Bible Encyclopedias
Meteorology

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 by 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 yy `N Arms, 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 during1906-1909with Angstrom'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 FIG. 6. - Marvin-Hargrave Kite, with Meteorograph in position.

is almost identical with that now recognized by Elster (see Terrestrial Magnetism, Jan. 1900, iv. 213). 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 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 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 of 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 thefree atmosphere in numbers sufficient to indicate the normal. condition of the air.

The kite and meteorograph have now been adopted for use by alt 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. abovethe reel was attained by the use of 37,3 00 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 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.

e il ed I ? f ?' ? o o _ +.,,,,.,,?

a« a o FIG. 9. - Chart of Isotherms in Free Air above Trappes.

This diagram shows the height at which the isotherms of o°, - 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 Leon 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; ¦ l nl?I ' '1 l? ' 'I l I NIP I N _ ¦lN I i a Ssy.Ya, ' ? 1 ?a.?.? < w ?I?N'?OIY<>?././Il4? f??%Y., a a 0 FIG. 7. - Marvin Kite Reel for hand power.

] 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 during1871-1891by 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, Angstrom, 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 (I) 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. X (1 -{- a t), where a 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 = J,' - rgdh (2) where v 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 - ho=18400(1+000367t) (1 +0.378 (1+0.0026 cos 2q) ('+ 671) (1 +0.00157) log '°. (2a) 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, the pressure at the bottom, cjo 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 dQ = Cvdt + Apdv = C v dt + 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 a 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 ap + a (p u) + a(nv°) + a(pw) o (4) - at ax ay az where p is the density, t is the time and a 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: 1, in, n, be cosines of the angle between the pressure p, and S the inwardly directed normal to the boundary surface. Then will a(T+V+W) '_' m y +n v) dS . (5) at 1 b. Equations of acceleration and inertia. Let P be the potential of the external forces acting on a unit mass of the atmosphere; µ, be the coefficient of viscosity or internal friction. Then will aP 1 ap - au au au au ax - P ax at + u. a x + v. a y +w. az _ 02,202,2a2 u g[ax2+ay2+az2 aP 1 ap = av av, av aw a y - - P ay at + U. a x + v. - y +W . az ra 2 v 0 2 v 02v g Lax2 + ay2 + az2 aP 1 ap = aw aw aw aw - az - P az at + u ax + v. ay +w az (a 2 w 0 2 w 02wi L a e 2 ay 2 az2 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 interconversions 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 (6)> 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 Gottingen in a memoir published in the Met. Zeit., 18 93, 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 t 0). 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 0) fv N=-6Ccos 0 sin04 0 = D [sin 0 (1 - 3 cos t 0) go- + 6 cos t 8y0-].

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 southeastern 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 e 0-0.0836), 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 Tokyo, 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 Tokyo 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 1875-1884, 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 tradewind 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 211 v sin 0, while the curvature of the path of the wind is measured by its radius of curvature, which is v/211 sin 0, where v is the velocity of the wind, n is the equatorial velocity of the earth's rotation, and 0 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 ' Recherche sur le mouvement des projectiles dans l'air en ayant egard a l'influence du mouvement diurne de la terre; dated 1837, printed Paris, 1839.

expressed by the following formula for the pressures that prevail at sea-level: - G = [(2n sin 4 -cos iv/r)v sec i] /183,000,000].

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 of1888-1891showed 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 ioo 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 Ober die Energie der Stiirme (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 p r2 wdV 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 Muller-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 Sandstrom, 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: - Hydrodynamics. velocity of unit mass I. Magnetics.. magnetic induction Electrics. .. electric induction Hydrodynamics. intensity of the field II. Magnetics. .. „ „ „ Electrics .

Hydrodynamics. velocity of energy III. Magnetics. .. intrinsic magnetic polarization Electrics. „ electric „ Hydrodynamics. velocity of expansion per unit volume IV. Magnetics.. density of the true magnetic mass Electrics. electric Hydrodynamics. density of the dynamic vortex V. Magnetics.. „ „ steady magnetic current Electrics. .. „ „ „ magnetic „ Hydrodynamics. specific volume VI. Magnetics. .. magnetic permeability Electrics dielectric constant ' " On the Construction of Isobaric Charts for High Levels in the Earth's Atmosphere and their Dynamic Significance," Trans. Am. Phil. Soc. (1906). 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 Sandstriim 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 Sandstrom, 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°-fix), where x is the local hour angle of the sun. In higher latitudes either north or south the coefficient A l =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 A2 = (0.988 mm. - 0.573 mm. sin 24,) cos 20 as given by Hann, or A2 = (0.92 mm. - 0.495 sin 2 4)) cos 24 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 Mecanique celeste were at fault from a rigorous analytical point of view. The process by which a diurnal temperature wave produces a semidiurnal 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 X and A 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 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 eo the unit volume can contain only a definite number of grams of [After Hertz.

water, and this condition is repreFIG. i 0. - Diagram for Graphicsented by a set of moisture lines, Method of following Adiabaticindicated by short dashes, showChanges.

ing the temperature and pres sure 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 II 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 a a. When this line intersects the inclined moisture line for I I 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 # ,6. 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 a y. 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 'y y, 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 o c.

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 a, 1 3, y and 8 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 o6°. 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 H1 - h1 sin A h1 cos where A 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 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 e 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 4,; 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 4 _ - ] 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. i i, prepared for the U.S. Monthly Weather Review (Oct.

After Brillouin.

FIG. I I.- Diagram illustrating Clouds due to Mixture.

1897), gives five of the cases elucidated by Brillouin. 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 Stiirme (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 l 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: R+S(K+P) +8A =0 SI -SA=Q R-}-S(K+P)+SI =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 moistures 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 expan sion 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 Po) nK(cKI) P T0 In our fig. I 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, Xviii. Io. 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 I a 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 Bornstein 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, 5906) as being a systematic encyclopaedia. 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.)