eet ee a) ane ee eo a te PN ELL re SL Se I atl PCR eae S i 2 SEC et , PRT Nee - ee, Oe PET LY % ee Y, t z y Rete TD : . % AARNE NES REARS A Law ee ee ee ee ee eae ee Cee ree oe ee v BF ee Pe, Qc Pb] H& Cl rwovrn [ovr Ch WHERE Iam stony N ew York State College of Agriculture At Cornell University Ithaca, N.Y. Library ty Librai wii PHYSICS OF THE AIR PROPERTY OF Ut DEPT, OF iETEGROLOGY PHYSICS OF THE AIR BY W. J. HUMPHREYS, C.E., Px.D. PROFESSOR OF METEOROLOGICAL PHYSICS, UNITED STATES WEATHER BUREAU, WASHINGTON, D. C. “. PHILADELPHIA PUBLISHED FOR THE FRANKLIN INSTITUTE OF THE STATE OF PENNSYLVANIA BY J. B. LIPPINCOTT COMPANY 1920 ae £6 | Hé Copyright, 1920, by THE FRANKLIN INSTITUTE 1'70901 INTRODUCTION THE physical phenomena of the earth’s atmosphere are exceedingly numerous and of great importance. Nevertheless, the explanations, even of those well understood, still remain scat- tered through many books and numerous journals. Perhaps this is because some of the phenomena have never been explained, and others but imperfectly so, but, however that may be, it is obvious that an orderly assemblage of all those facts and theories that together might be called the Physics of the Air would be exceedingly helpful to the student of atmospherics. An attempt to serve this useful purpose, begun in a course of lectures at the San Diego Aviation School (Rockwell Field) in 1914, led to the production of the following chapters—revised and re- printed from the Journal of The Franklin Institute, 1917, 1918, I9IQ, 1920. The author begs to express his indebtedness to Prof. C. F. Marvin, Chief of the United States Weather Bureau, for numer- ous helpful criticisms; to Dr. C. F. Brooks, Editor of-the Monthly Weather Review, for many excellent suggestions; to Prof. C. F. Talman, Librarian of the United States Weather Bureau, for valuable aid in locating original sources; and to Major R. B. Owens, D. S. O., Secretary of The Franklin Institute, for his encouraging interest in the work and invaluable attention to the details of its publication. § emmy ge 1 Ta te & ea hae bed HP web Be ee CONTENTS INTRODUCTION gag ewes zs Sebel exo Sey oak a ads Se 2 dasa ad deer dea aw base v PART I MECHANICS AND THERMODYNAMICS OF THE ATMOSPHERE CHAPTER TH OBSERVATIONS} aia Sasedie aa dines a. dig Now nee, Deealaus BA ania noed I Temperature, Pressure, Wind Velocity, Wind Direction, Humidity (Absolute, Relative, Specific, Dew Point, Saturation Deficit, Instrumentation), Cloudiness, Precipitation, Evaporation, Sun- shine, Radiation, Electrical Condition, Optical Phenomena, Tur- bidity. Sources of Meteorological Information. II. Some THEORETICAL TEMPERATURE RELATIONS OF THE ATMOSPHERE 28 Various Relations Between Temperature, Pressure, Volume and Altitude, Temperature Changes of a Rising (or Falling) Isolated Mass of Air. III. OBSERVED VERTICAL TEMPERATURE GRADIENTS...........-000005 37 Average Vertical Distribution of Temperature During Summer and During Winter, Why the Temperature of the Atmosphere Decreases With Increase of Elevation. IV. Tue IsOTHERMAL REGION, OR STRATOSPHERE..........-.-0000055 43 Physical Explanation of the Existence of the Stratosphere, Inequal- ity of Seasonal Temperature Change of Lower and Upper Atmos- phere, Height of the Isothermal Region (Base of Stratosphere), Storm Effects on Temperature Gradients, Relation of the Iso- thermal Region to Latitude. V. COMPOSITION OF THE ATMOSPHERE..........0 00000 e eee ee teens 60 Composition of the Surface Air, Barometric Hypsometry, Compo- sition of the Upper Air, Density of the Atmosphere. VE. INSOGATION cjecg.cs tien ae gh a Ree Fee awd MER eu Deed ee ee Ray 74 Factors of Insolation, Solar Output of Radiation, Distance from the Sun, Solar Altitude, Transmission and Absorption, Surface Temperature and Absorbing Gases. vii viil CONTENTS VII. ATMOSPHERIC CIRCULATION. 0.00000. c ccc cece cence ene enn teens Introduction, Vertical Convection (General Considerations), Local Convection, Classification of Winds, Whirlwinds, Auto-convection Gradient, Cumulus Convection, Valley Breeze, Sea Breeze, Land Breeze, Mountain Breeze, Glacier Winds, the Bora, Mistral, Nor- wegian Fallwinds, Continental Fallwinds, Thunderstorm Winds. VIII. ATMosPHERIC CIRCULATION (Continued)................00000 eee Winds Due to Widespread Heating and Cooling (General Remarks), Irregularities (Gusts or Puffs), Interzonal Drift, Change of Velocity with Change of Latitude, Law of Conservation of Areas, Deflection Due to the Earth's Rotation, Rate of Change of Wind Direction, Centrifugal Deflecting Force of Winds, Relative Values of Centrif- ugal and Rotational Components, Total Horizontal Deflecting Force, Gradient Velocity, Gradient Velocity Nomogram, Auto- matic Adjustment of Winds in Direction and Velocity, General Relations of Wind to Elevation, Local Wind Velocity and Elevation, Horizontal Pressure Gradient and Elevation, Level of Maximum Horizontal Pressure Gradient, Constancy of Mass Flow—Egnell’s Law, Relation of Velocity to Altitude above 5 Kilometres, Season of Greatest Winds, Latitude of Greatest Winds, Hours of Greatest and Least Winds, Diurnal Shift of the Wind, Normal State of the Atmosphere, Equatorial East-to-West Winds, Probable Inter- zonal Circulation of the Stratosphere. IX. ATMOSPHERIC CIRCULATION (Continued).............0 00000002005 Monsoons, Trade Winds, Antitrade Winds, Tropical Cyclones, Distinction Between Tropical and Extra-tropical Cyclones, Place of Occurrence, Size and Shape of Storm, Direction of Wind, Velocity of Wind, Direction of Travel, Velocity of Travel, Origin and Maintenance. X. ATMOSPHERIC CIRCULATION (Continued) ................00 00000 ee XI. Winps ADVERSE TO AVIATION XII. BAROMETRIC FLUCTUATIONS Extra-tropical Cyclones, Size, Direction of Movement of the Cyclonic Centre, Chief Paths of Cyclonic Storms, Velocity of Travel, Frequency, Direction’ of Winds, Deflection Angle, Wind Velocity, Convection, Velocity of Travel and Amount of Precipitation, Classi- fication, Thermal, Insolational, Mechanical, Tentative Hypothesis of the Origin and Maintenance of Migratory Cyclones, Anticyclones, Mechanical, Velocity and Path of Travel, Wind Velocity, Radia- tional, Thermal, Eddics, Foehn (Chinook), Tornado, Waterspouts. Air Fountains, Air Sinks, Air Cataracts, Cloud Currents, Keria} Cascades, Wind Layers, Wind Billows, Wind Gusts, Wind Eddies, Air Torrents, Air Breakers. Seasonal Pressure Changes, Regional Pressure Changes, Storm Pressure Changes, Barometric Ripples, Diurnal and Semidiurnal Pressure Changes, Tidal Pressure Changes. 93 123 1S 214 226 CONTENTS ix XIII. EVAPORATION AND CONDENSATION... 0.0.0... 0000 eee eee eee ees 241 Evaporation, Evaporation into Still Air, Evaporation in the Open, Salinity, Dryness of the Air, Evaporation into a Steady Horizontal Wind, Barometric Pressure, Area of Surface, Temperature of the Water, Empirical Evaporation Equations, Condensation, Conden- sation due to Contact Cooling, Condensation Due to Mixing, Con- densation Due to Dynamic Cooling, ‘‘Pseudoadiabatic’’ Convec- tion, Principal Forms of Condensation, Why the Atmosphere Generally is Unsaturated, How Raindrops are Formed, Velocity of Fall of Raindrops, Intensity of Precipitation, Summer and Winter Precipitation. DOV: ROGS: AND: CLOUDS: 5.4) (edie oa cgi sean eo eta see ad ea oe AS 271 Distinction Between Fog and Cloud, Radiation Fog, Advection Fog, Clouds, Classification, Cirrus, Cirro-stratus, Cirro-cumulus, Alto-stratus, Alto-cumulus, Strato-cumulus, Nimbus, Fracto- nimbus, Cumulus, Fracto-cumulus, Cumulo-nimbus, Stratus, Bil- low Cloud, Lenticular Cloud, Crest Cloud, Banner Cloud, Scarf Cloud, False Cirrus, Mammato-cumulus, Tornado or Funnel Cloud, Relation of Cloud Height to Humidity, Levels of Maximum Cloudi- ness, Regions of Minimum Cloudiness, Cloud Depth or Thickness, Cloud Velocities. SV. THE LHUNDERSTORM A caccnss sew ee Gowen aA Ka os oa OS 311 Origin of Thunderstorm Electricity, the Violent Motions of Cumulus Clouds, Convectional Instability, Periodic Recurrence of Thunder- storms, Daily Land Period, Daily Ocean Period, Yearly Land Period, Yearly Ocean Period, Cyclic Land Period, Cyclic Ocean Period, Geographic Distribution, Pressure and Temperature Dis- tribution, Thunderstorm Winds, the Squall Cloud, Schematic Illus- trations, Thunderstorm Pressures, Thunderstorm Temperatures, Thunderstorm Humidity ,‘‘Rain-gush,”’ Thunderstorm Velocity, Hail. AVI. LIGHTNING: suxrys deisa diesuceie ides er eebee tas ge aed teades eee 367 Lightning, Streak Lightning, Rocket Lightning, Ball Lightning, Sheet Lightning, Beaded Lightning, Return Lightning, Dark Lightning, Duration, Length of Streak, Discharge Where to Where, Discharges Direct not Alternating, Temperature, Visibility, Spec- trum, Thunder, Rumbling, Distance Heard, the Ceraunograph, Chemical Effects, Explosive Effects, Crushing Effects, Quantity of Electricity in Discharge, Danger, Lightning Protection, Conductors, Terminals, System, Joints, Bends, Attachment, Ground Connec- tions, Connection to Neighboring Conductors, Special Dangers. CONTENTS PART II ATMOSPHERIC ELECTRICITY AND AURORAS T. ATMOSPRERIC ELECTRICITY. .......... 00 0c cece cece eee e eee eats Chief Discoveries, Electrical Field of the Earth, Potential Gradient Near the Surface, Location Effect, Annual Variation, Diurnal Vari- ation, Potential Gradient and Meteorological Elements, Potential Gradient and Elevation, Surface and Volume Charges, Electrical Conductivity of the Atmosphere, Annual Variation, Diurnal Vari- ation, Relation to Weather, Conductivity and Elevation, Ionic Density, Ionic Velocity, Langevin Ions, Electric Currents in the Atmosphere, Penetrating Radiation, Origin and Maintenance of the Earth’s Charge. TD. AURORA (POLARIS icc adie accede BAH QAR Gen Raduge eo Sid MUL ie dba aaa bande aceD I. Ill. IV. V. Aurora Polaris, Latitude Variation, Periodicity, Color, Height, Cause. PART III ATMOSPHERIC OPTICS INTRODUCTION—CLASSIFICATION. 2.00.00. nee . PERSPECTIVE PHENOMENA..........0 000 eee etre eee eee nae Stairstep Clouds, Arching of Cloud Bands, Crepuscular Rays, Auroral Streamers, Sky Vault, Apparent Size of Sun and Moon, Apparent Distance Between Stars. REFRACTION PHENOMENA: ATMOSPHERIC REFRACTION............. Astronomical Refraction, Scintillation, Scintillation of Planets, Shadow Bands, Terrestrial Scintillation, Shimmering, Optical Haze, Times of Rising and Setting of Celestial Objects, Green Flash, Terrestrial Refraction, Looming, Towering, Sinking, Stooping, Superior Mirage, Inferior Mirage, Lateral Mirage, Fata Morgana. REFRACTION PHENOMENA: REFRACTION BY WATER Drops......... Rainbow, Principal Bows, Supernumerary Bows, Deviation of Rays, Minimum Deviation, Formation of the Bow, Minimum Brightness Between Bows, Origin of Supernumerary Bows, Equation of Wave Front, Variation of Intensity, Distribution of Colors, Relation of Size of Drop and Wave-length to Intensity, Popular Questions, Reflected Rainbows, Reflection Rainbows, Horizontal Rainbow. REFRACTION PHENOMENA: REFRACTION BY ICE CRYSTALS......... Prismatic Refraction, Deviation, Minimum Deviation, Total Re- flection, Illumination of Sky by Ice Crystals, Parhelia of 22°, Halo of 22°, Arcs of Lowitz, Tangent Arcs of Halo of 22°, Relative Fre- quency of Horizontal and Vertical Tangent Arcs, Parhelia of 146°, Halo of 46°, Halo of 90°, Bouguer’s Halo, Circumzenithal Arc, Kern’s Arc, Circumhorizontal Arc, Lateral Tangent Arcs of Halo of 46°, Infralateral Tangent Arcs of Halo of 46°, Supralateral Tangent Arcs, Secondary Halos. REFLECTION PHENOMENA......00000 0000 cece cece cence eee neeeeeens Parhelic Circle, Anthelion, Oblique Arcs of the Anthelion, Parhelia of 120°, Parhelia of 90°, Pillars, Crosses, Recent Halo Complexes. 422 426 427 431 456 483 518 VI. VII. VII. II. IIl. IV. bot fo: 8 amie ber Tbe ey CONTENTS xi DIFFRACTION PHENOMENA... 0.000000 ccc cece ccc cee ee eeeee 528 Coronas, Size of Cloud Particles, Iridescent Clouds, Bishop's Ring, Glory. PHENOMENA DUE TO SCATTERING: COLOR OF THE SKY.........-.-- 538 Early Ideas, Modern Theory, Extinction Coefficient, Prevailing Color, Twilight Colors, Duration of Twilight, Twilight Illumination. PHENOMENA DUE TO SCATTERING: SKY POLARIZATION...........- 551 Condition of Primarily Scattered Light, Condition of Secondarily Scattered Light. PART IV FACTORS OF CLIMATIC CONTROL ¢ GENERAL, SUMMARY) <4 23 u's od ast ow tad en tea eae Se spear uieeRes 556 Weather Recollection, Facts of Climatic Changes, Existing Factors of Climatic Control. PRINCIPAL ICE-AGE THEORIES. ...........000 00 cece eee eee eees 563 Solar Variation Theory, Croll’s Eccentricitv Theory, Carbon Dioxide Theory. VUECANISM:® “LHEORY: 5 «see sex Maver dencoa wep da 8 aware saelat a 569 Effect of Change in Surface Covering, Dust in the Upper Atmos- phere, Size of Dust Particles, Time of Fall of Dust, Action of Dust on Solar Radiation, Action of Dust on Terrestrial Radiation, Num- ber of Dust Particles, Temperature Correction Due to Radiation from Dust,Total Quantity of Dust, Effect of Dust on the Interzonal Temperature Gradient. VULCANISM: (OBSERVATIONAL 9:95.05 a0 sasg oe Seed HEE ES Rw EEE Se ES 585 Pyrheliometric Records, Temperatures at the Surface of the Earth, Relation of World Temperatures to Pyrheliometric Values, Sun- Spots and Temperature, Temperature Variations since 1750, Volcanic Disturbances of Atmospheric Temperature since 1750, Magnitude and Importance of Annual Temperature Changes. . OTHER FACTORS OF CLIMATIC CONTROL..........00 000000 eee eens 604 How Sun-Spots may Change Earth Temperatures, Influence of Carbon Dioxide on Temperatures, Temperature Effects of Land Elevation, Temperature Effects due to Changes in Land Area, Temperature Effects of Atmospheric and Oceanic Circulation, Present Atmospheric and Oceanic Circulations, Possible Changes in Oceanic Circulation and their Obvious Climatic Results, Relation of Temperature to Surface Covering, Chronological Relation of Geological Events, Conclusion. APPENDIX I.—GRADIENT WIND VELOCITY TABLES eaenenhis tare gat aves 630 Table I, Gradient Wind Velocity for Cyclonic Movement; Table IT, Gradient Wind Velocity for Anticyclonic Movement. APPENDIX II.— CONSTANTS AND EQUIVALENTS..........-..00000055 655 PHYSICS OF THE AIR PART I. MECHANICS AND THERMODYNAMICS OF THE ATMOSPHERE. CHAPTER I. OBSERVATIONS. Berore discussing any of the physical laws of the atmosphere it will be instructive briefly to consider the observational data upon which they are based; that is, to enumerate the meteoro- logical phenomena which commonly are measured, and to indi- cate in each case the type of instrument generally used. No effort will be made to describe apparatus in detail, nor to discuss the minutiz of every correction. These important matters are fully taken care of by observers’ instructions issued by the United States Weather Bureau and other meteorological services. Be- sides, they pertain to the technique of the collection of data rather than to the science deduced therefrom, which latter, and not the former, is the object of the present discussion. MEASURED PHENOMENA. Temtperature.—Probably the most obvious, satisfactory defi- nition of temperature describes it as that thermal state of an object which enables it to communicate heat to other objects. Whenever the heat interchange that always takes place between two objects in thermal communication results in a net loss to the one and gain to the other, the temperature of the former is said to have been higher than that of the latter. If, however, there is no net loss or gain by either, the objects are said to have the same temperature. Detection of net loss or gain of heat may be accomplished in any one of many ways, some of which are: change of volume; change of state; change of electromotive force; and change of electrical resistance. All these, according to circumstances, afford con- venient means of comparing the temperatures of different ob- jects, and of establishing a scale for ready reference. Thus the I 2 PHYSICS OF THE AIR ordinary mercury thermometer, the alcohol thermometer, adapted to low temperatures, and others of this nature, are based on the fact that the coefficient of volume expansion of the vessel is not the same as that of the contained fluid. Such thermometers, though capable of a high degree of accuracy, are not adapted to cheap and convenient registration, except of extremes; that is, the maximum or minimum temperature reached since last adjust- ment. Nevertheless, differential expansion does afford several means of obtaining continuous mechanical registration of tem- perature. The most compact and satisfactory apparatus of this kind in general use consists essentially of a curved closed tube of oval cross-section—a Bourdon tube—completely filled with a suit- able liquid. Inequality of expansion between tube and liquid in this case demands change of volume, and that in turn changes the curvature of the tube. Hence by making one end of the tube fast and connecting the other with a tracing point it at once becomes possible to obtain on a moving surface a complete record of tem- perature changes. The unequal expansion of the two sides of a bimetallic strip is also utilized in obtaining temperature registration. Variation with temperature of electrical resistance, and of the electromotive force at a thermal junction, both provide means of measuring temperature changes to a high degree of accuracy. In the case of the atmosphere, however, temperature com- monly is measured at stated intervals, and whenever desired, by the readings (corrected when necessary) of a good mercurial, or, in very cold regions, alcohol, thermometer exposed to full circula- tion of the air, but protected from both solar and sky radiation. An excellent shelter for this purpose, with maximum and mini- mum thermometers in place, is shown in Fig. 1. Normally, of course, the door is closed. A less accurate but continuous record of atmospheric temperature usually is secured by the use of either a bimetallic or a Bourdon tube thermograph (Fig. 2). The con- nection between the thermal element and the tracing point may be either mechanical, as shown, or electrical. In the latter case the two may be separated any desired distance, the first placed out- doors, say, and the second conveniently located in an office. Other methods of measuring and even continuously recording the tem- *For the theory of this extensively used gauge, see H. Lorenz; Zeit. des Ter. Deutsch. Ingen., 54, p. 1865, IgI0. Fic. 1.—Thermometer shelter and rain gauge for codperative observers. 4 PHYSICS OF THE AIR perature of the air have been devised, though at present they are but sparingly used, and then, as a rule, only for special purposes. Pressure.—The pressure of the atmosphere, upon the distribu- tion of which winds and storm movement so vitally depend. ordinarily, is not determined. Measurements, however, equally good for intercomparison, are made to which it is directly pro- portional, and from which pressures readily might be computed in dynes per square centimetre, or any other specified units. On land the measurement usually taken for this purpose is the height of the barometric column; that is, the difference in level FiG: 2: Thermograph. between the two free surfaces of a continuous mass of mer- cury, one of which is open to the atmosphere, the other in vacuo, slightly corrected for temperature effects, capillarity, scale errors, and degree of vacuum. From this corrected height and the local force of gravity the actual air pressure is easily obtained. Fur- ther, by reducing the barometric heights simultaneously obtained at different places to what they presumably would be if the sta- tions all had a certain common level—for which operation appro- priate equations are used—data are obtained which, when plotted ona map of the region concerned, show the approximate pressure distribution, from which, in turn, the strength and course of the winds during the next 12 to 24 hours may be closely predicted. OBSERVATIONS 5 As a rule, the mercurial barometer is read by eye and only as occasion may require, but it also has been so constructed as to give excellent continuous records. The aneroid, or, as its name implies, non-liquid, barometer, though involving many sources of error, is conveniently portable and capable of fairly satisfactory use in many places—on kites, aeroplanes, etc.—where the mercurial barometer would be wholly impracticable. It consists essentially of a disk-like vacuum cell, or series of such cells, a few centimetres in diameter, whose cor- Fic. 3. (a oR EArt Dd Barograph. rugated, flexible top and bottom are held apart by a short, stiff spring. .\ny change in the atmospheric or external pressure obviously must lead to a corresponding flexure of the spring, which motion may be communicated to either an index hand or a recording pen. In the ordinary barograph (Fig. 3) the pen commonly is actuated by a number of aneroid cells placed in series. Most aneroids, whether single- or multiple-celled, require careful attention and frequent comparison with a standard mer- curial instrument. They also are inherently subject to lag errors due to the imperfect elasticity of the cells that varv according 5 6 PHYSICS OF THE AIR to the pressure conditions and the characteristics of the par- ticular instrument, and which, for accurate readings, must al- ways be allowed for. IVind Velocity—The velocity of the wind may be deter- mined by triangulation on clouds, balloons, and other floating objects; by noting the speed of rotation, easily automatically re- corded, of a windmill anemometer, air meter, or other similar device, and applying the necessary corrections; by the pressure on a flat surface squarely facing the wind; by the difference in level between the two free surfaces of a liquid in a U-tube or equivalent vessel when one surface is protected and the other exposed to the full force of the wind; and by a great many other but generally less accurate methods. The Robinson cup anemometer (Fig. 4) appears to be the most convenient and reliable instrument wherever it can be properly exposed. The theory of its action, however, is but im- perfectly understood.%* Rapid velocity changes, manifesting themselves in irregular puffs and of great importance to the avi- ator, the architect, and the engineer, generally are observed and recorded by some quick-acting pressure apparatus, such as the Dines pressure tube anemometer, or the Pitot tube, or Venturi tube. The Pitot tube, of which the Dines anemometer is only a modi- fication, consists of a tube with a “ dynamic” opening facing the wind, or current of other fluid, and one or more “ static’ open- ings facing at right angles to the direction of the flow. When the respective openings communicate with closed chambers, obvi- ously the head /: of the fluid in question that would balance the difference between the dynamic and the static pressures in a per- fect instrument (the best gives very nearly theoretical values) is given by the equation, h= 28 in which V’ is the velocity of the current, and g gravity accelera- tion; allin C.G.S. units. In practice the pressure difference is given by a column of liquid, a compressed spring, or other device, differentially con- nected with the two chambers, dynamic and static. In each case a Chree, Phil. Afag. 40, p. 63, 1895. OBSERVATIONS NI v= yi 7eeP when / is the corrected reading of the indicator in whatever terms, and c the value of i per unit of p. If, for instance, p is dynes per square centimetre, c is the thickness in centimetres of a FIG. 4. or! Robinson’s cup anemometer. horizontal layer of the air, say, that would produce a gravity pressure of one dyne per square centimetre; and similarly for other types of graduation. The Venturi tube which measures velocity of flow in exactly the reverse manner from that of the Pitot tube, that is, by de- crease of pressure, consists of two oppositely directed hollow 8 PHYSICS OF THE AIR " cones joined together coaxially by a short throat of uniform cross-section. The angular opening of the receiving cone, which may have a short cylindrical mouth, is relatively large, while the discharge cone is comparatively long and tapering. Let this tube be mounted parallel to the wind whose velocity I” it is proposed to measure, and let r be the ratio of the cross- section of the mouth to that of the throat, in which the velocity, therefore, is ry’. Clearly, then, if the flow through the tube is smooth (in good tubes it is very nearly so) the pressure against the wall of the mouth cylinder and that against the throat are each less than the outside static pressure. Furthermore, if My, /to, and h, are the heads of the current atmosphere that would give the static, mouth, and throat pressures, respectively, then, neglect- ing the effect of the wind outside the tube, V2 re V2 In + —— = hs + = I 28 28 and fogtn a) — © .. fortia th | 2 g (iz hts) Vom af teh) — gt leq r—t To determine /” by this method it clearly is only necessary to connect the mouth and throat cylinders through small openings to the opposite sides of a manometer, or either opening to one side of a manometer the other side of which is connected to a static chamber. If, as in the Pitot tube, p is the manometer reading and c the value of /: per unit of /, r= Miao _ ate 7" = 2 gcps : V fol for the several connections, as indicated. Obviously, a Pitot and a Venturi tube can easily be combined by connecting the dynamic opening of the first and the throat of the second to opposite sides of a manometer, and the reading of the latter thereby made approximately double that given by either tube alone. Wind velocities at considerable heights in the free air com- monly are obtained by triangulation on clouds, or, less satisfac- torily, owing to constantly changing altitude, on small free balloons. Wind Direction—The direction of the wind, as the term OBSERVATIONS 9 is used in meteorological literature, always means the direction from which the wind is blowing at the point in question. IJt may be determined approximately by the course of smoke, clouds, or other floating objects, by the set of a wind vane (Fig. 5), drift of a pennant, flexure of trees, or other simple methods. Vari- ous devices for automatically recording this direction, either in its entirety or for selected points only, are possible, the simplest, perhaps, being electrical and under control of contacts made by a rod connected to and rotated by the wind vane. In common practice only a small number of directions, usually eight, are registered, each covering an angle of 45 degrees. That is, a wind from any point between W. 22.5° S. and W. 22.5° N. is regis- tered as a west wind; and similarly for the other octants. This division may seem very coafse, but it is sufficient for most meteorological uses. Humidity, Definitions —The mixture of water vapor with the permanent gases of the atmosphere has occasioned a number of “humidity problems” over which the student is in danger of becoming more or less confused. And this danger is increased by the use in this connection of the same word by recognized authorities to connote quite different ideas. For the sake of clearness, therefore, this subject will be briefly discussed under several sub-heads. I. Absolute Humidity. Two entirely different definitions are in use for the common expression “absolute humidity” : a. The mass of water vapor per unit volume. b. The gas pressure exerted by the water vapor per unit area. According to the first definition, the absolute humidity may be expressed in terms of any units of mass and volume, as, for instance, grammes per cubic metre. According to the second definition, it may be expressed in terms of any units of force and area—dynes, say, per square centimetre; or any measurable pressure effect, such as height of the mercury column the vapor pressure would sustain. Accepting the simple definition a as being correct, as every one does, it remains to show the equivalence to it of definition b. But this follows at once from the well-known fact that the pressure exerted by any constituent in a uniform mixture of gases is to the total pressure as the number of its molecules Guy RODS (3) ONTACT BOX CONTACTS Ww RON STEP uf SHOES FOR GUY RODS(3) pity BASE PLATE Bm me i . 7 Wind vane and anemometer support, pattern 1913 (showing 4-foot wind vane on ball tearings) OBSERVATIONS II per given volume is to the total number in the mixture... Vapor pressure, therefore, varies directly as vapor density, or mass per unit volume. Hence the two definitions, a and b, of absolute humidity are equivalent to each other, for any given temperature. II. Relative Hunudity. Different definitions are also in use for the expression “rela- tive humidity”: a. The ratio of the actual to the saturation quantity of water vapor, at the same temperature, per unit volume. b. The ratio of the actual to the saturation pressure of water vapor at the same temperature. In these definitions the expressions “saturation quantity” and “saturation pressure” refer to the maximum quantity of water vapor per unit volume and maximum pressure of water vapor per unit area, respectively, that can exist in the presence of a flat water surface, at the given temperature. IIL. Specific Humidity. > The term “ specific humidity,”’ occasionally found in meteoro- logical literature, means the weight of water vapor per unit weight of moist air. IV. Dew Point. The expression ‘dew point,” as used in humidity tables and elsewhere, means simply that temperature at which, without change of pressure, saturation is just reached. It might also be defined as that temperature at which the saturation pressure is the same as the existing vapor pressure. V. Saturation Deficit. “ Saturation deficit,” a term much used by plant physiologists, is susceptible of several definitions, especially: (1) Amount of water vapor, in addition to that already present, per unit volume, grammes per cubic metre, say, necessary to produce saturation at the existing temperature and pressure. (2) Difference be- tween actual and saturation pressure. (3) Ratio of the vapor pressure deficit to the saturation pressure at the existing tem- perature. The third is relative, the others absolute. Humidity, Instrumentation —The absolute humidity, in the sense of mass of water vapor per unit volume, can be determined 12 PHYSICS OF THE AIR by noting the increase in weight of phosphorus pentoxide or other suitable drying agent on absorbing a known volume of the vapor. This direct determination of the humidity, however, is impracticable for routine observations. On the other hand, as partial pressure ratios are independent of temperature, the determination of the absolute humidity in the sense of vapor pressure merely requires measuring the loss of pressure due to absorption of the vapor in a closed space, for which there are several devices ;’® or, as more commonly practised, finding the dew point and referring it to a table of predetermined saturation pressures. Similarly, the difference between the cur- rent and dew-point temperatures is sufficient to determine, from suitable tables, the relative humidity. The dew point may be found by any one of several slightly different methods, all of which have for their basis the deter- mination of that temperature at which moisture just begins to collect on a cooling surface. A thin-walled silver tube, burnished on the outside, is an excellent vessel for the cooling mixture. The temperature of the liquid, if well stirred, and that of such a tube will be very nearly the same; and, besides, the dulling of the surface promptly reveals the slightest condensation. It should be noted, however, that if carefully taken the ob- served temperatures of the silver hygrometer will be slightly below the actual “dew point.”” This is because the initial deposit is in the form of minute droplets, whose vapor pressure is greater than that of a flat surface at the same temperature, in accordance with the equation,”® 2 Tp» R (pu——pv) Ap= which may be derived as follows: Let & be the radius of a capillary tube standing in a vessel of water, Fig. 6; / the height of the water in the tube when satura- tion is attained; T the surface tension; ,, and p, the densities of the water and the saturated vapor, respectively; and g the gravity acceleration. Then, obviously, 27 RT=7 R? (Pu—pe) gh; and *b A. N. Shaw, Trans. Roy. Soc. Can., 10, p. 85, 1916. *c Sir William Thomson, Proc. Roy. Soc., Ed. 7, p. 63 (1870). OBSERVATIONS 13 being the difference between the vapor pressures at the inner and outer surfaces. Hence _Adb_ 2T __ 2T by = Pug R (Pw—pz) g’ and Ae ~R (Pu—pa) At ordinary temperatures and for droplets whose radii are 10% cm. (a possible size) the temperature depression, or error, amounts roughly to 0.02" C. According to the equation, the error obviously might have any value, though actually it seems Fic. 6. ~N a <= SS Relation of curvature of surface to saturation vapor pressure. always to be small, owing to limiting values of R, and presum- ably also to other causes; that is, this too, like many other physical equations, has its limitations. In taking humidity measurements the observer must be care- ful that his presence does not affect the amount of moisture in the air under examination—he must stand to the lee of his apparatus. Although the dew-point apparatus and other absolute hygrom- eters are extremely simple in theory, they generally are too com- plicated in structure and too difficult to manipulate to be suitable for routine observations. On the other hand, the psychrometer, presently to be explained, which depends on the maximum cool- 14 PHYSICS OF "THE. AIR ing of water by evaporation when amply ventilated, is less obvious in theory,’ but both simple in construction and easy to use. A convenient form of the psychrometric equation is: e=c'—AB (t—?’), in which t= the air temperature. t/= the temperature of a vigorously ventilated wet-bulb thermometer. e=the vapor pressure. e’=the saturation pressure at temperature ?’. B= barometric pressure. 4=a number that, in the case of ample ventilation, varies only with ¢’, and with it but slowly. Obviously, the relatively cool wet-bulb gains heat by conduc- tion from the adjacent atmosphere and loses heat through evapo- ration. There is also absorption and emission of radiation, but when the ventilation is ample—3 metres per second or more— the net gain or loss of heat by this process is negligible in com- parison with that by conduction or evaporation, respectively. Radiation effects may be still further reduced by surrounding the thermometer and its stem with a suitable wet-lined, reflecting shield, preferably of the Dewar bulb type. For most purposes, however, the use of a shield is unnecessary. It may be assumed, then, that the equilibrium or steady temperature of an amply ventilated wet-bulb thermometer is that at which the heat it gains by conduction from the passing air is equal to the heat it loses from evaporation. The details of the processes of evaporation and heat conduc- tion involved are not all fully known. But it 1s known that when radiation effects are excluded, the equilibrium temperature is measurably independent of the rate of ventilation, which, under these conditions, is only a convenient means of quickly attaining a steady state. In the extreme case of simple molecular diffusion in an otherwise stagnate atmosphere it seems safe to assume that *dIvory, Phil. Mlag., 60, p. 81, 1822; August, Ann. der Phys., 5, 60, 1825; Apjohn. Trans. Roy. Irish Acad., 1834; Regnault. C. R., 20, p. 11273, 1220, 1845; 35. Pp. 930, 1852; Maxwell, Ency. Brit., oth Ed., “ Diffusion,” 1878; Stefan. Zeit. Ost. Gessell. fiir Mcteorologie, 16, p. 177, 1881. Ferrel. Annual Report, Chief Signal Officer, Appendix 71, “‘ Hygrometry,” 1885; Carrier, Trans. Amer. Soc. Mechan. Eng. 33, p. 1005, 1912; Grossmann. dan. d. Hydr. usw., 44, p- 577, 1916. OBSERVATIONS 15 the space immediately adjacent to the wet surface is fully satur- ated at the temperature of the wet-bulb, and that heat is supplied by molecular bombardment of the air. Furthermore, if the tem- perature is not affected by ventilation (all radiation effects ex- cluded) it seems that identically the same conditions just stated, or their equivalents, must hold whatever the ventilation. In so far as these assumptions are true, it follows that during a steady state the gain of heat, Q, per unit time, say, is given by the equation Q=mys (t—t) in which mm is the mass of previously free air, temperature t, that during the time in question comes into actual contact with the wet-bulb, temperature ¢’, and s its average specific heat, at con- stant pressure, between these temperatures. Similarly, the equal amount of heat simultaneously lost is given by the equation _e—e C= oer rm Ly in which e’ is the saturation vapor pressure at the temperature ?’, e the vapor pressure in the free air, B the current barometric pressure, ¢ the ratio of the molecular weight of water to the equivalent molecular weight of the free air, and Ly’, the latent heat of vaporization at the temperature ?’. Hence, equating the two values of Q. e=e'—A B(t-") in which 5 r Ly The value of A, therefore, varies slightly, but to known amounts with e and ¢’. At t/=o0°C. it also depends upon the phase, liquid or solid, of the evaporating water. But as vapor pressure at 0° C. is the same over ice as over water, it seems that the abrupt change of A at this temperature must be accommodated by an equivalent opposite change in the value of t—?’. The general agreement between this theory and the best psy- chrometric observations, such as those of Hazen, Marvin and others of the Weather Bureau (Signal Corps),** while not per- te“ Annual Report Chief Signal Officer,” Appendix 24, 1886. U.S. Weather Bureau : Fic, 7 —Sling psy- chrometer. PHYSICS OF THE AIR fect, is sufficiently close to make it doubtful which is in greater error, and thus to increase confidence in each. When ¢, ce’, and B are expressed in millimetres of mercury under standard conditions and ¢ and t’ in centigrade values, observation gives e=c’—0.000660 B (t-t’) (1+000115 17), approximately. In practice f and ft’ commonly are obtained with a properly constructed and adequately venti- lated (usually whirled) psychrometer carrying both a wet and a dry bulb thermometer. The sling psychrometer (Fig. 7), whirled by hand, is a simple device for this purpose. The observer has only to note the air temperature, the wet bulb depres- sion (that is, difference between the wet and dry bulb temperatures), and barometric pressure. With these values he reads off from tables the vapor pressure and the dew point. Assmann’s aspiration psychrometer (Fig. 8), however, appears to be the most accurate instru- ment for this purpose. This consists of two par- allel double-walled tubes, silvered to minimize radiation effects, containing a wet and dry bulb thermometer, respectively, united into a common stem and surmounted by a small ventilating fan. Several kinds of instruments for automati- cally recording humidity have been devised, but of these only the hair hygrometer is in general use. It resembles some forms of thermograph except that the actuating member instead of being a thermal element is a strand of clean hairs, freed of oil, that increase in length with the humidity. With reasonable care the data thus obtained on a cali- brated scale are both consistent and fairly reliable. Cloudiness.—The degree of cloudiness gener- ally is expressed in tenths (estimated) of the sky actually overcast. Kinds of Clouds.—As an indication of the approaching weather and general state of the at- mosphere, the kind or kinds of clouds present OBSERVATIONS 17 is more important than the mere total percentage of cloudiness. For convenient reference clouds: have been divided into four pri- mary and nine secondary (combination, alto, and fracto) forms. These are: Primary Forms: Cirrus—or curl cloud; stratus—or layer cloud; cumulus—or wool-pack cloud; and nimbus —or rain cloud. Fic. 8. THERMOMETER SUN SHIELD * Aspiration psychrometer. CoMBINATION ForMs: Cirro-stratus, cirro-cumulus, strato- cumulus, and cumulo-nimbus. Ato Forms: Alto-stratus and alto-cumulus. Fracto Forms: Fracto-stratus, fracto-cumulus, and fracto- nimbus. The foregoing names are used in the International Cloud Classification, now generally accepted. 18 PHYSICS OF THE AIR It will be noted that several names possible in accordance with this scheme of nomenclature are omitted, even though a few of them have occasionally been used in certain other schemes of classification. Thus there is no cirro-nimbus, for the reason that rain clouds never have the cirrus form; no strato-nimbus, because all rain clouds are flat-bottomed; no alto-cirrus, because cirri usually are high; no alto-nimbus, because rain clouds, except the cumulo-nimbus, are never high; and no fracto-cirrus, because cirri are always broken and detached. Most of these clouds may be grouped according to their re- spective altitudes: Uprer CLoups: Cirrus, cirro-stratus. INTERMEDIATE CLoups: Cirro-cumulus, alto-stratus, alto- cumulus. Lower Cxoups: Strato-cumulus, nimbus, fracto-nimbus, stratus, fracto-stratus. The cumulus, fracto-cumulus, and cumulo-nimbus (base), all caused by diurnal convection, vary in altitude from low to intermediate. — Precipitation —The amount of precipitation is measured in the actual or, in case of snow, equivalent depth of horizontal water layer. The details in respect to the manner of catching and measuring precipitation have been greatly varied. The meas- uring, of course, is simple enough, but it is far from easy to secure a correct catch, owing chiefly to the influence of the vessel itself on the wind currents over and about its mouth and the consequent effect on the amount of precipitation actually caught. The details of a simple rain gauge are shown in Fig. 9, and its installation in Fig. 1. Many gauges are provided with a small tipping bucket just beneath the spout of the receiving funnel, by which the time of occurrence and rate of each rainfall are elec- trically recorded at any desired place. Evaporation.—Evaporation is measured in terms of the depth of a flat laver of water, of area equal to that of the evaporating surface. This, too, like precipitation, has been measured by many kinds of apparatus, some of which have been designed with the view of simulating the surface of leaves. or meeting other spe- cial conditions. Manv attempts have also been made to find from theoretical considerations a correct equation between rate of evaporation and the various factors upon which it depends, OBSERVATIONS 19 such as shape of surface, extent of surface, temperature of the superficial layer, temperature of the air, humidity, barometric pressure, wind velocity, and anything else that might be consid- ered of importance. A few special cases, such as evaporation from flush circular and elliptical water surfaces at constant tem- perature and in absolutely stagnant atmosphere, appear to have been completely analyzed.2_ But this work, however ingenious, Fic. 9. Front View. Vertical Section, a at ee ¥ 1 F a e d oe Lid i B cts a ! Horizontal Section, EF. | i | | | | | Hemel O72 3 ¢ 56 FE 9 10H l2 kK MIS 161718 19 2021 2223 OKINCHES Seok SS ee ee SCALE. Rain gauge, has contributed very little to the solution of the general problem, because in Nature water surfaces are of irregular outline, and all the factors that control evaporation are in such a maze of flux and reflex as to render equation-testing and evaluation of con- stants of doubtful accuracy and value. Evaporation, therefore, like most biological and many other phenomena, must be observed and measured; it cannot be computed very accurately as a func- tion of given conditions. For discussion see Chapter XII. Sunshine.—Sunshine generally is expressed in terms both of ? Stefan, Sitz. der K. Akad., 73, 943, 954 (1881). oo 20 PHYSICS OF THE AIR hours of its actual and percentage of its possible duration. It is recorded automatically, usually through electrical contact made or broken by the movement of a mercury piston in the stem of a vacuum-enclosed black bulb differential air-thermometer (Fig. 10) ; by charring on prepared cards in the focus of a glass sphere; or by photographic traces on sensitized paper. Sunshine recorder. fadiation.—In relation to the atmosphere, radiation from three sources is of importance: from the sun, from the sky, and from the earth. Each may be measured integrally (that is, in terms of the amount of that energy delivered per minute, say, per unit normal area at the place of observation), or spectrally (that is, as distributed according to wave-length). The first kind of measurement, the integral, usually is made by some type of pyrheliometer, and the second (so far applied only to solar and sky radiation) by a bolometer. Electrical Condition—Measurements of the electrical condi- OBSERVATIONS 21 tion of the atmosphere generally are confined to the vertical po- tential gradient, determined by any one of several methods, ioni- zation and the consequent conductivity. Optical Phenomena.—Various optical phenomena of the at- mosphere are observed and recorded. These include, especially, mirages, sky colors, sky polarization, rainbows, coronas, and halos. For several of them—mirages, sky colors, and rain- bows—mere eye observations are sufficient. Sky polarization, however, cannot be measured or even detected without the aid of suitable apparatus, while the data pertaining to halos and even coronas are far more valuable when they include accurate angular measurements. Turbidity.—The turbidity or haze of the atmosphere, whether caused by dust particles (dust haze) or by irregular temperature distribution (optical haze), though often a matter of importance, seldom is measured, and even then only indirectly, since the usual method is to note the maximum distance at which a -given ob- ject or certain of its details may be distinctly seen. Strictly speaking, this process measures only transparency, from which, however, the inverse, opacity, may be inferred. Typical Installation A typical roof installation of the more common meteorological instruments is shown in Fig. 11. The wind vane is at the top of the tower, the whirling Robinson cup anemometer just below and to the left of the vane, and the sunshine recorder slightly lower, on the cage or platform rail- ing. The thermometer shelter, with the door open, is in the lower portion of the tower. Finally, two rain gauges—one simple, the other tipping bucket—are shown in the lower left corner of the picture. SOURCES OF METEOROLOGICAL INFORMATION. As a further introduction to a discussion of the physics of the air, it will be helpful to consider a sort of vertical cross- section of the atmosphere as a whole with reference to the sources of meteorological information concerning each particular level. Other cross-sections that show its temperature, pressure, density, and composition at various elevations will be given later. Fig. 12, an adaptation of Wegener’s profile of the atmosphere, indicates the principal present sources of this information and the distribu- tion of meteorological phenomena at various levels. 5 Phys. Zeitsch., 12, Jahrg., 1911, p. 170. 3 PHYSICS OF THE AIR 1, 22 5 = Fic. t1—Forty-foot steel wind instrument tower; typical installation for high office building (Lynchburg, Va., January, 1914.) OBSERVATIONS 23 Mountains and other irregularities of the earth’s surface make it practicable to examine the atmosphere minutely and to record continuously all its changes at every elevation from sea level up to nearly six kilometres. In fact, many continuous records have already been obtained at the summit station on El Misti, Peru, whose altitude is 5852 metres. Occasional and partial records have been obtained by this means as far up as about 7 kilometres, but no higher, since this is the limit to which any Fic. 12. It. on 300 4 2007 J z 9° 9 AURORAL oa DRAPERIES Z 0 1007 2 qf an = T5tZ--- a 9- HE~LA MEE - => es ao w Oo Zn 7 uzr wih < nL<_* z= MOUNTAINS. + T | [REGIONS oF cLlouns & ORDINARY DUST T Sources of meteorological information. one has ever yet been able to climb. But all-such records, whether obtained at high levels or low, of course are more or less affected by the surface conditions. Hence some means of obtaining observations and records other than apparatus carried about on the surface of the earth is essential to a knowledge of the conditions and movements of the free atmosphere. One obvious source of information as regards motion only, and which has been extensively used, is the observation of drifting clouds, which occur at all levels from the bottom of the atmos- phere up to 11 kilometres, or thereabouts, in middle latitudes, and occasionally, in the tropics, even as high as 15 kilometres. 24 PHYSICS OF THE AIR There are several methods of determining the elevation, direction of motion, and velocity of clouds, but all depend upon simple processes of triangulation. Thus, simultaneous theodolite observations made on the same spot in a cloud from two sta- tions whose elevations and distance apart are known obviously furnish all the data necessary for an easy and fairly accurate determination of the height of the particular spot in question, while a single subsequent observation by either instrument on this spot, provided the time interval between the first and second observations is known, clearly gives all the additional data neces- sary to the determination of its velocity and direction of travel— assuming uniform motion and constancy of elevation. Excellent results, also, are gotten from cloud negatives simultaneously ob- tained with phototheodolites provided with fiducial lines. In this way, if several successive exposures are made, the height and movement of each distinguishable point in the cloud can be deter- mined, and therefore not only the general height and drift of the cloud as a whole, but also its dimensions and something of its internal motions. However, the general motion of the wind at the point observed and time of observation, though interesting and often valuable, is by far the chief information about the atmosphere that clouds give, and, indeed, some, such as those formed by air billows over mountain crests and elsewhere, do not give even this. Besides, they are not always present, so that on clear days even this modicum of information about the upper air would be impossible to obtain if we had no other means of inves- tigation. But there are others, the most fruitful of which is the carrying of self-registering thermometers, barometers, hygrom- eters, and the like into the free air by means of : a. Kites (Fig. 13) to over 7 kilometres, the record being 7.26 kilometres. b. Aeroplanes; present limit about 11 kilometres. c. Manned balloons; maximum elevation, roughly, 11 kilo- metres. d. Sounding balloons (Figs. 14-and 15), with a record of 35.08 kilometres. Upper air movements are also shown by the flights of pilot balloons (small balloons without apparatus); record 39 kilometres. The registering apparatus sent aloft by these various methods furnish reliable information concerning the composition (in- OBSERVATIONS 25 26 PHYSICS OF THE AIR cluding humidity), temperature, pressure, direction of motion, and, in some cases, velocity of the air, from the surface of the earth up to the greatest elevation reached. And it is this auto- matically recorded information, gathered, with but little excep- tion, since the beginning of the twentieth century, that has so Fic. 14. Sounding balloons. greatly extended our accurate knowledge of meteorology, and done so much to make of it an interesting and profitable branch of both theoretical and applied physics. Beyond the reach of the pilot balloon, or, for the present, at elevations greater than 39 kilometres, our information of the atmosphere is limited to such deductions as properly may be OBSERVATIONS 27 drawn from the height of the twilight arch—roughly, 75 kilo- metres; the paths of shooting stars, rarely, if ever, seen as high as 200 kilometres; and the phenomena of the auroras, those curi- ous and but partially explained electrical discharges that seldom occur at a lower level than go kilometres or higher than 300. Fic. 15. Sounding balloon. The above, obviously, are all, or nearly all, the means by which our knowledge of the atmosphere has been obtained. Up to 35 kilometres it is comparatively well known, but beyond that level only deductions, growing less certain with increase of ele- vation, can possibly take us at present, or at any time until higher soundings have been made. CHAPTER II. SOME THEORETICAL TEMPERATURE RELATIONS OF THE ATMOSPHERE. In order to acquire a clear understanding of the causes of the actual distribution of temperature in the atmosphere, it will be convenient, first, to consider some of the thermodynamic equations of gases, especially those that give relations between temperature, pressure, and volume. If to a unit mass of air or other gas at constant pressure p a quantity of heat dQ be supplied, the energy so added will divide itself into two parts. One portion will change the tem- perature of the gas and the other will change its volume. Hence, if the work is expressed in its heat equivalent, or if each por- tion of the energy is expressed in heat units and not in units of work, then RG wt Ae di co cpa aa acne (1) in which Cy is the specific heat of the gas in question at constant volume, dT and dV the resulting changes in temperature and volume, respectively, and A the reciprocal of the mechanical equivalent of a unit of heat. But to secure the relations desired, the relation of p to T, for instance, when both are variable, it is necessary to have an additional equation involving dT, dp, and dV. From Boyle’s and Charles’s laws, we have the equation, pv Vo i ie which expresses the fact that for a given quantity of gas the product of pressure and volume varies directly as the absolute temperature, T. So long, then, as the quantity of gas involved and its temperature are constant, so also is the product pV But when this quantity is one gramme and the temperature 0° . A « 3 po Vo C., it is convenient to speak of the quantity, “7, > as the characteristic constant, R, of the gas in question. In general, then, pV = RT, in which the value of R depends solely upon the kind of gas. Hence, differentiating, Par ap Se OF 5 cea ea canara (2) 28 THEORETICAL TEMPERATURE RELATIONS 29 To find the relation between dp and dT in an adiabatic proc- ess (that is, a process in the course of which no heat is either given to or taken from the gas involved, such as closely obtains in the case of rapidly rising or falling air), it is only necessary, by aid of equation (2), to eliminate dV from equation (1) and to put dQ =o. Thus Cy, dT +4.(R dT —V dp) =0 or (Gy oP AR) GT = AV Gbs cnabsociiaeeetnasieess (3) Also, since the excess of the specific heat at constant pressure over the specific heat at constant volume is simply the amount of heat necessary to perform the external work incident to expan- sion as a result of increasing the temperature 1° C., we have, Cy — C, = AW, the heat equivalent of the external work. And from pV = RT, we get, with p constant, p dV = R dT. If dT = 1° C., then Ap dV is the heat equivalent of the ex- ternal work done as a result of increasing the temperature of the unit mass of the gas in question 1° C. Hence, Cee On substituting this value of R in (3), we get, Cp dT = AVdp, or ATE UM eNO Soest ctabesh I ascaiennet urate gage ead (4) From this it appears that the ratio of the change of tem- perature to the change of pressure, in an adiabatic process, is directly proportional to the apne temperature and inversely proportional to the pressure. In the case of dry atmospheric air at ordinary temperatures Cp = 0.241, about.4 Hence, ART. us dT = dp — . p 0.241 But putes. fe, To Po To from which, assuming fo to be the pressure in dynes per square *Moody, Phys. Rev., 34, p. 275 (1912); used by Bureau of Standards. 30 PHYSICS OF THE AIR centimetre when the barometer under gravity g =981 and at 0° C. stands at 760 mm., and po the corresponding density of dry air at o° C,, it follows that, numerically, pic SOR AOE gi ee rok 0.001293 X 273 and I . (a 4.19 X 107 Therefore, dp T ar = 4, PB 3.5172 and aT _ dp, T +2843, > In the special case where the pressure is one atmosphere (barometer reading 760 mm.) and the temperature 0° C. (273° absolute), such as often happens on the surface of the earth, an adiabatic change of pressure represented by 1 mm. of the barometer produces a temperature change given by the equation, Pa = 2S 0°.10213 C. 760 3.5172 From equation (4) we get dT _dp AR T p Cp Hence TAR, ts loge T, Cp loge be or, AR Cp— Cv vei ss ce) Cp _ co Ge (2) T2 po 2) =\ pe , or, pi = oe pa (7, : If we wish to find the rate of adiabatic cooling with change of elevation, dh, a matter of great meteorological importance, it is necessary to find the value of dp in terms of dh and sub- stitute it in equation (4). It must be remembered, too, that pressure p decreases as the height / increases. THEORETICAL TEMPERATURE RELATIONS 31 But — dp = 981 p dh, where ¢ is the density of the gas in question, or gpa 28th _ 981 p dh V RT Hence, by substitution in equation (4), as explained, a eNO a iors oa Ry Seedatss Ges (5) dh Cp —- 10293 Clearly, then, when the atmosphere is dry and its temperature decreases with increase of altitude at the above adiabatic rate of 1° C. per 102.93 metres, any portion of it transferred with- out gain or loss of heat from one level to another has, at every stage, the same temperature and density as the adjacent air, and therefore, if abandoned at rest, will neither rise nor fall. If, however, the temperature decreases with altitude at a less rate ‘than the above, an isolated mass of air, on being adiabatically lifted or depressed, becomes colder and denser or warmer and rarer, respectively, than the adjacent air, and consequently, if abandoned, will return to its initial level. Finally, if the tem- perature decrease with altitude is more rapid than the above rate, an isolated mass of air, on being elevated or depressed, will be- come warmer and lighter or colder and denser than the adjacent air, and, if permitted, will continue to rise or fall, respectively, until arrested by a change in the temperature gradient, or, if descending, perhaps even by the surface of the earth. In short, the atmosphere is in neutral, stable, or unstable equilibrium according as the temperature decrease with increase of altitude is the same as, less than, or greater than the adiabatic rate of 1° C. per 102.93 metres (more or less, as g is less or more). From equation (5) it is obvious that the adiabatic rate of temperature decrease of the atmosphere with increase of alti- tude is independent alike of altitude (except as gravity is so modi- fied), temperature, and pressure, unless, possibly, its specific heat at constant pressure may slightly vary with temperature or pres- sure, or both. When, however, the composition of the atmos- phere is changed, it is obvious that its specific heat, and therefore its temperature gradient, must also change. Now the chief vari- able constituent of the atmosphere is water vapor, and, since its specific heat is approximately 1.95 that of dry air, it follows that the greater the amount of water vapor present the less rapid will 32 PHYSICS (OF ‘THE AIR be the adiabatic decrease of temperature with increase of altitude. If, for instance, 3 per cent. of the pressure is due to water vapor, the adiabatic decrease of temperature, before satura- tion is reached, will be at the rate of about 1° C. per 103.59 metres increase of elevation, and proportionately altered for other percentages. Water vapor also frequently causes another and most im- portant change in the temperature gradient. As soon as con- densation sets in the latent heat of vaporization, and, if ice is formed, of fusion, is liberated, and thus the rate of temperature decrease with altitude is reduced. The amount of this reduction, often at least half the original value, depends, of course, slightly upon what becomes of the condensed vapor. If it is carried along with the rising air the process remains adiabatic, except as modified by conduction and radiation, but if, as in great meas- ure must happen, it is left behind as precipitation, then the process becomes that special case of the nonadiabatic which von Bezold, followed by others, has called pseudoadiabatic. This whole sub- ject has been more or less discussed by several writers, but most fully, first, by Hertz® and, later, by Neuhoff.