinuity as to velocity, temperature and cloudiness in one special case only. Analytical methods permit us to resolve complex questions only for limited areas in longitude and for contiguous zones within which the movements are steady, but not necessarily uniform nor parallel. But it is evident that one can learn much as to the condition of permanence or destruction of annular zones having uniform and parallel movements. Thus simplified, the questions can be treated by elementary geometric methods, by means of which we at once rediscover and complete the results given by Helmholtz for zones of clear air and discover a whole series of new results for zones of cloudy air.” Among Brillouin’s results are the following theorems:—
A. If the atmosphere be divided into narrow zonal rings, each extending completely around the globe, thus covering a narrow zone of latitude, and if each is within itself in convective equilibrium so that the surfaces of equal pressure shall be surfaces of revolution around the axis of rotation, then within any such complete ring in convective equilibrium the angular velocity of any particle of the air will vary in inverse ratio of the square of its distance from the axis of rotation, or ar$^2$ is constant; that is to say, the air will not move like a rotating solid, but will have a variable angular velocity, smaller far from the axis and greater near to it.
B. The surfaces of equal pressure are more concave towards the centre than is the surface of the globe itself, and they are tangent to the latter only along the parallel where calms prevail.
C. A heavy gaseous atmosphere resting upon a rotating frictionless globe divides itself into concentric rings whose angular movements increase as we pass from the polar region towards the equatorial ring; the central globe rotates more rapidly than the equatorial atmospheric ring.
D. The surface of separation between two contiguous concentric rings must be such that the atmospheric pressure shall have the same value as one approaches this surface from either direction, and the surface of separation is stable if the differences of pressure in different parts of this surface are directed towards the surface of equilibrium. As the distribution of pressure along a line parallel to the axis of rotation is independent of the velocity of rotation, the ordinary condition of stability, viz. that the gas of which the lower ring is composed shall be denser than that above, will hold good for this line. In general, any inclination of the surface of separation to the horizon amounting to 10° must be associated with very small differences of density and large differences of velocity; in practice the inclinations are far less than 10°.
E. If the surfaces of equal pressure or isobars are nearly horizontal, as in ordinary cases, the calculations are comparatively easy to make. Let the inclination of the isobaric surface ascending towards the pole be φ; let h$_1$ be a distance counted along the axis of the earth, and H$_1$ the distance measured in the direction of the attraction of gravity; then the angle of inclination of the isobaric surface is given by the equation
$\tan \phi =-{\frac {\mathrm {H} _{1}-h_{1}\sin \lambda }{h_{1}\cos \lambda }}$
where λ is the complement of the angle between the direction of gravity and the line drawn to the poles, or the axis of rotation of the earth. The surface of separation is that over which the pressure is the same in two contiguous masses or zones, and is identical with a vertical plane only when the densities and velocities in the two layers have certain specific relations to each other. It can never lie between the isobaric surfaces that Brillouin designates as 1 and 2. In order that the equilibrium may be stable, it is necessary that when ascending in the atmosphere along a line parallel to the polar axis one should traverse layers of diminishing density. In the midst of any zone there cannot exist another zone of limited altitude; it must extend upwards indefinitely. Whenever there is any zone of limited altitude it must necessarily have, near its highest or lowest point, an edge by which it is attached to the surface of separation of two other neighbouring zones. In other words, the surfaces of separation of the three zones, of which one is limited and the other two are indefinite, must all run together at a common point or edge, very much as in the problem of the equilibrium of thin films.
F. When the contiguous zones are cloudless the mixtures take place under the following conditions: Starting from the stable conditions, the cloudless mixture ascends on the polar side when the west wind which prevails on the equatorial side of the surface of separation is warmer, but descends between the pole and the equatorial side of the horizon when the west wind which prevails on the equatorial side of the surface of separation is colder. The mixtures of cloudless air rapidly occupy the whole height of the two layers that are mixing. When they form along a surface that becomes unstable the whirlwind that is thus engendered is sensibly cylindrical at first, but finally becomes extremely conical; This whirlwind may be limited as to height when the two contiguous masses that are mixing are surmounted by a third clear or cloudy layer which intersects the other two and whose lower surface is stable. (Brillouin suggests that possibly this corresponds to the formation of water-spouts and tornadoes.)