® Undoubtedly much of the condensation drops out, or begins to drop out, as soon as formed, so that the actual temperature gradient, while lying somewhere between the really adiabatic and the “pseudoadiabatic’’ curves, probably follows the latter more closelv than the former. Presumably, therefore, in prac- tice it would be better, or at least quite as well, to determine the latter gradient (the adiabatic will be considered later, under “ Condensation,” in chapter XII) and then to add such correc- tions to it as the circumstances of individual cases suggest. The main curve can be determined as follows: As before. dQ = C, dT + Apdl. But pV = RT, (RF being appropriate to the existing mixture of air and water vapor). Hence dQ = C,dT + A(R dT —V dp) - (C, + AR)dT — AV dp = C,dT —AV dp ® Deutsch. Met. Zeit., vol. i, 1884, p. 421. * Abh. d. K. P. Met. Inst., vol. i, No. 6, Berlin, 1900. THEORETICAL TEMPERATURE RELATIONS 33 But where g is gravitational acceleration. Therefore, dQ = C,dT +g A dh. Now the heat, dQ, is added as the result of a quantity of water vapor, dw, being extracted. Hence dQ =—s dw, in which s is the heat of vaporization, and therefore, —sdw = C,dT + g A dh. From this equation it is obvious that to obtain the ratio of dT to dh in terms of measurable quantities it is necessary and sufficient to express dw in similar terms. But w = p0.622 - in which w is the total mass of water vapor per cm.’, p the density of the air, 0.622 the ratio of the molecular weight of water vapor to the weighted mean of the molecular weights of the constituents of dry air, e the partial pressure of the water vapor in terms of millimetres, say, of mercury, and b the height, in millimetres, of the barometer. Hence dw _ de _ db, w e b But, if D is the density of mercury, _, _ pdh _ Dbgdh —Ddb=pdh= Rl RF Hence db_ | ah, ~~, 8 RT and d dh dw=w = + wg RT Hence, by substitution, de dh Cp dT + sw 5 + swg PT +A dh=o 34 PHYSICS OF THE AIR or de. sw = (Got sw-p) a0 + (er +4 )edh =o and Sw ee) Nes cia eater aarta aN tear (6) ate Cp + sw iia a edT All the terms on the right-hand side of this equation are known for any definite temperature and assumed value of dT. From this equation, therefore, tables can be written and curves constructed that give the “pseudoadiabatic” gradient under all conditions of temperature and pressure. Temperature Changes of a Rising (or Falling) Isolated Mass of Air—tThe above discussion of the temperature decrease with elevation of dry air applies only to an atmosphere whose potential temperature (temperature any portion would have if carried adiabatically to some given level, usually mean sea level) is the same throughout, such as it would be on thorough adiabatic mixing. As a matter of fact, the actual potential temperature of the atmosphere rarely, if ever, is uniform, and hence it is of some interest to trace the temperature changes with elevation of an isolated mass of air, or other gas, as it rises or falls adiabatically through an atmosphere whose potential tempera- ture is non-uniform. This subject has recently been discussed by several authors, but most concisely, perhaps, by Exner in his Dynamische Meteor- ologie, and, in substance, as follows: Let the absolute temperature at a given point within the adia- batically-cooling (or warming) isolated mass of air be T, and that of the surrounding air at the same level, and where the pressure, therefore, is also the same, 7’. Then, as already ex- plained, at any point within this mass aT __ ART dp pC, whatever the cause of the pressure change, dp. Now, let dp be due wholly to change of level of the isolated mass in the surrounding air; then gpdh ~ ob = “Rp THEORETICAL TEMPERATURE RELATIONS 35 Hence the temperature gradient of (not within) the rising mass at the place in question is given by the equation dT gAT T GS: BEE dh C,T’ ge in which a is the adiabatic temperature gradient. That is, the rising air will cool at a greater or less rate than the “ adiabatic” according as its temperature is higher or lower than that of the adjacent atmosphere, and by roughly 0.4 of one per cent. of the adiabatic rate for each 1° C. difference. Let the height under consideration be h, and let the tempera- ture of the free air decrease uniformly with elevation. Then, if T’, is the temperature of the free air at the elevation /, and T'o its temperature at the surface, T,/ = T,! — th, in which / is the uniform lapse-rate, or ratio of temperature change to change of elevation, of the free air. Hence (dT), ee es TT,’ —lh or dT dh Be Oa and log T, = 7 log (T,’ — th) + a constant If To is the initial or surface temperature of the rising mass, then ae ( T,!— th i fe re Hence, in general, the cooling with elevation is given by the equation () 7 ey z fae oO ee Fi! When the temperature of the free air has the “adiabatic” distribution, or /=a, 7 __4k a | Re 36 PHYSICS OF THE AIR That is, the rising air then also cools at a constant rate, but one more or less different from the “ adiabatic,” except in the special case when it has the same initial temperature as the adjacent air. When /=0, or the temperature of the free air remains con- stant with elevation, as it does in the isothermal region, the value of dT/dh clearly can not be determined from the above equation. However, from me r.=1.(:-#) ’ it appears that when /=0, —ah/T’ f= 73 0, T. -ah/T', € . (4 +) = opt Hence in an isothermal region the rate of cooling of a rising mass of air decreases with elevation. Finally, from the equation fii r,=7.( —*) T, =T, — ih, and it appears that or that the rising air comes to the temperature of the surrounding atmosphere, and thus into a position of rest, at the elevation fa 1 p22 |= (2 )e]. L T,’ If, for instance, = a/2, T’e=290" A., and T,= 300° A., then h=1.99 kilometres, approximately; whereas, if the rising air cooled according to the adiabatic rate (1° C. per 103 metres), as usually assumed, the value of /: would be 2.06 kilometres. If the roughly approximate value of the adiabatic rate, 1° C. per 100 metres, is used, the above values of become 1.93 kilo- metres and 2 kilometres, respectively. Cuaprer III. OBSERVED VERTICAL TEMPERATURE GRADIENTS. THE temperature of the surface air is well known at many places and at various altitudes, from sea level up to about six kilometres. But the temperature records obtained by the aid of kites and balloons, both manned and free, show that the mountain air temperatures generally differ materially from the tempera- ture of the free air at the same elevation and latitude. According to Hann,’ the average temperature of the surface decreases approximately at the rate of 1’ C. per each 180 metres, 200 metres, and 250 metres increase of elevation on mountains, hills, and plateaus, respectively. In the free atmosphere, how- ever, the result is quite different. Here the decrease of tempera- ture with increase of altitude, except at very great elevations, is, roughly, the same at different parts of the world. The records obtained by kites, manned balloons, and sound- ing balloons all agree, of course, so far as they apply to the same levels, but as the free or sounding balloon, with its automatically registering apparatus, has gone far higher than either manned balloons or kites, and as ascensions by it have been quite numerous, only the records thus obtained will be considered in what follows. Again, and for the sake of still further uniformity, the first part of the discussion will be confined to only those records which were obtained at Munich, Strassburg, Trappes, and Uccle, four Euro- pean stations of about the same latitude and more or less similar climates. It seems also desirable to divide the records of verti- cal temperature distribution according to season, winter (Decem- ber, January, February, and March) and summer (June, July, August, and September), and prevailing type of weather, or, to be more exact, the height of the barometer, high, low, and neutral. Spring and fall observations will not be used in the typical or most general temperature distributions, owing to the transitional nature of these seasons, or the overlapping and con- fusion at these times of summer and winter conditions. At the time these data were assembled, the middle of 1918, all the available records of the stations mentioned were used, ™ Lehrbuch der Meteorologie,” 3d ed., p. 126. 4 37 38 PHYSICS OF THE AIR there being 185 winter records and 231 summer records. A larger number of flights would, of course, furnish a somewhat more reliable average, but, as the several stations gave substan- tially the same results, it would seem that no great change would be made in the season averages, however large the number of combined observations. Fig. 16 gives the average winter and summer vertical tem- / Fic. 16. =-60" ~55° -50°-45° -40° -35°-30" -25° 20° -I5° -10" -5°_0° 5° 10° 15° = 19 20 19 18 \7 16 15 \4 13 I2 ti 10 Oo oF NWSE UY DN © ~60°-55° -50°-45°-40" -35°-30°-25° 20°-I5°-10"-5" 0° 5° 10° 15° TEMPERATURE °C, Winter and summer vertical distribution of temperature. perature gradients of the stations in question, or the graphs ob- tained by plotting the average temperatures (derived from the average of the observed temperature gradients) of the given season against the corresponding altitudes at which they were obtained. A number of interesting points are brought out by these two curves, each of which calls for an explanation. Among other VERTICAL TEMPERATURE GRADIENTS 39 things, the two gradients are, roughly, parallel to each other throughout their whole range. This is because the tempera- ture of the atmosphere from top to bottom is determined by the same factors in the winter that determine it in the summer; that is, by radiation, conduction, and convection, all mainly from the surface of the earth and the lower atmosphere. Since all these factors are less in winter than in summer, it follows that their combined result, the temperature of the higher atmosphere, must also be less at every level; hence the substantial parallelism of the two gradients. Again, it appears, as shown by the figure, that up to about 2% kilometres the temperature decreases less rapidly with in- crease of elevation during winter than it does during summer. The reason for this, while not quite obvious, will become apparent from the following considerations : The surface of the earth, which is a much better radiator than the atmosphere, often cools, especially during clear nights, to a decidedly lower temperature than the air 100 metres or so above it. Hence, late at night, when the sky is clear and the wind is light, the temperature near the surface usually increases with increase of elevation, and even when there is sufficient wind to prevent this “temperature inversion,” as it is called, the lower atmosphere still is colder than it otherwise would be. Obviously, too, the amount of this surface cooling, and therefore the mag- nitude of the temperature inversion, depends jointly upon the rates of radiation to and from the sky and the time.involved. Now the rate of the output of surface and lower air radiation is less in winter than in summer, both because of their lower tempera- tures at that time and because the atmosphere then contains less water vapor, its chief radiating constituent. Nevertheless, even though the radiation loss from the surface of the earth and adjacent air is greater in summer than in winter, the concurrent radiation gain from the upper air may, perhaps, usually render the difference, or net loss, somewhat less. At any rate, partly for this reason, it may be, but mainly because of the relatively greater length of the nights and greater dryness and consequent diathermacy of the atmosphere, the total surface cooling, and therefore the morning temperature inver- sions, is much more pronounced in winter than in summer. Hence the average decrease of temperature with increase of elevation 40 PHYSICS OF THE AIR through the first one or two kilometres is decidedly less during the colder than during the warmer season. Another peculiarity shown by the curves is the fact that be- tween the elevations of approximately four and eight kilometres the temperature decreases rather more rapidly during winter than summer. Throughout this region the temperature of the at- mosphere depends in part upon convection from lower levels and in part upon its gain and loss of heat through radiation. But even this midair, or radiational, change in temperature can result only in immediate convection. Consequently, so long as satura- tion is not reached, the convectional temperature gradient must be very approximately that of a totally dry atmosphere. If, how- ever, condensation takes place, the latent heat of vaporization be- comes sensible heat, and the decrease of temperature with increase of altitude is correspondingly less. When a condensation tem- perature gradient is once established in this mid-region of the atmosphere it tends to persist, even after condensation has ceased and the clouds have evaporated, because, whatever condition— the presence or absence of sunshine, for instance—produces a tem- perature change in one part of it is likely to produce similar temperature changes in other parts, and therefore approximately the same variation for each level, a variation which would leave the general temperature gradient substantially as before. We should, then, expect to find the average vertical temperature gradient following, roughly, the gradient for saturated air for the given temperature, and such, indeed, are the gradients actu- ally found. Hence, as the atmosphere between the elevations of four and eight kilometres is quite out of the reach of surface inversions, and as it is also warmer and more humid during summer than during winter, we should expect the summer temperature of this region to decrease less rapidly with increase of altitude than does the winter temperature, precisely as balloon records show to be the case. Another point brought out by Fig. 16 is the fact that up to eight kilometres, or thereabouts, the ratio of the decrease of tem- perature to increase of altitude itself increases with altitude. The explanation of this phenomenon is precisely the same as that of the difference between the winter and summer gradients from four to eight kilometres. That is to say, it depends upon the VERTICAL TEMPERATURE GRADIENTS 41 amount of water vapor necessary to produce saturation at the various levels, since the less this vapor is in proportion to the total gases present the more nearly does the actual temperature gradient follow the adiabatic curve for dry air. One striking feature of each of the temperature gradients is its gradual change, between the levels of nine and twelve kilo- metres, from a rapid decrease of temperature with increase of elevation to an approximately isothermal condition. Normally, however, the temperature gradient changes from a rapid to prac- tically a zero decrease, and even, as usually recorded, to a slow increase of temperature with increase of elevation, much more abruptly than one would infer from the given curves. But this more or less abrupt change varies considerably in altitude from day to day. Therefore, when a large number of actual gradients are averaged an apparent gradual transition is indicated. Two other features calling for some attention are shown by the lower portion of the summer gradient; namely, the fact that through the first half kilometre the temperature decreases but slowly, and the further fact that through the second half kilo- metre it decreases more rapidly than anywhere else, short of very considerable altitudes. Now nearly all the observations from which this summer gradient was constructed were obtained during the early forenoon. Hence the average slow decrease of temperature with increase of elevation is the result only of ordi- nary morning inversions. On the other hand, the rapid decrease of temperature through the second half kilometre is expressive of the adiabatic gradient of unsaturated air that commonly exists during summer afternoons up to a level of at least one kilometre. In this case it has persisted in its upper portion throughout the night, and been modified, as explained, by temperature inversions only in its lower half. Vhy the Temperature of the Atmosphere Decreases with Increase of Elevation.—lIt is not, perhaps, obvious why the tem- perature of the atmosphere should rapidly decrease with increase of elevation, as it does through at least the first several kilo- metres, as shown by Fig. 16. Essentially, however, this phe- nomenon depends on the following facts: 1. The atmosphere, as is known from observation, transmits directly to the surface of the earth half, roughly, of the effective radiation received from the sun—that is, half of the portion 42 PHYSICS OF THE AIR absorbed and not lost by reflection. Consequently, it is this sur- face, where the energy absorption is concentrated, and not the atmosphere, through which it is diffused, that is chiefly heated by insolation. The heated surface in turn warms the air above it, partly by contact and partly by the long wave-length radiation it emits, and of which the atmosphere is far more absorptive than it is of the comparatively short wave-length solar radiation. 2. Furthermore, and this is an equally vital part of the ex- planation, the lower atmosphere (below about 10 kilometres), under all ordinary conditions, emits more radiant energy than it absorbs. It is these two phenomena, (a) the net loss of heat by radiation (cooling above), and (b) the surface heating (warming below), that together establish and maintain the vertical con- vections of the atmosphere under which, since the descending portions grow warmer through compression and the ascending colder through expansion, the whole of the convective region is made to decrease in temperature with increase of elevation. But since the coefficient of absorption of the air, as of other objects, changes but little, if at all, with temperature, while its emissive power decreases rapidly as it grows colder, and since the intensity of the incident terrestrial (including atmospheric) radiation remains roughly constant up to an altitude of many kilometres beyond the first 4 or 5, it follows that the upper limit of the convective region is not, as formerly supposed, the outer- most limit of the atmosphere, but at that elevation at which the temperature is so low that the loss of heat by radiation is no longer in excess of, but now equal to, its gain by absorption. Beyond this level temperature does not decrease, or does so but slightly, with increase of elevation; nor would it so decrease, at least at nothing like the present rate, beyond any level, however low, at which absorption and radiation became equal. In short, then, the air grows colder with elevation because (1) owing to its transparency to solar radiation it is heated mainly at the surface of the earth, and (2) because at ordinary temperatures it emits more radiation than it absorbs. These together so affect the density of the atmosphere as to induce vertical convections, and thereby to establish and maintain, throughout the region in which they are active, a rapid decrease of temperature with increase of elevation. CHAPTER IV, THE ISOTHERMAL REGION, OR STRATOSPHERE. Or all the conditions indicated by the temperature gradients of Fig. 16, by far the most surprising, and most difficult fully to explain, is the approximately isothermal state of the upper atmosphere. Indeed, the discovery of the fact that the tempera- ture of the upper atmosphere changes but little with altitude, and the supplementary discovery of its physical explanation, constitute one of the most important advances in modern meteorology. The exploration of the atmosphere by small balloons carrying meteorological instruments was suggested in 1809,° but the idea was first carried out by Hermite® on March 21, 1893, when an elevation of 16 kilometres was attained. In April, 1808, ‘Teisserenc de Bort,'® with improved apparatus, began at Trappes, France, a long series of frequent atmospheric soundings. Among other things, he soon found temperature records that indicated something unsuspected: either errors in the thermometers them- selves or surprising temperature conditions in the upper atmos- phere. However, numerous temperature records subsequently ob- tained by himself and many others in various countries and with different kinds of apparatus have shown that, in general, the tem- perature of the upper atmosphere actually does change but little with change of elevation. Indeed, as a rule, the change is so small that the whole region characterized by this approximate constancy of temperature has been called the “ isothermal region.” At present it is more generally known as the “stratosphere,” though the older and less used term certainly is more suggestive of its distinguishing characteristic. The height at which this region begins and its temperature both depend upon season, upon storm conditions, and upon lati- tude; but, while all these are important details, they are secondary to the fact that there is an isothermal region at all. As soon as observations left no doubt of the actual existence of the isothermal region many explanations of it were proposed. ® Ann. Harvard Obs., 68, pt. I, p. I. ° TL’ Aérophile, 1, p. 45 (1893). *C. R., 129, p. 417 (1899). 43 ay PHYSICS OF THE AIR but for a number of years all such suggestions proved unavailing. Finally, however, independently and nearly simultaneously, the generally accepted explanation occurred to Gold?! of England and Humphreys !? of America. The same subject has also been discussed at length by Emden.1* The key to the explanation 1s this: The temperature of every portion of the atmosphere 1s determined, in part at least, by counteracting radiation—radia- tion absorbed and radiation emitted—and wherever these two are equal there is substantial constancy of temperature. Mr. Gold’s method of procedure was to take the best-known data concerning atmospheric absorption and radiation and to ob- tain, by the aid of suitable mathematics, a general solution of the problem. The chief difficulty in the application of this direct and elegant method, apart from the troublesome equations in- volved, is that due to our imperfect knowledge of the necessary radiation and absorption constants. Numerical values in these particulars are not accurately known and certainly not easy to determine. On the other hand, the solution offered by Humphreys, while not so direct, reduces the necessary mathematics to a minimum. In brief, it is as follows: Since the average yearly temperature of the atmosphere at any given place does not greatly change, it follows that the absorption of solar radiation by the earth as a whole is substantially equal to the total outgoing earth radiation, and in amount approximately equal to that which a black or per- fectly radiating surface, equal in area to the surface of the earth would emit if at the absolute temperature 259° C14 Further. since at ordinary atmospheric temperatures water vapor, in any considerable quantity, absorbs and, presumably, also radiates sub- stantially as does a black body at the same temperature, while dry air is exceedingly diathermanous, it follows that the plane- tary radiation of the earth is essentially water vapor radiation. Now the records of sounding balloons show that at some alti- tude, in general about 11 kilometres above sea level in middle latitudes. the average temnerature ceases to decrease with increase of elevation. Individual flights show many peculiarities that call ™ Proc. Roy. Soc., series A, vol. 82, 1G09, p. 43. ® Astrophys. Jour., vol. 20, 1900, p. 14. ® Sitz. der K. Bayr. Akad. der Wis., Jahr., 1913, p. 55. “Abbot and Fowle, Annals of the Astrophysical Observatory of the Smithsonian Institution, vol. 2, p. 174. THE ISOTHERMAL REGION 45 for special explanation, but the purpose here is to consider only the general explanation of the main effect, and therefore average conditions are considered. lf, then, as is approximately true, the temperature does not decrease with increase of altitude above 11 kilometres, it follows that this must be the limit of anything like a marked vertical convection. And from this in turn it follows, since conduction is negligible, that the upper atmosphere must be warmed almost wholly by absorption of radiation, in part solar and in part ter- restrial; but exactly how much of the final temperature of the upper atmosphere is due to the one source of heat and how much to the other it is not possible to say. However, there are certain facts that seem clearly to indicate the relative importance in this respect of the two sources. Thus the summer and winter gradients as given by Fig. 16 show a difference of temperature in the iso- thermal region of only about the amount that might be expected on the assumption that the temperature of the upper air is wholly dependent upon the radiation from the lower. That is to say, the seasonal temperatures of the lower atmosphere differ dis- tinctly more than do those of the upper. It should be clearly kept in mind, too, that the particular seasonal gradients given in Fig. 16 were obtained at a latitude of, roughly, 50 degrees, where the number of hours of summer and winter sunshine differ greatly, and therefore where the seasonal temperature of the iso- thermal region, if essentially determined by absorption of solar radiation, should differ somewhat correspondingly. But, as no such great difference in these temperatures exists it would ap- pear that the temperature of the isothermal region must be due chiefly to absorption of long wave-length radiation given off by the water vapor and other constituents of the atmosphere at lower levels, and to only a very minor degree to the absorption of solar radiation. Hence, as a first approximation, one may consider this radiation alone, and for the lower atmosphere as it actually exists substitute the radiationally equivalent black sur- face at the absolute temperature of 259° C. Obviously, too, this surface, surrounding as it would the entire earth, could be re- garded as horizontal and of infinite length and breadth in com- parison to any elevation attainable by sounding balloons, and therefore as giving radiation of equal intensity at all avail- able altitudes. 46 PHYSICS OF THE AIR Now consider two such surfaces, parallel and directly facing each other, at a distance apart small in comparison to their width, and having the absolute temperature T,, and let an object of any kind whatever be placed at the centre of the practically en- closed space. Obviously, according to the laws of radiation, the final temperature of the object in question will also be ap- proximately T,. If, now, one of the parallel planes should be removed, the uncovered object would be in substantially the saine situation, so far as exposure to radiation is concerned, as is the atmosphere of the isothermal region in its exposure to the radiation from the lower atmosphere. Of course, each particle of the upper air receives some radiation from the adjacent atmos- phere, but this is small in comparison to that from the lower water vapor and may, therefore, provisionally be neglected. Hence the problem, as an approximation, is to find the final temperature to which an object, assumed infinitesimally small, to fit the case of a gas, will come when exposed to the radiation of a single black plane of infinite extent. Now, whether between the parallel planes or facing but one, the object in question is in temperature equilibrium when, and only when, it loses as much energy by radiation as it gains by absorption. Furthermore, so long as its chemical nature re- mains the same, its coefficient of absorption is but little affected by even considerable changes in temperature. Therefore, what- ever the nature of the object, since it is exposed to twice as much radiation when between the two planes as it is when facing but one, it must, in the former case, both absorb and emit twice as much energy as in the latter. Or, using symbols, Ey = 2k; in which F, and £, are the quantities of heat radiated by the object per second, say, when between the two planes and when facing but one, respectively. Again, Ree. and Behn in which T, and T, are the respective absolute temperatures of the object under the given conditions, and K and n its radiation constants. THE ISOTHERMAL REGION 47 For every substance there are definite values of K and n which, so long as the chemical nature of the object remains the same, do not rapidly vary with change of temperature. Hence, assuming K, = K, and m, = m, we have, from the equation EE, - 2E; Ties V2 Ti From this it appears that there must be some minimum tempera- ture T, below which the radiation of the earth and lower atmos- phere will not permit the upper atmosphere to fall, though what it is for a given value of T, depends upon the value of n. Presumably the radiation of the upper atmosphere is purely a thermal radiation, and therefore in full agreement, as is the thermal radiation of water vapor, carbon dioxide, and certain other gases, with the Kirchhoff 15 law. In other words, the ratio of emission to absorption for any given wave-length, presum- ably, is wholly a question of temperature, and is numerically equal to the radiation of a black body at me same temperature and wave-length. In symbols, (#),, t = Aye in which H is the incident energy, 4 the energy absorbed, and e the energy emitted by the body or gas in question at the wave- length A and temperature ¢, and E the black body emission at the same wave-length and temperature, all per equal area and time. To fix the ideas, let the body of gas under consideration be a shell one centimetre thick, surrounding the earth at a fixed distance—z2o kilometres, say, above sea level—and let the black body be a very thin shell at the same temperature inside and outside, that may, if we wish, take the place of the gas shell. Now, since nearly all the incident radiation under consideration, the radiation of the earth and its atmosphere onto a shell at 20 kilometres elevation, or anywhere else in the isothermal re- gion, comes from below, we may assume it, or its normal equiva- lent, to be substantially the same for all levels of the upper at- mosphere, and assume the emitted radiation to be all the energy * Pringsheim, “ Congrés International de Physique,” Paris, 1900, vol. 2, p. 127. 48 PHYSICS OF THE AIR sent out by the shell on either or on both sides; only, whatever the assumption for one shell, the same must be made for the other. Returning to a consideration of the temperature of the upper atmosphere under the influence of radiation from the lower gases: Since the composition of the upper atmosphere is not appre- ciably changed by a change of even 50° C., it follows that such a change of temperature will not materially alter its coefficient of absorption. Hence a change in the intensity of the incident radiation H will make substantially the same proportionate change in the rate of absorption h, whatever the alteration in tempera- ture. In short, = =X a constant, presumably. Hence £4, ty Ey, 4 “te Fan or A, “A, te Ei,t Er, t Unfortunately, nothing is known of the spectral distribution of the energy radiation of the cold upper atmosphere, though possibly it is of the irregular, but more or less continuous broad band, type. If this is its distribution, and if for each wave- length the increase of black body radiation, for a small increase of temperature, is proportional to the total radiation at that wave length, which it is to a rough first approximation, then to about the same average approximation, en — Eu, etz En in which the symbols stand for the total radiation of all wave- lengths. But from the Stefan law in regard to the total radiation of black bodies, we know that En _ PY Et, ~ ToS in which T, and T, are the respective absolute temperatures. Hence, as explained above, if the spectral distribution of the radiation of the upper atmosphere is continuous, or nearly so THE ISOTHERMAL REGION 49 (no matter how irregular), and not confined chiefly to lines with zero radiation between them, it follows that in the equation, T= V2 the numerical value of m must be 4, roughly. But, as already explained, the value of T, is substantially 259° C. absolute; hence, on the assumption that m = 4, it follows that T, = 218° C. absolute. And this is the value, approximately, that observa- tion gives. Whatever the facts in regard to the radiation constants of the atmosphere, the laws of radiation and absorption demand that the temperature of the upper atmosphere shall change but little with change of elevation. Besides, while the exact value of this temperature—the temperature of the isothermal region— is, of course, best determined by actual observation, it also may be computed approximately from the known intensity of out- going radiation, together with the thermal properties of the gases of the atmosphere. Doubtless solar radiation affects the temperature of the iso- thermal region to some extent, but, presumably, not very much, since the radiation from the lower levels seems competent not only to produce an isothermal condition in the upper levels, but also to maintain them at substantially the observed temperature. Further, the lower atmosphere obviously is slightly warmed and its radiation correspondingly increased by return radiation from the upper, but this presumably does not affect the general validity of the above reasoning, which is based on the action of the total outgoing radiation. Given the isothermal condition of the upper atmosphere, it follows that the heated surface air can, under favorable circum- stances, rise till, but only till, by expansion it has cooled down to that temperature (the temperature of the isothermal region) below which the radiation from the lower atmosphere will not allow it to fall. The existence of an upper isothermal region and the vertical temperature gradient (Fig. 16) suggests rational explanations of a number of otherwise obscure meteorological phenomena— why the clouds of a given region have a fairly well-defined ‘maximum elevation; why this elevation is greater in summer than in winter; why it is a level of maximum cloud formation, 50 PHYSICS OF THE AIR and the like—but all these are special phenomena that will be discussed independently later on. INEQUALITY OF SEASONAL TEMPERATURE CHANGE OF LOWER AND UPPER ATMOSPHERE. As just explained, if T, is the absolute temperature of the black surface that gives off radiation equivalent to that sent out by the convective portion of the atmosphere and 7, the absolute temperature of the isothermal region, then T= Ta/-W/2 =0.84 T2, roughly. Hence the greater T,, or the warmer the lower atmosphere, if its composition remains the same, the greater the difference between 7, and 7., or the greater the contrast between the tem- perature of the lower atmosphere and that of the isothermal re- gion. This is in keeping with the observed fact (Fig. 16), that the seasonal difference in the temperature of the isothermal region, while in the same sense as that of the lower atmosphere, is not so great as is the latter. Because of seasonal differences in the composition of the lower atmosphere, especially in the average amount and distribution of water vapor, there can be no constant relation between the above temperature differences—only the qualitative relation as given. HEIGHT OF THE ISOTHERMAL REGION. If H, is the height and 7, the temperature of the under sur- face of the isothermal region above the level H,, whatever that may be, whose temperature is Ty, then ‘Ti Hy=Ho+ 4H ap T. ai 0 As above explained, the greater the temperature of the lower atmosphere, the greater the difference between this temperature and that of the isothermal region, or, in symbols, the greater Ty the greater 7-7, and therefore the greater H,. Hence the iso- thermal region should be at a greater elevation during summer than during winter. Another way of showing this same thing is as follows: Let the difference between the summer and winter tempera- tures of the lower atmosphere be AT, throughout, and the cor- THE ISOTHERMAL REGION 51 responding difference between the temperatures of the upper atmosphere AT,, then, according to the above theory, AT, = 0.844T,, roughly. This, as already explained, is a radiation re- sult. The inequality or 0.16AT, is produced by convection. Now if h is the change in elevation corresponding to 1’ C., we have AH = 0.16AT:h. But, AT,, winter to summer, is roughly 12” C., and h about 110 metres. Hence the change in the seasonal elevation of the isothermal region, if there is constancy in atmospheric composi- tion, and other conditions, except temperature, is, roughly, AH =0.16 X' 12 X 110 = 211.2 metres. It must be distinctly noted, however, that many disturbing elements, such as quantity and distribution of water vapor, fre- quency and extent of cirrus clouds, and the like, so modify these simple relations that they apply only to average conditions, and to them but approximately. STORM EFFECTS ON TEMPERATURE GRADIENTS. The average of a season’s (winter or summer) vertical tem- perature gradients gives a fairly regular curve, and, of course, tke same would be true of the average of these averages, or what might be called the annual gradient for any given locality. How- ever, each particular flight yields its own temperature-altitude curve, which differs more or less from others of the same place and season, especially in the values of the gradients in the first two or three kilometres elevation, in the absolute temperatures at other levels, and in the location of the upper inversion. With the view of determining the causes of some of these flight-to-flight irregularities, both the summer and the winter records from which the corresponding seasonal gradients were determined were grouped, according to the heights of the barome- ter at the times and places of observation, into “ highs,” “ neu- trals,” and “lows.” Thus the “highs” belong, to barometric readings of 5 mm. or more above, and the “ lows”’ to readings of 5 mm. or more below, the seasonal normal, and the “neutrals” to the various intermediate values, all reduced to sea level. Fig. 17 shows the winter averages, respectively, of 54 highs, 72 neutrals, and 59 lows. Commonly, as the figure shows, a high barometer in the winter is accompanied by low surface tempera- 52 PHYSICS OF THE AIR tures, a slow decrease of temperature up to an elevation of about three kilometres, relatively warm air, in general, between the levels of two and nine kilometres, a high upper inversion, a cold isothermal region, and a marked minimum temperature 1n the lower portion of the stratosphere. A winter low, on the con- trary, and in comparison with a high of the same season, 1s accom Tie.. 17. = -60"-55"-50"'-45"-40" 35°-30° 25° 20° 15° 10° -5° 0° 5° 10° 15° ig i9 | 18 17 17 16 16 15 15 14 14 — HIGH -—— NEUTRAL i 13 O- NW BO DONA DW OO SOD -NwWhtSOAANOD OO -60°-55° -50°-45° -40°-35° 30° -25°-20" -I5° -10° -5° 0” «5° 10° 15° TEMPERATURE °C Temperature gradients at different pressures, winter. panied by warm surface temperatures, a more rapid decrease of temperature with increase of elevation through the first three kilometres, relatively cold air from, roughly, two to nine kilo- metres elevation, a low upper inversion, and a warm isothermal region. The normal barometer, as one would expect, is accompanied. by intermediate values in all particulars. The corresponding summer gradients (averages, respectively, THE ISOTHERMAL REGION 53 of 32 highs, 161 neutrals, and 38 lows), given in Fig. 18, show, except near the surface, where the lows remain cold and the highs warm, the same characteristics as do those of winter. Both the summer and the winter curves follow exactly the averages of the observations, as per the accompanying table. An obvious contributing cause of these differences in tem- Fic. 18. = -60° -55°-50° -45°-40°-35"30° -25°-20° -15*-10° 5° 0° 5° 10° 15° 5 20 4 19 \8 18 17 17 6 16 15 15 \4 4 13 13 2 NEUTRAL 16 l2 LOW 38 " 10 10 9 8 7: 6 5 4 3 2 | N\ 0 OG 0°-55°-50"-45°-40° -35°-30" 25° -20"-15°-10" 5° O° 5° 10° 15° TEMPERATURE °C. Temperature gradients at different pressures, summer. perature is the warming of the air by compression and its cooling by expansion incident to barometric changes; an amount which, starting with dry air at 0° C., is given, as explained on page 30, by the equation aT _ 77:6 dp pp’ in which p is the pressure, expressed in millimetres of mercury, and dT the change of temperature in degrees Centigrade. 5 PHYSICS OF THE AIR + wm gr L6gr— SI gé6gh— i S$ fg LS— | ° : a 1 Lo-6b— Res 41 gg:6b— sured g tg Lo— sr S oz gS— ge Lr-oS— £ Logr— zz gt'oS — g zges— fr eg LS— S$ eg lo— 9 of gS— ai 6b LoisS— b LelLp— gf giris— 6 zebS— iz €94S— L eg lS— 6 oo'gS— ¢ Sg'gS— zg LgrS— g Liregb— Ig ggIS— | fr zesg— ee ¢f2S— | or €boS— | zi of'gS— | 11 SS-gS— oir 2Z61S— | 241 LE-Lb— 1g ge'cS— | gr zess— 6b €rlZS— | o1 fbSS— | 91 oz gS— | 41 Sggs— Zbr L&zS— | 12 Lelb— | vor ghzS— | zz zgqS— zZ €S9S— | be EL4S— | zz oLLS— | gz SEgS— wZ1 LLeS— | Le Legr— | Zir glzS— | Le zglS— g6 €€9S— |] of EzbS— | FE olgS— | FE So'6S— 61 LezS— | of Lo6r— | Er gorzS— | of zoZS— |] ozr EzLS— | LE L6bS— | Sh oggS— gf SLog— tiz LooS— | r¢ Legr— | 6hr gowoS— | 1€ zgrzS— || Zhr EgqS— | Lr LoSS— | 9S oS-gS— | br C9'6S — zzz Lebr— | 9f Lobb— | SSr gg bh— | 1€ ee-Sh— Sor €ftS— | eS EzbrS— | bo of bS— | gr Sgrs— dzz lege— | Ze LL6f— | 6S1 goge— | 1€ zgoLE— || blr Co-6b— | LE EEI1S— | Lg OL Ob— | OS So-gbh— 1fz LLof— | gf recf— | 191 6Sof— | z& zg-6z— zgr ¢gokb— | 6S ErLbp— | of orer— | S Lgor— 1€z gz€z— | g& ogbz— | 191 zifz— | ze grzz— |] bgr Lg-of— | 6S Lgob— | 14 ogSe— | PS Loee— 1€z 6z91— | gf og Zi— | 191 Srg1— | ze msi1— Sor €f6z— | 6S LEee— | cL obge— | FS gI-gz— fz £66 — | gf ee11— | 191 Lg6 — | zc bLg — Sg. bteee— | 6S 16Sz— | zl 6hIiz— | PS zz61— fz gzb — | g& PLS — | 191 git — | z€ ore — |] Sgr ofS1— | 6S thgi— | zZ 6obI— | PF 69z1—- 1fz zor ge 6ho — | 191 611 ze 00% Sgr br6 — | 6S SLI1r— | zL Sog — | VS z69q — fz Lge ge zie I9l_ bet ze LEP Sgt gbho — | 6 9989 — | zZ org — | PS og — fz 679 ge Sob 191 $9 ze 604 Sgr grt — | 66 26S — | zfZ gL — | oS SkLz — 1fz 06 ec etal 191 +f6 ze LS°6 Sgt gzz — | 6S oS — | zLZ LL1 — | PS QS — 1fz Ig'll gt 366 I9I Zizi zl 6LZI Sgt fg — | 6S ogo — | zl bro — | f§ Lgr°0 — gZI og f1 gz f61l Izi o6'f1 6z -g6°E1 Zbr fz 1 6b LL gS 10! fr Lego efi oflb1 gz gSE1 zl 7gbl 6z bS'Sr Ler zly 6b Sez cS Ig! fr go N L N L N L N L N E N L N I N L uray MOT yesqneN ys ues MO'T yeayna N ys aaWWNS UALNIM o'0z 061 o’gl oli o'9g1 o'St oti ofl oat oll ool 9200000 OrMNC ROH Sz 218 O19'9 Sonu pPAa eas 9A0ge “Wy ur apnaaTy "N Sasv9 fo zaqunu ‘J aanqosadua [ ‘eIOI—-OOO1 ‘ynun pUuDd ‘Sungssv.jg ‘399Q ‘saddvay yD syysiyf uooyjpg Surpunos grb mos (Sjuarposd adnjosagual adpdaan WoLsf) apDAéd1juay ‘saanjo1adua} advizap | alavy THE ISOTHERMAL REGION 55 According to Figs. 17 and 18, the temperature at the altitude of four kilometres is considerably warmer both winter and sum- mer in the regions of high barometric pressure than it is in the regions of low pressure. But to secure a temperature difference of 7° C., say, as a result of pressure change only, would require a rise or fall of the barometer at this level of about 40 mm., or some- thing like 70 mm. at sea level; and, since this is of several-fold the average pressure change, it is obvious that the observed tempera- ture differences, often more than 7° C., cannot in the main be accounted for in this way, though, of course, the pressure effect must be present to some extent. Another contributing cause of temperature differences, gen- erally associated with the height of the barometer, is the clear and cloudy condition of the sky, or the humid and the dry state of the atmosphere. A barometric high, as we know, commonly is accompanied by clear skies and a dry atmosphere, while in the region of a low the sky ordinarily is overcast, the atmosphere relatively moist, and precipitation abundant—conditions that have much to do with air temperatures. Thus, generally, at the end of any consecutive 24 hours of clear weather the surface of the earth will be warmer in the summer time and colder in the winter because of the unequal lengths during those seasons of the day and night. On the whole, the earth gains heat, especially in clear weather, during summer and loses it in the winter. A cloud covering, however, greatly reduces the rate of this gain or loss, and therefore during winter the surface temperature is lowest when the barometer is high and the earth can radiate most freely to space, while it is warmest when the barometer is low and the sky so overcast as to check radiation loss. In the summer time, as explained, the conditions of gain and loss of heat are the reverse of those during winter, consequently the highest summer surface temperatures accompany the high barometer, or clear weather, while the lowest accompany cloudy skies. When the barometer is distinctly above normal the tempera- ture fall with increase of altitude near the stratosphere gen- erally follows approximately the adiabatic curve for dry air. When, however, the barometer is low the temperature gradient usually is far less constant at all elevations, owing to irregularities in the humidity distribution and the consequent varying amounts 56 PHYSICS OF THE AIR and places of precipitation. In many cases the temperature gra- dient over varying heights is essentially the adiabatic curve for saturated air at the prevailing temperature and pressure ; that is, a fall of temperature per given change in altitude is less, other things being equal, the greater the amount of uncondensed mois- ture present. Since the curves of Figs. 17 and 18 are the averages of a number of flights, it may be approximately correct, in an effort to account for their differences, to start with something like aver- age conditions and trace the consequences. Let these conditions be a moist atmosphere in the one case and a dry one in the other, each having the same temperature as the other at all levels. The moist atmosphere, because a better radiator than the dry, will, under the same conditions of exposure and at the end of the same interval of time, cool to a lower temperature, but in so doing— that is, in getting rid of its own heat most rapidly—it at the same time supplies heat at greater rate to any neighboring region that receives it by radiation only. Therefore when the lower atmosphere is moist it will, under like conditions, radiate heat most rapidly to and through the always dry air of the isothermal region, and while getting cold itself will at the same time warm this region to a temperature above its average. On the contrary, in the region of a high barometer the lower air, being relatively dry and therefore a poor radiator, will conserve its own tempera- ture, but in so doing will allow the isothermal region to get cold in comparison with its temperature during the prevalence of a low at the same season. Since the temperature of the isothermal region depends es- sentially upon the amount of radiation received from the lower atmosphere, it follows that, on the average, the temperatures of the two regions must vary in the same sense, or warm and cool together, and this, indeed, is just what happens, as the winter and summer gradients of Fig. 16 indicate. It is surprising, therefore, when we find the temperatures of these regions varying in the opposite sense, the one getting warm while the other is getting cold. But it must be remembered that the lower atmosphere is warmed convectionally. in large part, while the upper air is warmed almost wholly hy radiation. Hence whatever increases radiation from the lower air, increase of humidity or tempera- ture, or both, must tend to increase the temperature of the iso- THE ISOTHERMAL REGION 57 thermal region, and whatever decreases this radiation, decrease of humidity or temperature, or both, must decrease its tempera- ture below that which it otherwise would have. Now the aver- age seasonal change of the lower atmosphere is primarily one of temperature, while the average storm difference of a given season appears to be largely one of humidity. The high tem- perature of summer obviously affords a more abundant radia- tion than the relatively low temperature of winter and should give, as we have seen, a warmer isothermal region. Similarly, the different intensities of radiation from humid and relatively dry air would lead one to expect the stratosphere to be warmer over a cyclonic than over an anticyclonic area. Another important factor, presumably the controlling one, in the temperature contrasts between cyclonic and anticyclonic regions is the vertical movement of the atmosphere, upward in the former, downward in the latter. Probably, at least, a large portion of the anticyclonic excess of air that gives the increase of pressure and makes good the loss by outflow is fed in at con- siderable altitudes, though below the isothermal level. If the air movement is as here supposed, there necessarily must be dynamical heating throughout the lower atmosphere, partly because of the initially increased pressure, but mainly through descent. At the same time, the atmosphere of the isothermal region would be more or less lifted and cooled by the resulting expansion. Conversely, if, as there is much reason to believe, the chief removal of atmosphere over cyclonic areas is also from con- siderable altitudes, but below the isothermal region, the lower atmosphere must be dynamically cooled, partly by virtue of the immediately decreased pressure, but chiefly through ascent. The stratosphere would be lowered and its temperature thereby in- creased. It seems likely, too, that under these conditions there would be a somewhat continuous slow movement of air from the stratosphere down into the region of the troposphere (convection region), with, of course, counterflows elsewhere and subsequent readjustments of the level of the isothermal region as temperature and other conditions changed. Radiation intensity, barometric pressure, and vertical circula- tion, therefore, appear all to codperate in lowering the tempera- ture of the troposphere and in raising that of the stratosphere in cyclonic regions. Conversely, they appear equally to cooperate o 58 PHYSICS OF THE AIR in raising the temperature of the troposphere and lowering that of the stratosphere in anticyclonic regions. ; The above temperature conditions are averages, respectively, for the whole of cyclonic and anticyclonic areas. Subdivisions of these areas show temperature contrasts between their several quadrants, owing, in part at least, to differences in horizontal wind direction and the distribution of condensation and evapora- tion. This interesting detail, however, scarcely belongs to a dis- cussion of the isothermal region, but rather to an account of the two types of weather concerned, under which heads it will receive further consideration. RELATION OF THE ISOTHERMAL REGION TO LATITUDE. It is well known that both the height and temperature of the stratosphere are functions of latitude. In the northern hemi- sphere, during summer, the under surface of the stratosphere gradually rises from about 10 kilometres above sea level at lati- tude 60° to approximately 15 kilometres at the equator, while the temperature correspondingly changes, roughly, from —45° C. to —70° C. Similar altitude and temperature changes of the stratosphere with latitude obtain, so far as observed, during all seasons and in both hemispheres, though the exact cause, or causes, of these variations is not known. Changes in the amount of radiation from below and changes in the diathermacy of the upper air at once occur as possible ex- planations of the above latitude effects. The warm surface tem- peratures of equatorial regions necessarily cause, through vertical convection, abundant cloudiness at high altitudes. These clouds, in turn, intercept much of the radiation from below, either re- flecting or absorbing it. The portion reflected obviously does not directly warm the cloud, but somewhat raises the temperature of the troposphere, while a portion of that which is absorbed merely produces evaporation rather than a change of temperature. Hence, presumably, the high clouds of equatorial regions, and also the considerable humidity there at great altitudes, owing to the persistent vertical convection, raise the level and thereby de- crease the temperature of the effective radiating surface, thus diminishing the intensity of the radiation that reaches the strato- sphere, and permitting its temperature to be correspondingly low. Some of the heat thus absorbed in the lower atmosphere con- THE ISOTHERMAL REGION 59 ceivably may manifest itself in an acceleration of interzonal cir- culation in equatorial regions and an increase of outgoing radia- tion at higher latitudes. There is, of course, abundant cloudiness over the higher lati- tudes as well as in equatorial regions, but there the atmosphere is more generally descending instead of ascending, the clouds low, the humid layer shallow, and consequently the effective radiating surface and the stratosphere comparatively warm. Conceivably, too, the composition of the stratosphere may differ with latitude. Because of auroral concentration and be- cause of any poleward drift there may be of the upper atmos- phere, perhaps there is more ozone, intensely absorptive of earth radiation, over high than over low latitudes. Doubtless, also, there are local differences in the water vapor content of the stratosphere, but at most the absolute humidity of this region must be exceedingly small, as is obvious from its excessively low temperature, and from the fact that marked temperature changes of the upper atmosphere, amounting at times to 20° C., or more, never, so far as known, produce clouds above the high cirrus; that is, above the upper levels of the troposphere. As previously stated, the essential cause of the relation of the temperature of the stratosphere to latitude is not known, but it seems probable that this relation may depend, in part at least. upon the distribution of clouds, water vapor, and ozone, and therefore that each deserves further observation and study in this connection. CHAPTER V. COMPOSITION OF THE ATMOSPHERE. In the previous discussions the actual composition of the atmosphere was of little or no importance. In some that follow, however, barometric hypsometry, for instance, or the determina- tion of altitude from pressure, it is a factor that cannot always be neglected. It will be convenient, therefore, before considering such subjects, to note of what substances the atmosphere consists and in what proportions they occur. If we disregard such obviously foreign things as dust, fog, and cloud, then whatever remains appears to be ideally homo- geneous, under ordinary conditions, and in many discussions, such as most of those of the previous pages, it conveniently may be so treated. The Greek philosophers, indeed, regarded the at- mosphere as one of the four elements that singly and combined constituted the whole of the material universe. To them it was an element in the strictest sense—a thing that cannot be divided into dissimilar parts. In reality it is not even a single substance like water, much less a single élement, but a mixture of a number of gases and vapors that radically differ from each other in every particular; nor are even the relative percentages of the several distinct con- stituents at all constant. The story of the chemical conquest of the atmosphere, from the calcination and combustion experiments of the seventeenth and eighteenth centuries that established its complexity down to the refined analyses of the present day that note and account for even the faintest traces, is full of instruc- tion and inspiration. However, it is practicable to give here only some of the final results. According to Hann,'® the chief independent gases that are blended into a dry atmosphere at the surface of the earth, and their respective volume percentages, are as follows: e Carbon Element...... Nitrogen Oxygen Argon dioxide Hydrogen Neon Helium Volume, per cent. .78.03 20.99 0.94 0.03 0.01 0.0012 0.0004 In addition to these, krypton and xenon also occur as perma- nent constituents of the atmosphere. There are also many sub- *“Tehrbuch der Meteorologie,” 3d ed., p. 5. Oo 60 COMPOSITION OF THE ATMOSPHERE 61 stances, such as radio-active emanations, the oxides of nitrogen, ozone, and, above all, water vapor, that are found in varying amounts, but of these only water vapor commonly forms an appreciable percentage of the total atmosphere, a percentage that depends chiefly upon temperature in the sense that, for any given pressure, the higher the temperature the greater the possible per- centage of water vapor. This relation holds up to the boiling- point of water at the given pressure, when, assuming saturation, there will be nothing but water vapor present, as in the spout, for instance, of a vigorously boiling kettle. Because of this relation of water vapor to temperature its volume percentage decreases in the lower atmosphere from the equator towards the poles, while that of each of the other con- stituents of the atmosphere correspondingly increases. The annual average values, again quoting from Hann,” are: Carbon Nitrogen Oxygen Argon Watervapor dioxide Equator .... 75.99 20.44 0.92 2.63 0.02 GON a dsceess GF32 20.80 0.94 0.92 0.02 FO" Na «see 26 77.87 20.94 0.94 0.22 0.03 Except for the change in the amount of water vapor, the com- position of the surface atmosphere is substantially the same at all parts of the earth. Its composition at different elevations, however, probably differs greatly, as considerations presently to follow will indicate. But this discussion requires the use of barometric hypsometry. Therefore an equation must be developed for this purpose. BAROMETRIC HYPSOMETRY. Let p be the density of the atmosphere at the height h, and p its pressure in dynes per square centimetre. Then at the level h the decrease in pressure, —dp, due to the increase in height, dh, is given by the equation, SAPS pk Casa sas a sinlied WA weal ene he ie A aia WAN Non Dog Mae OS HRS (1) in which g is the acceleration of gravity at the point in question. To within practically negligible limits the density of the at- mosphere is directly proportional to the pressure—Boyle’s law; " Tbid., p. 5. 62 PHYSICS OF THE AIF inversely proportional to the absolute temperature—Charles's law; and directly proportional to the sum obtained by adding together the molecular weights of the several gases present, each multiplied by the ratio of its partial pressure (the pressure which it alone produces) to the total pressure—Avogadro’s law. If, now, p, is the density of dry air at the temperature 0° C., and under the pressure p, then I+at in which zw is the partial pressure of the water vapor present, ¢ the existing temperature in degrees Centigrade, and a the co- efficient of gas expansion, org#,, at o° C. Substituting the value of p, as given by equation (2), in equation (1), we have w —0.378 > — dp =pog ce li Further, let H be the height of the ‘“ homogeneous ”’ atmos- phere, or height it would have if everywhere at the same tem- perature and pressure, and therefore of constant density. Obvi- ously, according to Boyle’s law, the value of H is independent of the actual value of the pressure. If, for instance, the amount of gas is doubled, p becomes doubled and the density doubled, and consequently H remains unchanged. Similarly for any other multiple or submultiple of the pressure. At any given place the pressure, p, clearly is equal to the con- tinuous product of the gas density, local acceleration of gravity, and homogeneous height; that is, pb =pogH stag ay Bed og alginate cates Walia aca ue Ipeaeiale: glia Gedy ye ee Ass at eg (4) Hence, substituting in (3) w ipo? icc onuaiseieasssdenmsianbaseisn cease (s) W 1+at But, as is seen from equation (4), H is inversely proportional to g. Hence before we can assign a numerical value to H it is necessary to specify the value of g to which it applies. Now the height of the “ homogeneous ”’ atmosphere corresponding to tem- x COMPOSITION OF THE ATMOSPHERE 63 perature ¢ and gravity g is found by multiplying any barometric height b, representing, under gravity g, a pressure p, by the ratio of the density of mercury at the temperature for which b was de- termined to the density of dry air at the given temperature t, and assumed pressure p. For 0° C. and normal gravity G (that is, the value of gravity acceleration at sea level at latitude 45° N.), He = 7991 metres. Therefore H, or, specifically, Hy, = rog1c metres. Hence, substituting in (5), and measuring in metres, (x 0.378) dp p a pb I+at G Integrating this from ho, po to h, p, we have : ( ene 7991 toge(*) = : ah Plvpen te leeastaenetede (7) I-+at However, the integration is not rigidly possible, since ¢ and the ratio ™ both are more or less irregular and variable func- tions of h. The value of g is also a function, but, for any given place, a fixed one, of h. Nevertheless, when the coincident values of p, t, and w are closely known, as they may be, it is possible to determine with equal accuracy the corresponding values of h; that is, to obtain an approximate solution of the above noninteg- rable equation. This, of course, is most accurately done by divid- ing the total height into intervals over each of which ¢t and the ratio 3 both change very nearly uniformly. If at the elevation h, we have the ratio > and at fh the ratio ~, then, when h — hy is not too great, we may, with but little error, assume the ratio constant and its value for the interval in question to be (Fe +5) ei gaeas aye eae ORs pak Gea Roehe (8) Also, if the temperature varies approximately uniformly be- tween the given levels, we can assume, again with but little error, 64 PHYSICS OF THE AI the mean, tm, of the two limiting temperatures to be that of the whole layer between / and hy. Finally, as the value of g changes but little through all attainable levels in the atmosphere, its mean value, gm, between the two levels, may be used as a very close approximation. Hence, with all these approximations, poet ees | Lo |e ae Os canadian Danie (9) ieee ep. ? s Z ¥ Tr . . 2 It will be noticed that since 1 + at =3,,' which T is the absolute temperature, a should, theoretically, be used in place of I + atm, where 7 is the harmonic mean (= =atnt : +7) of the absolute temperatures (average) of the equally spaced short intervals between the given levels. Probably, however, this refine- ment is seldom justified by the data, except for elevations greater than 4 or 5 kilometres. If, instead of natural logarithms with base e, ordinary loga- rithms with base 10 are used, equation (g) becomes h = 18400 1 Oi US gE iss oa yaa aeees 10 e ogi (Be) 7 £m ( Z Now gm differs in general from G both because of difference in latitude and because of difference in elevation. Thus the shape of the earth causes the value of gravity so to vary at sea level that at latitude / g:=G(1I —0.00264 cos 2/ + 0.000007 cos? 2/), while with elevation it varies inversely, nearly, as the square of the distance from the centre of the earth. Let R be the radius of the earth at the place of observation, and d the elevation at which the value of g is desired. Then SOs GE nearly (increase of g due to mass of air left below is negligible), gf WR and, to the same approximation, Spi (roe Ey sate. gn=eo(x 25+3(2) 4(Z) +.) Ese c ee Ris Sud beaut loetesete eet (11) ‘ ‘ ‘ . d. But even if d is as great as 10 kilometres, the fraction —% is still so small, roughly 4, that an error of less than 1 in 400,000 will be made by writing ee Choke l= 2 A COMPOSITION OF THE ATMOSPHERE 65 Hence, finally, £1,g=G (1 —0.00264 cos 2/ + 0.000007 cos?2!) (: -25) , nearly, and = ) I+dtn I I h = 18400 logio ( I1—0.378W (1 —0.00264 cos 2/ + 0.000007 cos?2/) ( -2$) nearly ...(12) But as the amount of water vapor in the atmosphere seldom amounts to more than 2.5 per cent. of the total gases present, it follows that oa75W = 1 + 0.378 IV, to within 1 part in 10,000, Simi- larly, « I 1 —0.00264 cos 2/-+ 0.000007 cos’2]= 1+0.00264 cos 21—0.000007 cos” 2l, usually to within 1 part in 1,000,000 and I ay d : Sed (2 )-4, when d = 10 kilometres, to within 1 part in 100,000. Hence, for convenience, if d= moth we may write as a close approximation, h=18400 logio (2) (1+4tm) (1+0.378W) (1 +0.00264 cos 21 — 0.000007 cos? 2/) (42) ...08) If standard gravity gs, that is, 980.665 c.m./sec.’, is used in- stead of normal gravity G, the term I + 0.00264 cos 2/ — 0.000007 cos? 2i in equation (13) must be replaced by the term 1 +#—® gs Since the two pressures, py and p, occur in this equation as a ratio, it is correct and customary to substitute for them the corre- sponding barometric readings—properly corrected, of course, for tand g. But as the value of g, in turn, depends upon h, the evaluation of the latter would appear to require a series of ap- proximations. Rigidly this is true, but, as the value of g varies so little through attainable altitudes, a very rough approximation to the value of / is sufficient for the altitude correction of g. Obviously, in general, the recorded values of t, W, and the barometric reading b are all in error, and therefore it will be well 66 PHYSICS OF THE AIR to see what effects such errors will have on the computed value of h. Assuming an error to be made in } only, amounting to db, we have from (13), substituting ie for 2 and using natural logarithms, dh =- 7991 & (1 + atm) (1 + 0.378 W) (1 + loth R : db dh=—7991 - (1+4atm) 0.0026 cos 2/) (: + ) or, very approximately, Hence the greater the altitude, or the smaller the value of 0, the more important become the errors in pressure. Under the reasonable conditions that tm = 0° C., db = 1 mm., and b = 500 mm., corresponding to an altitude of, roughly, 3350 metres, the error dh = 16 metres, nearly. Hence, to avoid serious errors in barometrically ascertained altitudes, the value of b must be deter- mined with great care. Assume, now, an error in the temperature amounting to df, then dh = 18400 logs (7) a dt, approximately. Hence dh _adt dt dt h 1+0lm tm+273. = in which T is the absolute temperature. Again, let b = 500 mm., tm=0° C., and dt=1°C. Then dh =12.25 metres, approximately. Clearly, then, to avoid considerable errors in hypsometric alti- tude determinations the temperature must also be known with considerable accuracy. Finally, assume an error in the value of WW, that is to say, in (@+5) /2, As there should be no error of consequence in 0 W,, assuming it to be the vapor tension at the surface of the earth, it follows that the chief error is likely to be in w, the vapor tension at the elevation where the total pressure is p. Let w and p both be expressed in terms of barometric height, then db dh =18400 logo (3) (1+atm) 0.378 COMPOSITION OF THE ATMOSPHERE 67 If, as above, we let b= 500 mm., then w will usually be less than 4mm. Hence, assuming bo = 760 mm., tm = 0° C., and a 25 per cent. or I mm. error in w, dh = 1.25 metres, approximately. Hence an error in the value of the humidity produces only a small effect on the altitude determination in comparison with that due to an error of the same order in either the temperature or the total pressure. Errors in the force of gravity, whether from latitude or from elevation, have already been shown to be very small. For all ordinary purposes, therefore, altitudes in metres may be determined by the greatly simplified equation, h=18400 logio (@) GEG han) Son oe cca yeeey ance hake Aw a hind (14J Obviously these hypsometric formule apply only to so much of the atmosphere as is of substantially constant composition, since the same ‘‘ homogeneous” altitude, 7991 metres, is assumed throughout. Clearly, too, this condition of constant composition must apply, very approximately, up to the greatest altitude to which vigorous vertical convection extends, or in middle latitudes, as we shall see later, to an elevation of about 11 kilometres above sea level. Beyond this level, up at least to the greatest altitude yet reached by sounding balloons and presumably much higher still. the temperature changes comparatively little with change of eleva- tion. Hence in this region there can be relatively little vertical movernent of the atmosphere, and therefore a chance, presumably, for the several gases, oxygen, nitrogen, and others, to distribute themselves, each as though it alone were present. For this more or less isothermal region, then, it is sufficient for most purposes to use the simple equation, —ap=p'y wet a atie eta bebe a ce sa ce ets vad Saal dav abe wise Suen ockaw eeatio elie Ieee (15) in which p is the partial pressure of the gas under consideration at the place in question, dh the change in elevation, and H the virtual height of the given gas, or its height, assuming its density throughout to be the same as at the initial level, necessary to pro- duce the pressure p. This equation neglects any changes in the force of gravity, but, as already explained, such changes are small, and therefore the equation as it stands gives a close first approx!- 68 PHYSICS OF “LELE. ALK mation. It is not convenient, however, for numerical calculations, but for this purpose can be put into the following form: oO. logiop = logiopo — H Equation (14) is applicable as far up as the composition of the atmosphere is essentially constant, or to an elevation of about 11 kilometres, while above that level, where, owing to the practi- Fic. 19. bn 140 130 120 uo 100 90 80 70 60 50 40 30 20 is Ul 5 ote “ <7 40 50 VOLUME PER CENT Composition of the atmosphere at different levels. cal absence of vertical convections, each gas presumably is dis- tributed substantially as though it alone were present, equation (16) may be used, with, of course, the proper value of H for each gas considered. This value is given by the following equation: oo De F H=7991 D 37% COMPOSITION OF THE ATMOSPHERE 69 in which T is the absolute temperature, Da the density of dry air, and D that of the gas in question, both at the same pressure (no matter what) and at 0° C. Table II, computed by the aid of equations (14) and (16), and Fig. 19, drawn i in accordance with this table, give the approxi- mate composition and barometric pressure of the atmosphere at various levels. The assumptions upon which they are based are in close agreement with the average conditions of middle latitudes, and are as follows: TABLE II. Percentage Distribution of Gases in the Atmosphere. Gases Height in oe Wat Carb Hyd: Total pres- metres | Argon |Nitrogen Ganon Oxygen dioxide cea Helium | sure in milli- metres 140 apne 0.01 doa hte“ tity 99.15 0.84 0.0040 130 a 0.04 whi Smee ages 99.00 0.96 0.0046 120 esis 0.19 erat weiag i otek 98.74. 1.07 0.0052 110 aid 0.67 0.02 0.02 oe 98.10 1.19 0.0059 100 FA 2.95 0.05 O.II sete 95.58 1.31 0.0067 go ate 9.78 0.10 0.49 aie 88.28 1.35 0.0081 80 jaws 32.18 0.17 1.85 kane 64.70 1.10 0.0123 70 0.03 61.83 0.20 4.72 in bancs 32.61 0.61 0.0274 60 0.03. | 81.22 0.15 7.69 oe 10.68 | 0.23 0.0935 50 0.12 86.78 0.10 10.17 ee 2.76 0.07 0.403, 40 0.22 | 86.42 0.06 | 12.61 er 0.67 0.02 1.84 30 0.35 | 84.26 | 0.03 15.18 | 0.01 0.16 | 0.01 8.63 20 0.59 81.24 | 0.02 18.10 0.01 0.04 bigs: 40.99 15 0.77. | 79.52 0.01 19.66 | 0.02 0.02 sale 89.66 II 0.94 78.02 0.01 20.99 0.03 0.01 sees 168.00 5 0.94 77.89 0.18 20.95 0.03, 0.01 ges 405. oO 0.93 | 77.08 1.20 | 20.75 0.03, 0.01 ar 760. 1. That at the surface of the earth the principal gases of the atmosphere and their respective volume percentages in dry air are: Nitrogen .............. 78.03 IN CGR. Sean y ecelensealels 0.0012 ORY SEM esas cueicicyeens 20.99 Helium isn caccc ce accas 0.0004 AIgon oo... eee ee eee 0.94 Carbon dioxide ...... 0.03 Hydrogen .............. 0.01 2. That at the surface of the earth water vapor supplies 1.2 per cent. of the total number of gas molecules present. 3. That the absolute humidity rapidly decreases, under the 6 70 PHYSICS OF THE AIR influence of lower temperatures, with increase of elevation, to a negligible amount at or below the level of 10 kilometres. 4. That the temperature decreases uniformly at the rate of 6° C. per kilometre from 11° C. at sea level to —55° C. at an elevation of 11 kilometres. 5. That beyond 11 kilometres above sea level the temperature remains constant at —55° C. 6. That up to the level of 11 kilometres the relative percent- ages of the several gases, excepting water vapor, remain con- stant—a result, of course, of vertical convection. 7. That above 11 kilometres, where the temperature changes but little with elevation, and where vertical convection, therefore, is practically absent, the several gases are distributed according to their respective molecular weights. A number of atmospheric gases—neon, krypton, xenon, ozone, etc.—are omitted both from Table I and from its accompanying figure. This is because all these occur—in the lower atmosphere, at any rate—in quantities too small for graphical illustration in the same diagram and to the same scale as are the principal gases. In using this diagram it should be distinctly remembered that it is supported by direct experimental observations only from the surface of the earth up to a level of about 30 kilometres, and that, while the extrapolated values are based upon apparently sound logic and not mere surmises, they necessarily become less and less certain with increase of elevation. The table and the figure bring out a few points not generally realized. One of these is the fact that the total amount of argon in the atmosphere is much greater than the average total amount of water vapor. Another is the surprisingly small amount of water vapor, especially in view of the wonderful things it does, and of its vital importance to life of every kind. There may also be a little surprise that, according to calculation, the percentage of water vapor reaches a certain maximum at an elevation of 70 to 80 kilometres, where it is, roughly, twenty-fold what it is at, say, tt kilometres. This, however, does not mean that the total amount of water vapor increases with elevation, but that it de- creases less rapidly than do the heavier constituents, and more rapidly than the two lighter ones, hydrogen and helium. COMPOSITION OF THE ATMOSPHERE 71 DENSITY OF THE ATMOSPHERE. Fig. 19, though serving the useful purpose of graphically rep- resenting the percentage distribution of the several gases of the atmosphere, nevertheless, is likely to be misleading in respect to their combined pressure and density, especially at great eleva- tions. This latter information is given in the accompanying Fic. 20. ALT. 50 100 150 200 250 = 2 6 7 10 KM. 21 19 2e 18 23 (17 24 16 25 15 26 14 27 |3 28 2 29 Il 30 10 3] 32 33 34 35 36 37 38 39 40 ee Oo-nouotaonwxz © © —- rN wr UHA™~ OO 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 600 PRESSURE MM Summer and winter pressures at various elevations. table and shown by Figs. 20 and 21, in which the abscissas at every altitude are proportional to the corresponding atmospheric pressure, and density, to as great elevation, about 40 kilometres, as the size of the figures will permit. In computing the pressure and density values in the accom- panying table the complete hyposometric equation was used. That is, the effect of water vapor, and of both the latitude and 72 PHYSICS. OF THE AIR TABLE III. Average Grammes per Cubic Metre (p x 10°, p=density) and Miilimetres Pressure (total, and Water Vapor) from 231 Summer and 185 Winter Sounding Balloon Flights at Trappes, Uccle, Strassburg, and Munich, 1900-1912. SUMMER WINTER pide Km. above sea leve. Tota Grammes 1 Vapor Grammes << ee cee ce pee pressure pee saute 0.0 762.55* 10.46 1224.42 763.35* 4.69 1287.58 0.5 718.75 9.17 1159.17 717.42 4.35 1212.31 1.0 677.24 7.81 1099.61 674.11 3-56 1147.23 1.5 637.81 6.21 1046.50 633-12 2.93 1084.23 2.0 600.31 4-97 995.19 594.37 2.27 1025.03 2.5 564.67 3:97 945.56 557-71 1.71 970.08 3.0 530.82 3-12 897.73 522.99 1.30 919.87 4.0 468.23 1.87 808.07 458.91 0.72 826.62 5.0 411.93 1.06 726.57 401.32 | ...... 743.33 6.0 361.32 0.57 653-35 349-62) | cies 666.41 7.0 BI5<84 9] ites 3 587.39 80334.) weateye 596.05 8.0 Q27A08 | ap saui-s 527.26 20804. | skin ss 530.41 9.0 238.39 | ...... 471.70 225.37 | aaaaeus 468.61 10.0 20597. | if! Sena vebale 418.94 T9819) | es gews 410.34 II.0 176.95 | ...... 368.66 165.19 | ...... 355-20 12.0 151.80 | ...... 319.03 I41.1I | ow... 303.43 13.0 TZOMTA | ||. eoatyisia 273.51 T2055 | seahass 259.22 14.0 WIL§8 | ees ae 234.50 102.99 | ....... 221.46 15.0 95:07 f) aeexee 201.06 87.99 | ...... 189.20 16.0 82:03 |}! “ganda 172.40 PSUS. seas 161.66 17.0 7034 | weeaws 147.83 64524 I ages 138.13 18.0 60:32 | ee sews 126.77 54.89 | ...... 118.03 19.0 GIL73 |. bod aeidsd 108.72 46.901 | asxecan 100.87 20.0 BASE ees yee 93.25 40,00. | gee ess 86.20 21.0 BSI05. lh. Waie tes 79.97 34.26 | ow... 73.67 22.0 32:64. | - ssisccc 68.60 29.28 | ...... 62.96 23.0 27:00! | anvacnns 58.82 ZEO2 b hneance 53.80 24.0 24.0% | sauces 50.46 QT3O% eon dc 45-99 25.0 20.60) | eseue 43-29 T8280 scdev wa 39-31 26.0 17:67 || scawned 37-14 15-63 | ...... 33-61 27.0 W516 | canes 31.86 13.36: |) wdcuseee 28.73 28.0 - T3/0F | sacs 27.34 THEG2 eed eytn 24.56 29.0 TE:TG | cscs 23-45 Qa77 | aw acess 21.01 30.0 9258 | aiaadissien 20.13 8.35 | gecnes 17.95 31.0 B22 6 eames 17.28 Fel || vesicle 15.35 32.0 705. | teas 14.82 OO) Rawlins 13.12 33-0 6.05 | ...... 12.72 B22 hates 11.24 34.0 5319- | iene 10.91 GAG) | gestae 9.59 35.0 BAO | ow cw di 9.37 B22 iC cxesebees 8.21 36.0 3:83 | esses 8.05 B27 || foc aes 7.03 37.0 3:28) | ee rer 6.89 2.79 | sevens 6.00 38.0 2B |) oxen ag 5-93 2339) || aeons 5-14 39.0 Deda Oep cece 5.09 2004] Feasts 4.39 40.0 BOB | seg tes 4.37 Li75 | sn aes 3-76 * Normal for the season. COMPOSITION OF THE ATMOSPHERE 73 altitude changes of gravity were all allowed for. No allowance, however, was made for the probable change with altitude in com- position of the upper atmosphere because a, the exact amount of Fic. 21. ALT. 100 200 300 400 500 600 700 1100 1260 1300 KM. 20 2! 19 19, 22 18 18 23 17 7 24 16 16 25 15 15 26 14 14. 27 13 13 28 12 l2 29 II Wl 30 10 10 31 9 9 32 8 8 33 7 7 34 6 6 35 5 5 36 4 o 37 3 3 38 2 = 2 39 | st" 40 0 a 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 DENSITY X 10° Summer and winter densities at various elevations. this change, is not certain, and b, at most, could not alter the values at the level of even 40 kilometres by more than about I per cent. Cuapter VI. INSOLATION. THE temperature variations of the atmosphere, both as to time and to place, and also the actual average temperature for any given locality, all obviously are of the utmost importance within themselves, and of equal importance indirectly through such meteorological elements as humidity, precipitation, wind di- rection, wind velocity, and nearly everything else that contributes to the sum-total of both weather and climate. Hence it is im- perative that in any general discussion of meteorology some con- sideration be given to the question of the source, or sources, of the heat energy necessary to these conditions, where it is de- livered, and how distributed. A little heat is given to the surface of the earth and the atmos- phere surrounding it by conduction from the heated interior, a little as a result of certain chemical changes, some from tidal action, and another small amount by the absorption of stellar and lunar radiation. But the sum-total of all these several amounts is so small in comparison to that which results from the absorp- tion of solar radiation that for even a close approximation to the total amount of thermal energy given to the atmosphere it is sufficient to consider the sun as its only source. The rate at which heat is delivered to any place on the earth from the sun depends upon: a. The solar output of radiation. b. Distance from the sun. c. Inclination of the rays to the plane of the horizon, or solar elevation. d. Transmission and absorption of the atmosphere. These factors, then, determine the earth’s heat income, and will be considered seriatim. How this heat is conserved, dis- tributed, and expended also are important problems, which will be taken up later. SOLAR OUTPUT OF RADIATION. There is no @ priori reason for assuming that the total out- put of radiation from the sun must remain strictly constant from 74 INSOLATION 75 age to age, from year to year, or even day to day. Neither is there any known a priori reason for supposing that the solar radia- tion must greatly vary, either periodically or irregularly. Hence it is distinctly a subject for continuous and careful observation, a sort that, fortunately, is already well under way. Beginning with the summer of 1905, Messrs. Abbot and Fowle, of the Astro- physical Observatory of the Smithsonian Institution, and others working with them, have made numerous determinations of the solar constant, or intensity of the solar radiation as received at the outer surface of the atmosphere. Many of these observations were made on consecutive days, especially those obtained on Mount Wilson, California, and show irregular changes both as to time and quantity, changes often amounting to several per cent. in from five to ten days. In general, the observed values of the solar constant varied from one extreme to the other grad- ually and not by jumps. Besides, observations taken simultane- ously, or at least on the same day, at stations so widely separated as Mount Wilson, California, and Bassour, Algeria, gave values that varied substantially together. “Hence,” they say, “ the most probable conclusion is that the sun actually varies from day to day in its output of radiation within limits of from five to ten per cent. in quantity and in irregular periods of from five to ten days.” But further observations are much needed. Some hold that the variations of even these short periods pro- duce noticeable weather effects; 18 while a change of, say, five per cent. in the solar constant, if long continued, obviously would be a matter of very great climatic importance. A five per cent. increase in the amount of radiation received means, of course, a correspondingly higher temperature equilibrium and, when that is established, a like increase in the amount of radiation that must somehow be sent out to space. An increase in temperature would, among other things, increase the cloudiness to some extent and therefore the amount of solar radiation directly reflected, but probably the chief increase of the outgoing radiation would be due to the greater temperature of the earth and the atmosphere. Suppose the terrestrial radiation to be increased by four per cent.. roughly the amount that might be expected from a long-continued five per cent. increase of solar radiation. Then, since the effective absolute temperature of the earth as a full radiator is approxi- * Clayton, Smithsonian Miscellaneous Collections, 68, No. 3, 1917; 71, No. 3, 1920. ‘ 76 PHYSICS OF THE AIR mately 260° C.,!° it follows, from the fourth power law, that the effective temperature increase, essential to this four per cent. greater terrestrial output of radiation, would be 2.6° C., an amount that, if continued for a number of years, would be very important. But, as already stated, the observed periods of solar variations, while irregular, appear always to be short, in fact so short as to produce only much smaller variations from the average temperature. There is, however, some evidence that, in addition to all short period changes, there are also other changes of the solar constant coincident in period and time with the sunspot variation, and which therefore go through a complete cycle in about 11 years. The evidence in favor of this 11-year cyclic change is not conclusive, but it is found both in the relative pyrheliometric values and in the absolute determinations of the solar constant. Both indicate that the solar constant may be, roughly, two per cent. greater at the times of sunspot maxima than at the times of sunspot minima. This indicated change probably is in the same sense that most persons would anticipate from the fact that the solar surface is most agitated at the times of spot maxima. Nevertheless, it apparently is in direct conflict with the conclu- sion, supported by much statistical evidence, that the atmosphere as a whole is slightly warmer at the times of spot minima than at spot maxima. There is, however, a logical way out of the paradox which will be given later. DISTANCE FROM THE SUN. If the apparent disk of the sun radiated equally all over, it would be strictly accurate to say that the intensity of its energy received at any particular point is directly proportional to the solid angle subtended by it at that point. But it does not radiate equally from all parts, either in amount or kind. The quantity of radiation per unit area of the apparent solar disk decreases from centre to circumference, while at the same time the spectral region of maximum intensity gradually shifts to longer and longer wave-lengths. Hence the total insolation at a given point cannot be rigidly proportional to the solid angle indicated. How- ever, this departure from exact proportionality must in most cases ” Abbot and Fowle, Annals Astrophys. Obs. Smithsonian Institution, 2, p. 175 (1908). INSOLATION 77 be wholly negligible. Besides, the size of the solid angle sub- tended by the sun at the surface of the earth is so small that but little error would be made in problems of total radiation by re- garding this angle as strictly zero and therefore applying without correction the law of inverse squares. At aphelion the distance of the earth from the sun is, roughly, 3-3 per cent. greater than at perihelion. Hence the solar con- stant at perihelion, other things being equal, must be approxi- mately 6.6 per cent. greater than at aphelion. And, since the earth may be regarded as a full radiator at about 260° C. absolute, it follows that its effective temperature must be greater when a maximum than when a minimum by about 1.6 per cent. of the average value, or, roughly, by 4° C. , All these calculations assume complete equilibrium between radiation and absorption, and, while there necessarily is some lag, an approach to equilibrium, as a little calculation will show, probably comes much sooner than one might suppose to be the case. Hence northern winters are not only shorter but also warmer than they would be if they occurred at times of aphelion instead of, as they do, at times of perihelion; while the winters of the southern hemisphere, during which the earth is farthest removed from the sun, have now a maximum both of duration and severity. Notwithstanding—really, because of—the marked difference between the perihelion and aphelion intensities of the solar radia- tion at the limit of the atmosphere, it is easy to show that the total amount of insolation on the earth as a whole is constant per con- stant angular travel along its orbit; and that each hemisphere, regardless of the perihelion phase, or exact date on which peri- helion occurs, receives during the course of a whole year exactly the same amount of solar radiation as does the other. This is shown as follows: Let FR be the solar distance, dé the angle at the sun swept over by the earth in the time dt. Then, from the law of equal areas, R’d@ = Cdt, in which C is a constant. Also, if dQ is the amount of solar energy incident upon the earth in the time dt, o=% dt 78 PHYSICS OF THE AIR in which J is the solar constant at unit solar distance. Hence I dQ= 48, or the energy received by the earth from the sun, assuming the solar output to be constant, is directly proportional to the angular distance between the initial and final radii vectors. Since the direction of the earth’s axis is practically fixed in space, it follows that, to the same degree of approximation, each hemisphere must be inclined toward or from the sun over exactly one-half the angular orbit, and hence that the total yearly amount of heat received by one hemisphere is the same as that received by the other, and also that the earth as a whole gets precisely the same amount of radiant energy during the aphelion half of its orbit that it does during the perihelion half—what it loses in distance it exactly makes up in time. It must not be supposed that this equality of heat supply means equality of world temperatures. Indeed, it means quite the re- verse, for the equal quantities are delivered in unequal times; the time being longest and therefore the world temperature the lowest, except in so far as there may be a lag, or, perhaps, counter land and water effects, during aphelion, and shortest with highest temperature, as previously explained, during perihelion. SOLAR ALTITUDE. Leaving out, for the present, all questions of atmospheric absorption, it is obvious that the intensity of insolation is directly proportional to the sine of the angle of solar altitude, or to the cosine of the sun’s zenith distance. But neither of these angles is directly known, and therefore can be expressed only in terms of those that are known. Each, however, is a function of latitude, of the time of day, expressible as an hour angle, and solar declina- tion, as will be explained by the aid of Fig. 22. Let P be the point of observation, with its zenith at Z, and let the sun be off in the direction OS or PS. Clearly, then, the plane of OZ and OS intersects the surface of the earth in a great circle, and the angle ZOS, measured by the arc PV of this circle, is equal to the sun’s zenith distance. But in the spherical tri- angle NPV it is obvious that the arc NV, V being directly under the sun, is the codeclination, NP the colatitude, and the angle h at N, measured by the arc CD on the equator, the hour angle, or INSOLATION 79 angle through which the earth must turn to bring the meridian of P directly under the sun. Hence I, =I cosa =I (sin ¢ sin § + cos ¢ cos 8 cos A), in which J is the normal component of the full solar intensity J, g the latitude of the point P, § the solar declination, and h the hour angle, as explained. Fic. 22. N Z Va SS S ‘e e s a Yr P a Vv o1B v nt A 0 C Ss Relation of insolation to latitude, declination, and hour angle. To find the amount of solar energy delivered at a given point we have the equation, dQ=I,dt=I (sin g sin + cos yg cos 8 cos h) dh/w in which dh is the change in the angle /: in the time dt, and » the angular velocity of the earth with reference to the sun or » = ., radians per hour. To obtain the total energy delivered per unit area in the course of a day we may consider J and 8 constant for that time, and therefore write, Q=2l (sing sin 6 H+ cos ¢ cos 6 sin H)/o in which H is the hour angle between noon and sunrise or sunset. H obviously is a function of gand 8. Thus at sunrise, say, a= = . Hence, cosa =o=sin g sin 6+ cos ¢cos § cos H and cos H =—tan ¢ tan 6. 80 PHYSICS OF THE AIR Now ¢, the latitude of the place in question, is known, and 8, the solar declination for any given day, is obtainable from an ephemeris. Hence, assuming a constant output of solar energy and allowing for variations in solar distance, the relative per diem amounts of insolation delivered to the earth (outer atmosphere) at different latitudes and different times may readily be computed. A few of these values, in terms of the total insolation received at the equator on the day of the vernal equinox, are given in the Fic. 23. LATITUDE Relation of insolation to season and latitude. following table, and the complete data for all seasons and all latitudes in Fig. 23, both of which are copied from Davis’s “Elementary Meteorology,” Ginn & Co.: Latitude.......... 0° + 20° + 40° + 60° +90° — 90° March 20......... 1.000 0.934 0.763 0.499 0.000 0.000 JUNE QE sec ss es 0.881 1.040 1.103 1.090 1.202 0.000 September 22...... 0.984 0.938 0.760 0.499 0.000 0.000 December 21...... 0.942 0.679 0.352 0.000 0.000 1.284 Annual total. ... 347 | 329 | 274 197 143 143 TRANSMISSION AND ABSORPTION. The rate of solar output of energy, distance from the sun, length of day, and solar altitude are all, as above explained, of vital importance in determining the amount of radiant energy INSOLATION 81 delivered to unit horizontal area during any interval of time— any consecutive 24 hours, say. But they give only the quantity of insolation delivered, and not the amount of energy actually absorbed and thereby. rendered effective in maintaining tempera- ture. This smaller quantity, the absorbed energy, depends upon not only the total insolation and therefore upon each of the above factors, but also upon at least two others; namely, reflection and scattering. Thus it is obvious that all the solar radiation which is reflected back to space, whether by clouds or by the surface of the earth, is immediately and completely lost, so far as heating the atmosphere is concerned, and that the same is also true of that smaller portion lost through the process of scattering, whether by dust particles or by air molecules. The total loss of insolation by these two processes, reflection and scattering, amounts, according to Abbot and Fowle,”° to about 37 per cent. for the whole earth. In other words, more than one-third of all the energy delivered to the earth is unused— merely scattered to space. When solar radiation is minutely analyzed spectrally it ex- hibits thousands of irregularities in the wave-length distribution of energy that were present even before the outer atmosphere was reached. The minima, indicating strong absorptions in the solar atmosphere, constitute the well-known Fraunhofer lines. In addition to the vast number of intensity deficiencies, absorption or Fraunhofer lines, as they are called, inherent in solar radiation, there are also many similar deficiencies resulting from its passage through the earth’s atmosphere. These are caused by oxygen, carbon dioxide, water vapor, and ozone, and possibly even by other substances. Three of these, carbon dioxide, water vapor, and ozone, are also strongly absorptive of the long wave-length earth radiation. Oxygen and water vapor have many exceedingly restricted regions of absorption—so restricted, indeed, that in mere appearance they are indistinguishable from the narrow Fraunhofer lines. But in addition to these numerous narrow lines there are also a number of broad absorption bands, certainly of water vapor, ozone, and carbon dioxide. Oxygen, too, seems to have a broad absorption band in the region of exceedingly short wave-lengths. It is possible that many, if not all. of the bands are simply aggregates of large numbers of ” Annals Astrophys. Obs. Smithsonian Institution, 2, p. 163. 82 PHYSICS OF THE AIR individual lines, but this is not known to be true of any of them. Whatever the actual process of absorption, it is certain that to within observational errors the amount of energy absorbed increases arithmetically with the intensity of the incident radiation and, for monochromatic radiation, geometrically with the quantity of the absorbing material passed through, provided it is all under the same physical condition. Thus, if J, is the initial intensity of a parallel beam of monochromatic radiation, and a/, its intensity after passing normally through a homogeneous layer of absorbing material of unit thickness, then its intensity after traversing a dis- tance of m units in the same material is given by the equation, I = Iha™, In the case, also, of scattering of monochromatic radiation the extinction progresses according to the same laws that apply to absorption. That is to say, it is always a constant fraction of the remaining radiation that gets through a unit quantity of the scattering material. , The coefficients both of direct absorption and of extinction by scattering are radically different for radiations of different wave-lengths. But if J) is the initial intensity of the radiation of a given wave-length and aJ, its intensity after it has passed normally through a layer of absorbing material of unit thickness, then after normal transmission through layers m and units thick respectively, Im =Ina™, and In = Ina" Hence, I m o-(#)" *, and Ip=Im (=) eas Now, in the case of the atmosphere, while in a vertical direc- tion there is neither homogeneity in dust content nor in density, there is approximate horizontal homogeneity in respect to both conditions. Hence by observing the sun at different angles of elevation a considerable range in the ratio between m and n can be obtained for the atmosphere as a whole. For simplicity it is desirable to take n= 2m, from which, In= 7 (equation of Bouguer). am INSOLATION ; 83 As both Jm and Jn are measurable, anywhere at the surface of the earth, J,, or the intensity of the radiation outside the atmos- phere, is at once determined to approximately the same degree of accuracy. The equation, however, is accurate only for monochro- matic radiation. If applied to the whole, or even any considerable part, of the solar radiation as a unit the value thus obtained for the intensity of the initial radiation will be too small, as Langley showed long ago. This can be seen as follows: Let the intensities of the several monochromatic radiations be Ao, By, Co, etc., and their respective coefficients of transmission a,b,c, etc. Then their combined residual intensities after passing through the thicknesses m and 2m of the absorbing medium will be, respectively, Apa™ + Bob" +Cyc™+, etc. =Rm and Ayam +Bob?™ + Coc2m+, etc. = Rem Hence the initial intensity, as computed by the Bouguer equa- tion, is _ Rn ~ Rom But the difference between the actual and the computed initial intensity is Ro AyptBotCot+, etc. —Ry= (Aoa™ + Bob” +Cycm +etc.)? Aa Bot Oat eles Aut BPC PR bate, = A oBo(a™ —b™)? +A oCo(a™ —em)? +... + BoCo(b™ —c™)? Fete. A,a?™ + Bob?” + Coe?" + etc. An occasional term in the numerator of this final fraction may reduce to zero, since possibly a = k, c =], etc., but in general no two of the coefficients, a, b, c, etc., are equal to each other. Hence every term in the numerator, except the few zero ones, if such exist, and consequently the fraction as a whole, is both real and positive. The Bouguer equation, therefore, when applied to complex radiation, always gives too small a value for the initial intensity. Clearly, then, to determine to the highest degree of accuracy the intensity of the radiation reaching the outer atmosphere (that is, the amount per unit normal surface per unit time) it is necessary first to analyze it into its spectroscopic components and 84 PHYSICS OF THE AIR then either to determine the initial intensity of each or else to adopt some equivalent process. The direct method of measuring the energy in each small spectral range would be very tedious, and, besides, would involve a difficult instrumental standardiza- tion, hence the following method has been found more convenient : 1. Analyze the insolation and obtain, with the bolometer, the relative distribution of energy through the spectrum for differ- ent solar altitudes but, as nearly as possible, constant sky con- ditions. In each case the value of m, the air mass as it is called, is proportional to the secant of the solar zenith distance. Hence when the solar altitudes at which the bolograms were taken are known, the ratios of the corresponding 1’s, being the ratio of the respective zenith distance secants, are also known. 2. Measure with a pyrheliometer the rate at which solar energy, exclusive of sky radiation, is delivered per unit normal area during the same time that one of the bolograms was ‘being obtained. 3. Extrapolate, according to the Bouguer equation, each por- tion of the bolograms to zero atmosphere and thus obtain the initial bologram, or energy distribution through the solar spec- trum outside the atmosphere. 4. Measure the areas between the base line, corresponding to zero insolation, and the two bolograms, the extrapolated and the one corresponding to the pyrheliometric reading. 5. From these areas, A, and A, respectively. and the observed solar intensity 7, compute J,, the intensity of solar radiation out- side the atmosphere, by the equation, Ao Io=I7 When expressed in terms of gram-calories per square centi- metre normal surface per minute the average value of J,, known in this form as the solar constant, is about 1.93.7? As stated above, careful estimates show that about 37 per cent. of this radiant energy is wholly lost to the earth, leaving only some 63 per cent. directly absorbed in roughly equal amounts by the earth and the atmosphere. And since the air usually is nearly opaque to terrestrial radiation, it follows that approxi- * Abbot and Fowle, Annals Astrophys. Obs. Smithsonian Institution, 3, p. 134 (1913). INSOLATION 85 mately 60 per cent. of the incident solar energy ultimately heats the atmosphere. The more conspicuous notches in the bolometric curve coin- cide with water vapor absorption bands, from which it is inferred that most of the direct absorption of solar energy in the atmos- phere is due to water vapor. All these bands, however, are of longer wave-length than the region of maximum intensity in the solar spectrum, as are also the absorption bands of carbon dioxide and the stronger bands of ozone. Nitrogen and argon have no known absorption bands, while oxygen, the only other important constituent of the atmosphere, has only one, and that in the ex- treme ultraviolet or Schumann region, except some fine lines in the red. Further, the general absorption of all three is so feeble that, to a first approximation, it may be regarded as wholly neg- ligible. Hence, atmospheric absorption of radiation, whether solar or terrestrial, obviously is due almost wholly to water vapor, carbon dioxide, and ozone; and, since the approximate amount of carbon dioxide in the atmosphere is always known and that of water vapor at least often determinable, it frequently is possible, by the aid of laboratory data, to know roughly the actual absorption in any portion of the spectrum due to these two sub- stances, either singly or jointly. The magnitude of the ozone effect, however, is always un- certain because the quantity of this gas in the atmosphere is not known. In the presence of moisture and at ordinary temperatures it soon reverts to ordinary oxygen—a sufficient reason, perhaps, why only traces of it are found in the lower atmosphere. In the high atmosphere, on the other hand, where there must be very little moisture and where the temperature is about —55° C. in mid-latitudes, and even lower in the tropics, it obviously is far more stable. Hence, since extreme ultraviolet radiation, such as there is every reason to believe is emitted by the sun, on passing through cold dry oxygen converts much cf it into ozone, it appears exceedingly probable that this substance must exist to appreciable amounts in the higher portions of the atmosphere. Indeed, the presence of ozone in the upper, atmosphere has been fully demon- strated spectroscopically by Angstrom,?? Fabry and Buisson,”* 2 Arkiv. for Matematik, Astronomi och Fysik., 1, p. 395 (1914). = Tournal de physique (5), 3, P. 196 (1913). 7 86 PHYSICS OF THE AIR Fowler and Strutt,23* and Abbot.”*® Strutt °° also proves, spec- troscopically, that it is not nearly so concentrated, if present at all, in the lower atmosphere as in the upper. The form of the solar energy spectrum curve outside the atmosphere as determined by Abbot and Fowle and its compari- son with “ black-body ” curves at 6200° and 7000° absolute C. are given by Fig. 24 (a copy of Fig. 29, vol. iii, Annals of the Astrophysical Observatory of the Smithsonian Institution). The Fic. 24. 00% 02 04 06 O08 1.0 1.2 1.4 1.6 18 #20 22 24 26 28 3.0 Comparison of solar and ‘‘black-body”’ energy distribution. curve of terrestrial radiation intensities, on the other hand, is not known, but it obviously must be within that of a full radiator at the earth’s temperature, but close to it, because of the universal presence of the highly absorptive substances, water vapor, espe- cially, carbon dioxide, and ozone. That is, it must be within, but close to, the black-body curve for 287.2° C. absolute, as shown in Fig. 25, copied from Plate XX, vol. ii, Annals of the Astro- 2a Proc. Roy. Soc. v. 93 A, p. 77, 1917. > Proc. National Acad., vol. 4, p. 104, 1918. *e Nature, vol. 100, p. 144, 1917; Proc. Roy. Soc. A. 94, p. 260, 1918. INSOLATION 87 physical Observatory of the Smithsonian Institution (Abbot and Fowle). The absorptions of earth radiation by water vapor, carbon dioxide, and ozone are shown in Fig. 26. The outer or envelop- ing curve, a copy of Fig. 25, gives the intensity distribution of - radiation from a black body at the temperature 287.2° C. absolute. The area of this curve below the irregular full line near its top, at least up to 20m, and, presumably, through much, if not all, the region of longer wave-lengths, shows the absorption of earth radiation by a column of 1.13 grammes of water vapor per square centimetre cross-section, as computed by Bouguer’s equation from Fic. 25. ora 5 10 15 20 25 30 35 40 45 50 AL ‘‘ Black-body "’ radiation at earth temperature. the laboratory data of Rubens and Aschkinass.** Similar data by Fowle,** however, give smaller coefficients of absorption. The amount of water vapor assumed, 1.13 grammes per square centi- metre cross-section of the column, is that which Abbot and Fowle * have computed to be the average amount in the atmos- phere as a whole above the 1780-metre level. The areas below the two broken curves show the absorption by carbon dioxide above the same level, as computed from the experimental data of Schae- fer,2® and Rubens and Aschkinass.?7 Finally, the area below the dotted line gives some idea of the absorption of earth radia- 4 Ann. der Phys., 64, p. 584 (1808). *4a Smithsonian Misc. Col., v. 68, No. 8, 1917. * Annals of the Astrophys. Obs. Smithsonian Institution, vol. ii, p. 168 (1908). Ann. der Phys., 16, p. 93 (1905). 7 Loc. cit. 88 PHYSICS OF THE AIR tion by ozone, computed, after making certain assumptions ex- plained below, from the observations of Ladenburg and Leh- mann.** The amount of the ozone absorption, however, is uncer- tain, as implied, for several reasons: (a) Laboratory measure- ments have not extended beyond 124. (b) While Ladenburg and Lehmann give the length of the absorbing column used, one metre, and describe minutely their ingenious manometer, they do not state the actual pressures at which their data were obtained. But as their ozone was nearly pure, and as they refer to the color of the gas at 50 mm. and 200 to 300 mm., it would seem that they used the equivalent, roughly, of a column 30 centimetres Fic. 26. ABSORPTION INTENSITY 0 2 4 6 86 0 2 4 16 B 2 22 24 26 2 3 32 34 36 38 40 WAVE -LENGTH, £2 Water vapor, carbon dioxide, and ozone absorption. long at, say, 15° C. and 760 mm. (c) The amount of ozone in the atmosphere is not known. Pring,?® who appears to have done the most careful work on this subject, estimates it to be the equivalent of a layer of the pure gas 4.2 centimetres thick at normal temperature and pressure. Hence the assumptions re- ferred to above were (1) that the ozone in the absorption tube was the equivalent of a column 30 centimetres long, and (2) that the ozone in the atmosphere is equivalent to a layer whose thick- ness is only 4.2 centimetres, each at atmospheric pressure and room temperature. It appears, then, as shown by Fig. 26, that the absorption of * Ann. der Phys., 21, p. 305 (1906). ”® Proc. Roy. Soc., A, vol. 90, p. 204 (1914). INSOLATION 89 earth radiation by water vapor is nearly perfect, even beyond the level of one to two kilometres; that neither at this level nor, perhaps, at any other (consult Fig. 19 and its accompanying table for probable distribution of carbon dioxide and water vapor) does the carbon dioxide appreciably affect the amount of absorp- tion—already complete (through the presence of water vapor) in the regions of its bands; and that, since ozone absorption is very strong where that of water vapor is weakest and imperfect and earth radiation at its maximum, the presence of this gas in the atmosphere has a slight heat-conserving or warming effect. _ It is also obvious that, although each of these substances is an effective absorber in the region of appreciable to strong solar radiation, their joint effect on earth radiation is far greater, so much so, indeed, that for low levels absorption is practi- cally complete. SURFACE TEMPERATURES AND ABSORBING GASES. The radiation from a particle of water vapor, or any other substance in or of the atmosphere, clearly, is equal in all directions. Hence the amount of radiant energy incident on the surface of the earth and the resulting temperature are generally different from what they would be in the absence of any such absorbing and radiating medium. During the night, when there is no incom- ing radiation to consider, the process of absorption and radiation by the constituents of the atmosphere manifestly checks the rate of surface cooling, and thereby insures higher night tempera- tures than otherwise would obtain. Whether this process also increases day temperatures is not so obvious. It does, as the following argument will show, when, and only when, the substance involved, whether the ozone shell, presumably in the isothermal region, the water vapor shell of the lower atmosphere, or any other such shell, is more absorptive of the outgoing terrestrial radiation than of the incoming solar radiation. The numerical solution of the problem as applied to any one of these shells is complicated by the alternation between night and day; by constant changes in the solar inclination; by reflec- tion; and probably by many other conditions of importance. However, since the coefficient of absorption is independent of intensity of radiation, it is possible to obtain an approximate evaluation of the temperature effect due to any given absorbing layer or shell. Let J be the average intensity of the normal component of the go PHYSICS OF THE AIR absorbed portion of solar radiation. Then, assuming, as already explained, that 37 per cent. of the incident solar energy is wholly lost by reflection, representing the solar intensity outside the atmosphere by Jo, and dividing the cross-section of the beam, multiplied by its effectiveness by the area over which it is distributed, I= 0.6310 R? qr? =0.16 Ip, about, in which & is the effective radius of the earth as an intercepter of incoming radiation. Also let al be the average intensity of solar energy, including both the direct and the reflected, absorbed by the outermost shell, say, or by the ozone of the upper atmosphere. Half this absorbed energy is radiated to space and half to the earth, including the lower atmosphere. The earth, which for convenience may be considered initially cold, now receives radiation of the average intensity (1-a) I from the sun, and of the intensity = I from the absorbing layer under consideration. Together these amount to J (1- =). After a time the earth will return an equal average radiation, but of very different spectral distribution. Let bJ (1- <) be the part of this long-wave earth radiation absorbed by the layer in question. As before, one half, or ° I (1- - ), will be radi- ated back to the earth, there absorbed, because of its long wave- length, and again sent out. The next amount returned by the shell is ()? I (1- = ), and so on infinitely. Hence the total average intensity, [,, of the radiation reaching the earth and lower atmosphere is given by the equation, perf Babe a)"} mfr roo} 208) = 1 1+K(b -a)}, since b cannot exceed unity, in which INSOLATION gI Now, b is positive and therefore K is also positive. Hence > I {1 + K(b—a) \S1 according as a < b a That is, the total amount of radiation reaching the earth is increased, unchanged, or decreased by the presence of an absorb- ing shell according as its coefficient of absorption of terrestrial radiation is greater than, equal to, or less than its coefficient of absorption of solar radiation. But water vapor, carbon dioxide, and ozone are all more absorptive of earth radiation than of the comparatively short wave-length solar energy, and therefore each, but water vapor especially, keeps the average temperature higher than it otherwise would be. Suppose b = 20 per cent. and a = 2 per cent., then, Ee fr +K(-a)} =1.1/, about. That is, the incoming radiation, and hence also the outgoing radiation, is increased 10 per cent. over what it would be if such an absorbing layer did not exist. But as the earth, largely because of its water vapor, radiates substantially as a black body, or in proportion to the fourth power of the absolute temperature, it follows that a 10 per cent. increase of radiation implies approxi- mately a 2.5 per cent. increase of the absolute temperature. In other words, an absorbing shell with the properties assumed, properties that possibly are of the same order of magnitude as those of the existing ozone in the upper atmosphere, would maintain the average temperature of the earth about 7° C. higher than it otherwise would be. Any increase, then, in the amount of ozone, or other similar absorbing material, in the outer atmosphere must more or less increase the average temperature of the earth. Hence variations in the output from the sun of the ozonizing or very short wave- length radiation presumably would alter the ozone content of the upper air and through it, as above explained, the average temperature of the earth. Other things being equal, it would seem that there should be a maximum of this extreme ultraviolet radiation and, consequently, maximum average temperature at the 92 PHYSICS OF THE AIR time of a sunspot minimum when the solar atmosphere is com- paratively clear, as indicated by a minimum corona; and a mini- mum, with minimum average temperature, at the time of a spot maximum when the “ dustiness”’ of the solar atmosphere, as shown by a maximum corona, is very great. Even if the solar constant should be a little greater at the time of a spot maximum than at a spot minimum, the above variation of ozone, if it occurs, might lead to the paradoxical concurrence of maximum average temperature with minimum average insolation and minimum average temperature with maximum average insolation. A greater general prevalence of cirrus and cirrus haze during spot maxima than during spot minima would also account for this paradox ; because such clouds, owing to the size of their par- ticles, shut out the short wave-length solar radiation more effec- tively than they shut in the long wave-length earth radiation. And perhaps these clouds really are generally most prevalent during spot maxima, and therefore at least a contributing factor in the cause of the observed temperature changes. At any rate the auroras are then most frequent, and they obviously generate nitrous oxide and other hygroscopic compounds which, because of their density, slowly fall to the cirrus level where they may produce cloud particles in an atmosphere whose humidity is much below that which otherwise would be essential to cloud formation. CHAPTER VII. ATMOSPHERIC CIRCULATION. INTRODUCTION. ATMOSPHERIC circulation, whether manifesting itself in a monsoon, for instance, or in only a gentle lake breeze, is a gravi- tational phenomenon induced and maintained by temperature differences. This can be well illustrated by the flow of water between two adjacent tanks when connected by an upper and a lower pipe and kept at different temperatures. Let the two tanks, A and B, Fig. 27, be filled to the same level slightly above the upper pipe u, and let them have the same temperature. Under these conditions there will be no flow of water from either tank to the other. Now let the pipes be closed and let the water in tank A be equally warmed throughout. It will expand, providing its original temperature was not below 4° C., and the amount of water above each level in 4, at and below the initial surface, be increased in proportion to its dis- tance from the bottom. Hence the pressure due to gravity is everywhere throughout the original volume correspondingly in- creased—the maximum increase being at the level of the initial surface. If the lower pipe J be now opened, there still will be no flow of water from either tank to the other. But if the upper pipe be opened, water will flow from A to B, and in so doing will decrease the pressure on all parts of A and increase it on all parts of B. If/ is also open, water will flow from B to A. If both pipes are left open and the water in A kept constantly warmer than the water in B, there will be continuous circulation of the water from A to B through the upper pipe and from B to 4 through the lower. Obviously the same results could be obtained by applying a cooling process to B instead of a warming one to A. That is, since the circulation in question is a gravitational phenomenon induced by a temperature difference between the water in the two tanks, it clearly is immaterial how this tempera- ture difference is established, whether by heating the one tank or by cooling the other; similarly in the case of the atmos- phere. If two adjacent columns of air, or the masses of air over two adjoining regions, whether large or small, are kept at 93 94 PHYSICS OF THE AIR different temperatures, there will exist, through the action of gravity, a continuous overflow from the warmer to the colder, and an underflow from the colder to the warmer. Neither does it make any difference in this case how the inequality of tempera- ture is established and maintained, whether by heating the one section or by cooling the other. Fic. 27. I | ft Circulation between warm and cold tanks. VERTICAL CONVECTION OF THE ATMOSPHERE. General Considerations.