G. When the contiguous zones are cloudy and the mixtures produce decided condensations, and sometimes even precipitation, the study of these must follow closely in the train of thought followed out by von Bezold. When the contiguous winds are feeble, but the temperatures are very different and the zones are near the equator, then the position of the mixture can be inverted by condensation, since the influence of difference of pressure becomes predominant. At the equator, whatever may be the difference of temperature, a mixture that is accompanied by condensation always rises if the surface of separation is stable. The condensation increases by the expansion, each zone of mixture being an outburst of ascending cumuli. At the equator, whatever may be the difference of ​temperature, a mixture accompanied by condensation always descends when the surface of separation is unstable; moreover, the adiabatic compression rapidly evaporates the mixture.
In the last three chapters of his memoir, Brillouin applies these principles and other details to almost every observed variety of mixtures due to the pressure of one current of air against another. Fig. 11, prepared for the U.S. Monthly Weather Review (Oct. 1897), gives five of the cases elucidated by Brillouin.
* After Brillouin.
* Fig. 11.—Diagram illustrating Clouds due to Mixture.
In each of these the left-hand side of the diagram is the polar side, the air being cold above and the wind from the east, while the right-hand side is the equatorial side, the air being warm above and the wind from the west. The reader will see that in each case, depending on the relative temperatures and winds, layers of cloud are formed of marked individuality. As none of these clouds appear in the International Cloud Atlas or the various systems of notation for clouds, one is all the more impressed with the importance of their study and the success with which Brillouin has opened up the way for future investigators. “We have no longer to do with personal and local experience, but with an analytical description of a small number of characteristics easy to comprehend and applicable at every locality throughout the globe.”
From a thermodynamic point of view the most important study is that published by Margules, Ueber die Energie der Stürme (Vienna, 1905). This work considers only the total energy and its adiabatic transformations within a mass of air constituting a closed system. Truly adiabatic changes in closed systems do not occur within any special portion of the earth’s atmosphere, neither can our entire atmosphere be considered as one such system—but Margules’ results are approximately applicable to many observed cases and complete the demonstration of the general truth that we must not confine our studies to the simpler cases treated by Espy, Reye, Sohncke, Peslin, Ferrel, Mohn. All imaginable combinations of conditions exist in our atmosphere, and a method must be found to treat the whole subject comprehensively and rigorously.
The three equations of energy on which Margules bases his work are:—
* $\mathrm {R} +\delta \left(\mathrm {K} +\mathrm {P} \right)+\delta \mathrm {A} =0$
* $\delta \mathrm {I} -\delta \mathrm {A} =\mathrm {Q}$
* $\mathrm {R} +\delta \left(\mathrm {K} +\mathrm {P} \right)+\delta \mathrm {A} =\mathrm {Q}$
where R＝energy lost by friction or converted into heat; K＝kinetic energy due to velocity of moving masses; P＝potential energy due to location and gravity and pressure heat; A＝work done by internal forces when air is expanding or contracting; I＝internal energy due to the existing pressure and temperature; Q＝quantity of heat or thermal energy added or lost during any operation and which is zero during adiabatic processes only.
These equations are applied to cases in which masses of air of different temperatures and, moisture’s are superposed and then left free to assume stable equilibrium. It results in every case that there is no free energy developed. Any condensation of moisture by expansion is counterbalanced by redistribution of potential energy and by the work done in the interchange of locations. The idea that barometric pressure gradients make the storm-winds is seen to be erroneous and the primary importance of gravity gradients is brought to light. “The source of a storm is to be sought only in the potential energy of position and. in the velocity of ascent and descent, although these are generally lost sight of owing to the great horizontal and small vertical dimensions of the storm areas The horizontal distribution of pressure seems to be a forced transformation within the storm areas at the boundary surface of the earth, by reason of which a small part of the mass of air acquires a greater velocity than it could by ascending in the coldest or sinking in the warmest part of the storm areas. But here we come to problems that cannot be solved by considering the energy only.”