—Vertical convection of the atmos- phere may be divided into two classes: (a) mechanically forced convection, as the rise of air on the windward side of a mountain or other obstruction and its fall on the leeward side; (b) thermal convection. The latter, involving both warming and cooling, is by far the more important; in fact, it either constitutes or is associated with all natural air movements. It commonly is said to consist of the rising of warm air and the sinking or flowing in of cold air to take its place; but, while this describes the phenomenon of thermal convection, it seems to imply the false ATMOSPHERIC CIRCULATION 95. concept that warm air has some inherent ascensional power, whereas, in reality, thermal convection is only a gravitational phenomenon, consisting in the sinking of relatively heavy air and the consequent forcing up of air which, volume for volume and under the same pressure, is relatively light, The terms “heavy” and “light” are used here advisedly instead of “ dense” and “ rare,” because it is the relative weights of two adjacent masses of air of equal volume under the same pressure and not their densities that determine which shall fall and which shall be raised. Three factors enter into the question of weight per unit volume when pressure is constant: (a) temperature, (b) com- position, and (c) horizontal velocity, including speed and direc- tion. The first of these weight factors varies widely and is very effective. A change in temperature by any given amount + t, say, changes the original weight per unit volume, W,, to the new weight, W, + w in the ratio, hee is L 7 : (Charles’s or Gay-Lussac’s law), in which T is the original absolute temperature. Thus if the original temperature is that of melting ice, and it is increased or decreased by 1° C., the weight per unit volume will be decreased or increased, respectively, 1 part in 273. The effect of the second of the above weight factors, the composition of the atméSphere, is obvious from the following consideration: Since the number of gas molecules per unit volume under a fixed temperature and pressure is independent of the nature of the gas—-Avogadro’s law—it follows that under these conditions an increase or decrease of water vapor, say, in the atmosphere implies a corresponding decrease or increase of the other molecules present, mainly nitrogen and oxygen. Now the equivalent molecular weight of dry air is approximately 28.94 and the molecular weight of water 18, hence a change in the water vapor, the only constituent of the atmosphere that appreciably varies, amounting to 1 per cent. of the total number of gas mole- cules present, alters the weight per unit volume by Ze = W, in which W is the weight of the unit volume of dry air under the same conditions of temperature, pressure, and gravity. On very warm days water vapor may amount to 5 per cent. or more of the total gas molecules present, and the air, therefore, be, roughly, 96 PHYSICS OF THE AIR 2 per cent. lighter than it would be if perfectly dry. Of course, changes from saturation to utter dryness, or the reverse, do not occur in nature, but a variation of as much as 50 per cent. in the absolute humidity at a given place does occur through evapora- tion, condensation, and air movement. Hence on very hot days a change of 1 per cent. in the weight per unit volume of the lower air as a result of altered composition alone is quite possible, and indeed often occurs. This produces a difference in buoyancy Fic. 28 N 9 r Wi, Pp Q Ww 0 E Ss Decrease of weight due to rotation of the earth. of the same order as that caused by a 3° C. change in tempera- ture and therefore may be decidedly important. The third factor that affects weight and convection, namely, horizontal velocity, while comparatively small, occasionally may be of some importance. Its numerical value can easily be com- puted. Let NS, Fig. 28, be the axis of the earth’s rotation, and let P at latitude ¢ be the point under consideration. The cen- trifugal force f acting on the mass a at the point P is given by the equation, =mrao, in which © is the angular velocity of the earth's rotation, and r the distance of P from the axis. Numerically, 2a oe 86,164 ATMOSPHERIC CIRCULATION 97 Since the mean radius of the earth is about 6368 kilometres, and since weight equals mass times gravitational acceleration, or g8im, approximately, in the C.G.S. system, it follows that at latitude 4o° w f=-—, roughly, 378 in which w is the weight of the object considered, while the de- crease, dw, in the weight, or the component of f at right angles to the surface, is given by the equation, dw=—f cos 40° = — ae about At latitude 40° a velocity of 22.4 metres per second (50 miles per hour) from east to west is equivalent to decreasing ? by I part in 8, approximately, and an equal velocity from west to east to increasing it a like amount. That is, at latitude 40° a given mass of air in a west wind of 22.4 metres per second (50 miles per hour) weighs less than an equal amount in an east wind of the same velocity by about 1 part in 1972: similarly for other latitudes in proportion to their cosines. Hence, other things being equal, an east wind tends slightly to underrun an adjacent west wind. The above special solution of this problem may suffice for most purposes, but the following outline and conclusions of a more general solution probably will be of interest. Referring to Fig. 29, let V cos ¢ be the horizontal velocity of the surface of the earth at latitude ¢, v the horizontal velocity of the air with reference to the surface, a the angle between the east direction and the path, and assume the earth to be spherical and concentrically homogeneous. Further, let mg, be the gravita- tional pull on the mass m, or the weight the mass m would have when at rest if the earth were nonrotating, and let mg be its actual weight. Then,. (V cos ¢+2 cos a)? —-_m(v sin a)? mg =mgo —m-—__, ——— — —_, R R x m(V cos $)? _ mv(2 V cos ¢ cos a+») ea ae R But, mgy— MAY cos 6 = the weight of the mass m when at rest on the surface of the rotating earth. Hence, when the mass m 98 PHYSICS OF THE AIR is given a horizontal velocity v, its still-weight, W. is changed by an amount, AI’, given by the equation, ; (2V cos $ cos a+y) R Since the latitude is limited by 0° and go’, it follows that the sign of the change (that is, whether the change consists of a decrease or increase from the still-weight) depends upon the value of a, or the direction of motion. Obviously, whenever cos @ is positive, or the velocity has an easterly component, the AW=—mn Fic 29 N S Change of weight due to horizontal velocity. change of weight is negative—maximum when ¢ and @ are both zero, or when the motion is east on the equator. Similarly, since 2V cos ¢ is nearly always large in comparison with v, the change of weight ordinarily is positive whenever the velocity has an appreciable westward component. This increase of weight clearly is a maximum when ¢ = 0° and a= 180°, or when the motion is west on the equator. Further, the direction of the wind in order that there be no change of weight is conditioned by the equation, Uv cos a =—_——__- 2Vcos¢ But, as above stated, 2 V cos ¢ nearly always is large in comparison with v, and therefore the direction conditioned by ATMOSPHERIC CIRCULATION 99 zero change in weight commonly has only a small westerly com- ponent. For example, let v = 44.7 metres per second (100 miles per hour) and let ¢=60°. Then, under these somewhat excessive conditions, for zero effect, cos a =-s, about, or the direction along which there is no change of weight is less than 6° west of the meridian. : From the above it appears that of the three factors that alter the weight of a given volume of air and thereby determine whether it shall rise to higher levels, sink to lower, or remain where it is, temperature is by far the most important, and horizontal velocity the least important. As a rule, the former alone need be con- sidered. Local Convection.—There are two distinct ways of thermally inducing convection: (a) by heating below; (b) by cooling above. Each is of great importance, both in general atmospheric movements and also in those restricted or local winds to which special names have been given. Where heating alone occurs the rising air does not return, but remains in equilibrium at its new level, where its final temperature is the same as that of the adja- cent atmosphere. Similarly, when cooling alone occurs the sink- ing air does not again immediately rise. In other words, neither heating nor cooling, acting alone, can produce closed circulation in which the same mass passes through a complete cycle of posi- tions, though, of course, a compensating’ movement must occur somewhere. A strong local uprush, for instance, except in the case of the thunderstorm, to be explained below, is nearly always compensated by a wide settling, so gentle that it cannot be meas- ured. Similarly, restricted down-rushes of air, again except in connection with the thunderstorm, are compensated by wide and gentle upward movements. Whatever the type of atmospheric disturbance under con- sideration, the most important general facts to remember are: that all vertical movements of the air are accompanied by dynami- cal heating or cooling; that rising air cools, roughly, at the adia- batic rate of about 1° C. for each 103 metres increase of eleva- tion; that descending air warms at substantially the same rate; that dynamic cooling limits the height of upward convection; and that in many cases dynamic heating, and not the surface of the ground, limits downward convection. 100 PHYSICS OF THE AIK + CLASSIFICATION OF WINDS. All the above is entirely general and of universal application, Gravity and temperature differences enter directly or indirectly into all atmospheric circulation, both the fundamental and con- tinuous circulation that exists between the warm equatorial and cold polar regions, and those secondary circulations that occur only locally and occasionally. Nevertheless, clearness in any detailed discussion of all winds requires their grouping according to some basis of classification suitable to the purpose in view—in the present case a discussion of their initiating causes and modifying influences. Unfortunately, none of the current classifications of winds (e.g., those listed in Milham’s “ Meteor- ology,” p. 164 et seq.) is adapted to this end, and, therefore, pro- visionally a somewhat different grouping will be used. Obviously no subdivision of air movements is possible on the basis either of gravitation or of temperature difference, since, as just explained, each is involved in every such movement. But there also are modifying factors—friction, viscosity, turbulence, local heating, local cooling, deflection by mountain barriers, deflection due to the earth’s rotation, and many others that make one circulation different from another in time of occurrence, extent, duration, direction, and intensity. Hence in considering the origin and nature of winds, it will be convenient to classify them as follows, according to the conditions that initiate or materially modify them, and to discuss separately, under its appropriate head, each distinct and well-recognized sub- division. : A.—Winds due chiefly to local heating—whirlwinds, cumulus convection, valley breezes, sea breezes. B.—Winds due to cooling—land breezes, mountain breezes, glacier winds, bora, mistral, Norwegian fallwinds, continental fallwinds. C.—Winds due to simultaneous adjacent local heating and local cooling—thunderstorm winds. D.—Winds due to widespread heating and cooling—gradient winds, monsoons, trades, antitrades, tropical cyclonic winds, extratropical cyclonic winds, anticyclonic winds. E.—Forced winds, or winds caused by other winds—eddies, foehns (Chinooks), tornadoes. ATMOSPHERIC CIRCULATION 101 WINDS DUE TO LOCAL HEATING. Whirlwinds. During clear, calm summer afternoons, particularly during a dry spell when vegetation is parched and the ground strongly heated, dust whirls often develop, and occasionally travel con- siderable distances before losing their identity. The flatter the region, the more barren, the hotter the surface, and the quieter the air, the more violent these whirls become. Hence, level deserts are especially frequented by such winds, amounting at times to violent storms, though never more than a few metres in diameter. The development of these storms in which convection is strong is not simple, but an understanding of them will materially help to an understanding of convection due to heating in less obvious cases. It is well known that those regions in which violent dust or sand whirls occur are also the places where inferior mirages are most frequent. The reason for this coincidence is the fact that the density gradient of the atmosphere essential to the production of a mirage simulating a lake, namely, an increase of ce with elevation, is most favorable to strong vertical convection. Under these conditions the air is in that same unstable equilibrium that applies to a column of liquid whose under layer is lighter than the upper—whose under layer is oil, say, and upper layer water. At first sight it might seem that no such condition of con- siderable extent can occur in nature; that as soon as the under layer became specifically lighter than the one next above, they would change places. Whenever a cork, for instance, is let go under water it bobs up. Similarly, a balloon rises, without ex- ception, whenever the combined weight of gas, envelope, etc., is less than that of the atmosphere displaced. Why then should not surface air, whenever it becomes specifically lighter than the air above it, also rise immediately? This undoubtedly is just what a limited volume of light air would do if actually sur- rounded on all sides by heavier air. But surface air is not com- pletely surrounded by other air; its condition is somewhat anal- ogous to that of a cork whose flat surface is pressed against the bottom of a vessel of water. The cork in this case does not rise, simply because it is pressed down by water above and not pushed up by water beneath. Similarly, warm air covering an extensive flat surface is pressed down by the superincumbent atmosphere 8 102 PHYSICS OF THE AIR and not pushed up by denser air below—there is no denser air below to push it up. Obviously, though, even surface air under the given con- ditions is in an unstable condition. Hence it is important to deter- mine that vertical temperature gradient which reduces super- adjacent layers of air to the same density. Auto-convection Gradient—Suppose the atmosphere is per- fectly quiet, what temperature gradient must any layer of it have in order that it may just initiate its own convection? Clearly this gradient must be such that density shall just increase with elevation. That is, the ratio, 2, must be just dh ’ positive. From p V=*+RT p p we get meee PRT Therefore, pb (@_ar do-azl BF But te = —98tdh_ 981 pah. dp = —981 pdh= yo RT Therefore, ____b (981 dh af) | ie op RT tr) and dp_ Pp (e + aa) dh RT?\ R dh}* Hence, since is negative in the case under consideration, dp _ dh” when aT _981 ; dh R But for dry air, R=2.871X 108 and OF oo 000 Gh = 0:0903417- ATMOSPHERIC CIRCULATION 103 Hence when dT =- 1° C., dh = 29.27 metres, That is, in order that an under layer shall have the same density as the next above it the temperature must decrease 1° C. with each 29.27 metres increase of altitude, or 3.52 times faster than the adiabatic rate of 1° C. per 102.93 metres. In order that the lower layer shall be distinctly lighter than the upper, the temperature decrease with increase of altitude must be four or five times the adiabatic rate. Obviously an extensive layer of warm, light air cannot all rise at the same time. It must rise locally and in streams, if at all. Similarly, the upper air must settle locally, if at all. But during the time mirage conditions are maintained the surface is strongly heated, so that any air that might reach it is not only warmed dynamically by the compression to which it is subjected, in settling down, but also by the heat acquired from contact with the surface. Hence, any settling of colder air from above amounts only to a partial removal of the hot and therefore light surface air. It might seem, however, that the streams of rising air, above referred to, would ascend with great rapidity and in such volume as quickly to exhaust the supply of warm air. But, as already stated, the heat is being constantly supplied, and therefore the surface layer of hot air continuously renewed. Besides, the difference in weight between a given volume of a rising filament of warm air and an equal volume of adjacent air is at first only an exceedingly small fraction of the weight of either. Hence the acceleration with which it moves is correspondingly small. In nearly all cases the feeble streams of rising hot air presumably are pinched off by the adjacent denser air, and in this manner the breaks, as it were, in the integrity of the hot surface laver mended and the entire convection divided into innumerable dis- continuous filaments—mere fitful leaks from the constantly re- newed reservoir of hot air. It occasionally happens, however, that because of some dis- turbance an unusually large volume of warm air breaks through and rises in a columnar form. Such a column necessarily pro- duces a chimney-like draft, since the air composing it is warmer and therefore lighter than the adjacent air on the outside. Hence, however established, such a column of warm air will maintain its integrity, or, rather, perpetuate itself, so long as the air that 104 PHYSICS OF THE ALK is forced into it from the base is warm and light. In this con- nection it apparently cannot be too strongly emphasized that the ascending air is not “ drawn” up any more than air is “ drawn” up a chimney. In each case the weight of the column of warm air is less than the weight of an adjacent equal column of cooler air, and the static unbalance is compensated kinetically; that is, air is forced up the column in question, as up a chimney, because of, and in proportion to, the difference between its density and that of the cooler descending air outside. Even a vena con- tracta, or restricted section, is formed in the column a short dis- tance—one to five metres often—above the surface, as, and for the same reason that, such a restriction occurs in a jet of any fluid shortly after its issuance from an ordinary orifice. The incoming air is almost certain to be directed to one side of the centre of the rising column, and, as the angular momentum thus established tends to remain constant, a correspondingly vigor- ous whirl is developed as the place of ascent is approached that gathers up such loose materials as dust, straws, leaves, etc. Furthermore, this rotation, whether clockwise or the reverse, perpetuates itself, though the details of how it does so are, per- haps, not fully understood. Pictet,?° for instance, reports ob- serving a dust whirl near Cairo, Egypt, that began on a small sand mound, remained stationary for nearly two hours, then, in re- sponse to a gentle breeze, wandered away, but maintained its sharply defined outlines and great altitude until lost in the dis- tance, more than three hours later, or about five and a half hours after its inception. The diameters of these whirls (seldom more than a few metres near the ground) are too small for the direction of their gyration to be, greatly influenced, by the rotation of the earth. Hence nearly as many turn in one sense as in the other. They have even been reported to reverse, but it is probable that the apparent changes were only optical illusions similar to that which causes the cup anemometer to seem to reverse its rotation. The height to which the whirling column rises (that is, the distance between the base of the column and its mushroom capi- tal), the violence of the whirl, and, in some measure, even its duration, all depend upon the amount of surface heating and the * Hildebrandsson et Teisserenc de Bort, “Les Bases de la Météorologie dynamique,” vol. 2, pp. 286-288. ATMOSPHERIC CIRCULATION 105 extent to which the lower temperature gradient has been made greater than the adiabatic. When this heating is slight, only those small and gentle dust whirls with which all are familiar can be generated and sustained. When, however, the heating is pronounced, as it often is over level, desert regions, the whirl may assume almost tornadic violence. But, however violent, this sort of storm is never a tornado; it originates near the surface and is sustained by the supply of warm air from below, while the true tornado is generated and developed by conditions that occur at the cloud level. When dust whirls pass on to regions where the surface air is not so strongly heated—over bodies of water, for instance, or green vegetation—they no longer are fed with air relatively so light and, as a rule, quickly come to rest. Naturally, too, their frequency varies with topography, ground covering, latitude, season, and time of day. Thus they are most frequent of after- noons and least of early mornings, most likely to occur during summer and fall and least during winter and spring; most gen- erally found in tropical and semitropical countries and least in regions of high latitude; more numerous over barren surfaces than over water and succulent vegetation; and, finally, more favored by level regions than by irregular and broken ground. Cumulus Convection. An interesting and important case of rapid vertical convec- tion resulting from the local application of heat and consequent establishment of strong horizontal temperature contrasts is that displayed by the turbulence of the cumulus cloud. That strong vertical and irregular movements of the air often occur in large cumulus clouds is known from the rapid boiling and rolling motions of their upper portions, from the descriptions of aero- nauts who have been caught up in the heart of a thunderstorm, and from the formation of hail within them. This latter phe- nomenon, the formation of hail, implies very definitely an uprush of at least 8 to ro metres per second (20 miles per hour). This, in turn, on the theory of the chimney-like action of a warm cen- tral column of air, would demand, even neglecting viscosity, the equivalent of a column 1500 metres high and 1’ C, warmer throughout than the surrounding atmosphere at the same level. 106 PHYSICS OF THE AIR The chief cause of the horizontal temperature contrasts neces- sary to this rapid uprush obviously is the difference between the current temperature gradient of the surrounding atmosphere and the adiabatic gradient of the saturated air within the cloud itself, full details of which will be given in the chapter on the thunderstorm. The common level, therefore, of a considerable number of detached but neighboring cumuli is one of rather vigorous con- vection—up within the clouds and down between them—however free from turmoil the atmosphere may be at other altitudes. Valley Breeze. During warm, clear days, when there is but little or no gen- eral wind, a gentle breeze, known as the valley breeze, commonly Fic. 30. Effect of mountain on levels of isobars. blows up the sides of mountains. ‘The strength of-this breeze varies greatly, owing to the size of the mountain, the material of its covering, and the conditions of its surroundings. The cause of some of these variations can be understood by reference to Fig. 30. Case 1.—Mountain Slope Connecting Wide Platcaus of Dif- ferent LevelLet AD be the upper plateau, BC the lower, and AB the slope connecting them. Further, let the insolation be vertical, or the sun directly overhead. If, now, the slope 4B is barren, or nearly so, it will become strongly heated and the adja- cent air correspondingly expanded. As this lighter air is buoyed up by the adjacent denser atmosphere there results a draft in toward the side of the mountain. But this draft is all along the mountain slope from top to bottom, and thus in a measure .the warm air is held in against the mountain side. Hence, the up- draft along the side of the mountain is analogous to that in a chimney. ATMOSPHERIC CIRCULATION 107 In addition to this obvious chimney effect of the mountain, there is, in the case under consideration, another source of up- ward winds that causes them to blow up along even shaded and cool ravines; unless snow-filled and very cold, in which circum- stance local density is the controlling factor and air drainage, or a downward flow of the air, usually prevails, as will be more fully explained later. The early morning isobaric levels, 1, 2, 3, etc., are raised by heating during the day to higher levels, 1’, 2’, 3’, etc. From any point directly above the foot of the mountain the amount of this expansion obviously drops off, as indicated in the figure, as the side of the mountain is approached. Hence a pressure gradient is established toward the mountain side and plateau beyond. If both plateaus are broad, a perceptible breeze of several hours’ duration up the mountain slope and onto the higher plateau may be induced in this manner. Such winds grow stronger as the top of the mountain is approached. At night, after sufficient cooling has taken place, the winds reverse. To form some idea of the possible magnitude of these effects, let the difference in level between AD and BC be 1.6 kilometres (one mile), and let the air between these levels be warmed on the average 5.5” C. (10° F.), then the increase of barometric pressure at A will be about 2.5 mm. (0.1 inch), with propor- tionate increases along the side of the mountain—quantities quite sufficient to produce a decided breeze. Similar overflow winds occur also on the slopes of the iso- lated mountain, BAE, whenever the air on the opposite sides is unequally heated. Thus the landward side of a coast mountain, for instance, on a still warm day should have a breeze blowing up it and out to sea. Case 2.—Isolated Mountain in the Midst of a Uniformly Heated Plain.—Here, too, the sides of the mountain are heated and corresponding upward currents induced. There also is ex- pansion of the air over the adjacent plains and a tendency to establish pressure gradients towards the mountain, as in the case just discussed. But, however great this expansion, the gradients thus produced never cause, in the present case, more than a negli- gible wind. To make this statement obvious: Let the ridge A of the mountain be 1.6 kilometres (one mile) above the plains EF and BC;; let the width of the base, EB, be 3.2 kilometres (two miles), and let the air be heated the same over one plain as over 108 PHYSICS OF THE AIR the other. Let the temperature increase of the air during the day be 5.5° C. (10° F.), or, suppose, 1 part in 50 of the absolute temperature. Under these conditions the compensating flow of air from the two sides must amount jointly to 1 part in 50 of the volume of the mountain; that is, the horizontal flow of the air from either side of the given mountain must average, from top to bottom, 1 part in 50 of 0.8 kilometre (0.5 mile). If, further, this is extended over a period of ten hours, as it may well be, the average velocity will amount to only about 1.5 metres (5 feet) per hour—certainly an imperceptible breeze. Clearly, then, the breezes that ascend mountain sides on still clear days have two causes: (a) a chimney or draft effect due to surface heating—always present—and (b) a pressure gradient effect due to expansion of the air over an adjacent plain or valley —present only when this expansion is unequal on the opposite sides of the mountain, or when the base levels are decidedly unequal on the opposite sides. Sea Breeze. Whenever a strongly heated region adjoins one whose sur- face is less heated, a local circulation from the one to the other obtains, unless prevented by winds of a general circulation. Thus along the seashore, beside lakes and even at the edge of favorably situated forests, a breeze (sea breeze, lake breeze, and forest breeze, respectively) of greater or less strength sets in during dry summer forenoons, after the land surface has become suffi- ciently warmed to establish decided convection. Since the sea breeze obviously ceases at that level where the barometric pressure is the same above the land that it is above the water, and since the change of pressure with change of alti- tude is a function of temperature, it follows that its depth, never great, may easily be computed by replacing certain general terms of a suitable equation by observed temperature and pressure data. To develop such an equation: Let p be the density of the air, then —dp=p gdh, in which —dp is the small decrease in pressure corresponding to the small increase, dh, in height, and g the gravitational accel- eration. From the general equation, verre, p ATMOSPHERIC CIRCULATION 109 in which p is the pressure, V’ the specific volume, R the gas con- stant, and T the absolute temperature, it follows that at Be ORE = 2 p =RT Hence, integrating from p,, corresponding to h = 0, to p, cor- responding to h = h, if T is independent of h, which, as a first approximation, its average value may be assumed to be, Therefore, fi RF The value of the first half of this equation obviously remains the same when the corresponding, but more convenient, barometric readings b and B are substituted for p and py, respectively. Hence, also, b gh But the top of the sea breeze clearly is where there is no hori- zontal difference of pressure, or where db = 0, when h is con- stant. Hence, on differentiating this equation, keeping h con- stant, it is. seen that b\ beh ay=aB(5)+ Be ar, and that the depth of the breeze, h, is given by the equation, gan Se dT gB Consider a typical case: Let the sea-level reading of the barometer on land, less that at sea, or dB = 0.5 mm.; let the tem- perature over the land exceed that over the sea by dT = 5° C.; let T = 300° A.; let B, the sea-level barometer reading at sea, be 760 mm. R for dry air = 2.871 x 108. Then the depth or thick- ness, h, of the sea breeze is given by the equation, ,a03 2.871 X10" X9= 34,657 cm. = 347 metres, approximately. 5 981X760 The sea breeze, usually, as just explained, not more than 500 metres deep, starts on the water, seldom attains a greater velocity than 4.5 metres per second (1o miles per hour: the greater the temperature contrast the stronger the breeze), and extends inland, growing feebler and warmer, to a distance of only 16 to 40 kilo- metres (10 to 25 miles). In a very important sense the circulation involved in this and all other local air convections is incomplete, since in such cases the path along which a given particle of the atmosphere flows is open and not closed. That is, the air that goes up over IIO PHYSICS OF THE AIR the heated land, in the case of the sea breeze, for instance, does not itself return by way of the water; it simply spreads out at the top of its ascent where its new temperature (above assumption of constancy of temperature not strictly correct), acquired by adiabatic expansion, is the same as that o1 the adjacent atmos- phere, while the return branch, or down-flowing portion of the circulation, is broad and gentle. Hence the surface air always flows from the cooler toward the warmer mass. By day the sea or lake breeze is on shore, because the soil gets warmer than the evaporating water, and the similar forest breeze, always feeble. away from the woods. WINDS DUE TO COOLING. Land Brecze. By night, when the direction of the horizontal temperature gradient is the reverse of that during the day (that is, when the water surface is relatively warm and the soil cool, because of its rapid radiation), the direction of the surface wind is also reversed or offshore. This is the well-known land breeze. Besides being reversed in direction and occurring at night instead of by day, the land breeze further differs from the sea breeze in usually being very much the weaker of the two, even though aided by the gravity flow of the cooler surface stratum of air. This is because a, the temperature contrast between land and water, is less by night than by day, and 0, the surface friction over land which retards the land breeze, is greater than the water fric- tion that affects the sea breeze. Hence, while the latter, as above stated, reaches 16 to 4o kilometres (10 to 25 miles) inland, the former seldom extends more than 8 to to kilometres (5 to 6 miles) to sea. The depth of the land breeze, usually less than that of the sea breeze, obviously may be computed in precisely the same manner as the latter. Mountain Breese, or Gravity Wind, During clear nights when there is but little or no general wind, there usually is a flow of the surface air, commonly most pro- nounced in ravines, down the sides and along the basin of every valley. At most places this movement is gentle to very slow, but in those exceptional cases where the valley is long and rather steep, especially if covered with snow and free from forest, and still better if fed by a gently-sloping plateau, the down-flowing ATMOSPHERIC CIRCULATION III air current may attain the velocity of a gale and become a veri- table aerial torrent. This drainage flow is known indifferently as the mountain breeze, or mountain wind; also canyon wind, katabatic wind, and gravity wind. For simplicity let there be no general wind; let the cross- valley profile be the arc of a circle, and let the covering of the walls be everywhere the same. But even thus simplified the problem of air drainage still requires the consideration of tem- perature changes of the free air, of the surface air, and of the surface itself. Free Air.—Largely, perhaps almost wholly, because of the dust and vapor always present, the lower atmosphere emits and absorbs radiation abundantly through much the greater portion of the spectrum. But during clear nights the loss, in the lower air at least, usually, if not always, is greater than the gain. However, even on such nights when radiation losses are greatest, the lower air, neglecting surface influences, cools too slowly and, on any given level, too nearly uniformly to produce more than very scattering and very feeble convection currents. Suppose, though, that a limited mass of free air is cooled to a temperature below that of the adjacent atmosphere at the same level, as must happen at night within a small isolated cloud. What will be the result? This problem, interesting within itself and essential to the present discussion, can easily be solved graphically. To this end let AB and A’B’, Fig. 31, be two adiabatic gradients of the free air, indicating a temperature decrease of 1° C. for each 100 metres increase in elevation (the customary approximate value), and let EE be any actual temperature gradient different from the adiabatic—in this case, for simplicity, assumed to be 1° C. per 120 metres change of elevation. If, under the given conditions, a limited mass of air at an elevation of 1000 metres, say, be cooled 1° C., or its position in Fig. 31 be shifted from W to C, it will immediately become denser than the neighboring air of the same level and therefore sink. As it sinks, if there is no interchange of heat by conduction, it will warm up adiabatically and finally come to equilibrium where the adiabatic gradient, AB, intersects the actual gradient EE, or at C’, where the falling air will have reached, through compression, the same temperature as the then adjacent atmosphere. That is, under the above gradient, a limited mass of air at any suffictent elevation cooled 1° C. will 112 PHYSICS OF THE AIR drop 600 metres, and in so doing increase its temperature by 6° C., or become 5° C. warmer than it originally was before the initial cooling. Similarly, if the original limited mass of air, with ele- vation and temperature indicated by C’, say, be warmed 1° C., it will be forced to assume a new equilibrium level and tem- perature indicated by JV. When the vertical temperature grad- ient is ‘reversed ’—temperature increasing with elevation as indicated by DD of the figure—the final gain in temperature is FIG. 31. € oO | 2@ @ 4 8 © F B&B SS 10 I DEGREES CENTIGRADE Oo Assumed temperature gradients. less than the initial loss. If, for example, the initial cooling is from WV” to C”, P will be the point of equilibrium and the final temperature will be less than the initial, In short, when air whose temperature decreases with elevation is warmed, it pro- ceeds at once to get colder than it was at first, as is evidenced by every cumulus cloud; and when cooled it quickly gets warmer than it originally was. If this gradient is reversed, that is, if the temperature increases with elevation, there still will be dynamical heating and cooling as before, but to an extent less than the initial ATMOSPHERIC CIRCULATION 113 cooling and heating, respectively. An initial temperature change different from the one just assumed, 1° C., would, of course, pro- duce, under the same temperature gradient, correspondingly dif- ferent alterations in level and final warming or cooling, provided always that the process is wholly adiabatic and that it takes place well above the surface of the earth. As a matter of fact, there necessarily is some interchange of heat between the moving limited mass of air and the surrounding stationary atmosphere. In so far, however, as the falling mass of air gains heat by conduction or radfation its equilibrium is reached at a correspondingly higher level and colder temperature. Similarly, so far as the rising mass of air loses heat by conduction or radiation, its equilibrium is reached at a correspondingly lower level and warmer temperature. It must be clearly understood that all the above reasoning applies only to free air. When the surface air of a level region or valley basin of negligible slope loses heat it gets colder and not warmer, simply because it cannot acquire dynamical heating by falling to a lower level—it is already at the bottom. It must also bé noted that the paradoxical results under discussion, ‘“ cooling by warming,’ as Shaw *? has called it, and its counterpart, warming by cooling, apply to isolated masses of air. When the whole of each layer of air of the same level undergoes the same temperature change, and when this change is but slightly different from that of the next higher or lower level, as obviously is the case over flat regions on still, clear nights, there can be but little local convection, and, therefore, but litthe dynamical heating: There still will be night-cooling, however, of the free air through at least the lower kilometre or more, but it will be distributed approximately uniformly and nowhere localized in that manner which, as just explained, is essential to marked convection. Valley Surface.—Since all portions of the valley surface are equally exposed, or nearly so, to the sky, and since the covering is uniform, it follows that on clear nights each portion must lose heat by radiation at a rate that varies closely only with its tem- perature. At the same time the surface also acquires heat partly by absorption and partly by conduction. But during still, clear nights the net loss of heat by the valley surface, whatever its nature, is more rapid than is the net loss of heat by the slowly- radiating free air. Indeed, it may even be assumed, as a- rough ‘approximation, that the atmosphere neither emits nor absorbs 4 Forecasting the Weather, p. 149, IQII. ‘ I14 PHYSICS OF THE AIR radiation; that only the surface covering is effective in these respects, and hence, that all temperature changes of the valley air are results of heat conduction to or from the valley surface and of dynamical heating or cooling. Surface Air—Any change in the temperature of the surface is communicated in greater or less measure by conduction, radia- tion, diffusion, and convection to all the neighboring atmosphere. But as chilled air tends to fall vertically, appreciable cooling in this case extends through only a relatively thin surface layer, as often is obvious to one on crossing a ravine. Consider then a thin layer of air close to the surface of one of the valley walls, and follow its movements and temperature changes on a still, clear night. As the surface cools, which it does everywhere, the temperature of the adjacent air is also reduced and its density thereby correspondingly increased. Hence as soon as this cooling has proceeded to a lower tempera- ture than that of the free atmosphere at the same elevation the surface air on the valley walls begins to flow to lower levels; overrunning, of course, any pockets of colder air that may be in its path. The turbulence resulting from this flow continuously, and at all places along its course, causes more or less of the ini- tially-chilled air to be separated from the surface, there aban- doned, temporarily or permanently, and underrun by other air. Clearly, too, the amount of turbulence and consequent depth of the affected layer, or amount of interchange between free air and surface air, vary owing to velocity of flow, slope of surface, nature of covering, etc. If the weight of a unit volume of this cooled air is w grams more than that of an equal volume of free air at the same level its contribution, f, to the total force producing, or tending ‘to produce, drainage, or flow down the sides of the valley, is,given by the equation, ; f=gwsin 6, in which g is the local acceleration of gravity and @ the angle of slope at the particular place along the valley wall where the small quantity of air under consideration happens to be. Sin @ varies, of course, from a minimum at the bottom of the valley, where it is o if the valley happens to be level, to a maximum where the sides are steepest. The value of the other variable, zw, depends on the difference between the temperature of the cooled air in ques- tion and that of the free atmosphere at the same level. A ATMOSPHERIC CIRCULATION 115 steady state, always more or less closely approached, obviously would give ea ha in which K is the coefficient of whatever opposition (friction, etc.) is encountered per unit volume due to the drainage veloc- ity V down the slope, and » a numerical exponent. Since w is proportional to 87, or difference in temperature between the surface air and free air at the same level, it follows that if 87, and therefore w, remains constant—that is, if the rate of temperature loss by the descending air through conduc- tion to the surface is equal to the rate of its temperature gain over the free air of identical levels, owing to compression during descent, then ate mS, dl where de/dt is the rate of loss of heat by the mass m of air to the surface at any given place, Sp» the specific heat of air at constant pressure, A the adiabatic gradient, dT/dh the actual vertical temperature gradient in the free air at the given level, and V the velocity in metres per second of the flow down the slope at the same level. Clearly, then, Y must increase with increase of de/dt. Also V must vary with dT/dh, but always be positive (down hill) so long as dT/dh is less than A, which it nearly always is except near the surface under strong insolation. If the temperature gra- dient of the free air should be super-adiabatic (dT/dh greater than A) V would become negative, or the surface air would need to flow uphill to maintain 8T constant. Actually, however, the air would flow down and not up the cooling surface. That is, if the free air were in this unstable condition 87, as applied to any given mass of surface air, instead of tending to remain constant, would rapidly increase. The more rapid the loss of heat by the surface the more rapid also the loss of heat by the adjacent air, and the swifter its flow, if the slope is sufficient; but, on the other hand, the swifter the flow the more rapid the dynamical gain of heat, and also the greater the retarding effect of surface friction, Hence an automatic adjustment between free-air gradient, velocity of flow, and rate of loss of heat to the radiating surface, is always in operation. Furthermore, as this automatic adjustment pre- vents the air next the surface from becoming greatly colder than the free air at the same level, and as the latter cools only slowly, aT = (A ——_) Vsin@ dh 116 PHYSICS OF THE AIR it follows that the temperature along the valley walls cannot decrease at all rapidly except below the inversion level (the nearer the bottom the more pronounced), as presently explained Initially, when the temperature of the free air everywhere over the valley decreases with elevation, the speed of the surface air down at least the steepest portions of the cooling walls is quite certain to be sufficient to make its dynamical gain of heat exceed its conduction loss and therefore to cause its tem- perature to increase with descent. As the bottom of the valley is approached, however, the rate of vertical descent and the conse- quent dynamical heating become less and less, and finally cease altogether, except in so far as there is drainage along the valley. At and near the bottom, then, where the dynamical heating is absent, or small, the temperature of the surface and the adjacent air necessarily decrease more or less rapidly. In a short while,. therefore, the valley basin begins to fill with a river of cold air. The first incoming air doubtless overflows the original bottom layer, but in so doing gets separated from the cooling surface, and in position itself to be underrun by such other air as has cooled _ to a lower temperature, and this in turn by still colder.air, and so on. In this way a temperature inversion is established in the valley. Below the inversion level (level of maximum tempera- ture) the surface flow, though still active, is so decreased in rate of descent that the contact cooling exceeds the dynamical heat- ing. The surface air could not otherwise here underrun the free air since the temperature of the latter decreases, as explained, with decrease of altitude below the inversion level. Above the inversion level the temperature of the down-flowing air, since it cannot anywhere greatly differ from that of the free air at the same elevation, necessarily increases, in general, with descent. A valley wall produces local cooling up in the atmosphere, guides the resulting drainage of cold air and more or less controls its velocity, while the temperature gradient of the free air (modi- fied over the valley bottom by the inflow from the sides) limits and largely determines the ratio of velocity of flow to rate of loss of heat (not cooling) by the surface air. In the case, there- fore, of well-defined valleys it appears that there must be on either side a belt at substantially the same elevation as the then inversion level along which during still, clear nights the dynamical heating and the contact cooling of the descending surface air are exactly equal. Above this level descending air grows contin- ATMOSPHERIC CIRCULATION 117 uously warmer, below it continuously cooler. Later in the night the inversion level attains a practically stationary elevation, and then intersects the valley walls in what are known as the “thermal belts.” In this connection it may be interesting to note that there are many practices in recognition of the above facts of air drain- age. Thus, for instance, the mountain camper tents above and not below his night fire, so as to avoid the smoke; the Swiss peasant builds his cottage on a knoll to keep above the valley flood of cold air; and the orchardist seeks the ‘“‘ thermal belt ” to escape killing frosts. Mountain Convections. Vertical convections on the sides of mountains due to tem- perature contrasts of different origin from those already men- tioned are also well known, and, though rarely if ever producing more than a gentle breeze, are worth mentioning. Thus, a considerable shower during the afternoon of a warm summer day, for instance, may leave the atmosphere, level for level, distinctly cooler than the side of a neighboring mountain. Consequently the air will then flow up the adjacent slopes~and occasionally carry with it masses of detached fog, or “steam,” that grad- ually merge into a long billow-like crest cloud. Similarly, as the cooler air on the clearing side of a cyclone invades a moun- tainous region, the relatively warm slopes often, when the general winds are light, induce rising currents. And as these currents also frequently are laden with patches of “steam” cloud the familiar mountain saying : “ When the fog rises the rain is over,” is well justified. On the other hand, the air on the stormy side of a cyclone is nearly always warmer during winter, and also frequently warmer during the other seasons, than are the mountains; and therefore on these occasions, as it passes over them, downward currents are induced along their slopes, a circumstance that equally justifies this other common saying of the mountain dweller ; “‘ While the fog descends it will continue to rain.” Glacier Winds. It is well known that a draft of cold air often is found blowing out from a cave-like opening in the lower end of a glacier, hence called glacier wind. Similar winds, blowing out during summer and in during winter, occasionally are found at the mouths of caves, called blowing caverns, on the sides of hills or mountains. 9 118 PHYSICS OF THE AIR In the volcanic mountains of Japan such places are numerous and extensively used for cold storage.** In each case the explanation of the phenomenon is the same and obvious. The cavity extends quite through the glacier, or earth, as the case may be, from its lower to its higher openings. Let this difference in elevation be 250 metres; let the average temperature of the air inside the cavity be o° C., and of that outside at the same level 15° C. The density of the inner air will be to that of the outer approximately as 19 to 18, and the pressure head, producing an inverse chimney effect, about 14 metres. Neglecting friction—usually, however, an extremely important factor—this would give the exit air a computed velocity of about 16.6 metres per second (37.1 miles per hour )—a very appreciable gale. The velocity or strength of this wind, other things being equal, varies as the square root of the difference in level between the lower and upper openings. In the case of a glacier, drainage obviously obtains in sub- stantially the same manner, whether the air passes in a concen- trated stream through a cavity or along a crevice within the ice, or merely flows in a broad sheet over the top surface. Clearly. too, the same sort of aerial cascades (exaggerated mountain winds) must occur, especially during summer nights, over any banks of snow that may exist in the upper and steeper reaches of canyons and mountain valleys. Such winds necessarily are shal- low and therefore, when swift, a treacherous source of danger to the landing aviator. : The Bora. From the above explanation and examples of aerial drainage it is obvious that similar winds must often blow down steep slopes that separate high, snow-covered plateaus or mountain ranges from adjacent bodies of relatively warm water. Thus when an anticyclone covers such a region during winter the surface air becomes very cold and correspondingly dense until, unless other- wise dissipated, it overflows restraining ridges or drains away through passes and gaps. Clearly, too, this flow must be most frequent and strongest during the early morning, since that is the coldest time of the day, and least frequent of mid-afternoons. In many instances during anticyclonic weather the air as it leaves the snow fields is so cad that in spite of dynamical heating it even reaches the sea at freezing temperatures and very dry. When, however, the drainage is amplified, if not even started, by “S. Suzuki and T. Sone, Tohoku Univ. Sci. Reports, 3, pp. IOI-IITI. ATMOSPHERIC CIRCULATION 119 the pressure gradients (to which the final velocity bears no special relation) due to a properly situated “ low,” it usually is associated with a counter cyclonic current above and therefore accompanied by rain, sleet, or snow. Probably the best known of all these violent fallwinds is the bora of the northeast Adriatic, especially at Trieste, Fiume, and Zengg. The boras of these places, however, are not from the north, as the name implies, but rather from the northeast and east-northeast. — Another excellent example of this kind of wind occurs at Novorossisk, a Russian port on the northeast coast of the Black Sea, where it blows down from a nearby pass in the mountains, occasionally with destructive violence. Probably, also, the brief but sudden and violent williwaws of steep, high latitude coasts have a similar origin. Mistral. Another instance of convection due essentially to cooling is the well-known mistral, or dry, cold northerly wind of the Rhone Valley. Here the more or less persistent winter low over the warm waters of the Gulf of Lyons to the south and the frequent highs over the snow-covered plateaus of southeastern France to the north often codperate in such manner as to produce extensive air drainage down the lower Rhone Valley. In general the cause of the mistral and its actions are the same as those of the bora. It is less violent, however—its path less steep, and therefore itself not so distinctly an aerial cataract. Similar winds occur, of course, under like circumstances in other parts of the world. but the mistral is the best known of its class. Norwegian Fallwinds. An extensive fallwind, which, because of its importance and the fact that it is more or less unique, deserves especial mention, frequently occurs during winter along the coast of Norway. Sandstrom,°** in one of his interesting atmospheric studies, de- scribes it as follows: ‘In winter, as one steams along the north- west coast of Norway, there is frequent opportunity to observe a peculiar meteorological phenomenon. Fine weather prevails over a narrow strip along the coast, while a heavy bank of cloud is visible out to seaward. Of course, coastwise traffic is greatly fv by this fine-weather strip and takes full advantage of it. "a Mount Weather Bulletin, 5, p. 129, 1912. 