This latter quotation emphasizes the necessity of returning to the equations of motion. The thermodynamics and hydrodynamics of the atmosphere must be studied in intimate connexion—they can no longer be studied separately. Apparently we may expect this next step to be taken in the above-mentioned work promised by V. Bjerknes, but meanwhile Professor F. H. Bigelow has successfully attacked some features of the problem in his “Studies on the Thermodynamics of the Atmosphere” (Monthly Weather Review, Jan.–Dec. 1906). In ch. iii. of his studies (Monthly Weather Review, March 1906) Bigelow establishes a thermodynamic formula applicable to non-adiabatic processes by introducing a factor n so that the pressure (P) and absolute temperature (T) are connected by the formula
* ${\frac {\mathrm {P} _{0}}{\mathrm {P} }}=\left({\frac {\mathrm {T} }{\mathrm {T} _{0}}}\right)^{n\kappa \left(c\kappa -1\right)}$
In our fig. 1 above given, Cottier has assumed n＝1·2, but as the values have now been computed for all altitudes from the observations given by balloons and kites, and have a very general importance and interest, we copy them from Bigelow’s Table 16 as below:—
The existence of such large values of n shows the great extent to which non-adiabatic processes enter into atmospheric physics. Heat is being radiated, absorbed, transferred and transformed on all occasions and at all altitudes. Knowing thus the thermodynamic structure of areas of high and low pressure we find the modifications needed in the energy formula for non-adiabatic processes—and Bigelow applies the resulting formula most satisfactorily to a famous waterspout of the 19th of August 1896 over Nantucket Sound, for which many photographs and measurements are available. The thermodynamic study of this waterspout being thus accomplished, it was followed by a combined thermohydrodynamic study of all storms (Monthly Weather Review, November, 1907–March 1909) with considerable success.
We have thus passed in review the steady progress of mathematical physicists in their efforts to unravel the complex dynamics of our atmosphere. The profound importance of this subject to governmental weather bureaus, and through them to the whole civilized world, stimulates diligent effort to overcome the inherent difficulties of the problems. An elaborate system of study and laboratory experimentation leading up to research in meteorology has been devised by Cleveland Abbe, culminating in experiments on models of the atmosphere as a whole by which to elucidate both the local and the general circulations on globes whose orography and distribution of land and water is as irregular as that of the earth.
The Formation of Rain.—Not only has dynamic meteorology made the progress delineated in the previous sections, but one of the most important questions in molecular physics is in process of being cleared up. The study of atmospheric nuclei and condensation and the, formation of clouds in their relation to daily meteorological, work began with the appointment of Dr Carl Barus in 1891 as physicist to the U.S. Weather Bureau, and his work has been laboriously continued and extended in his laboratory at Providence, Rhode Island. The formation of rain, from a physical point of view, ​is the ultimate step in the formation of cloud. The cloud consists, like fog, of extremely small particles, so light that they float indefinitely in the air; rain and snow represent those particles that have grown to be too large and heavy to be any longer sustained by the air—that is to say, their rate of fall through the air is greater than the ascending component of the air in which they float. The process by which larger drops are formed out of the lighter particles that constitute a cloud has not yet been satisfactorily explained. It is probable that either one of several processes contributes to bring about this result, and that in some cases all of these conspire together. The following paragraphs represent the hypotheses that have marked the gradual progress of our knowledge:—
A. Cloud particles may be driven together by the motions imparted to them by the wind, and may thus mechanically unite into larger ones, which, as they descend more rapidly, overtake the smaller ones and grow into rain-drops.
B. The particles on the upper boundary of a cloud may at nighttime, or in the shade, cool more decidedly than their neighbours below them, either by radiation or by mixture; then the air in their immediate vicinity becomes correspondingly cold, the particles and their envelopes of cold air sink more rapidly, overtaking, and therefore uniting, with other particles until the large rain-drops are formed.