120 PHYSICS OF THE AIR Throughout this zone of fine weather prevails a cuttingly cold wind so strong that one can scarce stand against it when on deck. The maximum velocity of this wind is attained near shore, where the water is whipped up into whirls and miniature waterspouts. Evidently the wind here plunges down upon the water from above, and with great force. “Upon leaving the steamer and travelling inland up the moun- tain slopes on skis, strong head winds oppose progress. This easterly wind is still very strong on the great divide of the Scandinavian Peninsula. But observations of the cloud caps on the highest peaks of the range show that a westerly wind is blowing at those great altitudes. It is clear that a lively inter- change of air between the North Atlantic Ocean and the conti- nent is taking place above the Scandinavian highlands. This exchange takes place along either side of a glide surface whose altitude above the ground at the divide may be estimated at about 1000 metres. In fact, at the kite station Vassijaur it proved almost impossible to raise the kites above that level, evi- dently because they there encountered a glide surface through which they cannot pass, since the wind has opposite directions on the two sides of this surface, and therefore calm must prevail at the glide surface itself. The altitude of this glide surface decreases to the Atlantic Ocean. The air below this surface flows toward the west, and above the surface it flows toward the east.” Continental Fallwinds. From the above discussion of winds that result from surface cooling it is obvious that they are of very general occurrence, especially during cold weather and down the valleys and slopes of high, snow-covered regions. Hence one would expect drainage winds to obtain to a greater or less extent during winter over the middle and high latitude regions of every continent. Where the elevation and slope are slight, however, as they are, with but minor exceptions, over all North America east of the Rocky Mountains, over Russia, and over Siberia, except the eastern portion, this drainage necessarily must be comparatively sluggish. On the other hand, there are two regions of continental ex- tent—Greenland, with an area of about 827,000 square miles, and Antarctica, with an area of, roughly, 4,600,000 square miles— that are ideally located for, and perfectly adapted to, the produc- tion of strong and almost continuous fallwinds. ATMOSPHERIC CIRCULATION 121 Greenland, as is well known, is continuously covered with an enormous ice cap that rises to a gently rounded plateau of, roughly, from 2000 to 3000 metres (7000 to 10,000 feet) ele- vation. This plateau, whose crest runs approximately north and south, has been crossed several times—six in all—at as many different places, and in each case nearly constant down-slope or drainage winds of greater or less strength were experienced. Throughout its great area, therefore, Greenland is a region of almost perpetual aerial cascades and cataracts. The continuous refrigerative influence of its enormous ice cap, covering an area 18 times that of the state of Pennsylvania and rising at places to an elevation of over three kilometres (two miles), not only controls the direction and velocity of nearly all local winds, but obviously must be of decided influence on the general circulation of the middle and higher latitudes of the whole northern hemis- phere—an important circumstance that will be taken up later. Antarctica, according to the reports of all its explorers, is quite as completely covered with ice as is Greenland, and it also rises, more or less dome-like, to fully as great altitudes. Hence it would seem that its general effect on the movement of the air must be very similar to that of its great counterpart in the northern hemisphere—an inference now fully borne out by the many accounts and records of those who have skirted its coasts, crossed its plateaus, or wintered on its borders. Sir Douglas Mawson, for instance, who spent many months during 1912-13 at Adelie Land, latitude 67° S., on the edge of the continent almost directly south of Tasmania, reports an average wind velocity for an entire year, from the interior toward the sea, of more than 22.4 metres per second (50 miles per hour). “‘ Day after day,’ he says, “the wind fluctuated between a gale anda hurricane.” Velocities of 100 miles and over per hour occurred, and gusts of even much greater velocity occasionally were re- corded. These measurements were made at the main station on the declivitous border that connects the inner ice plateau with the ocean, Back some distance inland, where the slope is gentle, the winds were less severe. At sea, also, these continental drain- age winds decreased in intensity with increase of distance from shore, and ceased altogether at a distance of about 300 kilometres (187 miles), where the westerlies became effective. Obviously, therefore, this particular station was located in one of the wind- iest places in the world—in an aerial cataract where the cold 122 PHYSICS OF THE AIR drainage air of the ice plateau rushes down a steep coastal slope to the sea. Similar winds of varying intensity and irregular duration are reported all along the Antarctic border, from every inland station and from end to end of every exploring trail. Clearly, then, the winds of Antarctica, though due essentially to cooling, neverthe- less, because of the extensive area they cover, belong also to those great circulations that are strongly influenced by earth rota- tion, and therefore constitute an important part of the general circulation of the atmosphere, under which head they will again be considered. WINDS DUE TO SIMULTANEOUS ADJACENT LOCAL HEATING AND LOCAL ‘ COOLING. Thunderstorm Winds. ‘ Shortly, say twenty minutes or so, before the rain of a thunderstorm reaches a given locality the wind at that place, gen- erally light, begins to die down to an approximate calm and to change its direction. At first it usually is from the south or southwest in the extra-tropical portion of the northern hemi- sphere; from the north or northwest in the corresponding portion of the southern, and in both more or less directly across the path of the storm itself. After the change, it blows for a few minutes rather gently, directly toward the nearest portion of the storm front, and finally, as the rain is almost at hand, abruptly and in rather violent gusts away from the storm and in the same direction, roughly, that it is travelling, a direction that usually differs appreciably from that of the original surface wind. Gen- erally this violent gusty wind lasts through only the earlier por- tion of the disturbance, and then is gradually but rather quickly succeeded by a comparatively gentle wind, which, though follow- ing the storm at first, frequently, after an hour or so, blows in the same general direction as the original surface wind. The chief cause of these and all other winds peculiar to the thunderstorm, except those within the cumulus cloud itself, is the juxtaposition of warm air immediately in front of the rain and a column or sheet of'cold air through which the rain is falling. How this temperature distribution is established and what the results are will be explained later in the chapter on the thunderstorm. Cuapter VIII. ATMOSPHERIC CIRCULATION (continued). Winds Due to Widespread Heating and Cooling. GENERAL REMARKS. SINCE the atmosphere is a fluid whose viscosity is not only small but also well known, one might suppose, with respect to any given portion, that it would be quite as easy, through the equa- tions of thermodynamics and hydrodynamics, to foretell its every movement and future position as by the equations of celestial mechanics to predict an eclipse or an occultation. But this is far from being the case, and for many reasons. Thus the irregu- larities of surface heating and surface friction, and the action of mountains, themselves irregular and broken, in deflecting winds, both horizontally and vertically, complicate the problem beyond exact solution. Besides, there are even discontinuities in the amount of atmosphere involved. Water vapor is added in large amounts by evaporation to the volume of circulating gases, mainly in the regions of “ highs,”’ while equal average quantities are withdrawn (not simultaneously) by precipitation, chiefly in the regions of “ lows.’ Hence an exact mathematical solution of the problem of world-wide circulation does not seem possible. Nevertheless, many details of this circulation are clearly under- stood from physical considerations and admit of at least approxi- mate analyses. Some of these details pertain equally to all the more general winds, and therefore a discussion of them will be given independently as a common introduction to the more ex- tended accounts of certain types of atmospheric circulation that follow under the captions monsoons, hurricanes, trade winds, cyclones, etc. Irregularities, Gusts or Puffs ——Though the wind at an alti- tude of 200 metres or more is comparatively steady, except in very rough or mountainous regions, near the surface of the earth any appreciable wind that may exist is always in a turmoil, owing to surface friction that checks the lower laver while the layers above tumble forward and down, and to numerous obstructing objects that block its course and introduce cross-currents. Hence 123 124 PHYSICS OF THE AIR its direction constantly changes through many degrees, while the velocity irregularly but persistently fluctuates from one extreme to another. At one instant the actual velocity may be anything up to 50 per cent. or more greater than the average velocity, while a second or two later it may be fully 50 per cent. less than the average. The greater the average velocity the greater, roughly, in the same proportion, the absolute change, as illus- trated by Fig. 32. So great, indeed, are these irregularities that places near the surface of the earth not more than 15 metres (50 feet) apart, though having the same average wind direction and velocity, commonly have different, often very different, simul- taneous directions and velocities, and therefore, for the instant, radically different winds. These facts are of great importance with reference to the wracking effect winds have on houses, bridges, and other struc- tures. They also deeply concern the aviator when starting and landing. But, however valuable for many reasons an exact knowledge of surface air movements would be, it is obvious that they defy all formule, and that mathematical equations can no more predict the course and speed of a given portion of turbulent surface air than they can mark the path and fix the velocity of water in the swirls and eddies of a mountain torrent. Neverthe- less, the average effect of a group of turbulent wind eddies, like the average effect of a large number of gas molecules, does profit- ably yield to mathematical discussion.%* Interzonal Drift—Although the atmosphere moves mainly from west to east in middle latitudes and from east to west in equatorial regions, it nearly always has a north-south component that produces an interzonal drift. This is simply because the major temperature contrasts of the surface of the earth are be- tween the equatorial and polar regions. Hence, whatever the local or secondary temperature contrasts, of which there are many, and whatever the deflecting barriers and other obstacles that prevent the latitudinal circulation from being free and rapid, it nevertheless must and does obtain to a greater or less extent. Change of Velocity with Change of Latitude.—The velocity of the earth’s surface at and near the equator, as a little calcula- tion shows, is about 1675 kilometres (1040 miles) per hour from west to east, while, with reference to this surface, the veloc- * Taylor, Phil. Trans. Roy. Soc., A, 215, pp. 1-26, 1915, and Richardson, Proc. Roy. Soc., A, 97, P. 354, 1920. 125 ‘FeqouOUTeUe oqny-sinssaid & Aq PazBOIPUL SE AJOOJ[AA PUTA BOEJINS ayy UI salqte[N Sa] /00Y ater 12d spunag wn 208 S2ug he ‘ i \ | | | : i i | Po. | pea | M8 eae cups Le ; i ole 0! eee Peet T t ‘ , bea) | ty) Pee lect Po 202 af : So = bet | af : S02 | aaa Ar Abe AMARA INN AW <= oOo 6 8 z 9 s + £ 2 ATMOSPHERIC CIRCULATION ee ees pci aay Se x “pa Bouse: Wl AMMbMAlT Cb EAT = 126 PHYSICS OF THE AIR ity of the atmosphere from east to west in the same region is only a small fraction of this value. In reality, therefore, the atmosphere of equatorial regions is also moving from west to east with a great velocity, though not so great as that of the surface of the earth itself. When this air moves to higher latitudes, as it does under the influence of the great temperature contrasts between equa- torial and polar regions, it is obvious that its velocity with reference to the surface of the earth must change. It might seem, as many have assumed, that the linear velocity of the air about the earth’s axis would remain constant, and that the wind would have a west to east component as soon as it had crossed that latitude on which the surface velocity is the same as the original west to east wind movement. This method, however, of considering the problem is theoretically incorrect, as has often been explained. A particle of the atmos- phere, or any portion of it moving as a unit, is mainly, at times wholly, rotating around the axis of the earth. In considering latitude effect, therefore, or effect of distance from this axis on wind velocity, it is necessary, as Ferrel first insisted, to remem- ber that the angular momentum mr? (in which i is the mass, r its distance from the axis of rotation, and » the west-east angular velocity), and not the linear momentum mv (in which w is the west-east linear velocity), is a constant. In other words, the law of conservation of areas applies. Hence as a given mass of air reaches higher latitudes the absolute value of its east-west component tends, not to remain the same as is often supposed, but actually to become greater, in proportion to the secant of the latitude. If the trend of the air is to lower latitudes, its west- east velocity obviously tends to get slower at the same rate that, when going to higher latitudes, it tends to become faster. Law of Conservation of Areas—The law of the conserva- tion of areas as applied to the atmosphere is of sufficient impor- tance to justify its brief demonstration. Let O, Fig. 33, be the centre about which a mass m is mov- ing with the linear velocity v, along the circular arc 4B whose radius is 7. Let m be constrained to follow its path by a cen- tral force; that is, a force directed towards O. For instance, let it move over a frictionless horizontal plane, and be kept in its orbit by the tension on a weightless string connecting it with ATMOSPHERIC CIRCULATION 127 the centre O. At B let the tension on the string be so increased that the mass m will be drawn in the distance BH in the same time that, undisturbed, it would have reached E. During this time the path will be something like BC. If the tension again becomes constant with the value appropriate to the point C, the new orbital velocity will be v, along the arc CD of radius r,. By taking the time interval smaller and smaller the velocity along BH, however irregular, approaches uniformity as its limit, while BE and BC both approach straight lines. With the two component velocities along BE and BH respectively uniform it is obvious that the resultant velocity along BC must also be FIG. 33. oO Velocities along arcs of different radii uniform. The problem of vectorial areas reduces, therefore, to finding the general relation of a radius vector to the component of the corresponding orbital velocity normal thereto. This rela- tion may be shown as follows: ‘Let BC, Fig. 34, be a rectilinear section of the orbit, usually of infinitesimal length, along which the velocity is uniform, and let OB and OC be two radii. From B draw BE perpendicular to OC extended, and from C draw CA perpendicular to OB. Hence AC_ BE w in which v, and v, are the components of the uniform velocity along BC at right angles to OB and OC, respectively. But 128 PHYSICS OF THE AIR from the similarity of the triangles OAC and OEB it follows that AC_OC BE OB and, therefore, that m _OC Vz = OB That is, rv k, a constant, in which r is the radius vector and wv the component of the orbital velocity at right angles thereto. Fic. 34. , ° Conservation of areas in a plane. But, by elementary geometry, rv =2a, in which a is the rate at which area is covered by the movement of r. Hence whatever the portion of the orbit, the radius vector sweeps over equal areas in equal intervals of time, or whatever the points selected, u_ tf V2 TL The kinetic energy FE, of the mass m while on the arc AB, Fig. 33, is given by the equation, Ey = 4m2,2. ATMOSPHERIC CIRCULATION 129 Similarly, its kinetic energy along CD is given by Eo=}mv2. These are unequal, the difference being m 2 (v2 —9?), ; and it will be interesting to find the source of inequality. At all parts of the orbit the tension f on the string is given by the equation, _ my ary and the work, dw, done on shortening the radius by the small amount dr is expressed by the equation, , mv dw = — ——dr. r But since rv = k, v = and m Rk? rh dw = dr. Hence on shortening the string from 7, to r, the work becomes, 2 2 vem pid «2B Bie Se Vr a Pr = w,7," = ete, Hence VW = : (02 — v7). But this is identical with the value already found for the dif- ference between the kinetic energies of m at the distances 7, and. r, from O. That is, this difference is equal and due to the work done on m by the tension on the string while decreasing the radius from 7, to rp. Consider now the velocity of a quantity of air or other mass moving as a unit frictionlessly over the surface of the earth. Let the mass m, regarded as a point (in the case of an extended body it is & mvr that remains constant), be at P, Fig. 35, rotating around the axis N.S on the small circle MP and held to the sur- face by gravity directed towards the centre O. If v is the linear velocity of m, it follows that the radially directed force f is ex- pressed by the equation, mo? _ mv" r DP On forcing this mass to a higher latitude, to P’, say, work is done against the horizontal component of f. But from the similarity of triangles it is obvious that at every point along the 130 PHYSICS OF THE ATR arc PP’, f sin 6, the force to overcome, is to f, the centrifugal force, as the rate of approach to the axis is to the rate of progress along the meridian. Thus the work done in going from P to P’ is the same as that which would be done in shortening the radius DP to DA. But, as above explained, this work on m, or transfer of energy to it, must appear as so much additional kinetic energy, friction being excluded. Hence the orbital velocity v at P’ is to the orbital velocity v at Pas DP is to D’P’. That is, Fic. 35. N e : M iD Ss Conservation of areas on a sphere. the conservation of areas holds likewise in this case, where the radius vector is the normal from the moving mass to the axis of rotation. This same law holds also on the slightly flattened earth. To make this clear, let PP” be a portion of a greatly flattened meridian, and let the mass m be taken from P to P’ as before, and thence to P’”. From P’ to P” the work is against the force f’ cos 6’, and obviously equal to the work against f’ over the dis- tance P’S. Hence the orbital velocity of m at P’’ is to its orbital velocity at P as DP is to D’P”. ATMOSPHERIC CIRCULATION 131 Suppose a quantity of quiet air,air moving strictly with the sur- face of the earth, at, say, latitude 30 degrees, is forced to higher latitudes, as it actually is by pressure gradients due to temperature differences, what, according to the law of the conservation of areas, will be its final surface velocity at, say, latitude 60 degrees? At latitude 30 degrees its orbital velocity, being the same as that of the surface, is, approximately, y = 273957.C0S 30° _ 9. , miles _ doris TEES. 24 hour second At latitude 60 degrees its orbital velocity is, from the prin- ciple stated, fay es 30° 1554 miles _ metres, cos 60° hour second while at latitude 60 degrees the orbital velocity of the surface is fs POS OT cag OES = say 6 24 hour second Hence the velocity of the transferred air in question with reference to the surface is i miles metres, v’ —s = 1036 = 463.1 S° hour ~ 4° second As a matter of fact, no such enormous velocities of the wind as the principle of the conservation of areas would lead one to expect in the higher latitudes are ever found, either at the surface or at other levels. This, however, does not argue against the applicability of the principle itself, but only shows that in the case of atmospheric circulation there are very effective damping or retarding influences in operation. The resistance due to the viscosity of the atmosphere is one of these retarding influences, but its effect probably is very small. A larger effect doubtless comes from surface turbulence induced by trees, hills, and other irregularities. A still greater velocity control, probably so great that all others are nearly negligible in comparison, except near the surface, is vertical convection. This phenomenon leads to extensive interchange between lower and upper layers of the atmosphere, thus indirectly increasing the effect of surface friction probably several fold and tending to bring all the lower, vigorously convective, portion of the atmos- phere to a common velocity. Because of these several means of control the actual wind velocity everywhere is different from that which, and at high latitudes much less than, it otherwise would be. 132 PHYSICS OF THE AIR Not only is the velocity of the wind changed through change of latitude, but also the rate at which its direction with reference to the surface of the earth varies or tends to vary, as will appear from what follows. Deflection Due to the Earth’s Rotation —The effects of the rotation of the earth on the direction of the wind are of extreme importance to the science of meteorology. It will be convenient, therefore, before going further, to consider how these important results are produced and to form some idea of their approximate magnitudes. An exact discussion of this problem is somewhat tedious, but a very approximate solution is readily obtained. To this end, let FIG. 36. Deflection, at pole, due to the earth’s rotation. P, Fig. 36, be one pole of the earth—the south pole, say—assume the surface to be flat, which it very approximately is, at and near this point, and let a particle of air cross it in the direction PA with the uniform velocity v; let the earth rotate in the direction AA’ with the angular velocity , and let the distance which the air particle under consideration has gone from P in the brief time dt be such that PA=dr=vdt. Let the meridian along which the particle started as it left P have the position PA’ at the end of the time dt, or when the particle, keeping a constant direction in space, has arrived at A. Obviously the velocity with which the earth moves under the particle increases directly with the distance from P. But as this latter is directly proportional to the time dt since the particle left ATMOSPHERIC CIRCULATION 133 P,v being a constant, it is clear that the distance, ds, travelled nor- mally to the instantaneous meridian, may be expressed in terms of a constant acceleration, a, in the direction opposite to that of rotation. That is, ds = 4 a(dt)’. Also ds = dr w dt =v dt w dt=V w (dt)’. Hence, % a (dt)? =v w (dt)’, or a= 204. Since a force is measured in terms of mass times acceleration, it follows that the west-east deflective force, f, that would keep a mass m, of atmosphere or anything else, next the pole in the same meridian, or the east-west force that, if the earth were still, would produce the given motion with reference to its sur- face, is very approximately given by the equation, f=ma=—2mMw?, where v and » have the values above assigned. Let the moving particle under consideration be not at one of the poles, but at some other point, such as P, Fig. 37, at latitude ¢. Resolve the angular velocity », about ON, into its components about the right-angled axes OP and OP’. These components, as is well known, are » sin ¢ about OP and © cos ¢ about OP’. Now all points on and exceedingly close to the equator of a rotating sphere have sensibly the same velocity, hence the direc- tion and velocity of horizontally moving particles at P are af- fected by the component of rotation about OP only, and not at all by the component about OP’. That is, at N, as already explained, a=2yv,andf = 2m wv, while at latitude ¢, where the angular rotation is sin 4, a = 2 sin ¢, and f = 2muwv sin dg, to the right (going forward with the particle) in the northern hemisphere, to the left in the southern. From this simple equation, assuming it to be exact, which it very nearly is, it follows that the deflective force due to the rota- 10 134 PHYSICS OF THE AIR tion of the earth acting on a quantity of moving air (that is, the force that, assuming the earth to be still, measures the existing tendency of wind to change its direction with reference to any fixed line on the adjacent surface) is: a. Directly proportional to its mass. b. Directly proportional to its horizontal velocity. c. Directly proportional to the angular velocity of the earth’s rotation. d. Directly proportional to the sine of the latitude of its location. e. Exactly the same whatever its horizontal direction. f. Always at right angles to its instantaneous direction and FIG. 37. N go] s Deflection, away from pole, due to earth's rotation. therefore wholly without influence on the velocity with reference to the surface. g. Opposite to the direction of the earth’s rotation. Hence to the right, or clockwise in the northern hemisphere; to the left, or counter-clockwise in the southern. Since the deflection acceleration is all the time at right angles to the path, it follows that an object moving freely over the sur- face of the earth would describe an endless series of curves. At each point on this path the acceleration at right angles to it, meas- ured with reference to the surface of the earth, is given, as ex- plained, by the equation, a@=2yvsin gs in which the terms have the values assigned above. It is also ATMOSPHERIC CIRCULATION 135 given by the well-known equation for acceleration along a radius of curvature. That is, a= 2 rT in which, since the force is tangent to the earth, r—=R tan a where F is the radius of the earth, and a the angle subtended at the centre of the earth by the radius of the path at the point under consideration. Hence, when the only deflective influence is that due to the earth’s rotation, v and tana= 2Rusin¢ : r= Z . 2wsing That is, the greater the linear velocity ot the moving object over the surface of the earth, and the nearer it is to the equator, the greater the radius of curvature. On the equator the radius of curvature is infinite, or the path a straight line. However, unless moving along the equator the object soon crosses to the other ‘hemisphere and its direction of curvature changes, as is well shown by the summer wind tracks over the Indian Ocean. Rate of Change of Wind Direction.—The theoretical rate of change of wind direction at any point on the surface of the earth obviously is the angular velocity »’ of the earth about an axis passing through its centre and the point in question. This change of direction, therefore, clockwise in the northern hemisphere, counter-clockwise in the southern, occurs at a rate wholly inde- pendent of wind velocity, and is given by the equation, w = sin ¢, in which ¢ is. the latitude of the place under consideration and the angular velocity about the axis through the north and south poles. But, as the earth turns completely around during a sidereal day, = see per second = 15° 2’ 26” per hour, or 15° per hour, roughly. Hence, w = 15° sin ¢ per hour, roughly. 136 PHYSICS OF THE AIR The approximate values of »’ corresponding to different lati- tudes may conveniently be tabulated as follows: Earth Rotation in Degrees per Hour at Different Latitudes. 20° 25° 30° ° ° ° 0° . 10° | 15° 0 3 5.14°| 6.36°| 7.52°| 8.63°| 9.68°] 10.64 5 0.00° 1.31°| 261°" | 3.89° 6 , 70° | 75° | 80° | 85° | 90° e | 50" | s5° | 60" | as? oho dla al 14.13°| 14.53°| 14.81°| 14.98°| 15.04°| w’ 11.52°| 12.32°| 13-.02°| 13.63° It must be clearly understood that the above values of rate of change of direction are based on the assumption that there is no friction and no disturbing horizontal pressure gradient, neither of which is true with reference to actual winds. Nevertheless, the values obtained are important, since they indicate the natural torque of the atmosphere, or its tendency to rotate when set in motion by pressure gradients. It is interesting and quite practicable, as Whipple?* has shown, to compute the path of a frictionless mass over the rotating earth when its direction and velocity are given for any definite point, but this will be omitted, since in the case of the actual atmosphere, because of viscosity, turbulence, surface obstacles, horizontal pres- sure gradients, etc., the departures from theoretical values are so great that it seems hardly necessary or even safe to go beyond the above simple and general relations. Centrifugal Deflecting Force of Winds.—Usually the paths of winds are more or less curved, and therefore the moving air exhibits a “centrifugal force,” or inertia force away from the centre of curvature in opposition to any applied. “ centripetal force.” The value of this force, f, in the plane of the curve, not the plane of the horizon, is given by the equation, my ar in which wm is the mass concerned, v its linear velocity, and r the radius of curvature of the path at the place and time under con- sideration, or radius of the “small circle” in which the air is then moving. Relative Values of Centrifugal and Rotational Components.— The ratio between the two deflective forces, rotational and cen- * Phil. Mag., 33, P. 457, 1917. y ATMOSPHERIC CIRCULATION 137 trifugal (centrifugal action of the earth’s rotation and centrifugal action due to curvature of path), varies greatly with the velocity of the wind, radius of curvature of its path, and latitude of its location. Within 20 degrees, at least, of the equator cyclonic storm winds commonly move on curves whose radii are compara- tively small, 150 kilometres (93.2 miles) or less, in which case the centrifugal deflective force generally is greater than the rotational. In middle and higher latitudes, however, the average radii of cyclonic wind-paths usually are much larger, say 600 kilometres (373 miles), and the rotational deflective force greater than the centrifugal. A few numerical examples will be interesting. No effort has been made to get average values, but only such as presumably often occur. Ratios of Deflective Forces Under Given Conditions. Latitude Radius of curvature Gradient velocity eKotatienal force: pee Centrifugal force Miles Miles per hour 10° 20 80 1/44 20° 20 70 1/13 30 100 50 10/19 40° 400 40 10/3 50° 400 35 14/3 60 | _ 400 35 26/5 In tropical cyclones, therefore, the pressure gradient is balanced mainly by the centrifugal force, while in those of middle latitudes it is balanced chiefly by the rotational deflective force. Ordinarily, except in the neighborhood of a well-marked low, the radius of curvature is much larger than any of the values above assumed, and consequently the ratio of rotation to centrif- ugal force correspondingly greater. Total Horizontal Deflecting Force.—lf the path of the air is at all curved, as it usually is, the total horizontal deflecting force, F, due to its velocity is given by the equation, 2 : my F=2meovsin¢ + 7 ’ in which r=7’ seca, r’ and a being the linear and angular (as seen .from the centre of the earth) radii respectively of the “ small circle”? in which the air is moving, or r = R tana, FR being the 138 PHYSICS OF THE AIR radius of the earth, and the other symbols have the meanings given above. The positive sign is used, or the deflective forces are additive, in the northern hemisphere when the course of the wind is counter-clockwise; in the southern hemisphere when the course is clockwise. The negative sign is used in each case when the sense of rotation is reversed. In cyclones, therefore, the total deflecting force is equal to the sum of the centrifugal and rotational deflec- tive forces ; in anticyclones to their difference. When the winds become approximately steady the deflective force obviously is balanced against the gravitational pressure gradient. In symbols, 1p _ . v rae =2evsing + ~ in which p is the density of the air, dp the slight difference be- tween the pressures at the ends of the short horizontal distance dn at right angles to the path at the place considered. The mean- ings of the other symbols are given above. If the gradient is zero (that is, if the air moves without lateral restraint), r = v 2w sing’ the equation just given, 2w uv sin ¢@ + S = 0. Hence, under as previously shown, or R tana = ; also, from 20 sing the assumed conditions, r = R tana = o; that is, a =9go°, or the path is a great circle. However, these latter equations have but little more than a theoretical interest, since’ without the driving force of a pressure gradient wind velocity can neither be acquired nor (because of friction) maintained. GRADIENT WIND. Gradient Velocity—That velocity of the air at which the de- flective force due to the rotation of the earth and the centrifugal force jointly balance the horizontal pressure gradient is called the gradient velocity. It does not occur near the surface of the earth, owing to surface friction, but ‘‘ from kite observations, it appears that at 1500 feet above the surface the agreement [be- tween the observed and ‘ gradient’ velocities] is generally very close,” °° especially in the absence of thunderstorms and other local disturbances. This does not mean that the wind has the same velocity at all levels beyond %4 kilometre, but only that above this height the velocity of an approximately steady wind * Shaw, “ Forecasting the Weather,” p. 45. ATMOSPHERIC CIRCULATION 139 is very nearly the gradient velocity appropriate to the atmospheric density, horizontal pressure gradient, and latitude at the place in question. If the sense of rotation is that which exists in a cyclone, the two deflective forces are additive, as stated above, and the gradient velocity is given. by the general equation, v= [PP + (raosin gro sing, ; ’ (A) in which the sign of the radical remains to be determined. But obviously v = o when cd = 0, as there can be no wind without a pressure gradient, from which it follows that the sign of the radical is positive, and that actually ml pant (rosin o}'—rasing ¢ bw x GB) Theoretically this wind at any place is along the correspond- ing isobar, parallel, roughly, through the first one or two kilo- metres of elevation; to the surface isobar, and always in such direction that one moving with it will have the lower pressure to his left. It must be distinctly noted, however, that the above equations presuppose absence of friction and the attainment of a steady state. They therefore give the approximate wind velocity and direction only for levels above the appreciable reach of sur- face turbulence, and even there in the cases only of smooth and regular isobars. Near the surface where the velocity is checked by friction the wind direction is correspondingly deflected toward the region of lower pressure. In the C. G. S. system of units: v = centimetres per second. (? _ difference in dynes pressure per square centimetre, per centimetre horizontal distance at right angles to isobars. r= 1’ sec a; 7’ = radius of curvature, in centimetres, of wind-path at time and place of observation, not distance to the centre of the low; « = angular radius (measured from the centre of the earth ) of the - stall circle” along which the wind is moving. Ordi- narily r differs from 1’ by less than 1 part per 100, and therefore, in practice, they may be assumed to have equal values. 140 PHYSICS OF THE, AIR p = grammes of air per cubic centimetre. w = angle through which the earth turns per second sin ¢ = natural sine of the angle of latitude. If the path of the wind is straight (that is, if there is no centrifugal force), the equation for gradient velocity is dp dn ; 2wp Sin © 27 > 86,164" In anticyclonic regions gradient winds, as explained, obey the equation, Tap = 2wy sing— 2 p dn r or, in ce a ees oS ASN SN (ro sin 6) dow si RR RR (C) As above, goanhen 2 = oO. dn Hence, in this case, the sign of the radical is negative and v= ro sino — u) (rasin yt Fat (rw sin 6)? —— DD ahs Phiriut seers ee (D) pdn Obviously, then, as pointed out by Gold,*° steady anticyclonic winds cannot become intense, since the maximum possible velocity is given by the equation, vmax = rwsin 6. For example, if r = 500 kilometres, and ¢ = 40°, vmax = 23.4 metres per second = 52.3 miles per hour. The gradient that produces this velocity is given by the equation, dp dn On substituting this gradient in the equation above for straight winds, it appears that it would give the velocity, = pr(osin 6) a pr(wsind)? — ‘ Sane yr wsing. That is, the limiting velocity of anticyclonic winds, ymax =rwsin9, *M. O., No. 190, “ Barometric Gradient and Wind Force,” London, 1908. ATMOSPHERIC CIRCULATION 141 is just twice that which the corresponding pressure gradient would give to straight winds. Since “ for the time being, we may regard the gradient winds as the best estimate we can give of the actual winds at, say, 1500 feet above the surface,” 37 it seemed advisable to construct tables (see Appendix I), one for cyclonic, the other for anticyclonic conditions, that give the theoretical wind velocities in metres per second, kilometres per hour, and miles per hour for various lati- tudes, radii of curvature, and pressure gradients, as indicated, each to be used in conjunction, of course, with the current weather map, corrected, if need be, by estimation or by special reports, for the hours that have elapsed since the observations were made from which it was constructed. As the equations demand and the tables indicate, the winds of an anticyclone, gradient for gradient, latitude for latitude, and curvature for curvature, are stronger, often much stronger, than those of a cyclone. This may seem to be flatly contradicted by the fact that anticyclones are characterized by relatively light winds, but the contradiction is only apparent, for, as the equations show, steep gradients cannot obtain in anticyclonic regions, nor, there- fore, heavy winds except near their borders, or when r is large. However, in general, strong anticyclonic winds cover only a narrow strip of territory, and their duration, therefore, is com- paratively brief. Figs. 38, 39, and 4o represent respectively the effect of lati- tude, pressure gradient, and radius of curvature on the “ gradi- ent ” velocity, other things in each case being constant. Surface gradients and surface isobars, when well defined and in the absence of local disturbances, may be used for approximate values up to elevations of, roughly, two kilometres, except wher- ever the horizontal temperature gradient is steep and opposite in direction to the horizontal pressure gradient. In such cases the temperature tends to weaken and finally reverse the pressure gradient with increase of elevation. Hence, since the temperature gradient is nearly always more or less poleward, in extra-tropical regions the east wind generally is the shallowest and the least likely to have, at an elevation of two kilometres, say, the direction and velocity computed from the surface system of isobars; and 7 Shaw, “ Forecasting the Weather,” p. 49. 142 PHYSICS OF THE AIR the west wind the deepest, with direction and velocity closest in agreement with the values thus computed. In short, with increase of elevation the isobars, usually closed on the surface, tend to Fic. 38. LATITUDE 1234567 89 10N 12 13 4 15 1617 18 19 20 21 22 23 24 25 2627 METERS PER SECOND Relation of gradient velocity to latitude. FIG. 39. > o Y oO nN a = an +. ae awo PRESSURE GRADIENT MM.MERCURY PER 100 KM. no ° 4 123456 7 89 101112 131415 1617 18 19 20 21 22 23 24 25 2627 28 29 30 31 32 33 METERS PER SECOND Relation of gradient velocity to pressure gradient. open out and roughly to follow the parallels of latitude with the decrease of pressure directed poleward, at least to well above the troposphere. ATMOSPHERIC CIRCULATION 143 Gradient Velocity Nomogram.—The general gradient velocity equation, F=2mevsing+™") reduces, on dividing by m, to Ie 4 &, r 2wvsino— ? pdn the upper sign being used for anticyclones and the lower for cyclones. Fic. 40. 3000 2000 1500 1200 1000 900 600 RADIUS OF CURVATURE IN KILOMETERS NWAY e000 CoO000 100 1234567 89 10M l2 131415 1617 1819 20 2122 23 METERS PER SECOND Relation of gradient velocity to radius of curvature. A straight line nomogram that solves this equation has been constructed by Mr. Herbert Bell, of the University of Chicago, after the method developed by Professor d’Ocagne in his “ Traité de Nomographie.” The solution is as follows: Writing u sae and w = 10° wsin¢, p dn 144 PHYSICS OF THE AIR w and w being scales along the lines » = —10 and » = Io respec- tively, the velocity equation becomes 2 v 2500u -uw= + 50,000 which is linear in w and w. If, then, a network is constructed of the two families _ |v — 2500 x=1 4 e508 # G) and ye 50,000 eS v + 2500 6.25 x 108 (10 + x)? r 10—x =+ - (2) the point c, say, determined by (1) and (2) from values of uv and r, will be collinear with the point A on the wu scale, fixed by the given value of db and the point B on the w scale indicated dn by the latitude. The resulting diagram, with gradients in terms of millimetres difference of barometer reading per 100 kilometres, and velocity in metres per second, is given in Fig. 41.* To find the gradient wind velocity, connect the known pressure gradient (marked on lower left border of the diagram) and the latitude of the place in question (given on the upper right border) * with a straight edge or stretched string and note where it cuts the curve representing the radius of curvature of the local isobar. For cyclones the vertical through this point gives the required velocity in metres per second. For anticyclones two velocities are thus indicated, but the smaller is the one to take, since it alone is physically possible. See equations C and D, above. This nomogram should be used in conjunction with the surface distribution of pressure only in the absence of local disturbances (thunderstorms, squalls, etc.), or strong horizontal temperature gradients; where the pressure gradient is well defined—isobars smooth, and for elevations between, roughly, 500 and 2000 metres. * Folded plate attached to inside of back cover. ATMOSPHERIC CIRCULATION 145 Automatic Adjustment of Winds in Direction and Velocity.— In discussing the more extensive winds it is convenient to con- sider the earth as stationary and the air as moving over it without friction under the influence of three distinct horizontal forces: (1)The deflective force, due to the earth’s rotation; (2) the horizontal component of the centrifugal force, due to the curva- ture of the path, and (3) the horizontal or gradient pressure, due to gravity. The first two are at right angles to the course of the wind and therefore help to control its direction, but do not alter its speed. The latter, however—that is, the gradient pressure— affects both the direction and the speed. Furthermore, as the velocity depends upon the horizontal pressure alone, and as the Fic. 42. Deflection and path of winds in frictionless flow under a force of constant magnitude and constant geographic direction. other forces depend in turn upon the velocity, and are zero when it is zero, it follows that of the three forces only the gradient pressure is independently variable. Consider, then, the result of applying a horizontal pressure p of constant magnitude and constant geographic direction to a small mass m of air, free, as above assumed, from friction: Let m, Fig. 42, be the mass in question initially at rest with reference to the surface of the earth, and let it be acted on by the force Pp, exactly poleward, say. Immediately the mass moves, under the applied pressure p, the deflective force d becomes operative, thus curving the path (to the right in the northern hemisphere, to the left in the southern) and introducing the centrifugal force c. So long, however, as the angle between the path and the force p is 146 PHYSICS OF THE AIR less than go degrees there will still be a component of the latter in the line of motion; accordingly the speed of m will continue to in- crease, and therefore also the deflective force d. If this angle should exceed go degrees, the force p would have a component opposite to the direction of motion, which consequently would be slowed up and d thereby correspondingly decreased. In the end, therefore, a poleward force along the meridians on an object free FiG. 43. Path of winds in frictionless flow under a converging force. to move gives it an exactly west to east velocity of such magni- tude that, except in very high latitudes, the resulting deflective force is nearly equal to the horizontal pressure—the horizontal component of the centrifugal force being then comparatively small, except near the poles. Whatever the direction of the gradient force, whether poleward, as above assumed, or any other, the final motion is normal thereto. A change in the magnitude but not in the direction of p, above, would only shift the latitude of the path and change the velocity so as to be nearly proportional to p. If the horizontal pressure is not everywhere in the same direc- tion, but converges, as in Fig. 43, or diverges, as in Fig. 44, the path, in adjusting itself normally to the directions of this ATMOSPHERIC CIRCULATION 147 pressure, obviously curves, as in cyclonic and anticyclonic regions, respectively. In all cases, then, the wind automatically follows approxi- mately the isobar of its position, with substantially the gradient velocity. General Relations of Wind to Elevation —Knowledge of the directions and velocities of the winds of the earth is still frag- FIG. 44. Path of winds in frictionless flow under a diverging force. mentary and incomplete. Over large areas even the surface winds are unknown, and over regions best studied these alone are well known. The continuous records obtained at mountain stations have given much information in regard to air movements, but stations of this nature are comparatively few, and, besides, their data, however valuable, are always affected to an unknown extent by local topography. Cloud observations have also given a large amount of valuable information, but it, too, is only fragmentary. At best a cloud observation seldom gives more than the direction and velocity of the air at one level, nor does such an observation ever apply to the stratosphere, since this region is never visited by clouds. In many respects kites and sounding balloons have 148 PHYSICS OF THE AIR furnished the most valuable data in regard to the movements of the upper air and their causes, but, unfortunately, aerological investigations of this nature, with relatively few exceptions, have been restricted to the northern hemisphere, and even there mainly to the summer season. Nevertheless, by combining the data gathered from these various sources a number of tentative con- clusions, subject, of course, to modification, have already been reached in regard to the winds of different parts of the world from the surface up to great elevations. Some of the more important of these conclusions are: 1. That there is no continuous and rapid overflow of the atmosphere at all longitudes from the equatorial to the polar regions. At an elevation of 10 kilometres, for instance, the wind of middle northern latitudes seems to have southerly components about as often as northerly. From this it follows that the equator-polar circulation is irregular and probably complex even at the higher altitudes. 2. That the equatorial winds are not always and at all levels from the east; that, on the contrary, west winds occur (how regularly is uncertain) at elevations of about 18 to 20 kilometres, with east winds again prevailing (certainly at times) at still greater elevations. The cause of this layer of equatorial west wind has never been explained. Indeed, it may be only a local and temporary phenomenon. 3. That layers of air in which the temperature in- creases with increase of elevation, and others in which the temperature is constant, exist at different levels, espe- cially through the first two or three kilometres. This stratified condition of the lower atmosphere appears to be universal. It is found even over tropical oceans, and is exceedingly well developed over the ice plateau of Antarctica. Each layer usually shows such different humidity and such different wind velocity from those of the adjacent layers as to indicate a distinct origin, which it well may have. For example, as explained in an earlier section, a rising convection current on reaching its equilibrium level flows away substantially at that ATMOSPHERIC CIRCULATION 149 particular elevation, and obviously retains its own humidity (pro- vided condensation has not taken place), dust content, and other peculiarities. Its viscosity is not the same as that of the adjacent air, because its humidity or temperature, or both, are different. Hence, as shown by billow clouds, any such layer with a distinctly independent velocity tends to retain its integrity and to glide over another from which it differs physically without rapid interming- ling. And there are still other obvious causes of temperature and humidity irregularities and consequent stratification of the atmos- phere, such as reflection from, and evaporation of, clouds, surface cooling, and air drainage. Clearly, then, one should expect to find in the lower atmosphere substantially the kind and amount of temperature inversions and other irregularities that it actually shows. 4. That the upper winds are exceedingly variable along the edges of the high-pressure belts, and that marked disturbances occur in the antitrades. 5. That the north-poleward pressure gradient in the upper atmosphere becomes very small long before the arctic circle is reached—in fact, between 50° and 60° N. 6. That in high northern latitudes, where the pole- ward pressure gradient of the upper atmosphere is small, the westerly winds are not constant. Local Wind Velocity and Elevation—Everyone knows that the wind increases with increase of elevation. Even casual ob- servations of such objects as sails of ships, tops of trees, columns of smoke, or isolated clouds suffice to show qualitatively that wind velocity increases with height above the surface; while measurements made by triangulation on freely drifting clouds and balloons, or by anemometry on tethered kites, fully support the conclusions reached by the simpler methods just mentioned. Near, the surface of the earth—up to from 2 to 8 metres over an open plain—the condition of the wind, upon whose force this limit depends, may be summarized as follows: Actual velocity: exceedingly irregular. Average velocity: increases rapidly with elevation. a, increases with average velocity. Rate of velocity increase: 13 decreases with elevation. II 150 PHYSICS OF THE AIR Above this thin surface layer the wind increases so nearly regularly with elevation that its approximate velocity at any level up to 16 metres may be computed, according to Stevenson,** from its observed velocity at some other height by the empirical equation, lH +72 v= "Na+72° in which [” is the computed wind velocity for the level H in terms of the known velocity v at the height h, both elevations being expressed in feet. If heights are given in metres, this equation becomes, H+22. k + 22 V=v Other empirical equations expressing the relation of wind velocity to elevation have been given for greater heights. Archibald,®® for instance, finds that his velocity observations be- tween 100 metres and 600 metres elevation fairly satisfy the simple equation, v=(2e v ( h ) Shaw *° suggests as a likely formula, ee Ve, ae 7 V in which ’ is the wind velocity at the height H above ground, Vo the observed anemometer velocity at a fixed position, and a a constant, obviously depending upon surrounding topography, anemometer exposure, and, perhaps, other factors. Among the most interesting observations on the relation of wind velocity to altitude are those of Dr. Cesare Fabris,*! based on some 200 pilot balloon flights made at nearly equal intervals during the year June, 1g10, to May, to11, at Vigna di Valle, the principal aerological station of the Royal Italian Oceanographic Committee. This station is about 25 miles northwest from Rome. % Tour. Scot. Meteor. Soc., 5, p. 348, 1880. ® Nature, 33, P- 593, 1885. * Advisory Committee for Aeronautics, “ Reports and Memoranda,” 66, No. 9, p. 8, 1909. “R. Comitato Talassografico Italiano, Memoria 8, pp. 37-46, 1912. ATMOSPHERIC CIRCULATION I51 Its codrdinates are: Latitude 42° 04' 41” N.; longitude, 12° 12’ 43” E.; altitude, 272.4 metres. The general results of all the observations are summed up in Fig. 45, which shows four distinct regions: a. The region of rapid linear increase of velocity with Fic. 45. 5 10 Wind velocity and elevation. (After Fabris.) increase of altitude, extending from the surface (272 metres above sea level), where the velocity is least, to an elevation above ground of, roughly, 300 to 500 metres. This obviously is the region in which the winds are affected by surface friction and the resulting turbulence. Clearly, too, the average number of eddies and their consequent effect on velocity must rapidly de- 152 . PHYSICS OF THE AIR crease with increase of elevation, at least near the surface, sub- stantially as indicated by the given velocity-altitude curves. b. The region of velocity decrease with increase of altitude; about 200 metres thick and coming immediately above a. This decrease probably is not what one at first would expect, but it may be of fairly general occurrence (known to occur in other localities) in analogy to the well-known fact that the maximum velocity in rivers, canals, and other streams is not at the surface, but, roughly, one-third the depth below it. This surprising rela- tion between velocity and depth is due to the retarding drag of the bed and banks, together with the viscous pull of the swifter centre that draws the sluggish surface water away from either side; and, since the surface of the earth exerts a similar drag on the atmosphere, it appears that an analogous effect on wind velocity might be suspected, not, of course, because of overflow, for there are no retarding banks, but as a result of convection. Obviously the amount of interference to the flow of a given stratum of air, exerted by a convecting mass, depends upon the difference of their velocities and the duration of their contact. But near the surface of the earth vertical movements necessarily are slow, and again slow near the limit of convection, and there- fore most rapid at some intermediate point. Hence the least inter- ference to its flow and the maximum velocity, or at least a tendency to a maximum, of the turbulent layer of air may occur below its pseudo surface—the upper limit of convection—just as the maximum flow of a river occurs below its surface, though chiefly for a different reason. c. A region of irregular winds slowly increasing with increase of altitude, extending, roughly, from about 500 to 1500 metres above the surface. These conditions are of very general occur- rence between the levels given.4? The irregularity probably is due to convectional mixing induced during the day by insolation and at night by cloud evaporation. d. A region of approximately constant increase of velocity with increase of elevation, beginning at about 1500 metres above the surface and extending to at least the maximum height ob- served, 5000 metres. The wind velocities of this region, being out of the reach both of frictional and convectional disturbances, are determined by the prevailing horizontal pressure gradients. “Berson, Wissenschaftliche Luftfahrten, 3, p. 205, 1900. ATMOSPHERIC CIRCULATION 153 Cloud and balloon observations show that increase of wind velocity with increase of altitude beyond 1500 to 2000 metres above the surface holds practically to the top of the troposphere, where the velocity in middle latitudes may amount to as much as 90 metres per second (200 miles per hour) or even more. At higher levels—that is, in the stratosphere—the average velocity is decidedly less. Horizontal Pressure Gradient and Elevation.—All these facts are well known, but there are no generally accepted and satisfac- tory discussions of the reasons why the average wind velocity at levels above the limit of appreciable surface influence should go on increasing with increase of elevation up to the isothermal base and then decrease. Indeed, data sufficient for a complete solution of this problem are not yet available, and it is only recently that enough facts have become known to indicate at all clearly the several links in the chain of cause and effect that deter- mine the average atmospheric movements in middle and higher latitudes. Because of the actual distribution of insolation over the earth the temperature of the lower atmosphere, as shown by observation, is warmest, on the average, in equatorial regions and coldest beyond the polar circles, with intermediate values over middle latitudes. Hence, since the temperature of the air above the earth depends mainly upon convection and radiation from below, it follows that the latitude distribution of temperature in the upper air must be substantially the same as that at the surface; that is, warmest within the tropics and coldest in the polar regions, with intermediate values between. And this, indeed, according to kite and balloon records, does apply at each level up to 10 to 12 kilometres, or to fully three-fourths of the air mass. At much higher levels, 15 to 20 kilometres, for reasons that need not be discussed here, the rare atmosphere is coldest over equatorial regions and warmest over high latitudes. This inverse condition, however, does not apply to the winter and summer atmospheres of the same place, nor, presumably, to those of neighboring places on approximately the same latitude. On the contrary, the atmosphere is warmer, on the average, at all explored levels during summer than during winter, and warmer, so far as known, over regions whose temperatures are relatively high than over others of the same latitude that are comparatively cold. * 154 PHYSICS OF THE AIR As a crude first approximation to conditions as they actually exist, assume (1) that the temperature distribution is the same along all meridians, (2) that the temperature changes from one latitude to another is the same for all levels, and (3) that sea- level pressure is the same at all latitudes. Assumption (1) ap- proximates the conditions over much the greater portion of the southern hemisphere, but, on account of the irregular distribution of land and sea, has to be modified for any detailed study of the winds of the northern hemisphere. Assumption (2) conforms roughly to average conditions between the thermal equator and Fic. 46. 20° 10° S10’ 0° 10° 20° 30° 40° 50° 60° 70°N Relation of temperature to altitude and latitude. (After Siring.) latitude 50° to 60°, except near the surface and at altitudes above 10 to 12 kilometres. This is well shown by Fig. 46 referring to the northern hemisphere during its summer, and copied from Suring’s paper,** on the present state of knowledge concerning the general circulation of the atmosphere. Assumption (3), as applied to normal pressure, is also approximately true except for restricted areas, whose secondary and local effects will not here be discussed. Consider an atmosphere of the same composition through- out, and having initially the same temperature at any *® Zeitschrift der Gesell. fiir Erdkunde, p. 600, 1913. ATMOSPHERIC CIRCULATION 155 given elevation, resting on a horizontal plane. Let the tem- perature be uniformly increased from north to south, say, and by the same amount from top to bottom, thus simulating the tem- perature distribution that actually obtains in the earth’s atmos- phere over middle latitudes, as above explained. Find the result- ing horizontal pressure gradient at the different levels. At the height / the horizontal pressure gradient, ae obviously directed from the warmer toward the colder region, is very approximately given by the equation, _ dp Ah dn? HL’ in which L is any given horizontal distance along which dn is taken, p the pressure at the level , above the colder end of L, Ah the difference of vertical expansion of the air below the level in question at the ends of L, or difference of distance through which the level, whose original pressure was ~, was lifted at these two places, and H the virtual height of the atmosphere, approxi- mately 8 kilometres, or height it would have above any point if from there up it had the density which exists at that point. The negative sign is used because the pressure decreases as 1, measured from a warmer toward a colder region, increases. For simplicity let L be in the direction of maximum rate of horizontal temperature change, north-south, in this case. Under the assumed conditions Ah=a ATh, approximately, ’ in which a is the average coefficient of volume expansion of the atmosphere below the level 4, and A T the difference of tempera- ture change at the ends of L. At any two levels, then, / and h’, the horizontal pressure gradients in the same direction are given approximately by the respective equations, dp _ padTh ~ dn HL and dp’ _ pia ATR’ | ~ dn H'L But L may be taken the same in both equations, while a, H, and AT generally are not greatly different respectively from a’, H’ and AT’. In reality, 156 PHYSICS OF THE AIR and a’ is slightly greater than a when 7” is less than T. But in this case it appears from observations that actually AT’ is slightly less than AT, so that dp dn __ ph . dp ph ee approximately. dn FIG. 47. mm Km L i06 LK 1024 15 Ee = 94 224 220 | ee | ps L216] WE ne ; + 208 + 204 a L200 L 424 oon 422 | te Ls 5 E415 = 414 t-410 «Pr _] |_ 406 ——__ [E402 |_760—] sich ia 0 [ 758 ia ee 510° Oo 1? 20° 30 40° 50 60 70N Relation of pressure to altitude and latitude. (After Siring ) Again, from the 5- to the 1o0-kilometre level, and even to some distance below the former and above the latter, p h' , =a roughly. Hence, commonly, dp dn h'h : aa =a h approximately. dn That is, through these levels, or from below 5 kilometres to above 10 kilometres, the horizontal pressure gradient established by the temperature difference between adjacent regions of air ATMOSPHERIC CIRCULATION 157 is roughly constant. This conclusion is fully supported by obser- vations, as shown in Fig. 47, referring to the northern hemisphere during its summer, and also copied from Siiring’s paper.*# Level of Maximum Horizontal Pressure-Gradient.—The ap- proximate level of the maximum horizontal gradient may be found as follows: As just explained, in the equation, _ dp — Pa daTh dn HAL the factor, or is roughly constant. Writing G for the gra- *. dient and K for the “ constant,” the equation takes the form, , G=Kph. Hence G has a maximum value when pdh=—h dp. But dh EP Hence the pressure gradient is steepest when h pdh= 7 p dh, that is, when h =H =8 kilometres, roughly. The following is a slightly different method of arriving at the same conclusion: The maximum horizontal pressure gradient resulting from a constant temperature difference between two neighboring columns of air obviously is at that level at which the vertical pressure is most changed by the expansion of the air below due to a constant temperature increase. Let h be any height, and let a be the average coefficient of volume expansion of the air below this level. Then, Ah =ah, nearly, and Ap=pgAh=pg ah, nearly, in which p is the density of the air at the level h and g the local gravity acceleration. But p=C?, in which C is a constant, and Ap=pCgah=K ph, say, in which K may be regarded as a constant. * Loe. cit. 158 PHYSICS OF THE AIR Hence, as before, A p has its maximum value when p dh=—hdp= f dh That is, the horizontal gradient is steepest when h=H. But, as is well known, H =8 kilometres, approximately. Hence the horizontal pressure gradient, resulting from a temperature dis- tribution substantially that which actually obtains in the atmos- phere, is greatest at a height of about 8 kilometres. According to this conclusion the maximum seasonal pressure change should occur at the elevation of 8 kilometres, or a little higher perhaps, since the surface pressure is slightly greater in winter than summer. And that is where it does occur, as shown by the table on page 72. Constancy of Mass Flow—Egnell’s Law.—At a distance above the surface of the earth sufficiently great to avoid appreci- able retardation due to friction and turbulence—that is, at eleva- tions greater than 2 kilometres (usually less)—the wind obviously must blow in such direction and with such velocity that there is an approximate equality between the pressure gradient on the one hand and the combined centrifugal force and deflection force 5 je ‘ due to rotation on the other. Hence, at these levels, if sf is the maximum horizontal pressure gradient, d i =—pv (2wsing + 7 tan ¢), approximately. in which p is the density of the air at the level under considera- tion, v the wind velocity, » the angular velocity of rotation of the earth, ¢ the latitude, and FR the radius of the earth. A little calculation shows that in the case of a wind following, roughly, a parallel of latitude the second term in the paren- theses is always small, except in very high latitudes, in comparison with the first. Thus for a 22.4-metres-per-second (50 miles per hour) west wind at latitude 45° the first is about 30 times greater than the second. Hence, under these conditions, dp “dn TT P22 sin ¢, approximately. But, as just explained, the horizontal pressure gradient, ae, is roughly constant between 5 and 10 kilometres elevation and di- rected polewards. Hence, at any given latitude, p v, the mass flow, or mass of air crossing unit normal area per unit time, tends to re- main constant with change of altitude from 4 or 5 kilometres above sea level up to the isothermal region. In other words, through this region, pv, at altitude /, equals p’ 7’, at altitude i’, nearly. This re- ATMOSPHERIC CIRCULATION 159 lation between the density and velocity of the atmosphere at differ- ‘ent levels is known as Egnell’s law,** determined empirically by himself, as previously by H. H. Clayton, ** from cloud observa- tions. Obviously p v has a maximum value at that level at which the horizontal pressure gradient is a maximum; that is, at about 8 kilometres above sea level. Relation of Velocity to Altitude Above 5 Kilometres.—Ob- viously, if the temperature is constant, as, for simplicity, we may assume it to be, pp ep But, as already seen, under this condition of constant tempera- ture, through a considerable range of altitude—that is, from below 5 to above to kilometres— h' ae roughly. Hence, p_h’ i at roughly. But, as explained above, pv=p’v’ Therefore, tai, approximately, Uv or the velocity of the wind through the levels in question is roughly proportional to the altitude. Above the isothermal level over the regions between the thermal equator and latitude 50° to 60° the horizontal temperature gradient decreases, and presently even reverses with increase of elevation, as shown by Fig. 46, and therefore the corresponding pressure gradient also decreases as shown by Fig. 47. Hence, the mass flow, pv, likewise decreases with elevation above this critical level. Further, the decrease of the horizontal pressure gradient, and consequently of 9 v, with altitude in the stratosphere appears usually to be more rapid than that of the density alone, from which it follows that the wind velocity generally must have its maximum value at or below the isothermal level. Season of Greatest Winds.—From the above discussion it is obvious that the general wind will be swiftest whenever the tem- perature contrast between the air of higher and lower latitudes is greatest. . But the temperature of the atmosphere in low latitudes *C.R., 136, p. 360, 1903. “Amer. Met'l Jour., 10, p. 177, 1893. 160 PHYSICS OF THE ALR does not change through the year nearly so much as does that of higher latitudes. Hence, the maximum horizontal temperature gradient, and therefore the greatest pressure gradient and strongest winds, must occur during winter. Latitude of Greatest Winds.—The latitude of strongest winds clearly is that at which the horizontal pressure gradient is greatest. In the northern hemisphere, according to Fig. 47, this occurs in the summer at about latitude 45°. It is obvious, however, since the pressure gradient depends in general upon the latitude rate of temperature change, that the belt of maximum winds must shift more or less from season to season—poleward with the com- ing of summer, equatorward with the onset of winter. Hours of Greatest and Least Winds.—On land, but not appre- ciably at sea, the velocity of the surface wind has a well-defined daily period. Over level regions this velocity is least, on the average, about sun-up and greatest from 1 to 2 p.M. The change is larger on clear days than on cloudy, and also most pronounced in summer, when it reaches an average altitude of about 100 metres, and least in winter, when it rises to only about 40 metres. The physical explanation of this phenomenon was given long ago by Espy. During the night, when there is no vertical con- vection, surface friction holds the lower air comparatively quiet, while the upper air glides over the lower with but little restraint. During the day, however, and especially during clear, summer days, vertical convection and the accompanying turbulence so mixes the surface layers of the air with those next above as to bring both to a more or less common velocity, which is greater than the undisturbed or night surface velocity, and less than that of the undisturbed upper layers before their mixture with the lower. Daily changes of wind velocity also occur on mountain tops, where the maximum is at night and the minimum by day, or just the reverse of the velocity changes that occur near the surface over plains. Three factors, possibly more, combine to produce this result: (a) Contraction of the lower air by night, thus bring- ing air of slightly higher levels, possibly 15 metres (50 feet) or so, and therefore of somewhat greater velocity down to the moun- tain top. (b) The presence by day and absence by night of sur- face disturbances, due to convection, in the air flowing over the mountain. (c) Overflow from the region of maximum expan- sion to the region of maximum compression. Since the greatest ATMOSPHERIC CIRCULATION 161 expansion of the lower air usually occurs at 3 to 4 P.M. and its greatest compression at 5 to 6 A.M., it follows that the overflow will be from west to east, or with the prevailing winds, through the night, and from east to west, or against them, during most of the day; that is, from sun-up to 3 or 4 P.M. Diurnal Shift of the Wind.—The average direction of the wind changes slightly during the day, both over plains and on mountain tops, the tendency being for it always to follow the sun, or, rather, the most heated section of the earth. That is, the wind tends to be east during the forenoon, south (in the northern hemisphere) during the early afternoon, and west during the late afternoon and early evening. This does not mean that at each instant the wind really blows directly from the then warmest region, but that the actual changes through the day in the average hourly wind directions can be accounted for by a velocity com- ponent away from that region. The whole sequence results from the thermal expansion of the atmosphere (progressive from east to west), which causes an increase of pressure and consequently an outward flow at all levels above the surface. The area covered is so vast that the time involved, only a few hours, is insufficient for the completion of the convection circuit, so that even the sur- face winds are away from the most heated regions, as stated, and not toward them, as in sea and land breezes, for instance. The compensating or return current occurs at night, when the com- ponent, outside the tropics at Jeast, is from the higher latitudes. In reality the entire phenomenon is only a diurnal surge, a flux and reflux, of the atmosphere due to diurnal heating and cooling. Normal State of the Atmosphere-—From the above explana- tions of the causes of general winds, especially those that pertain to cloud levels, it appears that the normal state of the atmosphere is one of considerable velocity with reference to the surface of the earth. In middle latitudes, at least, this velocity is from west to east more or less along parallels of latitude and so great as nearly to balance the latitudinal pressure gradient due to the zonal distribution of insolation. Calms, therefore, in this region must be regarded as disturbances of the atmosphere, and indeed often are comparatively shallow, with normal winds above. Equatorial East to West Winds.—East to west winds are quite as general and constant in equatorial regions as are west to east 162 PHYSICS OF THE AIR winds in middle latitudes. Along its borders, roughly 30° N. and 30° S., this equatorial belt of east to west winds is very shallow. Yoward the equator its thickness increases, as a rule, until it reaches at least the limit of vertical convection. There are, how- ever, great irregularities in these winds, just as in those of higher latitudes on either side of it. But the general conditions are as stated and require explanation. Conceivably the tidal action of the sun and moon on the atmosphere might set it rotating from east to west. But the baro- metric amplitudes of the atmospheric tides are very small, only about 0.0109 m.m. and 0.025 m.m., due respectively to the sun and the moon.4? Besides, they have but little phase lag, or follow closely under the disturbing body. Hence the tendency of the tide-producing forces to establish an east to west circulation of the atmosphere must be very small. The diurnal heating and cooling of the air presumably also tends slightly to produce a planetary circulation, possibly in the same direction as that due to the tidal action, or from east to west. In equatorial regions, and in general wherever and when- ever days and nights are approximately equal, the atmosphere is most condensed about daybreak, or, say, at 5.30 A.M., and most expanded at about 3.30 p.m. Hence at such times and places the gradient toward the east is to the pressure gradient toward the west substantially as the greatest and least distances, measured along a parallel, between the meridians of highest and lowest tem- perature; that is, as 7 to 5. On the other hand, the time of flow along the steeper gradient is to the time along the gentler as 5 to 7. But as the distance through which a given mass is moved, provided it is free to move, is proportional to the product of the force acting by the square of the time, it follows that the diurnal temperature changes, neglecting friction, which indeed may even reverse the sense of motion, should give the atmosphere an east to west velocity whose average magnitude would be determined in part by viscosity. The effect of the double diurnal pressure wave on this velocity is uncertain. However, this thermal effect on wind velocity, whatever its value, clearly is of secondary importance. Possibly it may have some relation to the unexpected east to west winds, the so-called upper trades, reported in the stratosphere over equatorial regions, “Lamb, Hydrodynamics, 4th edition, p. 552, 1916. ATMOSPHERIC CIRCULATION 163 but many more observations and a more rigid discussion of the theory of atmospheric circulation would be necessary to settle this interesting question. The only other obvious cause of east to west and west to east general or planetary winds is interzonal circulation, to which, indeed, they usually are regarded as being entirely due. Heating in equatorial and cooling in polar regions necessarily produce a more or less vigorous interchange of air, but, as already explained, one that is profoundly modified by earth rotation. Assume, as initial conditions, non-rotation, smoothness of surface, uniformity of surface temperature, and absence of local convection. Let the temperature of the surface and the atmos- phere now be decreased in proportion to the distance from the equator. There will be a poleward overflow and an equatorward underflow. Further, if, as assumed, there is no local convection— no intermingling of the air at different levels—the equatorward surface air obviously must remain at the surface throughout its course to lower latitudes and then, after rising in the general, not local, convection, move poleward at the top of the atmosphere. Similarly, any other layer must retain, in its equatorial course, a nearly fixed height above the surface and in its poleward journey a corresponding distance below the top. As a further modification assume again an initial uniformity of surface temperature, but let the earth and the atmosphere be everywhere rotating at the same rate, so that there shall be no winds of any kind. As before, let the temperature be decreased in proportion to the distance from the equator, but let there be no local convection. Again there would be established an upper poleward and an under equatorward circulation, but the air that started toward either polar region would quickly assume an east- ward component, while the under- or counter-current would have a westward component. In the absence of friction or other disturb- ing factor, the upper air moving under a pressure gradient from lower toward higher latitudes would approach along an asymp- totic spiral a certain limiting parallel, where the deflecting force due to its final velocity would equal the pressure gradient across that circle. At the same time the east to west under-current would give a deflective force counter to the equatorward gradient. Hence, perhaps, equilibrium would soon be reached with west to east upper winds balancing the poleward pressures and east to 164 PHYSICS OF THE AIR west lower winds balancing the equatorward pressures, and thus further interzonal circulation prevented. But surface friction, viscosity, local convection, and other disturbing factors so restrict the approach to equilibrium veloc- ities that interzonal circulation is continuous, though of varying intensity, both local and general. Hence the eastward moving upper air must gradually reach the surface and reach it as an eastward wind. In its subsequent course to lower latitudes it will become a westward wind, as already explained. In general, then, the areas of planetary atmospheric descent are the regions of west to east winds, while the similar areas of ascent are regions of east to west winds. Doubtless, too, these phenomena are accentu- ated at the surface—that is, the eastward and the westward surface winds are stronger than they otherwise would be—by the intermingling of the air of different levels through innumerable local convections. What latitude establishes the boundary between the east and west winds? This important question has no answer, not even a theoretical one, unless height is considered. At the surface the boundary is several degrees nearer the equator during winter than in summer, but its average latitude is, roughly, 30° to 32°. Near its border the east to west winds are very shallow, but in general they increase in depth as the equator is approached until they extend to the limit of vertical convection. If the temperature distribution were the same along all meridians, and gradually varied from highest at the equator to lowest at the poles, it would seem that the area of ascending air would be substantially the same as the area of descending air (really a trifle larger, because of the higher temperature and consequent greater volume of the ascending air), and therefore that the surface borders between east and west winds would be approximately 30” on either side of the equator. But tempera- ture is not distributed in this ideal way. There are restricted areas which are exceptionally warm, at least during a portion of the year, and others that are exceptionally cold, hence one would expect the area of ascent to be only roughly equal to the area of descent, and therefore the beundaries in question to be, as they are, only approximately at latitudes 30° N. and 30° S. The velocity of the west to east winds of middle and higher latitudes and the velocities of east to west winds of equatorial ATMOSPHERIC CIRCULATION 165 regions obviously depend ultimately upon the rate of interzonal circulation. If this circulation were zero, surface friction, facili- tated by local vertical convections, soon would greatly diminish and finally eliminate any cross-meridian velocity that originally might obtain. On the other hand, an extremely vigorous inter- zonal circulation would lead to violent east to west winds, partly because velocity is not altered by mere deflection and partly be- cause there would then be less time for the latitude (con- servation of area) effects on the velocity to be minimized by convectional turbulence—the total number of such disturbances becoming larger and their cumulative effects therefore greater with increase of time. Hence the moderate east winds of equa- torial regions and west winds of higher latitudes that actually exist are due to the fact that the interzonal circulation itself is moderate—being largely held in check, as already explained, by the automatic formation of gradient winds in the free atmosphere which roughly follow parallels of latitude. It appears, then, (a) that the temperature gradient, directed in general from the equatorial toward the polar regions, establishes an upper pressure gradient in the same direction and a lower in the opposite direction; (b) that in the absence of friction or other disturbance these pressures would produce east to west and west to east gradient winds with but little or no interzonal circulation; (c) that as the winds actually are more or less checked by surface friction, turbulence, convection, etc., they fail to attain full gradient velocities, and therefore cross the isobars at a small angle, except near the surface, where this angle is much larger, and thus maintain a correspondingly vigorous interzonal circulation even in the absence of cyclones and anticyclones; (d) that the actual west to east winds of the middle and higher latitudes and the east to west winds of equatorial regions are due chiefly to their ap- proach to gradient directions, and, finally, (e) that the strength of any steady wind is proportional, approximately, to the gradi- ent pressure, and its direction substantially normal thereto. Probable Interzonal Circulation of the Stratosphere.—-The primary circulation just explained involves all the atmosphere from the surface of the earth up to at least the highest cloud levels, but there is reason to believe that it does not extend to the greatest altitudes. Indeed, it appears probable that far above the upper- most clouds there may be another primary or fundamental circu- 12 166 PHYSICS OF “Tilt AIR lation in reverse direction to that of the lower. This inference is based on the fact that the stratosphere is so much warmer in high than in low latitudes that seemingly there must be an overflow of air from the former to the latter and a corresponding return; that is, a primary circulation in the stratosphere in which the upper branch is from the polar (in this case warmer) toward the equa- torial (in this case colder) regions and the under from the equatorial toward the polar regions, with, of course, longitudinal components in each due to the earth’s rotation. In a sense the upper circulation, if it exists as inferred, is the mirror image of the lower, though more regular. In addition to the primary circulation or circulations of the atmosphere as a whole, there are several secondary circulations or wind systems of magnitude sufficient to bring them markedly under the influence of the earth’s rotation. It will be convenient next to consider some of the more important of these winds. CHAPTER IX. ATMOSPHERIC CIRCULATION (continued). Winds Due to Widespread Heating and Cooling (continued). MONSOONS. SUMMER monsoons and winter monsoons, for convenience dis- cussed under the same head, bear the same relation to summer and winter that sea breezes and land breezes bear to day and night. It is the temperature contrast between land and water that estab- lishes the circulation that manifests itself on the surface as a sea Fic. 48. Z7 7" N LAND, NORTHERN » HEMISPHERE Li £7 2 y7- al of Prevailing directions of monsoon winds, northern hemisphere. or land breeze in the one case and as a seasonal or monsoon wind in the other. The direction of the surface wind in either case is always from the cooler toward the warmer of the adjacent regions, from the ocean toward the land by day as a sea breeze and during the warmer season as a summer monsoon; from the land toward the ocean by night as a land breeze and during the colder season as a winter monsoon. Hence monsoons may be regarded as sea and land breezes of seasonal duration, and might very well be classed with the latter under some common appro- priate caption. However, because of the immense areas involved, 167 168 PHYSICS OF THE AIR it cannot be said of them, as of sea and land breezes, that they are caused by mere local temperature differences. Besides, the dura- tion of a land or sea breeze is so brief that it covers only a narrow strip along the coast, as already explained, while the monsoon winds extend far from the coast, both inland and to sea and the directions of the former, since their paths are always short, are but little affected by the rotation of the earth, while the courses of the second are greatly modified by this important factor. The prevailing directions of monsoon winds, except where dis- tinctly modified by the general circulation, are given by the follow- ing table and by Figs. 48 and 49: Direction of Monsoon Winds i Hemisphere | Season Land south| Land west |Land north Land east | | | : | Summer: N.E. | S.E. ' SW. NLW, Northern = },————.~ Seo pn Winer. 6.W. ' Nav. wie. ' Sow. Summer) NW. NE. SE. S.W. Southern 4 2 || Winter | SE. | Sw. | N.w. | N.E. Since monsoons depend upon seasonal temperature contrasts between land and water, it is obvious that winds of this class must be most pronounced where such contrasts are greatest—that is, in temperate regions—and least developed where the temperature contrasts are smallest—that is, in equatorial and polar regions. It is even possible for secondary monsoons to develop, or for a monsoon to occur within a monsoon. This merely requires a favorably situated inland sea, such as the Caspian. In such cases monsoons or seasonal winds prevail between the inland sea and the surrounding land, and in turn between the continent as a whole and the adjacent oceans, just as, and for the same reason that on a still greater scale, there is a constant circulation between the perpetually warm equatorial regions and those about the poles that are continually cold. Another comparison between these several winds, the semi- daily (land and sea breeze), semi-annual (monsoon), and per- petual (interzonal), that is interesting and instructive concerns ATMOSPHERIC CIRCULATION 169 their depth. As already stated, the land and sea breezes seldom reach greater depths than 100 to 500 metres; the winter monsoon of India has a depth, roughly, of 2000 metres, and the summer monsoon 5000 metres; while the general or interzonal circulation involves the whole of the troposphere with a depth of 10 to 12 kilometres, and probably also, though perhaps to a less vigorous degree, even the stratosphere. If the term monsoon be extended, as it properly may, to include all winds whose prevailing directions and velocities FIG. 49. EN a LAND, SOUTHERN Ee HEMISPHERE 4 A = AS ANS AN Prevailing directions of monsoon winds, southern hemisphere. undergo distinct alterations as a result of seasonal changes in temperature, it clearly follows that this class of winds is well nigh universal. Nevertheless, it is generally thought of in con- nection with only those places where it is most strongly developed, and especially where the seasonal winds are more or less oppositely directed. Among these places are: India (Indian monsoons are the most pronounced of all and have been most fully studied), ‘China, the Caspian Sea, Australia, and portions of Africa. In the United States the chief monsoon effects are in the eastern portion, where the prevailing winds are northwest in winter and southwest in summer, and in Texas, where the pre- vailing winds are also northwest in winter, but southeast in summer: 170 PHYSICS: OF THE ALR TRADE WINDS. As previously stated, in equatorial ocean regions, or, roughly, over the oceans between latitudes 30° N. and 30° S., the winds usually have an east-to-west component. In the northern hemi- sphere they blow rather constantly from the northeast, becoming east-northeast and finally nearly east winds as the equator is approached. Similarly, in the southern hemisphere, starting from the southeast, they gradually back through east-southeast to nearly east. In each case they blow “ trade ”’; that is, ina fixed or nearly fixed direction. It is because of this steadiness of direc- tion and not because of any relation they may have to the paths of commerce that they are called trade winds. Along each border of this belt, or along both the northern and southern horse latitudes, calms are frequent, while such winds as do occur generally are light and variable in direction. Besides, the barometric pressure is high, humidity low, and sky clear. Hence it generally is inferred that throughout the horse latitudes the air is descending. This evidence, however, as applied to places other than the centres of maximum pressure is not quite conclusive—it only shows that the air is not ascending. Another narrow belt of calms or light variable winds, known as the region of the doldrums, approximately follows the equator (more exactly the thermal equator), where the two systems of trade winds, the northern and the southern, come together. Here, however, the barometric pressure is low, humidity high, and skies often filled with cumulus and other clouds that give conclusive proof of strong ascending currents. Trade winds in the sense here used—that is nearly constant winds blowing in a westerly direction—do not occur on land except along coasts and over islands. Besides being well-nigh peculiar to the oceans, they are even different from ocean to ocean, and also, since they tend to follow the thermal equator, somewhat different in latitude and intensity from season to season. According to Shaw the average velocities of the Atlantic trade winds are as follows: Trade-wind Velocities, Atlantic Ocean. Jan. Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. Year N.E.trade... 11.9 13.0 13.5 13.4 12.3 11.4 103 83 96 7.4 98 11.6 I0.5 aries S E. trade... 14.1 130 13.0 12.1 I1.0 12.1 12.1 15.0 17.0 I5.0 16.1 I5.0 13 o4 Gree From this it appears that the trades are strongest during the winter when their counterpart, the system of westerly winds of ATMOSPHERIC CIRCULATION I7I higher latitudes, is strongest; and weakest during the summer when their counterpart is weakest. It also appears that the south- east trades, or those pertaining to the southern hemisphere, are about one-third stronger than the northeast trades, due probably to the greater extent of the southern oceans and consequent less surface friction—the same reason, doubtless, that the westerly winds of the southern hemisphere are stronger, on the average, than the westerlies of the northern hemisphere. The trade winds of the Pacific Ocean are weaker than these of the Atlantic and not so constant in direction. On the Indian Ocean the trades are confined to the southern hemisphere. North of the equator the winds of this ocean, being controlled by the adjacent continent, are distinctly of the monsoon type. The seasonal shifting in latitude of the trade regions and belt of doldrums is shown by the following table, copied from Hann’s Lehrbuch, 3d edition, p. 463: Seasonal Latitude Limits of Trade Winds and Doldrums. March September Atlantic Pacific Atlantic Pacific N.E. trade.| 26°-3°N 25°-5°N. 25°-11°N. 30°-10°N.. Doldrums...} 3°N.-Equator 5°-3°N. 11° 3°N. 10° 7°N. e E. trade..| Equator-26°S.| 3°N.-28°S. 3°N.-25°S. 7°N.-20°S. ANTITRADE WINDS. As the heated and expanded air of equatorial regions overflows to higher latitudes it necessarily is deflected by the rotation of the earth. That portion which goes north changes from an east wind near the equator to a southeast, south, southwest, and, finally, at about latitude 35° N., a more nearly west wind. Similarly, that portion which goes south becomes northeast, north, north- west, and, finally, at about latitude 30° S. a more nearly west wind, At great altitudes, 10 to 15 kilometres, the east-to-west velocity near the equator is, roughly, 36 metres per second (80 miles per hour). Hence its west-to-east velocity around the axis of the earth is about 428 metres per second (957 miles per hour). As this air, assuming it to start from the equator and neglecting viscosity effects, moves to higher latitudes its west-to-east velocity 172 PHYSICS OF THE ALK must so increase, according to the law of the conservation of areas, that at about 16° N. or S. its angular velocity will be the same as that of the earth, and itself, therefore, be moving only poleward in the plane of the meridian. The exact latitude, however, at which the antitrades move directly poleward depends upon the position of the thermal equator and therefore varies with the seasons. Thus during August and September, when the centre of the doldrums is, roughly, 8° N., the inflection of the northern antitrades occurs somewhere between latitudes 20° N. and 25° N. At other seasons, because the doldrums are then nearer the equator, the place of inflection is also less removed. Beyond the turning point, wherever that may be, these upper or antitrade winds become westerly, and, except as modified by local dis- turbances, tend, as previously explained, to reach, under the in- fluence of the poleward pressure, a limiting or gradient velocity, and to follow parallels of latitude. However, there are innumer- able disturbances, mainly due to the distribution of land and water, that cause constant and abundant interzonal circulation which feeds and indefinitely maintains the antitrade wind portion of the general or planetary atmospheric circulation. The height of the antitrades (depth of the trades) is greatest, at any given place, during summer and least during winter. It also decreases with latitude, becoming zero, on the average, at about 30° N. and S. Thus during winter their height over Cuba, 22° N., is about 3.5 kilometres; over Hawaii, 19° 30’ N., about 3 kilometres; over Jamaica, 17° N., 6.5 kilometres; and over Trinidad, 12° N., 8 kilometres. But whatever their height it is always the same as the depth of the trades of which they are but the overhead continuation. Indeed, the trade winds as they ap- proach the equator ascend and gradually flow off poleward, thus producing in each hemisphere a great antitrade branch of the general circulation, which in turn becomes the westerlies of higher latitudes. These, in their turn, are confused by storms and other local disturbances, but after few or many vicissitudes, as cir- cumstances may determine, ultimately return to a similar starting- point, only to begin another of their endless cyclic journeys through trades, antitrades, westerlies, and the innumerable secondary winds such a course implies. ATMOSPHERIC CIRCULATION 173 TROPICAL CYCLONES. A tropical cyclone—the cyclone of the Indian Seas, the hurri- cane of the West Indies and South Pacific, and the typhoon of the West Pacific and China Sea—consists of a vast whirl of rapidly moving air currents surrounding a calm and relatively small centre or vortex. Distinction Between Tropical and Extra-tropical Cyclones.— Although tropical and extra-tropical cyclones have many simi- larities, such as low-pressure centres, abundant precipitation, same instantaneous wind directions, and the like, and although it may be impossible to say just when a tropical cyclone on its way to higher latitudes becomes extratropical in character, never- theless they usually differ from each other in several important respects. Among these differences are: (a) The isobars of the tropical cyclone generally are more symmetrical and more nearly circular than those of the extra-tropical. (b) The temperature distribution around the vortex of the tropical cyclone is practically the same in every direction, while about the extra-tropical it is very different. (c) In tropical cyclones rains are torrential and more or less equally distributed on all sides of the centre; in the extra-tropical rains usually are much lighter and very unequal in different quadrants. (d) Tropical cyclones usually have calm rainless centres 10 to 50 kilometres (6 to 31 miles) or more in diameter, while the extra-tropical rarely show this characteristic whirl phenomenon. (e) Tropical cyclones are most frequent during summer of the hemisphere in which they occur, while the extra-tropical are strongest and most numerous during winter. (f) Tropical cyclones often move to higher latitudes, where they assume, more or less completely, characteristics of the extra- tropical; the extra-tropical, on the other hand, never invade the region of the tropical nor assume its distinctive characteristics. (g) The pressure-drop of the tropical cyclone generally begins with the winds; in the extra-tropical it usually begins much sooner. (1) The tropical cyclone has no anticyclone companion; the extra-tropical usually has—to the west. Place of Occurrence.—Tropical cyclones occur over the warmer portions of all oceans except, possibly, the South Atlantic. They are most numerous, however, in the west Atlantic (includ- ing the Gulf of Mexico), Bay or Sea of Bengal, and west Pacific (including the China Sea), where their annual frequencies are, 174 PHYSICS OF THE AIR roughly, about 4, 8 and 24 respectively. They seldom originate closer than 5° or 6° to the equator but most frequently between latitudes 10° and 20.° In fact, they seem to originate almost entirely along the belt of doldrums, and therefore, since this belt follows the sun, to appear at higher latitudes during summer and lower, or not at all, during winter. Size and Shape of Storm.—The diameter of the tropical cy- clone varies greatly. Near their origin some storms may be no more than 80 kilometres (50 miles) across, while others, when well developed, may have diameters of 300 to 1500 kilometres (187 to 932 miles). The clouded area incident to typhoons, always much more extensive than the surface storm, may be even 3000 kilometres (1864 miles) across. The shape of the storm, as given by the isobars, appears usually to be that of an ellipse whose diameters are to each other, roughly, as 2 to 3, with the longer axis in the direction of travel. Direction of Ifind.—The direction of the surface wind is spirally in at an angle of 30 degrees, roughly, to the isobars, counter-clockwise in the northern hemisphere, clockwise in the southern. At an elevation of only 700 to 800 metres the inflow is said to cease, and above this level the circulation is outward. These horizontal motions necessitate a correspondingly strong upward component around the vortex or inner portion of the storm, and a slower downward component over a much greater surrounding area. Velocity of IV’ind.—The velocity of the wind in a tropical cyclone also varies greatly from one storm to another, and even more from one to another portion of the same storm. Near the centre, or within the eye of the storm, which may have any diameter from 8 to 50 kilometres (5 to 31 miles) or more, the wind is very light and the sky clear or only partially covered with high clouds. Away from this centre, especially on the poleward side, the winds often reach destructive velocities of 40 to 50 and even 60 metres per second (90 to 112 or even 134 miles per hour), but decrease in violence rather rapidly with increase of distance from the centre; dropping to only moderate winds of 50 to 60 kilometres (31 to 37 miles) per hour at a distance of, say, 300 kilometres (187 miles). Direction of Travel—Tropical cyclones of the northern hemisphere first move west, then usually northwest. Many turn ATMOSPHERIC CIRCULATION 175 north at latitude 20° to 25°, roughly, and finally move away to the northeast. In the southern hemisphere the corresponding directions of travel of the tropical cyclone are: West, southwest, south, and, finally, southeast. Velocity of Travel.—The velocity with which tropical cyclones travel varies from almost zero in certain cases, especially at or near the place of inflection when this happens to be abrupt, to perhaps 800 kilometres (497 miles) per day. Over the Bay of Bengal, Arabian Sea, and China Sea the velocity averages about 320 kilometres (199 miles) per day. O’ver the south Indian Ocean the velocity ranges from 80 to 320 kilometres (50 to 199 miles) per day. Over the west Atlantic the average velocity before and during recurvature is about 420 kilometres (260 miles) per day, but after recurvature—that is, when moving northeast over middle latitudes—about 640 kilometres (398 miles) per day. Origin and Maintenance.—Since tropical cyclones originate in a belt or region of doldrums where convectional rains are frequent and heavy, and since they rarely occur closer than 5° or 6° to the equator, it follows that both vertical convection and earth rotation are essential to their genesis. The atmosphere of a doldrum belt becomes very warm and humid, and therefore frequently is in a state of vertical convec- tion. The upward branches of this convection are nearly always limited to very restricted areas, where they break through, as it were, and often give rise to local thunderstorms. Occasionally, however, heating and expansion must take place more or less uniformly over a comparatively extended region. So long as the upward current is gentle and restricted to a small area, the com- pensating inflow from the sides is also gentle and can produce only a cumulus cloud and perhaps a thunderstorm. In the event that such a storm is formed, the inflowing counter-current to the ascending warm air is replaced by an equivalent column or sheet of descending cold air immediately to the rear. That is, the loss of warm surface air is compensated by a similarly concentrated and vigorous downflow of cold upper air. Hence, rotary circula- tion since it depends upon horizontal inflow from all, or at least several, sides, is not possible in the case of ordinary thunder- storms, whatever their location. On the other hand, an approximately equal expansion of air 176 PHYSICS OF THE AIR over a relatively large area, whether caused by an increase of temperature, or vapor density, or by both, must lead to an over- flow above and a corresponding surface inflow around the outer borders. Obviously the rate of volume overflow at any time is propor- tional to the area in question, while the corresponding inflow is proportional to the boundary multiplied by the average normal component of the wind. If the area is circular with radius R, it follows that the rate of outflow above is proportional to 7k?, and the rate of inflow below to 2*RVn, in which Vn is the average radially inward component of the wind at the distance k from the centre. But as the two currents compensate each other except as modified by precipitation, explained below, it follows that Vn, other things being equal, is proportional to R. Hence, when the area involved is rather large, 100 miles, say, in diameter, the relatively shallow and spirally moving compensating or return current may become very perceptible. This at once feeds the entire rising column with excessively humid air that renders it an even better absorber than before of both insolation and terres- trial radiation and increases its rate of expansion, thus initiating, perhaps, a widespread condensation. If so, the latent heat thus set free, while it does not actually raise the temperature of the air, reduces the rate of adiabatic cooling from approximately 1° C. to about 0.4° per 100 metres increase of elevation, and thereby establishes within the rising column temperatures distinctly higher than those of the surrounding air at the same level. In this way the circulation is accelerated, and thereby the rate of condensation and freeing of latent heat increased until, through growth of size, restricted supply of water vapor, and other causes, a limiting, somewhat steady, state is attained. When the conditions here described occur at some distance from the equator the rotation of the earth deflects the inflowing air and establishes a rotation around the region of lowest pressure —an effect all the more likely to occur (perhaps rarely else does occur ), when the existing convection takes place along the doldrum boundary between the rather oppositely directed (not opposing) trade winds, the one from higher latitudes, the other from across the equator. But whatever the radius of curvature, the angular momentum remains constant—the law of the conservation of areas obtains—except as modified by friction and viscosity, and there- ATMOSPHERIC CIRCULATION 77 fore, since surface-drag is effective at but small elevations, the atmosphere at only 100 to 200 metres above the water may, as it moves inward, soon reach that velocity at which its deflective force is equal to the horizontal pressure gradient. When such velocity is reached, as it obviously may be at any appreciable altitude, inflow at that place necessarily ceases. Near the water, however, this limiting velocity is prevented by surface friction. Hence, as soon as the whirl is well established, it must be fed almost exclusively by the lowest and therefore most humid air. In this way a maximum amount of precipitation, and, through it, a maximum amount of thermal energy, is secured—a condition important to the maintenance of the tropical cyclone, as is evident from the fact that it tends to go to pieces over dry land, especially before it has recurved and become essentially extra-tropical. Of course, similar atmospheric expansions may, and doubtless do, occur in the doldrums when they are on or very close to the equator, but in this case a whirl is impossible, and therefore a low so initiated will soon fill by gentle, somewhat radial, winds from all sides and at considerable altitudes, or, at most, mere local thunderstorms wil! develop. From the above it is evident that the seat, so to speak, of the tropical cyclone is where the sustaining energy is supplied; that is, where condensation is taking place. Hence the movement of the air at this level, and not at the surface, determines the course of the storm, and even carries it athwart shallow surface winds, CHAPTER X. ATMOSPHERIC CIRCULATION (continued). Winds Due to Widespread Heating and Cooling (continued). EXTRA-TROPICAL CYCLONES. General Remarks.—The strong winds and heavy precipita- tions of middle latitudes are associated with the occurrence of low barometric pressure, while gentle winds and clear skies as commonly are associated with the occurrence of high barometric pressure. Hence the cyclone, or that system of winds that accom- panies and surrounds any considerable region of minimum pres- sure, and the anticyclone, or that system of winds that belongs to and encircles a region of maximum pressure, deserve and have re- ceived a vast amount of observation and study. Nevertheless, in many respects—in their origin, in their temperature dis- tributions, and in the laws of their movements—cyclones and anticyclones still remain in great measure the meteorological mysteries they have always been. Although the cyclones and anticyclones of extra-tropical regions are as closely associated and as fully the complements of. each other as are hills and hollows, it nevertheless will be convenient to consider them independently. It will also be con- venient first to summarize the facts of observations, and then to string these facts together on the thread of a provisional theory. Size-——The area covered by an extra-tropical cyclone, the largest of all distinctive storms, nearly always amounts to millions of square kilometres. In North America the average diameter of these storms is estimated to be, roughly, 2500 kilometres (1553 miles), which probably is not greatly different from their average diameter on other continents. Over the North Atlantic their diameters are still larger, while the greatest of all in size is the semipermanent or winter Aleutian “low,” which appears usually to be much larger than the travelling cyclones of the Atlantic or even the great semipermanent Icelandic “ low.” Direction of Movement of the Cyclonic Centre-—The direc- tion the centre of a cyclone travels, wherever it may be located, is substantially the same as that of the higher clouds or of the atmosphere at 4 to 10 kilometres above sea level. In general, 178 ATMOSPHERIC CIRCULATION 179 therefore, the cyclones of middle latitudes travel from west to east, with (in the northern hemisphere) a southerly dip over con- tinents and a northerly deflection over oceans. Cyclones, for instance, that develop between latitudes 30° and 45°, in the western United States, usually turn northeast before reaching the Mississippi River. -Farther west they may move east, or even somewhat southeast. Locus of Maximum Cyclonic Frequency, or Chief Paths of Cyclonic Storms.—Probably no part of the earth’s surface more than 3 or 4 degrees from the equator is wholly free from cy- clonic storms, but the frequency of their occurrence varies greatly with respect to both time and place. Beginning with the West Pacific: During summer and fall many cyclonic storms come from the general region of the Philippines and move northeast across or on either side of Japan. Winter and spring’ cyclones enter on this same general course at latitudes 30 degrees to 40 degrees; some, presumably, being of oceanic origin, while others obviously either develop within or cross over China. In any case, the gen- eral track of these storms is along the Japanese and Kurile Islands, and thence east over the Bering Sea. The main path is then southeast across the Gulf of Alaska, with the storms, includ- ing off-shoots from the Aleutian “low,” crossing onto the con- tinent anywhere between latitudes 40 degrees and 60 degrees, but apparently most frequently in the general neighborhood of Van- couver Island. These Pacific storms usually cross the continent nearly from west to east, dipping slightly south over the Great Lakes, and finally leave it by way of Newfoundland. A smaller number of storms from the North Pacific dip far south, some- what like the Mediterranean branch mentioned below, to about latitudes 35 degrees to 4o degrees, but usually recurve west of the Mississippi and join the main course as they reach the Atlantic. Those that originate in or cross over the central and southern portions of the United States, as also those that come from the Gulf of Mexico, move northeast and gradually merge their paths with that of the Pacific storms anywhere from the Great Lakes to the Newfoundland Banks. Other cyclones coming up from the Florida and West Indies regions follow the coast, not far off shore, and also. merge their paths with that of the others in the neighborhood of Newfoundland. Half-way or more across the Atlantic the path of maximum 180 POYSICS OF THE AIR storm frequency breaks up into at least three distinct routes. The main route turns far north, usually by way of the Nor- wegian Sea, then southeast, entering Russia in the neighbor- hood of the White Sea, and passing on toward Central Asia. A second route turns southeast and crosses Europe generally along the northern side of the Mediterranean, and then turns north either across Austria toward northwest Russia or by way of the Black Sea toward Central Asia. A third and least frequented route, commonly running just south of Ireland, appears to cross both the North and the Baltic Sea, and then, like the others, to move on toward Siberia and central Asia. The cyclonic storms of central and northern Asia do not appear to be very numerous. Nevertheless, their track of maximum frequency seems to turn south, as does the similar track over North America, as far as Lake Baikal, thence probably to the Sea of Okhotsk and across or to the south of Kamchatka to the main storm path north of the Aleutians, as already explained. In the southern hemisphere the path of maximum storm fre- quency appears closely to follow the 60-degree parallel of latitude. Presumably it dips poleward at both the Ross and the Weddell Sea, as each of these is a region of semipermanent low pressure. It must be remembered, in this connection, however, that in both the southern hemisphere and the northern, cyclonic storms occur almost everywhere, and therefore that the routes above de- scribed are only paths of maximum cyclonic frequency and not of exclusive travel. Velocity of Travel—The velocity with which the centre of a cyclonic storm moves along its path varies greatly. It depends upon the season, being fastest in winter and slowest in summer; upon location, being faster in America than in Europe, for in- stance; and, finally, upon the individual storm. The following table gives average velocities of cyclonic centres for different parts of the northern hemisphere. Those pertaining to the United States were computed from a table of average 24-hour movements as determined by Bowie and Weightman *% from 16,239 observations, covering the years 1892-1912, inclu- sive. The others are from Hann’s “ Lehrbuch der Meteorologie,”’ 3d edition, p. 518. % Monthly Weather Review, Supplement No. 1, p. 8, 1914. ATMOSPHERIC CIRCULATION 181 Average Velocity of Cyclones in Metres per Second. (For the United States the velocity is also given in miles per hour.) | United States Japan Russia ao. a ¢ |Bering Sea. Winter......| (29.9) 13.4 12.4 10.8 8.2 8.0 8.5 Spring...... (23.7) 10.6 ILI 9.2 8.3 72 8.5 Summer.....| (20.7) 9.3 7.8 8.0 7.4 6.6 10.3 Ball sic sce (24.5) 11.0 10.6 9.6 8.3 8.2 9.3 Year........] (24.7) 11.1 10.5 9.4 8.05 7.5 g.1 Frequency.—The frequency of the occurrence of cyclonic storms varies not only from place to place, as already explained, but also at any given place, or even over an extensive area— probably an entire hemisphere—according to season. Tropical cyclones, it will be recalled, are far more frequent during summer and early fall than during winter. Mid-latitude cyclones, on the other hand, have exactly the opposite relation of frequency to season, being, in general, most numerous in winter and least numerous in summer. Exceptions to this rule apply to the paths of tropical cyclones next after the recurvature, provided we regard such storms as having then become extra-tropical. Perhaps ex- ceptions also apply to certain regions on the poleward sides of the main cyclonic routes, since these are farthest north in summer and farthest south in winter. This, however, is not certain. A statistical investigation might show that even the greatest increase due to latitude shift is more than compensated by the general seasonal decrease in frequency. When all storms are counted that appear in the United States or Southern Canada, whether short or long lived, weak or intense, it appears *® that the frequency of summer (June, July, and August) “lows” is to that of winter (December, January, and February) “ lows” approximately as 5 to 8. On the other hand, if only long-lived cyclones are considered, it appears °° that in the United States the frequencies of summer to winter storms are about as only 2 to 9, and those of Europe as 3 to Io, In either case, then—that is, whether only the longer lived and more intense “ lows’’ are counted, or whether all, of whatever magnitude and duration, are included—it seems that cyclonic “Bowie and Weightman, Monthly Weather Review, Supplement No. 1, p. 7, 1914. "U.S. Weather Bureau Bulletin A, p. 6. 1803. 13 182 PHYSICS OF THE AIR storms are most frequent during winter and least frequent during summer. Further, the extra-tropical storms of winter are not only more numerous than those of summer, but also, in general, longer lived, more intense, and faster moving. Direction of Winds.—From the directions of winds in and about a region of low barometric pressure, as given on synoptic charts, Fig. 99, for instance, it is often, perhaps usually, inferred that cyclonic winds circulate spirally inward and upward and then outward and upward, counter-clockwise in the northern hemis- phere, clockwise in the southern, around a storm axis. This indeed is, in general, the course of the winds in tropical cyclones, especially in those that are violent and of small diameter, as the eye of the storm and directions of cloud movements clearly indicate, but it does not apply to extra-tropical cyclones, except, perhaps, to the occasional ones of great violence and small diameter. Extra-tropi- cal cyclones rarely have clear centres, as they would if the circula- tion about them was closed or along spiral paths of repeated turns. Neither, in general, is a closed circulation indicated by the move- ments of the clouds. Again, it often happens that the velocity of the forward moving wind of a cyclone is less than that of the storm itself, so that instead of flowing around the storm centre it necessarily is left behind. Synoptic weather charts, therefore, show instantaneous wind directions, but not wind-paths. This is because the storm con- dition itself is moving forward—moving, indeed, with a velocity nearly always comparable to, and at times even faster than, that of the lower winds themselves. The main body of the storm winds, those below an elevation of 5 or 6 kilometres, except everywhere near the surface, and also generally about the poleward side above 2 to 3 kilometres eleva- tion, blow, in the cyclonic sense, roughly parallel to the surface isobars. This does not mean that the path of any given particle of air is around and around the centre of low pressure, because, as above explained, this centre itself and its system of isobars are both in rapid transit. Near the surface the velocity is so slowed down that the deflection forces no Jonger balance the horizontal pressure, and therefore the winds of this level are directed inward at a considerable angle across the isobars. Through the pole- ward half of the storm area the horizontal temperature gradient is nearly always opposite in general direction to the ‘horizontal ATMOSPHERIC CIRCULATION 183 pressure gradient at the surface. Therefore, with increase of elevation in this section the pressure gradient usually weakens from the start and later reverses at the height of only a few kilometres—often less than one kilometre; while the winds first increase (where the surface drag rapidly decreases) to a maximum, then decrease, and later more or less reverse in direction. Deflection Angle.