C. Some cloud particles may be supposed to be electrified positively and others negatively, causing them to attract each other and run together into larger ones, or, again, some may be neutral and others charged, which may also bring about attraction and union.
D. When any violent agitation of the air, such as the sound waves due to thunder, or cannonading, or other explosions, sets the particles in motion, they may be driven together until brought into contact, and united into larger drops.
E. The air—or, properly speaking, the vapour—between cloudy particles—that is to say, within fog or cloud, is generally in a state of supersaturation; but if it is steadily rising to higher altitudes, thereby expanding and cooling, the supersaturation must increase steadily until it reaches a degree at which the molecular strain gives way, and a sudden violent condensation takes place, in which process both the vapour and the cloud particles within a comparatively large sphere are instantaneously gathered into a large drop. The electricity that may be developed in this process may give rise to the lightning flash, instead of the reverse process described in the preceding paragraphs (C and D).
F. However plausible the preceding five hypotheses have seemed to be, it must be confessed that no one has ever yet observed precipitation actually formed by these processes. The laborious observations of C. T. R. Wilson of Cambridge, England, probably give us our first correct idea as to the molecular processes involved in the formation of rain. After having followed up the methods inaugurated by Aitken showing that the particles of dust floating in the air, no matter of what they may be composed, become by preference the nuclei upon which the moisture begins to condense when air is cooled by expansion. Wilson then showed that in absolutely dustless air, having therefore no nuclei to facilitate condensation, the latter could only occur when the air is cooled to a much greater extent than in the case of the presence of dust; in fact, dustless air requires to be expanded more than dusty air in the ratio of 4 to 3, or 1 1/3 times more. The amount of this larger expansion may vary somewhat with the temperature, the moisture and the gases. More remarkable still, he showed that dustless air, having no visible or probable nuclei, acquired such nuclei when a beam of ultra-violet light, or of the röntgen rays, or the uranium radiation, or of ordinary sunlight (which possibly contains all of these radiations), was allowed to pass through the moist air in his experimental tube. In other words, these rays produce a change in the mixed gas and vapour similar to the formation of nuclei, and condensation of aqueous vapour takes place upon these invisible nuclei as readily as upon the visible dust nuclei. Further, the presence of certain metals within the experimental tube also produces nuclei; but the amount of expansion, and therefore of cooling, required to produce condensation upon these metallic nuclei is rather larger than in the case of dust nuclei. The nuclei thrown into the experimental tube by the discharge of electricity from a pointed metal wire produced very dense fogs by means of expansions slightly exceeding those required for ordinary dust. Finally, Wilson has been able to show that when dust particles are electrified negatively their tendency to condense vapour upon themselves as nuclei is much greater than when they are electrified positively, and he suggests that the descent of the rain-drops to the ground, carrying negative electricity from the atmosphere to the earth, may perhaps explain the negative charge of the earth and the positive electricity of the atmosphere.
At this point we come into contact with the views developed by J. J. Thomson as to the nature of electricity and the presence of negative and positive nuclei in the atmosphere. According to him, “The molecules made up of what chemists call atoms must be still further subdivided, and the atoms must be conceived as made up of corpuscles; the mass of a corpuscle is the same as the mass of the negative ion in a gas at low pressure. In the normal atom this assemblage of corpuscles forms a system which is electrical and neutral. Though the individual corpuscles behave like negative ions yet when they are assembled in a neutral atom the negative effect is balanced by something which causes the space through which the corpuscles are spread to act as if it had a charge of positive electricity equal in amount to the sum of the negative charges on the corpuscles. I regard electrification of a gas as due to the splitting up of some of the atoms of the gas, resulting in the detachment of a corpuscle from such atoms. The detached corpuscles behave like negative ions, each carrying a constant negative charge which we shall call the unit charge, while the part of the atom left behind behaves like a positive ion with the units positively charged but with a mass that is large compared with that of the negative ion. In a case of the ionization of the gas by röntgen or uranium rays, the evidence seems to be in favour of the view that not more than one corpuscle can be detached from any one atom. Now the ions by virtue of their negative charges act as nuclei around which drops of water condense when moist dust-free gas is suddenly expanded. . . . C. T. R. Wilson has shown that it requires a considerably greater expansion to produce a cloud in dust-free air on positive ions than on negative ones, when the ions are produced by röntgen rays.” It would therefore appear that the moist atmosphere above us may, through the action of sunlight or the lightning flash as well as by other means, become ionized. The negative ions attract moisture to themselves more readily than the positive; they grow to be larger drops, and descending to the earth with their negative charges give it negative electricity, while the atmosphere is left essentially either positive or neutral. (See also Atmospheric Electricity.)