—The angle between the surface wind direc- tion at any place within a cyclonic storm and the normal to the corresponding isobar, the “ deflection” angle (Fig. 50), is great- est, or the surface winds most nearly parallel to the isobars, a, when the winds are swiftest and thus develop the strongest de- flective forces—therefore greatest to the south and east of the storm centre and least to the north and west, b, when the velocity Fic. 50. Deflection angle. of the storm as a whole is least, c, in the summer time, because during this season the storm movement is less than during other seasons, d, over water where it is roughly 80 degrees, because the surface drag is less here than over land where the “ deflection” angle averages only 40 degrees to 50 degrees. It is important to note also that usually the deflection angle does not greatly change with distance from the centre. This fol- lows from the fact that the horizontal pressure, the wind velocity, and the consequent surface friction and percentage loss of gradient velocity all are roughly constant in any given direction from the centre, so long as only points distinctly within the storm area are considered. With increase of elevation and consequent decrease of surface drag the deflection angle over land gets larger by 25 or 30 degrees in the first kilometre. Beyond this elevation it still gains, but relatively very slowly. At an elevation of several kilometres the velocity of the air is decidedly greater than that of the storm, 184 PHYSICS OF THE AIR and therefore air that may have risen to this level is carried forward. Hence the main outflow of the extra-tropical cyclone is toward the east. Wind Velocity—As just stated, the pressure gradient and wind velocity are roughly constant along any given radius from the storm centre. This is because at middle and higher latitudes the deflective force is essentially geostrophic (due to the rotation of the earth) and to only a small extent cyclostrophic (due to Cyclonic Wind Velocity in Metres per Second and (Miles per Hour). Altitude Surface} 500 1000 1500 2000 2500 3000 3500 4000 122m. m. m. ™. m. m. m. m. m. 6.16) 14.75, 15.09] 15.32} 15.79} 16.85] 18.28; 19.25] 20.30 = : a | Watters (13.8) |(33-0) |(33-8) (34-2) |(35-3) 1(37-7) |(40.9) | (43-1) |(45-4) * ) Gummer 5-42] 9.64] 10.69] 11.31] 12.22] 12.91] 14.08| 15.69) 17.21 2 (12.1) |(21.6) |(23.9) |(25.3) |(27-3) |(28-9) |(31-5) |(35-1) |(38.5) S| Vear 5-84) 12.24] 12.93 | 13.38] 14.07] 14.94] 16.24) 17.53] 18.81 3 (13.1) |(27.4) |(29.0) }(30.0) |(31-4) (33-4) |(36.3) 1(39.2) |(42.1) € : 6.70| 13.47] 13.39] 13-93] 14.75] 16.18] 17.31 | 17.31 £ Winter (15.0) (30.1) 1(30.0) |(31.2) }(33-0) |(36.2) |(38.7) (38.7) | .... a nnee 5.66 9.45 | 9.89} 9.91} 10.17] 10.65] 11.40) 12.07| 12.62 a (12.7) |(21.2) |(22.1) |(22.1) |(22.7) |(23.8) |(25.5) (27.0) |(28.2) 3 Vsse 6.06 | 11.34) 11.52! 11.80] 12.34] 13.29] 14.23) 14.56] .... E (13-5) |(25.4) |(25-7) |(26.4) |(27-6) |(29.8) |(31.9) (32.6) € : 4.72) 8.85) 8.95) 9.00] 9.09] 9.07] 9.32] 8.52) 8.02 5 Winter (10.5) |(19.8) |(20.0) |(20.1) |(20.4) |(20.3) |(20.8) |(19.0) |(17.9) Se) Garnier 4.84| 7.85] 8.37) 8.45] 8.81] 9.11] 10.26! 10.63] 10.63 a (10.8) cre) or oo? (19.7) ee Ce (23.8) |(23.8) 4-79 “3 : 72 94| 9.08) 9.7 9-57] 9-32 Bi eae (10.7) (18.7) |(19.4) |(19.5) |(20.0) |(20.3) |(21.9) |(21.4) |(20.8) = sit 4.50, 10.45] 10.02) 10.43] 10.58) 11.64| 12.11! 13.37] 14.59 ay Sate (10.1) (23.4) |(22.4) |(23-4) |(23-7) |(26.0) |(27-1) |(29.9) |(32.7) a Geer 4.11) 8.22] 8.64] 8.77] 8.98] 9.50} 9.50! 9.81) 11.86 5 (9.2) |(18.4) |(19.4) (1918) Pon) OLg) (21.3) (21.9) |(26.5) aly 4.34| 9.37] 9-37] 9.64] 9.82] 10.61] 10.84] 11.62] 13.25 Bee (9.7) |(20.9) | (20.9) |(21.6) |(21.9) |(23.7) |(24.3) |(26.0) |(29.7) circular motion). The winds, however, often are different in different portions of the storm area, and commonly strongest in its southern and eastern quadrants, where the isobars are most crowded and the direction of the winds roughly that of the storm movement. The actual average velocity of the wind in the different quad- rants of a cyclone and at different elevations is given in the pre- ATMOSPHERIC CIRCULATION 185 ceding table by Peppler,®! based on a large number of measure- ments made during 1903-1908, at Lindenburg; latitude 52° 10’ N.; longitude, 14° 15’ E. Probably other mid-latitude regions have approximately the same average cyclonic wind velocities. This, however, is not certain, nor are there available sufficient data for determining the question. Convection.—The vertical movements of the air, whether up or down, in an extra-tropical cyclone, or between such a cyclone and a neighboring anticyclone, are not known with much detail and accuracy. However, since the cyclone moves eastward with the air currents directed inward across the isobars, it is obvious that ordinarily the chief air convergence, due in part to increase of latitude, and hence the principal vertical convection, must be on the front or east side. Temperature also usually helps to locate the chief upflow in this quadrant, since its winds necessarily are from lower latitudes, and, therefore, relatively warm. This localization of the uprising air explains why, other things being equal, most of the precipitation due to cyclonic storms occurs to the east and southeast (northeast in the southern hemisphere) of their centres. Other things, however, are not always equal. Thus an ex- tensive plain rising gradually to great elevations may slope. in such direction that the mechanical or forced convection over it on any side of a cyclonic centre may approach, or even exceed, the thermal convection to the east. The Great Plains east of the Rocky Mountains illustrate this point. Here precipitation in the case of “stagnant” or slow-moving lows usually is most pro- nounced to the north of the centre where the winds are persistently up the slope. This is an extreme case, but it suffices to show that a rule relating to shifting winds and clear or foul weather that applies well in one place may not apply at all in another. Simi- larly, on the Pacific coast of North America, for instance, where the ocean is to the immediate west, the heaviest rains are to the south and west of the cyclonic centre. Velocity of Travel and Amount of Precipitation.—lIt is well known that the velocity of travel of an extra-tropical cyclone and the amount of precipitation accompanying it are to each other, roughly, in inverse ratio. This is simply because the slower the storm travels, the longer the winds blow into it at any " Beitrige sur Physik der freien Atmosphare, 4, p. 95, 1911. 186 PHYSICS OF THE ATK given place and, therefore, other things being equal, the greater the duration and the amount of the precipitation at that place. In extreme cases very fast moving cyclones may give but little or even no precipitation at all. Classification.—Cyclones occur in extra-tropical regions with so great frequency that several such storms are nearly always present in each hemisphere. Naturally they have been much studied and therefore variously classified, especially according: to duration, as semipermanent and migratory; to season of occur- rence, as summer and winter; to zone of origin, as tropical and extra-tropical; and to the place from which first reported as, for instance (referring to only those within or near the United States), Alberta, North Pacific, South Pacific, Northern Rocky Mountain, Colorado, Texas, East Gulf, South Atlantic, and Central. All these classifications are useful, but not adapted to the present purpose, which is to group the cyclones, as far as prac- ticable, according to their more important causes. Perhaps this end will be fairly well served by dividing them into thermal (identical with semipermanent), imsolational, and mechanical. Thermal (Due to Relatively IV arm Water).—The name semi- permanent cyclone—for which the alternate name, thermal cy- clone, is here proposed for reasons that will appear below—or semipermanent “ low,” has been given to that system of winds of any region over which the. barometric pressure habitually or seasonally averages lower than for the surrounding regions. The term generally is used as though it applied to but one and the same cyclone, however it might wander or even for a time wholly dis- appear. Thus, one always says the Icelandic “low,” not an Icelandic “low.” Similarly, the Aleutian “ low,” not an Aleutian “low.” But, as stated, this applies only to average conditions. In reality there is no one permanent Icelandic “ low,” for instance, that retains its identity wherever it may be, but only a series of sluggish or temporarily fixed lows, all of which originate over, or, on invading, become intensified over, practically the same restricted region. There are several semipermanent cyclones in various parts of the world. The most nearly continuously active of these, at least in the northern hemisphere, and at all seasons apparently productive of many migrating cyclones, lies southeast of Green- @ ATMOSPHERIC CIRCULATION 187 land and southwest of Iceland. Another such region, active during winters only and known as the Aleutian * low,” lies along and to the south and southeast of the Aleutians, extending into and including the Gulf of Alaska. The Norwegian Sea and, possibly, the Sea of Okhotsk are other such high-latitude regions. The Gulf of Lyons is a low-pressure haunt during winter, as is also the Black Sea, and the Caspian Sea, as its monsoon winds definitely show. The Gulf of Mexico, over which occasional winter cyclones appear to generate, may likewise be added to the above list. In the southern hemisphere the regions of most persistent lows are the Ross Sea and its counterpart, the Weddell Sea, on the other side of the continent. All the above regions have surfaces warmer than those that at least partially surround them. The circulation induced by such temperature distribution is converted into a system of cy- clonic winds by the deflective force due to the earth’s rotation. The warm waters off the coast of Greenland and Iceland, for in- stance, necessarily maintain the atmosphere above at higher tem- peratures, level for level, than that of the neighboring ice-caps. Hence a practically continuous overflow of air from the one place, with compensating drainage and inflow from the other, is enforced by the existing and perpetually maintained distribution of unequal surface temperatures. These temperature contrasts are most pro- nounced, and the resulting Icelandic ‘‘ low” most intense, during winter; but it prevails through summer also, for the simple reason that the necessary temperature gradients, though weakened dur- ing this season, are neither obliterated nor reversed—the water remains always warm in comparison with the ice-caps of both Greenland and Iceland, which persist from season to season and from year to year. The Aleutian “low,” on the other hand, is merely seasonal: it prevails only while the adjacent Alaskan and Siberian regions are snow-covered and relatively cold. When this snow is gone the temperature gradients are even reversed, and the off-shore drainage of winter is replaced by the on-shore winds of summer. Similar considerations and explanations obviously apply to all the other regions frequented by semipermanent cyclones. Insolational (Of Land Origin).—Since gulfs and seas flanked by relatively cold land areas induce, as explained, more or less 188 PHYSICS OF THE AIR permanent cyclones, it follows that peninsulas flanked by rela- tively cold water should also be generators of cyclonic wind systems. Similarly, any area of sufficient size that becomes heated through insolation to temperatures above those of the adjacent regions should likewise induce or tend to induce a circu- lation of the cyclonic type. The Spanish peninsula shows, during summer, the phenomenon in question. It also occurs over the Alaskan peninsula onto which summer winds blow from the Gulf of Alaska, from Bering Sea and from the Arctic Ocean, obviously producing, through rotational deflection, a distinct cyclonic cir- culation. Similarly, the Great Plains often show daylight or inso- lational lows from which occasional cyclonic storms appear to originate. Also many start over northwestern Australia. Of course, entire continents show low average pressure during summer and high during winter, while in each case the opposite condition applies to the oceans. Such conditions, however, are not especially productive of storms, because the areas involved are hyper-cyclonic in size—so large, in fact, that they only modify the general or planetary circulation without producing local dis- turbances within it. Neither do temperature contrasts between areas that are very small in comparison with that of the average cyclone produce extensive precipitation, but mere local disturb- ances quickly smoothed out by the general circulation, or, at most, only thunder showers. In short, for the development of cyclones by temperature contrasts the warm area must be neither too large nor too small, neither continental in extent nor in size a mere island or bay. Mechanical.—The mechanical “low” is divisible into two classes: (1) Permanent—in reality not a cyclone at all in the ordinary sense of a low centre with encircling isobars—and (2) migratory—the characteristic cyclone of middle latitudes. In the first class, certainly, and presumably in the second also, the low pressure is rather the result than the cause of the associated winds. Indeed, in the case of any steady wind, except those near the surface or close to the equator, its sustaining force (force in its direction) is small in comparison with the deflective force at right angles to its path due to the rotation of the earth. Mechanical (Permanent).—There are two well-developed, permanent lows of this type (mechanical) and also an imperfectly developed third. These are (a) The equatorial low, which ” ATMOSPHERIC CIRCULATION 189 roughly follows the equator through its entire course, due partly to the relatively high temperature of this belt (to that extent an insolational “ low”) and partly to the right and left deflective forces of the westward winds of the northern and southern hemispheres, respectively. (0b) The Aniarctic trough, encircling Antarctica generally between 60 degrees and 70 degrees S. and having an annual average pressure of about 740 mm., mechan- ically sustained jointly by the northward pressure of the swift west winds over the oceans and the southward pressure of the east to west component of the vigorous southeast air drainage or fallwinds of Antarctica. (c) The Arctic trough, irregular in outline and intensity and apparently only fragmentary. Mechanical (Migratory).—The great majority of extra- tropical cyclonic storms are migratory, and apparently originate either by breaking off from or in some manner being induced by the semipermanent and insolation lows, or, occasionally, by somehow forming at almost any other place, especially along the more frequented storm paths. The genesis, development, and detailed structure of these storms are by no means well under- stood, and therefore the following tentative hypothesis in respect to their origin and maintenance is offered chiefly as a convenient mnemonic by which the principal known facts concerning them may be remembered. Tentative Hypothesis of the Origin and Maintenance of M1- gratory Cyclones.—It will be recalled that the prevailing wind movement of middle latitudes is from west to east, and that to a first crude approximation (more nearly attained in the southern hemisphere than in the northern) parallels of latitude are fol- lowed with such velocity that the poleward pressure gradient is ‘ just balanced by the rotational deflection. Obviously, however, numerous surface inequalities, irregularities of temperature dis- tribution, cloudiness, precipitation, and the like, prevent this gradi- ent from being constant along any parallel of latitude or even remaining constant at any given place. Hence the prevailing winds themselves, being primarily under the control of this gradi- ent, correspondingly vary in direction and velocity. Also, be- cause of surface friction, there is much air leakage across the dynamical partition of swiftest winds (usuallv along parallels of 40 to 60 degrees) to higher latitudes, and, of course, an equiva- lent return flow. 190 PHYSICS OF THE AIR Now let a disturbance, due to whatever cause, deflect a con- siderable and rather deep section of the eastward flowing air toward the adjacent pole. Immediately it flows eastward faster than before, in accordance with the law of the conservation of areas, and thus crowds upon the air in front, unless it in turn has sufficient velocity to keep out of the way, a condition that probably does not usually obtain. Because this air comes from lower latitudes and therefore commonly is relatively warm and its ab- solute humidity often great, and also because it is flowing to regions where the meridians are crowded closer together, it necessarily rises, and in so doing usually yields abundant pre- cipitation, whose latent heat materially aids to perpetuate the storm—continuously to develop a “ low ”’ in the forward quadrant. Simultaneously as this broad body of air sweeps to higher latitudes an equivalent amount, necessarily to the westward, moves in the opposite direction. Indeed, this return branch may have contained the initial impulse; the results would be the same. Here, also, the law of the conservation of areas applies. The return current necessarily lags and in some measure checks the eastward flow of the air to the rear. In this manner the atmosphere between the two components of the horizontal circulation, the forward speeding up, the rearward lagging, is mechanically more or less expanded (stretched), while that on both sides is com- pressed. The lower air, especially in front of the storm centre, being retarded by friction and turbulence, flows spirally inward, then upward and out, largely in response to the decrease of pres- sure due to the increased eastward velocity of the upper winds. The “low” thus, or however, formed, constitutes a travelling break in the partition between the mid-latitude and high-latitude circulations. In front of the “low ” the primary circulation finds its way to colder regions, while to its rear return currents simul- taneously bring equivalent amounts of other air to warmer sec- tions. At any rate, whatever the origin of extratropical cyclones; it is obvious that much of the interzonal circulation between middle and high latitudes, perhaps by far the greater part of it, occurs simultaneously on their opposite sides. Between the tropi- cal and extra-tropical regions the chief intercirculation is through the trades and counter-trades—to lower latitudes by the former, mainly, and to higher chiefly by the latter. Since the area covered by a cyclone or anticyclone is very great, ATMOSPHERIC CIRCULATION IQI averaging, roughly 2x 107 square kilometres, it would seem, as abundantly supported by cloud movements, that each must directly involve at least the whole depth of the troposphere. On the other hand, the stratosphere, from its different temperature, hu- midity, and wind velocity, appears to be relatively passive, suffer- ing rather than causing either cyclonic or anticyclonic effects. According to this conception, the troposphere within a cy- clonic area is mechanically expanded and, besides, has a marked upward component. It therefore must be cooled, though in the east quadrant, where the wind is from lower latitudes, the warm- ing on that account may equal or even exceed the expansional cooling. Similarly, in an anticyclone the troposphere is mechan- ically compressed and also has a downward component, thus producing a temperature increase, except, possibly, on the east or forward side, where this’ effect may be equalled or exceeded by the transfer of colder air from higher latitudes. Hence, because of opposite directions of convection, upward (cooling) in the cyclone, downward (heating) in the anticyclone; contrary changes in pressure, decrease (cooling) in the cyclonic area, increase (heating) in the anticyclonic; and, presumably, inequality of radiating power due to differences of moisture content—the de- scending (warming) air of the anticyclone being relatively dry and thus heat preserving—one might expect to find, as observa- tions (referred to later) show, that the troposphere is compara- tively cold in cyclones and warm in anticyclones, except, perhaps, near the surface, where convection is less operative. If, as seems likely, cyclonic and anticyclonic winds involve the troposphere through its whole depth, it follows from Egnell’s law, pv=a constant, with change of elevation, that the pressure gradient is also a constant, and, finally, that the pressure differ- ence between a high and its neighboring low may be of the same order of magnitude at all levels up to the top of the troposphere. Further, if the stratosphere is essentially inert in respect to the genesis and progress of surface storms, it clearly must sink to lower levels over cyclonic areas and be raised to higher over anticyclonic, and thereby itself undergo pressure and temperature changes,®*? and also briefly (during the formative stage) manifest cyclonic and anticyclonic wind systems. Let a stratospheric column be dropped: bodily a distance dh, " Shaw, “ Perturbations of the Stratosphere,” M. O. 202, p. 47, 1909. 192 PHYSICS OF THE AIR and let the surrounding air come in until equilibrium is again established. At each level there obviously will result a change in pressure directly proportional to the pressure at that level. That is, throughout the column 7 = K, a constant. But, as is well known, = gy dp — = ee in which T is the absolute temperature, and C a constant, 0.2843 for dry air. Hence, since T is constant, roughly, in the strato- sphere, dT is also constant, and the upper air remains vertically isothermal, whatever the pressure increase or decrease. An in- crease of pressure in the stratosphere, such as presumably takes place over cyclones, increases its temperature, while a decrease of pressure, such as probably occurs over anticyclones, correspond- ingly decreases its temperature. In each case the pressure effect presumably is slightly enhanced by the coincident change in the intensity of radiation from below. Suppose the temperature of the stratosphere over a cyclone should differ from that at the same place over the following anticyclone by 10° C., what, according to the above conception, will be the approximate change of boundary level? Let h be this change, and let the temperature of the stratosphere be 220°, absolute: Then since dp _ dh =>) p 4 in which H is the height of the homogeneous atmosphere, about 6450 metres at the assumed temperature, it follows that 10 h a 0.2843 FH roughly, and h =1 kilometre, approximately, That is, the temperature of the stratosphere will increase or de- crease at the rate of approximately 10° C. per kilometre enforced fall or rise, respectively, under the influence of cyclonic and anti- cyclonic disturbances. While migratory cyclones of this nature, mechanical or counter-current, may originate almost anywhere outside the tropics, it is evident that some places are far more favorable to their genesis than others. Among such favorable places it is ATMOSPHERIC CIRCULATION 193 probable that the Gulf of Alaska is one of the most pronounced, at least during winter, since here the relatively warm water gradually creates a “low” that deflects in a northerly direction the air currents in the south and southeast, and to a southerly direction the air currents in the north and northwest. Hence a low formed over this gulf, or farther west along the Aleutian Islands, is likely to become accentuated on its eastern side through the advent of warm air and the onset of heavy precipitation, and therefore be carried away from its moorings, as it were, and set adrift along the great air currents, where, as already stated, it acts as a travelling centre of vigorous interzonal circulation be- tween middle and high latitudes. Of course, the very process that forces the cyclone away from its place of origin brings in colder air, usually from higher latitudes. But this, in turn, is slowly warmed from the great supply of heat in the water below, and thus all those conditions essential to the breaking off of another storm similar to the previous one are reéstablished, and so on in- definitely, or until the season and consequent temperature distribu- tions so change as to prevent such action. According to this conception, the permanent “low ” around which interzonal circulation tends to be active often produces that local disturbance or deflection of the general circulation necessary _ to the genesis of a mechanical or dynamical cyclone. Further, although the necessary mathematical demonstrations may not be obvious, it appears in a general way that such a cyclone would travel a course and tend to exhibit characteristics as follows: a. The storm would travel with the general circulation. This is fully supported by observations. b. .It would tend, in general, to follow the path of maximum winds, this being the course approached by the west-to-east circulation, and therefore to travel along (not down, but at right angles to) the maximum interzonal temperature and pressure slope. This inference is also supported by observations. ‘c. Its average annual course would follow annual isotherms. This, too, is in accord with observations. d. Because the winds to the east and southeast (north- east in the southern hemisphere) of the front gen- 194 PHYSICS OF THE AIR erally are relatively warm and humid, and because they are focused in direction, thus leading to con- gestion that forces the rear winds to climb over those in front, it follows that, except as modified by topography and proximity to oceans, these would be the quadrants of maximum precipita- tion, as indeed they commonly are, except along west coasts. e. The rising and, therefore, rain-producing air should flow off eastward with the general circulation. The cirrus and other high level clouds that forerun the cyclone amply support this inference. f. The mechanical cyclone should usually be accom- panied by a correlative anticyclone to its rear. There is much observational evidence in support also of this conclusion. g. The average latitude of cyclones should be greater than that of anticyclones, since the main mass of air of the one has a component toward, and of the other from, the adjacent pole. A statistical test of this conclusion is not at hand, but it seems - to accord with inspection. h. Since, as here conceived, the storm involves the gen- eral circulation from the surface to its top—that is, all the air up to the stratosphere—it seems possible that the pressure contrasts between “ low ”’ and ad- jacent ‘‘ high” may also extend to this level. Even this inference is supported by much observational evidence.*? , i. Since, according to the conception here offered, the atmosphere of the particular type of cyclone under discussion is mechanically rather than thermally expanded, and since the swift winds of the front would tend to draw upward and out such air as leaks into the “ low,” it seems that the atmosphere of a cyclonic region might be warm in the east quadrant, but cold in the centre and the other quadrants. 8 Dines, Jr. Scot. Meteorol, Soc., 16, p, 304, 1914. ATMOSPHERIC CIRCULATION 195 j. Since, according to this conception, the winds to the west of a cyclone are from higher latitudes, it fol- lows that they must spread out, coming where meridians are more separated, with the upper por- tions flowing to lower levels, and also, because flowing toward the equator, must lag behind and thus by a damming up process build, through over- flowing currents, a “ high ” in which the tempera- ture of the bulk of the atmosphere, because of its downward component, shall be relatively warm. k. The expansion of the lower air (below the strato- sphere) in the “low” and compression in the “high ” leads to lowering and warming the strato- sphere over the cyclone, and raising and cooling it over the anticyclone. The difference in intensity of radiation by the moist and dry air of the two regions probably accentuates these conditions. Furthermore, since the northerly winds of the anticyclone act as a partial barrier to the wester- lies of the general circulation, the latter must be deflected to unwonted altitudes, thereby cooling at top to a minimum temperature, more or less below that appropriate to the flux of terrestrial and other radiation. That is, a minimum tem- perature should occur at the base of the strato- sphere over the anticyclone, as shown in F[igs. 17 and 18. All the several inferences under 7, 7, and k (doubtful, because unsupported by analysis) are fully in accord with observations, whatever the physical cause or causes may be. This is shown by Figs. 17 and 18, which give, respectively, the vertical tem- perature gradients for winter and summer in regions of high (5 mm. and more above normal), neutral and low (5 mm. and more below normal) pressure, as determined by sounding balloons from Lindenberg, Munich, Strassburg, Trappes, Uccle, and Zurich. The figures of the legend give the number of flights from which the curves were determined. Abundant additional evidence of these formerly unsuspected temperature . relations 196 PHYSICS OF THE AIR between the cyclone and anticyclone is given by Wagner,** Gold,*® Dines,** and others. They must therefore be accepted as definitely established for the British Isles and Continental Europe, and tentatively accepted (until disproved if not true) for other parts of the world. Probably the above conceptions of the mechanism of the average extra-tropical cyclone could be elaborately developed from the standpoint of hydrodynamics and thermodynamics, but this would be too tedious to include here. The concept, however, even without such support, may be useful in helping to remember the chief facts learned by recent free air observations, “ Tropical.’’—As previously stated, a considerable percentage of the tropical cyclones (the actual number probably is only 2 to 3 per year in the northern hemisphere) migrate to extra-tropical regions. Shortly after recurving they gradually lose their original characteristics and become extra-tropical in type as well as loca- tion. Nevertheless, they generally still are called “ tropical cy- clones” (West India hurricanes, typhoons, etc.), however high the latitude actually reached. A causal name is not suggested for this cyclone, for the reason that it is not certain what is the chief factor in its origin. As already explained, these storms originate usually, if not always, in the doldrums, where the air is quiet, hot, and exces- sively humid. The stillness of the air, if long continued, leads to a high degree of humidity, and the humidity, in turn, decreases the local pressure and also increases the absorptive power of the atmosphere for both solar and terrestrial radiation. Hence an inwardly directed pressure gradient and a corresponding circu- lation, the latter increased when flanked by oppositely directed trade winds, are slowly established. The resulting precipitation, through the latent heat thus set free, if sufficiently abundant and properly distributed, accentuates the circulation and thus secures the perpetuation of the cyclone until it fails for want of moisture, as it often does on dry land, or spreads and loses itself in the world circulation. As it recurves and gets well away from the tropics, it generally spreads out, becomes less intense, has most of its pre- “ Beitrage sur Physik der freien Atmosphare, 3, 57, 1909. =“Tnternational Kite and Balloon Ascents,” 1913. (Geographical Me- moirs, No. 5.) Tr. Scot. Meteorol. Soc., 16, p. 304, 1914. ATMOSPHERIC CIRCULATION 197 cipitation on the east side, and otherwise gradually acquires the characteristics of a cyclone of extra-tropical origin, and, presum- ably, is maintained in the same way. The physical cause of these storms, if they originate, as seems probable, in the doldrums and between counter trades or similar winds, appears to be partly thermal and partly mechanical, and their subsequent maintenance, after reaching the middle and higher latitudes, the same (largely mechanical) as that of any other cyclone of the same place. ANTICYCLONES, ” Anticyclones, or “ highs,” are divisible, with respect to their genesis, into three classes: (1) Mechanical: a, permanent, and b, migratory. (2) Radiational: a, permanent; and 0, transitory. (3) Thermal. In this classification the relative ‘“ high”’ that obtains over an entire hemisphere during its winter, and also those seasonal highs of continental (during winter) and oceanic (during summer) ex- tent, have all been excluded. Like the lows of similar great size, they only modify somewhat the course of the general circulation and give direction to monsoon winds. . Mechanical (Permanent ).—Since the surface of the ocean is a gravitational equipotential surface, it follows that west winds, by virtue of their excess centrifugal force, will tend to climb up the bulge of the earth toward the equator, and east winds, because of deficiency in centrifugal force, will tend to slide down this bulge toward the nearest pole. Hence along the borders, between trade winds and the west winds of adjacent higher latitudes, the atmo- sphere must be subject to a mechanical squeeze. In other words, mechanically produced high pressure belts must encircle the earth at about latitudes 30’ to 35° N. and S. They must also be best developed over the oceans, where the trade winds, upon which they largely depend, are strongest and steadiest. These belts are clearly shown in Fig. 51. Nevertheless, they often do encroach to some extent onto land areas. Indeed, it seems probable that the high- pressure, droughty weather that occasionally prevails over the southern United States, and even much of the Mississippi valley, frequently is due, in part at least, to such an encroachment, inci- dent to the poleward summer shift of the northern high- pressure belt. Mechanical (Migratory).—The migratory anticyclone re- ferred to here, and assumed to be generated in the manner ex- 14 198 PHYSICS OF THE AIR plained in the discussion of mechanical cyclones, is the common one of middle latitudes. The directions of its system of winds, but in no sense the complete paths of the air particles, are given by synoptic charts, such as Figs. 100 and 101. These directions are spirally outward, clockwise in the northern hemisphere, counter- clockwise in the southern. Hence the relation of anticyclonic wind velocity to horizontal pressure gradient is given by the equation, oe = v(2 wsinge——): dn r in which r is the radius of curvature, nearly, of the wind-path at the place considered, and the other symbols have the usual sig- nificance as previously given. From the negative sign it appears that for a given radius of curvature the possible wind velocity ina “high ” is strictly limited, whatever the pressure gradient. Velocity and Path of Travel_—The velocity and normal path of the migrating anticyclone are by no means as well known as those of the cyclone, except, perhaps, through the studies of Bowie and Weightman °7 in respect to those that cross the United States. However, the size, frequency, and velocity of travel of anticy- clones are all roughly the same as those of similarly located cyclones. Furthermore, their most frequented paths, though, perhaps, generally beginning at higher latitudes over continents and running to lower over the oceans than the similar cyclonic routes, are roughly parallel thereto. | Just why these close relations hold is not certain. It may be interesting, however, to note that they appear to support the above assumption that generally the migrating cyclone and its neighbor- ing westerly anticyclone are correlative parts of a single great atmospheric disturbance. Wind Velocity.—The actual velocity of the wind in the differ- ent quadrants of an anticyclone and at different elevations is given in the following table by Peppler,®*® based on a large number of observations made during 1903-1909, at Lindenburg: latitude, 52° 10’ N.; longitude, 14° 15’ E. Probably other mid-latitude regions have approximately the same anticyclonic wind velocities, but this is not certain, nor are there at hand sufficient data to determine the question. Radiational (Permanent).—There are two extensive regions, 7M. W. R. Supplement, No. 4, 1917. _ 8 Beitrage zur Physik der freien Atmosphare, 4., p. 95, I9II. ATMOSPHERIC CIRCULATION 199 Antarctica and Greenland, where the barometric pressure always is high. At each place the high pressure appears to be the result of the very low prevailing temperatures, which in turn-are due in part to the great elevations and in part to the free and abundant radiation from the snow surface through the comparatively clear skies, kept generally free from clouds by the descent of the upper air induced and maintained by the vigorous fallwinds. That sur- Anticyclonic Wind Velocity in Metres per Second and (Miles per Hour). Ailitnda: “Szeses Ape | nope | 808 | vaya. ages | ayes: sym | ages € : 4.43, 8.48, 8.82| 8.68] 8.60 8.92| 9.71, 10.14) 10.97 | ee | 9) (19.0) (19-7) |(19-4) |(19.2) (19.9) |(21.7) |(22.7) (24-5) § » 3-92 19 6.25 3 7) 5.97 “19; 7.08) 7.83 se - (8.7) (13-9) |(14.0) |(14.2) |(13.8) |(13.3) |(13-9) |(15.9) |(17.5) 3 | Year , 416 7.32| 7-52) 7-51) 7.38) 7.-44| 7.94; 8.60) 9.39 3 e 3) (16.4) |(16.8) (16.8) |(16.5) |(16.7) |(17.8) |(19.2) |(21.0) € | winter 3-93, 7-60] 7.19) 7.35 7-23| 7-21| 7.57) 7-75) 8.41 5 (8.8) |(17.0) |(16.1) | (16.4)| (16.2)! (16.1)} (16.9)| (17.3) (17.9) S| Suramer 3-39) 5.26) 5.41] 5.18; 5.28 5.39] 5.20! 4.74) 5.04 a (7.6) | (11. 8) (12.1) (11.6) |(11.8) |(12.1) |(11.6) |(10.6) |(11.3) 9 Vat 3.74 6.51| 6.38] 6.35 6.34! 6.38} 6.46; 6.32] 6.65 E (8.4) i -5) |(14.3) |(14.2) |(14-2) |(14.3) |(14.4) (14:1) |(14.9) © : 4.21 9.69) 9.54| 9.78! 10.19| 10.69] 11.59] 12.29! 14.43 g | Winker (9.4) (21.7) |(21.4) |(21.9) |(22.8) |(23.9) |(25.9) |(27.5) |(32-3) s ‘Simime 4-05) 7-01! 7.68| 8.41| 8.85) 9.51] 10.04] 10.68] 11.45 x (9.0) |(15.7) |(17.2) |(18.8) |(19.8) (21.3) |(22.5) |(23.9) |(25.6) £1) Year 4.13! 8.35) 8.61] 9.09) 9.51) 10.09; 10.80| 11.47] 12.92 z (9.3) (18.7) (19.2) |(20.4) |(21.3) |(22.6) |(24.2) |(25.6) |(28.9) @/ Winter 4.29| 8.24} 8.83} 9.56| 10.92) 12.44] 13.52] 14.02] 15.68 & (9.6) ne ie) ee: (24. 4) (27.8) |(30.2) (1.3) (35.1) 3 3.92) 5. .42 55 98} 7.54] 7.31] 7.83] 8.2 a ee (8:7) |(13.2) (14-3) |(14.8) |(15-6) (16.9) |(16.3) |(17-5) |(18.5) 4 Vear 4.06| 7.01} 7.57| 8.00] 8.89) 9.93] 10.35] 10.86] II.91 a (9.1) }(15.7) |(16.9) |(17.9) |(19.9) |(22.2) |(23.2) |(24.3) |(26.6) face radiation is an essential factor in establishing and maintaining these low temperatures is obvious from the fact that air cannot flow down hill, as it does in these regions, unless it has a greater density and therefore lower temperature than the adjacent atmo- sphere of the same level. It is also obvious from the prevailing and excessive surface temperature inversions, in which, and be- cause of which, those ice fogs that doubtless furnish much of the interior precipitation are so common. It will be well to remember in this connection that snow, in addition to reflecting about 70 per cent. of the incident solar radia- 200 PHYSICS OF THE AIR tion,°** is also a good emitter of those long wave-length (12-15+) radiations appropriate to its temperature. In this way the low temperatures are maintained, not only during winter when air circulation and, to some extent, cooling ice supply the only available heat, but also during the long-continued insolation of summer. The air drainage thus produced is manifest in those strong and persistent southeast or anticyclonic winds that characterize the climates of the border and all explored portions of Antarctica, except, of course, near the pole, and, presumably, therefore, of the whole continent. Similar, though less vigorous, anticyclonic winds also prevail over and around Greenland. Each of these great regions but ‘especially Antarctica, by virtue of its strong and continuous refrigeration, obviously is exceedingly effective in its influence on the atmospheric circulation of its respective hemi- sphere. If there were no such extensive high and snow-covered areas in the polar regions, it is clear that our general circulation would be less vigorous and doubtless very different in many places. Radiational (Transitory).—During winter elevated snow- covered regions often become very cold and thus build “ highs ” similar to those of Greenland and Antarctica, though usually much smaller in extent, as well as only temporary. Occasionally these give rise to strong and cold surface winds, especially when the existing gradient is accentuated by the passage of a well- developed cyclone along lower latitudes. Examples of such winds are the mistral of the Rhone Valley and the bora of the Adriatic and Black Seas. The Texas norther and, probably, the blizzard of the Great Plains are other and important examples of the drainage of transitory radiational anticyclones. The well-known violent fallwind of the coast of Norway appears to have a similar origin, as indeed have innumerable other drainage winds in all mountainous and high plateau regions outside the tropics. Thermal (Senupermanent).—As is well known, there are five semipermanent “highs,” all of which occur on the oceans: Two, as Fig. 51 shows, about 35 degrees north of the equator and three about 32 degrees south of it. Two are on the Pacific Ocean—one west of southern California, the other off the coast of Chile: two on the Atlantic Ocean—near the Azores (known as %a Abbot and Aldrich, Proc. Na. Acad. Sci., 2, 335, 1916. ATMOSPHERIC CIRCULATION 201 the Azores “ high’’) and off the coast of southern Africa; and one on the Indian Ocean, about half-way between Africa and Australia. A sixth oceanic “ high” of this same class, but far less persistent than any of the above, often develops, especially during winter, in the region of the Bermudas. Obviously there must be a close relation between the inten- sities and locations of these highs and the directions and velocities of the surrounding winds, even to great distances, as shown by Figs. 52 and 53. Hence it is meteorologically iniportant to form some conception in regard to their origin. It will be seen from Fig. 51 that all these “ highs ” or centres of maximum pressure occur along the high-pressure belts, and from Fig. 54 that they occur at those places along these belts where the temperature of the air is low for that latitude; that is, where the isotherms are deflected equatorward. At these places, then, there are two causes of high pressure: (a) the mechanical pressure that produces the high-pressure belts, as already explained, and (b) -a relatively low surface temperature which allows the upper air to cool somewhat and correspondingly contract. It is known from sounding balloon records that the tempera- ture of the atmosphere even to great altitudes follows more or less closely any long-continued temperature changes of the sur- face. Hence one might reasonably expect the atmosphere over the cold regions, as shown by Fig. 54, to be colder at every level than that of the surrounding atmosphere over warmer regions. A change of 1° C. throughout would change the pressure by 2 mm. or more. Hence, since the regions in question, according to Buchan’s charts, are from 1° C. to 3° C. colder than those of the same latitude east or west, it appears that the pressure maxima of 2 mm. to 6 mm. probably are due to the continuous relatively low surface temperatures. In this case the “ high” appears to be due to the cooling of the superincumbent atmosphere to that tem- perature at which its radiation is in substantial equilibrium with the minimum radiation from below. But what is the cause of the local low surface temperatures ? Referring to Fig. 55, it will be seen that there are five different places, and only five, where a distinctly cold ocean current crosses a belt of high pressure, and that every one of these is associated with a region of maximum pressure. Neither is there a semi- permanent “ high ” anywhere else on the oceans. Wherever then. (Cueyong sozyy) “sreqost edeioae [enuuy OSt SET OFT OT Ost St OZT SOT 9st OST S9T O8t a9t O9T 06 SL 09 sh Of ST 0 at of 99 O98 SL 06 sot O2T 06 ch 098 Sb Of aT 0 st o€ Sh O09 SL 06 SOT OZT SET O9T S9T O8t S9T OST 1S ‘OY Fic. 52. 40 60 80 100 120 86 140 120 «6140 ~=—s:160 100 ) Oat LoAHy hilt gtt = 7 Zt : g g ‘| iz 2 ii = b2l a 23a = o x é £2 MY Ve. 74 , [ene PWV Z |, if p29 RU AA re No at iy IOS an f * tT 8 f Soe i << =e $a \ SL Z Sin “4 s Debs ” Lie , tas * SSIS Agen In, tien © ANSILQANS Zyl ER ppp . 4 60 80 100 120 140 160 7 Yah J — i € 4 + aE ‘) bso = a ~ > =~ SS 160 140 120 \\ N ENN s Lf oe Sy ~\ Wil /t : rite FAN Sil 3 3 & g 100 (Képpen.) Ocean winds, January and February. 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REREES. ost 09 OF (2am Ley peel Sa eae NN ee Ae | ___—+-—— | 4 A 0 SLE ee Te Y rs LA ae a : +t 3 2 le |} La a . 4 cbs qd —* oS Sh ee Bay al (tae LNEAT LL A/ Rey ciel lel anni 4 —= soar eee ss SOOM 1 4 2a i Ae SN ea ie =\ " al a soe ES SaaS de EE DD pl = L b<_| el P~ pe Se LL MSE Se Ee SS Cease : -—— San 4 : a ae AST See Ug ae GL BRR — . 4 ares ae fae See Lo ALES EE es OST S6t OZT SOT 06 09 SF of ST O st o8 09 $L 06 SOT OZt set ost ‘bS ‘Old Io REE REEP REE BE 5 > d SWE a Fr eae 3 os So 3 wo a o w °o ww o © o x ° “4 *sjueJInd =uead Ost SST OFT SOT 06 GL O08 GS OF S&T 0 st oc &F 09 GL 06 SOT OST SET OST SOT O8f S9T ONT i Ost SET OZT SOT 06 SL O09 Sh OF S&T 0 st Of8 9&F 09 SL O6 SOT OT SET OST SOT O8T S9T OST SS ‘oIg “SIBQOSt advioae [enuUe puUe ‘sUIJayyOSI ade1 QAR [eB nuue ‘sjuelins uesd Oo ‘ Ost Set O2T SOT 06 GL O98 Sb of ST 0 St Of Sb O89 GL 06 SOT O@T SET OST S9T O8T SST OST- 09 }— Sp 09 Ee SL 09 —_nJ = Se a a eed J EH ——— | or cee al SS as ee ee Np SS Sed FE 2 TS eas ; Sele aie 1 Re es a % ree ae o tere ey Ls ST OST SET OZT SOT O06 SL o9 6Sh)6OE~—OST 0 st 0& 9% O98 SL O06 SOT OT SET OST SOT OST Sot ost “9S “DIY 208 PHYSICS OF THE AIR the mechanical effect that produces a belt of high pressure is rein- forced by thermal contraction due to cold water, there, and only there, as illustrated by Fig. 56, are found a maximum of atmo- spheric pressure and the centre of a semipermanent anticyclone. During winter there is also a slight minimum temperature along the North Atlantic high-pressure belt near Bermuda, and a similar one along the South Pacific belt just east of New Zealand, and at each place a corresponding tendency to the maintenance of an anticyclone, One obvious effect of all these semipermanent highs is the location of branches or channels of interzonal circulation, anal- ogous to those of the cyclones and anticyclones of higher latitudes. Thus, much tropical atmosphere, in addition to that carried by the counter-trades, reaches middle latitudes by flowing around and to the west of the semipermanent “highs.” From here the next stage in the general circulation takes the air to still higher lati- tudes, and even to polar regions, around and to the east either of the semipermanent “lows” or of the migratory cyclones. In its return it passes to the west of the ‘“‘ lows” or east of the travelling “highs,” and finally around and to the east of the semi-permanent “highs.” These, however, are only general channels and, pre- sumably, average routes, upon which are superimposed innumer- able and ever-changing irregularities. FORCED WINDS. Although in greater or less measure all winds are interde- pendent, only a relatively small number obviously are generated and maintained by other and coexisting winds. Among these are eddy winds, Maloja winds, foehn or chinook winds, and, pre- sumably, the winds of the tornado and waterspout. Eddies.—Wherever the wind blows across a steep-sided hill or mountain, eddies are likely to be formed, especially on the lee side. In such cases the direction of the surface wind is approximately opposite to that of the general or prevailing wind, with a calm between them. For the practical purpose of the weather forecaster, wind eddies have but little significance, except in one important par- ticular. He must exclude from his forecasting data all reports of wind direction obtained at places where eddies are likely to prevail. Such eddies, however, may be of great importance to the ATMOSPHERIC CIRCULATION 209 aviator, since they produce, on their forward sides, troublesome down-currents and also shallow surface winds which, because oppositely directed to the winds, less, perhaps, than 100 metres above, may render landing at such places difficult or even very dangerous. Maloja Wind.—The “ Maloja”’ wind, named after the Maloja pass in Switzerland, below which, and for some distance along the valley of the Inn, it is well defined, is only a reverse valley breeze —treverse because such convectional tendency as the insolational heating of the valley in question may produce is more than coun- teracted by the similar heating of a suitable, and suitably situated, neighboring region. It is the controlling pressure distribution due to this latter heating that locates the up-draft and induces the down-valley Maloja wind. Similarly, the flooding of a basin by gravity winds often produces a forced breeze up a narrow pass, where ordinarily a down-current would be expected. Foehn, Chinook.—The foehn, or chinook, as it generally is called in North America, is a warm, dry wind blowing down a mountain side onto the valleys and plains beyond. It differs from the typical fallwind in being warm, level for level, and not cold, as is the latter, in comparison with the air of surrounding regions. Any system of winds, whether of trade, cyclonic, or other origin, extending to or near to the surface and blowing more or less normally across a mountain ridge, necessarily induces up- currents, dynamically cooled, on the windward side and down- currents, adiabatically heated, on the lee side, except along the under portions of such eddies as may be produced, where the directions and consequent temperature changes are just the re- verse. Therefore: 1. Foehns occur at all seasons. 2. The relative humidity of the foehn is always low. 3. The rise in temperature is greatest when the original ver- tical temperature gradient is least; hence greatest, other things being equal, a, when the upper air is warmest—that is, when there has been precipitation to the windward ; b, when the surface air is coldest—that is, when there has been free night radiation (clear skies) on the lee side; and c, during winter, when the vertical temperature gradient through the first several hundred metres may 210 PHYSICS OF THE AIR be. only 4° C., say, per kilometre, instead of the usual 7” to 8° C. of summer. The inertia of the wind crossing the mountain tends to carry it on well above the valley, or plain, beyond, but its drag on the lower air, due to viscosity, deflects it downward. Because of this deflection a foehn wind often strikes on the lower slopes, or adjacent region, with great violence, from which, and mainly because of its dynamical heating, it rebounds to higher levels. Along a belt, therefore, well down the mountain, or even a little beyond it, the surface wind may be exceedingly turbulent and violent, while both farther away and also nearer, or on the higher slopes, it is comparatively light. Furthermore, owing to changes in the general direction of the crossing current, or in its strength, or both, the wind belt may shift toward or from, or up or down, the mountain, or even vanish entirely. During its earlier stages a foehn is often accompanied by a crest cloud, by dissolving scud drawn down out of this cloud, and by a cumulus roll over the rebounding wind; and, a little later, by general precipitation. Another interesting phenomenon of the foehn is the trans- mission of sounds from the windward to the leeward side of a mountain, and often miles away, where ordinarily they are not heard at all. The explanation is obvious. The wind, which blows roughly parallel to the slopes, increases rapidly with dis- tance from the surface; hence the sound wave, because it is car- ried forward in the faster layers more speedily than in the slower, crosses the crest in an approximately vertical position, and then roughly converges, or focuses onto places some distance to the leeward. Since winds of this origin often are swift, and their dynamical heating pronounced, it follows that under favorable circum- stances a very strong foehn may even develop a secondary “ low ”’ —on the same side of the mountain, of course, as the centre of the primary one. TORNADO. The tornado,” in which the air travels in approximate circles, as its name implies, is well nigh peculiar to the United States east © For detailed discussion see: Finley, “Tornadoes,” New York, 1887, and Ferrel “A Popular Treatise of the Winds,” New York, 1880. ATMOSPHERIC CIRCULATION 211 of the Rocky Mountains. Nor is it at all equally distributed over even this area, since it occurs rarely in the Alleghenies, seldom along the Gulf and Atlantic coasts, frequently in central and northern Alabama, Georgia, and South Carolina, frequently also in Ohio, Indiana, Illinois, and southern Michigan, and most fre- quently in Missouri, Kansas, and Iowa. The tornado develops only in connection with a thunderstorm, usually just in front of the rain, and especially in connection with those particular storms that form along a valley “ low,” or between V-shaped isobars where opposing winds of widely different tem- peratures give rise to that exceptionally strong vertical convection essential to the genesis and growth of the thunderstorm. The season of most frequent occurrence, therefore, is spring and early summer ; in fact, during winter it is unknown, except occasionally near the Gulf and in other warm sections. Similarly, the time of most frequent occurrence is 3 to 5 p.m. Also, since it is only a local phenomenon, while the conditions favorable to its genesis are much more extensive, it often happens that a number of tornadoes develop, even close together, in connection with a single distorted cyclone. The diameter of the tornado averages only about 300 metres (984 feet) ; the length of its path varies roughly from 100 metres to possibly 500 kilometres (228 feet to 310 miles) ; its direction of travel is nearly always northeast: its rate of travel. though dif- fering greatly, averages ronghly 11 metres per second (25 miles per hour), thus passing a given place in half a minute or less; while its winds, always counter-clockwise, are the swiftest known, estimated at 45 to 225 metres per second (100 to 500 miles per hour). It is therefore bv far the smallest, briefest. and severest of all storms. Essentially it is a phenomenon of the middle atmosphere. In its genesis clouds whirl around each other with great velocity and turmoil, while from beneath their centre a funnel-shaped cloud develops, usually tapering off to a long pend- ent spout that may or may not extend to the earth. Wherever it does reach the surface it produces a deafening roar, and prac- tically everything in its immediate narrow path that can be blown down or tofn to’ pieces is desfroyed, though generally but little damage is done on éither sidé. On the other hand, wherever it does not conie to the surfacé its passage produces but little or no effect. eS a 212 PHYSICS OF THE AIR Cause.—From the characteristics of the tornado and from the meteorological conditions that normally accompany it, it appears that its origin must be purely mechanical. Thus its rotation ob- viously is derived essentially from that of the cyclone in which it occurs, since it is always in the same sense, counter-clockwise, however small its diameter, and never clockwise, as is often the case with large dust-whirls when formed in still air. But how is the rapid rotation started? From the directions of the V-shaped isobars it is clear that at the cloud level, say, there must be, as often observed, neighboring winds flowing in approximately opposite directions and, of course, more or less intermingling and over- running counter currents. Hence, under such conditions, the in- flow occurring at various levels that feeds the strong up-draft always just in front of a thunderstorm must occasionally so deflect these counter currents, by drawing both into the same rising column, as necessarily to produce a violent whirl. Here, too, as in all other cases of atmospheric motion, the law of the conservation of areas, or the constancy of the product of radius of curvature by linear velocity, applies, except as modi- fied by friction and viscosity. Hence, as the radii of curvature of the opposing currents may at first be comparatively large, and after the deflection relatively small, it follows that the wind velocity within the whirl, in which both the counter currents are taking part, may be very great. This rotation, however, does not check the up-current, hence that convection which is essential, as explained above, to the rotation is maintained, and therefore the rising currents brought in spirally with increasing angular and linear velocity as the axis of spin is approached. Each filament, so to speak, of the spirally rising air viscously drags along its under and slower neighbors, thereby bringing them nearer the axis and increasing their velocity. In this manner the whole of the rising column is set whirling with greater or less spin. Around the axis of rotation the pressure obviously is reduced in proportion to the centrifugal force, the temperature correspondingly lowered, and therefore a cloud spout often formed. Wherever the inflow of the surface air is greatly checked, or its course so altered by a deflecting hill or other obstacle as greatly to decrease the spin, there the tornado must lift. It may, however, retain its full vigor in the unaffected upper air, and soon reach the surface again. ATMOSPHERIC CIRCULATION 213 Why Essentially Pecutiar to the United States.—Since the tornado rarely occurs in violent form except in that portion of the Unied States which is east of the Rocky Mountains, it follows that that combination of meteorological conditions essential to its genesis seldom obtains in other parts of the world. This com- bination appears to be very simple—only a vigorous convec- tion between strong neighboring counter currents. But since vertical convection, as indicated by thunderstorms, is common enough in most parts of the world, it follows that the other factor —namely, strong counmer currents—is the distinctly American phenomenon. That such currents should often occur east of the Rocky Mountains is obvious from the position and trend of these mountains themselves, giving rise to southward winds; and the location of the Gulf of Mexico, from which winds turn north- ward, No other similar combination of mountain and ocean wind controls exists. and therefore no other place has in all respects the same kinds, frequencies, and intensities of storms. Waterspouts.