IV.—Cosmical Meteorology
Under this title have been included all possible, plausible or imaginary relations between the earth's atmosphere and interplanetary space or the heavenly bodies. The diffusion to and fro at the outer limit of the atmosphere, the bombardment by ions from the sun, the explanation of auroral lights and of magnetic storms, the influence of shooting stars and comet tails, the relation of the zodiacal light and the Gegenschein to the atmosphere, the parallelisms between terrestrial phenomena and the variations of the solar spots and protuberances, the origin of long or short climatic periods, the cause of special widespread cold days, the existence of lunar or solar gravitation tides analogous to oceanic tides, the influence of slow changes in the earth's orbit or the earth's axis of rotation—all are grouped under cosmical meteorology.
But, in the writer’s judgment these matters, while curious and interesting, have no appreciable bearing on the current important questions of atmospheric mechanics. There seem to be many widespread delusions and mistakes in regard to these problems, analogous to the popular errors in regard to astrology, and it is hardly necessary to do more than allude to them here. The leading meteorologists have relegated such questions to the care of theoretical astronomers and physicists until our knowledge is more firmly established. Undoubtedly the earth does come under other influences than that of the radiation from the sun; but in the present stage of dynamic meteorology we consider only this latter, and, assuming it to be constant as regards quantity and quality, we find the variable selective absorptions and reflections within our own atmosphere, and its complex internal mechanism afford us a bewildering maze of problems such that so long as these are unsolved it would be folly to spend time on those.
V.—Meteorological Organizations
During the latter half of the 19th century the prosecution of work in meteorology gradually passed out of the hands of individuals into the control of large national organizations. This was the natural result of the discovery that, by the spread of the electric telegraph and ocean cables, it had become possible to compile daily weather-maps for large portions of the globe and make predictions of the weather and the storms for a day or two in advance, of sufficient accuracy to be of the greatest importance to the material interests of civilized nations. The development of wireless telegraphy since 1900 has even made it possible for isolated ships at sea to exchange weather telegrams, compile daily maps and study surrounding storms. One by one every civilized nation has established either a weather bureau or a meteorological office, or a bureau of hydrography and marine meteorology, or an elaborate establishment for aerial explorations according as its special interests demanded. These governmental bureaus usually pursue both Climatology and theoretical meteorology in addition to their daily practical ​work of telegraphy, forecasting, and publication of charts. Although, of course, in most cases, the so-called practical work absorbs the greater part of the labour and the funds, yet everywhere it is recognized that research and the development of a correct theory of the motions of the atmosphere are essential to any important progress in the art of forecasting. Among other important general works in which the official weather bureaus have united, we may enumerate the International Meteorological Congresses, of which the first was held in 1853 at Brussels, the second in 1873 at Vienna, and others more frequently since that date; the establishment of an International Committee, to which questions of general interest are referred; the organization of a systematic exploration of the polar regions in the years 1882 and 1883; the general extension of the meteorological services to include terrestrial magnetism as an essential part of the physics of the globe; the systematic exploration of the upper atmosphere by means of kites and balloons; and the universal co-operation with the U.S. Weather Bureau in the contribution of simultaneous data for its international bulletin and its daily map of the whole northern hemisphere. The hydrographic offices and marine bureaus of the principal commercial nations have united so far as practicable in the daily charting of the weather, but have especially developed the study, of the climatology of the ocean, not only along the lines laid down by Maury and the Brussels Conference of 1853, but also with particular reference to the tracks of storm centres and the laws of storms on the ocean. The condition of these governmental organizations was discussed in the annual address of the Hon. F. Campbell Bayard, delivered before the Royal Meteorological Society of London in January 1899, and in the text accompanying Bartholomew’s Physical Atlas, vol. iii.
The development of meteorology, in both its scientific and its practical aspects, is intimately dependent upon the progress of our knowledge of physics, and its study offers innumerable problems that can be solved only by proper combinations of mathematical theory and laboratory experimentation. The professors in colleges and universities who have hitherto lectured on this subject have not failed to develop some features of dynamic meteorology, although most of their attention has been given to climatology. In fact, many of them have been engrossed in the study of general problems in molecular physics, and could give meteorology only a small part of their attention. The early textbooks on meteorology were frequently mere chapters or sections of general treatises on physics or chemistry. The few prominent early cases of university professorships devoted to meteorology are those of the eminent Professor Heinrich Wilhelm Dove at Berlin, Professor Adolphe Quetelet at Brussels and Professor Ludwig Friedrich Kaemtz at Halle and Dorpat. In modern times we may point to Professor Wilhelm von Bezold and George Hellmann at Berlin, Professor Julius Hann at Vienna and Gratz, Professor Josef Maria Pernter at Linz and Vienna, Professor Alexander Woeikof at St Petersburg, Professors Hugo Hildebrand-Hildebrandsson at Upsala, Henrik Mohn at Christiania, Elias Loomis at New Haven, Connecticut, W. M. Davis and R. de C. Ward at Cambridge, Massachusetts, Alfred Angot and Marcel Brillouin at Paris, Hugo Hergesell at Strassburg, Arthur Schuster at Manchester, Peter Polis at Bonn, and Richard Börnstein at the School of Agriculture in Berlin. With these exceptions the great universities of the world have as yet given but little special encouragement to meteorology; it has even been stated that there is no great demand for higher education on the subject. On the other hand, the existence of thousands of voluntary observers, the profound interest in the weather actually taken by every individual, and the numerous schemes for utilizing our very limited knowledge of the subject through the activities of the large weather bureaus of the world demonstrate that there is a demand for knowledge perhaps even higher than the universities can offer It would be very creditable to a nation or to a wealthy patron of science if there should be established meteorological laboratories in connexion with important universities, at which not only instruction but especially investigation might be pursued, as is done at the magnificent astronomical observatories that are so numerous throughout the world. Every atmospheric phenomenon can be materially elucidated by exact laboratory experiments and measurements. theory can be confronted with facts; and the student can become an original investigator in meteorology.
The great difficulties inherent to meteorology should stimulate the devotion of the highest talent to the progress of this branch of science. The practical value of weather predictions justifies the expenditure of money and labour in order to improve them in every detail.
Bibliography.—Those who desire recent additions to our knowledge should consult first Hann’s Lehrbuch der Meteorologie (2nd ed., Leipzig, 1906) as being a systematic encyclopedia. Of equal importance is the Meteorologische Zeitschrift (Berlin and Vienna, 1866 to date). The Atlas of Meteorology (Bartholomew, 1900), the Quarterly Journal of the Royal Meteorological Society (London) and the Monthly Weather Review (Washington) are the works most convenient to English readers and abound with references to current literature. The Physical Review Science Abstracts and the Fortschritte der Physik contain short notices of all important memoirs and will serve to direct the student’s attention toward any special topic that may interest him.  (C. A.)
* ↑ [We have here inserted the Washington data as interpolated from the figures given by Hann, Lehrbuch, 1906, p. 282.]
* ↑ Recherche sur le mouvement des projectiles dans l’air en ayant égard à l’influence du mouvement diurne de la terre; dated 1837, printed Paris, 1839.
* ↑ “On the Construction of Isobaric Charts for High Levels in the Earth’s Atmosphere and their Dynamic Significance,” Trans. Am. Phil. Soc. (1906).