—Only its well-established name requires that the waterspout shall be specifically mentioned, since mechanically it does not differ essentially from the tornado. In fact, a tornado becomes a waterspout as soon as it passes to sea, while a water- spout becomes a tornado immediately it invades the land. The waterspout, like the tornado, originates well up in the atmosphere, and is especially frequent in those regions where adjacent winds, usually the one above the other, have different directions: hence, where the counter trades, overrunning the trades, occur at ordinary cloud or convection levels; along the belt of doldrums, when considerably removed from the equator and flanked by opposing trade winds; and along boundaries of sharp temperature contrasts, such as the northern border of the Gulf Stream. In all such regions vertical convection may induce a more or less violent whirl in the same manner as that explained in the discussion of the tornado. Occasionally small whirlwinds start from the surface of lakes or other bodies of water during calm hot weather. The strongest of these produce cloud columns, due to expansion, and are often called “ waterspouts,” though of radically different origin from that of the waterspout above described. 15 CuHapter XI. WINDS ADVERSE TO AVIATION. SEVERAL local winds to which but little attention formerly was given, so little indeed that some of them are without special names, are now important through the art of aviation. These are here grouped together, however different in origin and type they may be, for the convenience of any one who may have occasion to consider them. General Statement.—Every aviator experiences in the course of his flights many abrupt drops and numerous more or less severe jolts. The cause of the first—the sudden drops—he has grouped together and called “ holes in the air,” while to the latter he has given such names as “bumps,” “‘dunts,” etc. There are, of course, no holes, in the ordinary sense of the term, in the atmos- phere—no vacuous regions—but at various places in the atmos- phere there are, occasionally, conditions which, so far as flying is concerned, are very like unto holes. Neither is the air ever “full of bumps,” in the sense of spots of abnormal density, but it often 1s turbulent in such manner as to render flying rough and uncomfortable. Both sets of atmospheric movements, those that produce appreciable drops and those that cause jolts, are indeed real; and the former, because of their general interest and prac- tical importance, will be considered in some detail. The latter, being of little importance, will only be mentioned incidentally. Furthermore, there are no “ pockets of noxious gas.” No single gas, and no other likely mixture of gases, has at ordinary tempera- tures and pressures the same density as atmospheric air. There- fore, a pocket of foreign gas in the atmosphere would almost certainly either bob up like a balloon, or sink like a stone in water. It is possible, of course, as will be explained a little later, to run into columns of rising air that may contain objectionable gases and odors, but these columns are quite different from anything likely to be suggested by the expression “ pocket of gas.” The above are some of the things that, fortunately, do not exist. The following, however, are some that do exist, and that produce sudden drops; usually small, so as to give only a negli- gible bump, but occasionally great enough to involve, when 214 WINDS ADVERSE TO AVIATION 215 near the surface, an element of danger. For clearness and sim- plicity these several kinds of air movements will be provisionally classified under terms suggested by water analogies. Air Fountains —A mass of air rises or falls according as its density is less or greater, respectively, than that of the surround- ing atmosphere, just as, and for the same reasan that, a cork bobs up in water and a stone goes down. Hence, any body of air is driven up whenever it is warmer and therefore lighter (less dense) than the surrounding air at the same level; and as the atmosphere is heated mainly through contact with the surface of the earth, which in turn has been heated by sunshine, it follows that these convection currents or vertical uprushes are most numerous during calm summer afternoons. The turbulence of some of these rising masses is evident from the numerous rolls and billows of the large cumulus clouds they produce, within, and immediately beneath, which, the air is always rough, however smooth it may be either above or con- siderably below; and it is obvious that the same sort of turbulence, probably on a smaller scale, occurs near the tops of such columns also as do not rise to the cloud level. Further, when the air is ex- ceptionally quiet, a rising column may be rather sharply separated from the surrounding quiescent atmosphere, as has often been reported by aviators, and as evidenced by the closely-adhering tall pillars of smoke occasionally seen to rise from chimneys. The velocity of ascent of such fountains of air whether con- tinuous, as in the dust whirl, or only intermittent, is at times surprisingly great. Measurements on pilot balloons, and also measurements taken in manned balloons, have shown vertical velocities, both up and down, of more than 3 metres per second (600 feet per minute). The soaring of large birds is a further proof of an upward velocity of the same order of magnitude, while the formation, in cumulus clouds, of hailstones of various sizes shows that uprushes of 10 to 12 metres per second (2000 to 2400 feet per minute), and occasionally much greater, not merely may, but actually do, occur. There are, then, “air fountains” of considerable velocity whose sides at times and places are almost as sharply separated from the surrounding atmosphere as are the sides of a fountain of water, and it is altogether possible for the swiftest of these to 216 PHYSICS OF THE AIR produce effects on an aeroplane more or less disconcerting to the pilot. The trouble may occur: 1. On grazing the column, with one wing of the machine in the rising and the other in the non-rising air; a condition that interferes with lateral stability, and produces a sudden shock both on entering the column and on leaving it. 2. On plunging squarely into the column; thus suddenly in- creasing the angle of attack, the pressure on the wings, and the angle of ascent. 3. On abruptly emerging from the column; thereby causing a sudden decrease in the angle of attack and also abruptly losing the supporting force of the rising mass of air. 4. Asa result of rotation, if rapid, as it sometimes is, of the rising air. That flying with one wing in the column and the other out must interfere with lateral stability and possibly cause a drop is obvious, but the effects of plunging squarely into or out of the column require a little further consideration, as does also the effect of rotation. Let an aeroplane that is flying horizontally pass from quies- cent air squarely into a rising column. The front of the machine may be lifted, as it enters the column, a little faster than the rear. If so, and, in any case, owing to the upward trend of the air, the angle of attack—that is, the angle which the plane of the wing, or plane of the wing chords, makes with the apparent wind direction—will be slightly increased. This will carry the machine to higher levels, which, of itself, is not important. If, however, the angle of attack is so changed by the pilot as to keep the machine while in the rising column at a constant level, and if, with this new adjustment, the rising column is abruptly left, a corresponding descent must begin. But even this is not necessarily harmful. Probably the real danger under such cir- cumstances arises from ovcradjustments by the novice in his hasty attempt to correct for the abrupt changes, instead of letting his ship mainly ride out the inequalities. If the rising column is in fairly rapid rotation (tornadoes are excluded—they can be seen and must be avoided), as sometimes is the case, disturbances may be produced in several ways. If the column is entered on its approaching side, the head-on wind may so decrease the velocity of the plane with reference to the WINDS ADVERSE TO AVIATION 217 surrounding air that on emerging there necessarily must be a greater or less drop, as explained below under the caption “ wind layers.” On the other hand, if entered on the receding side there will be a tendency to drop within the column, which may or may not be fully compensated for by the vertical component of the wind. Finally, such a rotating column, especially, perhaps, if crossed near its outer boundary, may quickly change the orien- tation of the plane, and therefore the action on it of the sur- rounding air, None of these conditions, however, except when encountered near the surface of the earth, is likely to involve any appreciable element of danger to the skilled aviator. But this does not justify ignoring them—no beginner is skillful, and all must start from and return to the surface. Rising columns of the nature just described occur most fre- quently during clear summer days and over barren ground. They also occur, even to surprising altitudes, over roads, sandspits, and other places of similar contrast to the surrounding areas. Iso- lated hills, especially short or conical ones, should be avoided on low flights during warm, still days, for on such occasions their sides are certain to be warmer than the adjacent atmosphere at the same level, and hence act like so many chimneys in produc- ing updrafts. Rising air columns occur less frequently and are less vigorous over water and over level green vegetation than elsewhere. They are also less frequent during the early forenoon than in the hotter portion of the day, and are practically absent before sunrise and at such times as the sky is wholly covered with clouds. Although, as just explained, rising currents are certain to be more or less turbulent and ‘“‘ bumpy,” they, nevertheless, are great aids to climbing. Hence, the experienced aviator often deliberately gets into them, as do soaring birds, when making a quick ascent. Air Sinks.—The air sink obviously is the counterpart of the air fountain and is most likely to occur at the same time. Indeed, it is certain to occur over a small pond, lake, or clump of trees in the midst of a hot and rather barren region. These cooler spots localize the return or down-branches of the convection currents, and generally should be avoided by the aviator when flying at low levels. Similarly, on calm, clear summer days, down-cur- 218 PHYSICS OF THE AIR rents nearly always obtain at short distances off shore, over rivers, and along the edges of forests. This type of down-current, how- ever, rarely is swift, except in connection with thunderstorms, and, therefore, while it may render flying difficult, or even impos- sible with a slow machite, it seldom involves much danger. Air Cataracts——The air cataract is caused by the flow of a dense or, what comes to the same thing, a heavily-laden surface layer of air up to and then over a precipice, much as a waterfall is formed. Such cataracts are most frequent among the barren mountains of high latitudes. The cold surface winds catch up, and become weighted with, great quantities of dry snow, and then, because of both this extra weight and their high density, often rush down the lee sides of steep mountains with the roar and the force of a hurricane. But the violence of such winds clearly is all on the jee side and of shallow depth. Hence, where such conditions prevail, the aviator should keep well above the drifting snow or other aerial ballast, and, if possible, strictly avoid any attempt to land within the cataract itself. Cloud Currents—It frequently happens that a stratum of broken or detached clouds, especially of the cumulus type, is a region of turbulent currents, however quiet the air at both lower and higher levels. In the case of cumuli, at least, the currents within the clouds are upward, and those in the open spaces, therefore, generally downward. Also each branch of this cir- culation is more or less turbulent. Hence, while passing through such a cloud layer the aviator is likely to encounter comparatively rough flying, though, owing to the height, of very little danger. Aerial Cascades—The term “aerial cascade” may, with some propriety, be applied to the wind as it sweeps down the lee of ahillor mountain. Ordinarily, it does not come very near the ground, where indeed there frequently is a countercurrent, but remains at a considerable elevation. Other things being equal, it is always most pronounced when the wind is at right angles to the direction of the ridge and when the mountain is rather high and steep. The swift downward sweep of the air when the wind is strong may carry a passing aeroplane with it, and lead ob- servers, if not the pilot, to fancy that a hole has been encountered, where, of course, there is nothing of the kind. Indeed, such cas- cades should be entirely harmless so long as the aviator keeps WINDS ADVERSE TO AVIATION 219 his machine well above the surface and thus out of the treacherous eddies presently to be discussed. Wind Layers.—For one reason or another it often happens that adjacent layers of air differ abruptly from each other in tem- perature, humidity, and density, and, therefore, as explained by Helmholtz, may, and often do, glide over each other in much the same manner:that air flows over water, and with the same general wave-producing effect. These air waves are scen only when the humidity at the interface is such that the slight differ- ence in temperature between the crests and troughs is sufficient to keep the one cloud-capped and the other free from condensation. In short, the humidity condition must be just right. Clearly then, though such clouds often occur in beautiful parallel rows, Figs. 79 and 80, adjacent wind strata of different velocities and their consequent air billows must be of far more frequent occurrence. Consider now the effect on an aeroplane as it passes from one such layer into another. For the sake of illustration let the propeller be at rest and the machine be making a straightaway glide to earth, and let it suddenly pass into a lower layer of air moving in the same horizontal direction as the machine and with the same velocity. This, of course, is an extreme case, but it is by no means an impossible one. Instantly on entering the lower layer, under the conditions just described, all dynamical support must cease, and with it all power of guidance. A fall, for at least a considerable distance, is absolutely inevitable, and if near the earth, perhaps a disastrous one. To all intents and purposes, a “hole’’ has been run into. The reason for the fall will be understood when it is recalled that the pressure of any ordinary wind is very nearly proportional to the square of its velocity with respect to the thing against which it is blowing. Hence, for a given inclination of the wings the lift on the aeroplane is approximately proportional to the square of the velocity of the machine with reference, not to the ground, but to the air in which it happens to be at the instant under consideration. If, then, it glides, with propellers at rest, into a wind stratum that is blowing in the same horizontal direc- tion and with the same velocity, it is in exactly the condition it would be if dropped from rest at the top of a monument in still air. It inevitably must fall unless inherent stability, or skill of the 220 PHYSICS OF THE AIR pilot, bring about a new glide after additional velocity has been acquired as the result of a considerable drop. Of course such an extreme case must be of rare occurrence, but cases less extreme are met with frequently. On passing into a current where the velocity of the wind is more nearly that of the aeroplane, and in the same direction, part of the supporting force is instantly lost, and a corresponding drop or dive becomes at once inevitable. Ordinarily, however, this is a matter of small consequence, for the relative speed necessary to support is again soon acquired, especially if the engine is in full operation. Occa- sionally, though, the loss in support may be large, and occur so near the ground, as to be more or less dangerous. If the new wind layer is against, and not with the machine, an increase instead of a decrease in the sustaining force is the result, and but little occurs beyond a mere change in the hori- zontal speed with reference to the ground, and a slowing up of the rate of descent. All the above discussion of the effect of wind layers on aero- planes is on the assumption that they flow in parallel directions. Ordinarily however, they flow more or less across each other. Hence the aviator, on passing out of one of them into the other, as a rule, has to contend with more than a disconcertingly abrupt change in the supporting force. That is, on crossing the inter- face between wind sheets, an aviator, in addition to suffering a partial loss of support, usually has to contend with the turmoil of a choppy aerial sea in which “bumps,” at least, seem to abound everywhere. Wind strata, within ordinary flying levels, are most frequent during weather changes, especially as fine weather is giving way to stormy. On such occasions, then, one should be on the watch for these strata, even to the extent of making test soundings for them with pilot balloons. It is also well, at such times, to avoid making great changes in altitude, because, since wind strata remain roughly parallel to the surface of the earth, the greater the change in altitude the greater the risk of passing from one stratum to another and thereby encountering at least a “bump,” and, perhaps, a “hole.” Also, to avoid the possibility of losing support when too low to dive, and for other good reasons, landings and launchings should be made, if practicable, squarely in the face of the surface wind. WINDS ADVERSE TO AVIATION 221 Wind Billows.—It was stated above that when one layer of air runs over another of different density, billows are set up between them, as is often shown by windrow clouds. However, the warning clouds are comparatively seldom present; hence, even the cautious aviator may, with no evidence of danger before him, take the very level of the air billows themselves, and before getting safely above or below them, encounter one or more sudden changes in wind velocity and direction due, in part, to the eddy- like or rolling motion within the waves, with chances in each case of being suddenly deprived of a large portion of the requisite sustaining force. There may be perfect safety in either layer, but, unless headed just right, there necessarily is some risk in going from one to the other. Hence, flying at the billow level, since it would necessitate frequent transitions of this nature, should be avoided. When the billows are within 300 metres, say, or less, of the earth (often the case during winter owing to the occurrence then of cold surface air with warmer air above) they are apt to be very turbulent, just as, and for much the same reason that, waves in shallow water are turbulent. For this reason, pre- sumably, winter flying sometimes is surprisingly rough—the air very “bumpy.” Fortunately, however, it is easy to determine by the aid of a suitable station barograph whether or not billows ate prevalent in the low atmosphere, since they produce frequent (5 to 12 per hour, roughly) pressure changes, usually of 0.1 mm. to 0.3 mm. at the surface, as shown by Fig. 57. Wind Gusts —Near the surface of the earth the wind is always in a turmoil owing to friction and to obstacles of all kinds that interfere with the free flow of the lower layers of the atmosphere and thereby allow the next higher layers to plunge forward in irregular fits, swirls, and gusts with all sorts of irrgular velocities and in every direction. Indeed the actual velocity of the wind near the surface of the earth often and abruptly varies from sec- ond to second by more than its full average value, and the greater the average velocity, the greater, in approximately the same ratio, are the irregularities or differences in the successive momentary velocities. This is well shown by pressure-tube traces, of which Fig. 31 is a fine example. ; Clearly, the lift on an aeroplane flying either with or against a gusty wind is correspondingly erratic, and may vary between 222 PHYSICS OF THE AIR such wide limits that the aviator will find himself in a veritable nest of “holes” out of which it is difficult to rise, at least with a slow machine, and sometimes dangerous to try. However, as the turmoil due to the horizontal winds rapidly decreases with increase of elevation, and as the aviator’s safety depends upon steady air conditions, or upon the velocity of his machine with reference to the atmosphere and not with reference to the ground, it is obvious that the windier it is the higher, in general, the minimum level at which he should fly. Probably, however, the chief disturbance due to gusty wind— excessive tipping and consequent side-slipping—occurs not during straightaway flying, to which the above discussion applies, but as the aviator turns at low levels from flying against the gusts to flying with them. This is not owing to change in direction, since the velocity of an aeroplane with reference to the air, and there- fore the sustaining force, is wholly independent of the velocity of either with reference to any third object, the surface of the earth, for instance. It may be, and presumably usually is, caused as follows: The aviator starts turning, suppose, while in and facing a relatively slow-moving portion of air. On banking, the plane is tipped with its under side more or less against the wind, whereupon the higher wing often runs into, or for brief intervals is caught by, a much swifter current than that into which the lower wing dips. Numerical values are not at hand, but the phenomenon of overrunning gusts is familiar from the action of winds on isolated tall trees. This obviously increases the tip, and, in extreme cases, sufficiently to induce a dangerous side slip. On the other hand, when turning from flying with to flying against the wind, the higher wing catches the increased impact on its upper side. Hence, in this case, the result is merely a temporary flattening of the bank, and a consequent skid of but little danger. Gusts that envelop the whole of an aeroplane while turning obviously affect the lift, as above explained, and even so, to some extent, when the path of the wind is at right angles to the course of the plane, but in this latter case seldom sufficiently to be of much importance. Wind Eddies.—Just as eddies and whirls exist in every stream of water, from tiny rills to the great rivers and even the ocean currents, wherever the banks are such as greatly to change the WINDS ADVERSE TO AVIATION 223 direction of flow, and wherever there is a pocket of considerable depth and extent on either side, and as similar eddies, but with horizontal instead of vertical axes, occur at the bottoms of streams where they flow over ledges that produce abrupt changes in the levels of their beds, so, too, and for the same general reasons, horizontal eddies occur in the atmosphere with rotation propor- tional, roughly, to the strength of the wind. These are most pronounced on the lee sides of cuts, cliffs, and steep mountains, but often occur also, to a less extent, on the windward sides of such places. The air at the top and bottom of such whirls is moving in diametrically opposite directions—at the top with the parent or prevailing. wind, at the bottom against it—and since they are close to the earth they may, therefore, as explained under “ wind layers,” be the source of decided danger. There may be some danger also at the forward side of the eddy where the downward motion is greatest. When the wind is blowing strongly landings should not be made, if at all avoidable, on the lee sides of, and close to, steep mountains, hills, bluffs, or even large buildings; for these are the favorite haunts, as just explained, of treacherous vortices. The whirl is best avoided by landing in an open place some distance from bluffs and large obstructions, or, if the obstruction is a hill, on the top of the hill itself. If, however, a landing to one side is necessary, and the aviator has a choice of sides, other things being equal, he should take the windward and not the lee side. Finally, if a landing close to the lee side be compulsory he should, if possible, head up the hill with sufficient velocity to offset any probable loss of support due to an eddy current in the same direction. He could, of course, avoid loss of velocity with reference to the air, and hence loss of support, by heading along the hill—that is, along the axis of the vortex—but this gain would be at the expense of the dangers incident to landing in a side or cross wind. His only other alternative, heading down the hill, might be correct so far as the direction of the surface wind is concerned, but it probably would entail a long run on the ground and its consequent danger. Eddies of a very different type, relatively small and so turbu- leut as to have no well-defined axis of rotation, are formed, as is well known, by a flow of strong winds past the side or corner of 224 PHYSICS. OF THE AIR a building, steep cliff, and the like. In reality such disturbances are, perhaps, more of the “breaker” type, presently to be dis- cussed, than like smoothly-flowing vortices, and should be avoided whenever the wind is above a light breeze. Air Torrents.—Just as water torrents are due to drainage down steep slopes, so, too, gravity winds strong enough to be called “air torrents” owe their origin to drainage down steep, narrow valleys. Whenever the surface of the earth begins to cool through radiation, or otherwise, the air in contact with it becomes correspondingly chilled and, because of its increased density, flows away to lower levels except when held in check, or even driven up, by opposing winds. Hence, when the weather is clear, and there is no counter-wind, there is certain to be air drainage down almost any steep valley during the late afternoon and most of the night. When several such valleys run into a common one, like so many tributartes to a stream, and especially when the upper reaches contain snow, and the whole section is devoid of forest, the aerial river is likely to become torrential in nature along the lower reaches of the drainage channel. A flying machine attempting to land in the mouth of such a valley after the air drainage is well begun is in danger of going from relatively quiet air into an atmosphere that is moving with considerable velocity, at times amounting almost to a gale. If one must land at such a place and time, he should head up the valley so as to face the wind. If he heads down the valley and thereby runs with the wind, he will, on passing into the swift air, lose his support, or much of it, for reasons already explained, and correspondingly drop. Air Breakers.—The term “air breakers’’ is used here in analogy with water breakers as a general name for the rolling, dashing, and choppy winds that accompany thunderstorm con- ditions. They often are of such violence, up, down, and sideways, in any and every direction, that an aeroplane in their grasp is likely to have as uncontrolled and disastrous a landing as would be the case in an actual hole of the worst kind. Fortunately, “ air breakers "' usually give abundant and noisy warnings, and hence the cautious aviator need seldom be, and, as a matter of fact, seldom is caught in so dangerous a situation. However, more than one disaster is attributable to just such tur- bulent winds as these—air breakers. WINDS ADVERSE TO AVIATION 225 Classification.—The above eleven types of atmospheric con- ditions may conveniently be divided into two groups with respect to the method by which they force an aeroplane to drop. 1. The Vertical Group.—All those conditions of the atmos- phere, such as air fountains, sinks, cataracts, cloud currents, cas- cades, breakers (in places), and eddies (forward side), that, in spite of full speed ahead with reference to the air, make it difficult or impossible for the aviator to maintain his level, belong to a common class and depend for their effect upon a vertical com- ponent, up or down, in the motion of the atmosphere itself. Whenever the aviator, without change of the angle of attack and with a full wind in his face, finds his machine rapidly sinking, he may be sure that he has run into some sort of a down-current. Ordinarily, however, assuming that he is not in the grasp of storm-breakers, this condition, bad as it may seem, is of but little danger. The wind cannot blow into the ground, and therefore any down-current, however vigorous, must somewhere become a horizontal current in which the aviator may fly away or land, as he chooses. 2. The Horizontal Group—This group includes all those atmospheric conditions—wind layers, billows, gusts, eddies (cen- tral portions), torrents, breakers (in places), and the like—that in spite of full speed ahead with reference to the ground deprive an aeroplane of a portion at least of its dynamical support. When this loss of support, due to a running of the wind more or less with the machine, is small and the elevation sufficient there is but little danger, but on thé other hand when the loss is relatively large, especially if near the ground, the chance of a fall is corre- spondingly great. Cuapter XII. BAROMETRIC FLUCTUATIONS. THE pressure of the atmosphere undergoes changes that may be classified as seasonal, regional, storm, “ ripple,” diurnal, semi- diurnal, and tidal. Most of these have already briefly been re- ferred to, but they deserve further and separate consideration. Seasonal Pressure Changes.—Since the atmosphere both ex- pands and becomes more humid with increase of temperature, and when cooled contracts and also loses moisture, it follows that the resulting circulation (due to gravity) decreases the mass of air, and therefore its pressure, over places at or near sea level in any warming region and increases it, and its pressure, at similar levels over cooling regions. Hence, in general, the normal reading of the barometer at sea level is greater during winter than summer. It is not much greater, however—perhaps two or three millimetres on the average—since the viscosity of the atmosphere is too small to enable it to maintain any considerable pressure gradient. At places of high elevation the average actual (not reduced) pres- sure is /ess during winter than summer because of the increased density, during the colder season, of the lower air. The approximate level at which January and July pressures, say, are equal may be computed as follows: Let the sea-level pressures differ by 2.5 mm. and let the Janu- ary temperature of the lower air be 20° C. colder than that of July. The pressure difference represents a stratum of the lower air about 27 metres thick, while the temperature difference is, roughly, 0.075 of the absolute temperature. Hence, under the above conditions, the height 4 at which the January and July pressures are the same is given approximately by the equation: = 27 metres 0.075 In addition to this seasonal pressure change over the whole of the northern and southern hemispheres, complicated to some ex- tent by local conditions and the shifting of the belts of high pressure, there also are similar but greater pressure changes be- tween the continents (high in winter, low in summer) and oceans (high in summer, low in winter) of each hemisphere itself. This 226 = 360 metres. BAROMETRIC FLUCTUATIONS 227 pressure swing between continent and ocean is due to the fact that the summer temperature of the land is much higher and its winter temperature much lower than that of the water. Regional Pressure Changes.—The great semipermanent lows and highs often shift more or less from their normal positions. These displacements may be in any direction (more frequent in some than in others) and may last for any length of time, froma day or two toa fortnight or even longer. Such pressure changes, whatever their immediate cause, obviously are not seasonal, since Fic. 57. Pressure changes (inches) cyclone to anticyclone, Drexel, Nebr. they occur at all times of the year. Neither are they of the migratory storm type, though themselves contributing to the gene- sis and development of storms and of great importance in the control of storm courses. Storm Pressure Changes.—The progressive travel of cyclones and anticyclones, or, rather, of cyclonic and anti-cyclonic condi- tions, necessarily implies a regular order of pressure changes, through a range often amounting to 25 mm. or more, at each point along the storm path (Fig. 57). This type of change, fre- quent in extratropical regions at all times of the year, seldom lasts longer than 24 to 36 hours, and averages, perhaps, about 18 hours. 228 PHYSICS OF THE AIR A secondary pressure change, due to the rapid rotation of a tornado or a waterspout, very intense but exceedingly brief— averaging less than one minute—occasionally develops under special conditions. Perhaps, too, the pulsatory irregularities of the barometer dur- ing a thunderstorm should also be included here. Their origin, however, is entirely different. Barometric “ Ripples.”’—Small pressure changes, amplitude Fic. 58. Barometric ripples. usually 0.1 mm. to 0.3 mm. and period of 5 minutes to 10 minutes, Fig. 58 (the regularly spaced vertical lines along the trace are hour marks), and continuing for hours or even days together, are very common during cold weather. As first demonstrated by Helmholtz,°° whenever layers of air that differ in density at their interface flow over each other long billows, analogous to gravity “ Sits. der K. P, Akad. Berlin, 1889, p. 761; 1890, p. 853. Translated by Cleveland Abbe, “ Mechanics of the Earth’s Atmosphere,” Smithsonian Institution, 1891. BAROMETRIC FLUCTUATIONS 229 water waves, are produced which conform approximately to the equation, di (u— V)? + dp (V—»)” = &ea— dy) in which V is the velocity of wave propagation, d, and d, the densities of the layers whose velocities are u and v, respectively, g the gravity acceleration, and the wave-length. If, now, the surface layer is colder than the next above, as it often is during winter, and rather shallow, 100 metres to 500 metres thick, say; the passage of the air billows, like the passage of waves in shallow water, necessarily produces greater or less corresponding changes in the pressure on the bottom—changes that appear as a series of Fic. 59. Barogram, Grand Turk Island, West Indies. ripples in the record of a sensitive barograph. Furthermore, such shallow air billows, like shallow water waves, doubtless are turbulent—a condition that accounts, presumably, for the sur- prisingly rough flying the aviator often experiences during winter at low levels—300 metres and less. During summer, when air billows rarely form near the sur- face, though frequently at greater altitudes, especially that of the cirrus cloud, neither barometric ripples nor shallow turbulences of the kind just mentioned often occur. This, doubtless, is be- cause wave disturbances in air as in water do not penetrate far beneath the wave level. Diurnal and Semidiurnal Pressure Changes.—It has been known now for two and a half centuries that there are more or less regular daily variations in the height of the barometer, cul- minating in two maxima and two minima during the course of 24 hours. The phenomenon in question is well illustrated by Fig. 59, a direct copy of a barograph trace obtained April 1-5, 1912, on 16 230 PHYSICS OF THE AIR Grand Turk Island, latitude 21° 21’ N., longitude 70” 7’ W. It is further illustrated, and shown to persist through all the seasons, by Fig. 60, which gives, from hourly values, the actual average Fic. 60. Average daily barometric curves, Key West, Florida. daily pressure curve for each month, and also for the entire year, as observed at Key West, latitude 24° 33’ N., longitude 81° 48’ W., during the 14 years, 1891-1904. The actual values are given in the accompanying table. 231 BAROMETRIC FLUCTUATIONS Zot fet Set Sz+ 674+ grt off of + Let Off CEH QE cBqpo ct VysUupI] | set gf4+ or+ oF+ 684+ OF +4 SE4+ oF PE L4H PE TE ttt Wd II of + ef+ o+ abt 68+ FE4 oF f+ CEH Let C+ OF + Qa THp crt Wd O1 Zvt get of + e4 bet Sr++ ezr4+ Sr op crt crf orp OE Tt Wd 6 go" — So or-+ lo+ Sor zi— V1 go" — Zz i grr— Cp IOT— teens Wd g ibe gz — gz — To zee Sore iv It — 09° — 09" — a gr — PE te eee wa Z 69° pads Oe Go 6S°— wes i So: — 69°— Sg — So — gL — iooS PCr edie R aie wd 9 6L°— ple Gfta J Peay 9¢°— 6L°— zl of gg — ob: — 6g°— €g— Ce eesti etd dune ong wa S 6f°— tg Lg-— Sg — 9g°— Tite Glia 6S°— CPx, og’ — te— 9g°— £g eee wav 9S — LL— LL zl — 09° — or — tres coe ph os: — 9S°— 39° — OG roe Ig— to — 6c°— Gok oc — to — gr roe 6o°— ger — of: — Lor ee ee ee Wv ¢ cre I— or— lo olr'— or— tr— oz — pre rre— olr'— So: — TE ttt eees Wy z ov So+ So+ zo tit Sr+ zu zo+ zu Sr+ Zot Sot lo cis SES OA Rr oe Se Wv I 69'°z9L PEboL Sor€gl gfo9Z o6'094 oz zl orto ogI9L gS194 oGz9L SSEgL govol ob Pgh ott ttt asVlaay Jaquraseq JaquiaaoN JaqoqQ Jequieydag ysnsny Ant aunt Av! ady yorrpy Areniqag Arenuef oul} ULIPMayy yySL leak ‘saagayy Z ‘uoyvaary “MM Sh oT§ apnyvsuoy “ny ,€€ bz apnyyvy ‘sag, Kay 7D ‘FoOI-I6gI ‘dajamosvg ay] fo ssuippay Kpanoxy aspsany 232 PHYSICS OF THE AIR Probably the earliest observations of these rhythmical daily changes in the atmospheric pressure were made by Doctor Beal “’ during the years 1664-65, and therefore very soon after the in- vention, 1643, of the mercurial barometer. Since Beal’s dis- covery the same observation has been made and puzzled over at every station at which pressure records were kept and studied, but without success in finding for it any adequate physical explana- tion. In speaking of the diurnal and semidiurnal variations of the barometer, Lord Rayleigh ® says: “The relative magnitude of the latter [semidiurnal varia- tion], as observed at most parts of the earth’s surface, is still a mystery, all the attempted explanations being illusory.” Fic. 61. Average daily barometric curve and its components, Washington, D.C. (After W. J. Bennett.) Obviously the average hourly pressures for a decade or longer at any given place are practically free from storm and other irregu- lar effects, but contain all diurnal and shorter period disturbances that may exist. On being analyzed these actual data show two well-defined sine curves, a diurnal and a semidiurnal, as illus- trated by Fig. 61,°* each of which requires a special explanation. Higher harmonics of very small amplitude have also been found, but, as neither the diurnal nor the semidiurnal disturbances can have true sine values throughout, it follows that the higher har- monics indicated by this type of analysis may not represent any actual force of the same periodicity. * Phil. Trans., 9 (1666), p. 153. ? Phil. Mag., 29 (1890), p. 179. “Bennett, Monthly Weather Review, 34 (1906), p. 528. BAROMETRIC FLUCTUATIONS 233 Diurnal Pressure Changes.—There are two classes of well- defined 24-hour pressure changes. One obtains at places of con- siderable elevation and is marked by a barometric maximum dur- ing the warmest hours and minimum during the coldest. The other applies to low, especially sea level, stations and is the re- verse of the above, the maximum occurring during the coldest hours and the minimum during the warmest. The first class of changes just mentioned, the one that con- cerns elevated stations, is due essentially to volume expansion and contraction of the atmosphere caused by heating and cooling re- spectively. Thus the lower atmosphere over that side of the earth which is exposed to insolation becomes more or less heated, and therefore, because of the resulting expansion, its centre of mass is correspondingly raised. Conversely, during the night the atmosphere cools and contracts and the centre of mass is propor- tionately lowered. Hence, so far as this effect alone is concerned, a mountain station, 1090 metres, say, above sea level, will have the greatest mass of air above it when the atmosphere below is warmest or most expanded, and the least when the lower atmos- phere is coldest or most contracted—that is to say, this effect tends to produce, at such stations, barometric maxima during afternoons and minima about dawn. There is, however, another effect resulting from the volume expansion and contraction of the atmosphere to consider ; namely, its lateral flow. To this, mainly, is due that daily barometric swing at sea level, as shown by harmonic analysis, the early evening minimum and the early morning maximum, that is the reverse of the high-level oscillation. The expansion and consequent vertical rise of the air on the warming side of the earth, together with the simultaneous con- traction and fall of the atmosphere on the cooling side, establishes a pressure gradient at all levels of the atmosphere directed from the warmer toward the cooler regions, a gradient that obviously causes the well-known heliotropic wind—the wind that turns with the sun—and thus leads to maximum pressures at the coldest places and minimum pressures at the warmest. But as these re- gions are along meridians, roughly, 10 hours, or 150 degrees apart, and perpetually move around the earth at the rate of one revolution every 24 hours, there must be a corresponding per- petual flow of air, or change of flow, as above described, in a 234 PHYSICS OF THE AIR ceaseless effort to establish an equilibrium which, since the dis- turbance is continuous, can never be attained. Semidiurnal Pressure Changes.—Both the actual barometric records and their harmonic analyses show conspicuous 12-hour cyclic changes that culminate in maxima and minima at approxi- mately 10 o’clock, 4.m. and P.m., and 4 o’clock, also both a.m. and P.M., respectively—the exact hour in each case depending somewhat upon season, elevation, and, presumably, weather conditions. Some of the observed facts in regard to this 12-hour cyclic change of pressure are :°* (a) The amplitude, when other things are substantially equal, varies with place approximately as the square of the cosine of the latitude. (b) The amplitude is everywhere greatest on equinoxes and everywhere least on solstices. (c) The amplitude is greater at perihelion than at aphelion. (d) The amplitude is greater by day than by night. (e) The amplitude is greatest on clear days and least on cloudy. (f) The day amplitude is greater over land than over water. (g) The night amplitude is greater over oceans than over continents. (h) Over the tropical Pacific Ocean the forenoon barometric maximum is about 1 mm. above and the afternoon minimum I mm. below the general average pressure. Obviously, other things being equal, both the daily change in temperature and the resulting change in convection are greater in the tropics than elsewhere; greater at perihelion than at aphelion; greater during clear weather than cloudy; greater over land than over water; and greatest when the time of heating and the time of cooling (day and night) are equal, and least when these are most unequal or at the times of solstice. Hence all the above facts of observation strongly favor, if they do not compel, the conclusion that the daily cyclic pressure changes are somehow results of daily temperature changes. There are, however, a * Angot, “Etude sur la marche diurne du barométre,” Annales du Bu- reau Central Météorol., 1887. Hann, “Untersuchungen tiber die tagliche Oscillation des Barometers,” Denkschriften der Wicner Akademic, Bd. 55, 1889. Hann, Meteorol Zeit., 15 (1808), 361. BAROMETRIC FLUCTUATIONS 235 number of other causes of slight pressure changes,®° but appar- ently only the following have any appreciable value: 1. Horizontal flow of the atmosphere from the regions where it is most expanded toward those where it is most contractea. The exact hour at which the atmosphere is warmest and most expanded depends upon a variety of circumstances, but on the average it is approximately at 4 o’clock in the afternoon. Hence, in general, at about this time the amount of air overhead, count- ing from sea level, should be least, and therefore at this hour a sea-level barometer should have its lowest reading. On the other hand, lowest temperatures and maximum contractions obtain soon after dawn, or shortly before 6 a.m. throughout the year near the equator, and everywhere at the time of equinox. The 24-hour swing of the barometer, therefore, does not ap- pear to be of even period, but rather of intervals that are to each other, roughly, as 5 to 7. To be sure, the barometer is lower at 6 o'clock in the afternoon than at the same hour of the morning, and hence one may assume an even period 24-hour swing, with a morning 6 o’clock maximum and evening 6 o’clock minimum, and partially correct this regular curve (the correction is never per- fect) by the superposition of one or more additional sine curves of convenient periods. But this approximation to the true curve does not prove the existence of actual forces with the periods assumed. It appears, then, that the physical causes of the 24-hour com- ponent of the diurnal pressure changes are such as to give a morn- ing maximum at about 6 o’clock and an afternoon minimum at about 4 o’clock. The above causes of pressure change, however, do not account for either of the 10 o’clock maxima. 2. Interference by vertical convection with free horizontal flow. It was long ago suggested by Abbe © that convectional inter- ference is the principal cause of the forenoon maximum pressure, which indeed it probably is, as the folowing consideration shows : Let the mass 7 of air be near the ground and have the hori- zontal velocity v, and let the larger mass M be at a higher elevation and have the greater velocity V in the same direction. If now these two masses should mingle in such manner as to be free from all disturbance, except their own mutual interference, the ®FHumphreys, Bul. Mt. Weather Obsy., 5 (1912), p. 132. ® Preparatory Studies” (1890), pp. 8 and 56. 236 PHYSICS OF THE AIR resulting final velocity, U, in the same direction, would be given by the equation— _ mu+ MV Ue m+ MM and there obviously would be no check in the total flow—no dam- ming up and consequent increase of pressure. But this simple mixing of the two masses is by no means all that happens in the case of vertical convection. The rise of the mass m is simul- taneously accompanied by an equivalent descent of air from a higher level, which in turn loses velocity, directly or indirectly, by surface friction. If the falling mass is also m, and if its velocity is reduced by friction to v, then from a single interchange, due to vertical convection, the total momentum becomes— 2mv+(M-—m) V and the total flow is reduced by the amount m (V—»v) But as this is for a single interchange, it is obvious that the more active vertical convection becomes, the greater will be its inter- ference with the flow of the atmosphere, the more the winds will be dammed up, and the higher the barometric pressure. As con- vection increases, reaches a maximum, and then decreases, sa, too, will the resulting interference go through the same changes. Now the general movement of the atmosphere is from east to west within the tropics and from west to east at higher latitudes. Therefore in either case such damming up of the air as vertical convection may produce will be essentially along meridians, and thus a function of the time of day. But, in general, convection increases most rapidly during the forenoon, say 8 to g o'clock, is most active at 10 to 11 o’clock, and reaches its greatest eleva- tion about 4 o’clock in the afternoon. Hence the damming up of the atmosphere, due to vertical convection, and the resulting in- crease of barometric pressure must increase most rapidly during the forenoon, and come to a maximum about 10 o’clock. After this the convectional interference decreases, while at the same time the amount of air in a vertical column of fixed cross-section diminishes as a result of expansion and overflow, until at about 4 o'clock in the afternoon the barometric pressure, as already ex- plained, has reached a minimum. BAROMETRIC FLUCTUATIONS 237 To form some idea of the magnitude of the barometric change due to convectional turbulence, consider the atmosphere between two parallels of latitude near the equator. This limited quan- tity may be regarded as a stream flowing around the earth, hav- ing its minimum velocity and maximum depth where convectional interference is greatest, and maximum velocity with minimum depth where convection is absent. And since the linear velocity of a point on the equator is approximately 1670 kilometres per hour, while during the forenoon the rate of increase of the barometric pressure at the same place is, roughly, 0.2 mm. per hour, it follows that a damming up, or check in the flow, of the given stream at the rate of 0.44 kilometre per hour would be suffi- cient of itself to account for the observed rise in the barometer. But if the average velocity of the wind, or flow of the stream in question, is Io metres per second, which it may well be, the rate of decrease in velocity requisite for the given rate of pressure in- crease could be produced by having only 1 part in 80 of the whole superincumbent atmosphere brought to rest per hour, or the equivalent thereof, an amount that perhaps is reasonable. At any rate, the assumed velocity decrease is of the same order of mag- nitude as that observed to take place during, and as the result of, diurnal convection. Summing up the effects of all the above causes of barometric changes, it appears: (a) That the afternoon minimum is caused essentially by overflow from the region where the atmosphere is warmest, or better, perhaps, from the meridian along which the temperature increase has been greatest, toward that meridian along which there has been the greatest decrease in temperature. (b) That vertical convection interferes with the free hori- zontal flow of the atmosphere and to that extent dams it up and correspondingly increases the barometric pressure; also, that the time of this interference agrees with the forenoon changes of the barometer, and that its magnitude is of about the proper order to account for the forenoon barometric maximum. The afternoon barometric minimum and the forenoon maxi- mum, therefore, are to be regarded as effects of temperature increase; the minimum as due to expansion and consequent over- flow; the maximum as caused by vertical convection and conse- quent interference with the free circulation of the atmosphere. 238 PHYSICS OF THE AIR The forced afternoon minimum would occur in an otherwise stagnant atmosphere, and substantially as at present; but not so with the forced forenoon maximum, since the interference or damming effect depends upon a flow or circulation of the atmos- phere, parallel roughly to the equator. It remains now to account for the night 10 o'clock maximum and 4 o’clock minimum. 3. Natural or free vibration of the atmosphere as a whole. This subject has been discussed by several mathematical physi- cists of great eminence. The latest and most complete of these discussions, and the one to which those interested in this phase of the barometric problem are especially referred, is by Lamb,*’ who concludes: “‘ Without pressing too far conclusions based on the hypothesis of an atmosphere uniform over the earth, and approximately in convective equilibrium, we may, I think, at least assert the existence of a free oscillation of the earth’s atmosphere, of ‘ semi- diurnal’ type, with a period not very different from, but probably somewhat less than, 12 mean solar hours.” Hence any cause of pressure change, having a semidiurnal period or approximately so, would, if of suffcient magnitude and proper phase, account for the 12-hour barometric curve. Such a cause, many think, may be found in the irregular daily march of temperature, since the curve expressing this march is more or less approximately resolvable into a diurnal and a semidiurnal sine curve. But the resolution is not perfect and, besides, there is no obvious cause for a temperature increase by night, and hence the reality of the semidiurnal component in the temperature curve 1s equally doubtful. All that is needed, apparentlv, to give the semidiurnal pres- sure curve is a pressure impulse of the same period, 12 hours, as that of the free vibration of the atmosphere asa whole. And this is furnished by the forced forenoon barometric maximum, fol- lowed six hours later at the same-place by the forced afternoon barometric minimum. In other words, taken together, the forenoon and afternoon forced disturbances appear to occur with the proper time interval necessary to set up and maintain the 12- hour free vibrations of the atmosphere. * Proc. Roy. Soc.. A. 84 (1911), p. 551. BAROMETRIC FLUCTUATIONS 239 The course of events at each locality appears to be substan- tially as follows: 1. A forced forenoon compression of the atmosphere, fol- lowed by its equally forced afternoon expansion, the two to- gether forming one complete barometric wave, with a 10 o’clock maximum and a 4 o’clock minimum, in harmony with the free vibration of the entire atmospheric shell. 2. Nondisturbance through the night or during the time of a single free vibration. 3. Repetition the following day of the forced disturbances in Fic. 62. | AN= woo inch Hg. A +0-01\ -0-01 mm. Ha} A’ Uppler Lowler Uppjer Tranjsit. Tran|sit. Tranjsit. Lunar semidiurnal atmospheric tide Greenwich, 1854-1917. synchronism with, and therefore at such time as to reénforce, the free vibrations. The series of disturbances is continuous, forced by day and free by night, but the resulting amplitudes of the barometric changes are limited, through friction and through the absence of perfect synchronism, to comparatively small values. Each point upon the atmospheric shell receives at every alternate swing a forced impulse in phase with the free vibration, and therefore at such time and in such manner as indefinitely to maintain the vibra- tions of the atmosphere as a whole. ie ; The forenoon maximum and the afternoon minimum are pri- 240 PHYSICS OF THE AIR mary disturbances equally forced but in different ways by the daily increase of temperature, while the evening maximum and the morning minimum are secondary disturbances caused by the joint action of the forced primaries through the 12-hour free vibration of the atmosphere. In short, the semidiurnal swing of the barometer is a result of merely fortuitous circumstances—of the fact that the mass of the atmosphere happens to be such that the period of its free vibration is approximately just one-half that of the earth’s rotation. Tidal Pressure Changes.—The theory of atmospheric tides is too tedious to include here, especially as it is easily accessible °* to all who may have any occasion to look it up. According to this theory the barometric amplitudes in equatorial regions, due to the gravitational action of the sun and the moon, should be about 0.0109 mm. and 0.025 mm., respectively, and rapidly de- crease with increase of latitude. These, of course, are not easily disentangled from the numerous other barometric changes. Nevertheless, efforts to do so have been made and, apparently, with fair success, notably by Chapman,*’? whose results from the Greenwich data of 1854-1917 are shown in Fig. 62. a Lamb, “ Hydrodynamics.” > Or. Jr. Roy. Meteorol. Socy. 44, p. 271, 1918; 45, p. 113, 1919. CHAPTER XIII. EVAPORATION AND CONDENSATION. INTRODUCTION. THE presence of water vapor in the atmosphere is of such vital importance in the economy of Nature, and the source of so many phenomena, as to demand a study of, among other things: evaporation, by which the vapor is gotten into and rendered a portion of the atmosphere, mainly from free surfaces, but also from vegetation and damp soil; and condensation, by which in various forms it is removed from the air. EVAPORATION. Evaporation, the process by which a liquid becomes a vapor, or gas, is a result of the kinetic energy of the individual molecules. Some of the molecules at or near the surface have such velocities and directions that they escape from the liquid and thus become an integral part of the surrounding gas or atmosphere; and as the chance of escape, other things remaining equal, increases with the velocity, it follows (a) that the average kinetic energy of the escaping molecules is greater than that of the remaining ones, or that evaporation decreases the temperature of a liquid, and (6) that the rate of evaporation increases with increase of temperature. Just as the kinetic energy of some of the molecules of the liquid carries them into the adjacent space, so, too, the kinetic energy of some of the molecules of the gaseous phase causes them to penetrate into and thus become a part of the liquid. In reality, therefore, evaporation from and condensation onto the surface of a liquid, though necessarily taking place by discrete molecular units, practically are continuous processes whose ratio may have any value whatever. As popularly used, however, and even as very commonly used scientifically, the term “‘ evaporation ” refers to the net loss of a liquid, and “‘ condensation” to its net gain, so that, in this sense, both are said to be zero when, as a matter of fact, they are only equal to each other. In the sense of net loss, which admits of accurate measure- ment, evaporation has been the subject of numerous investiga- 241 242 PHYSICS OF THE AIR tions. Vegetation, soil, and the free water surface each offers its own peculiar and numerous evaporation problems. In what follows, however, only the free surface will be considered. Evaporation into Still Air (a) from Tubes.—The rate of loss of a liquid by evaporation and diffusion, through a tube of fixed length and constant cross-section, into a still atmosphere has been carefully studied by Stefan.°* Obviously, when a steady state has been attained, the rate at which the vapor escapes per unit area of the cross-section of the tube is constant, directly proportional to the driving force and inversely proportional to the resistance. These in turn are proportional, respectively, to the pressure gradient of the vapor along the tube and the partial pressure of the foreign gas at the same place. In symbols, ppg. ~hym 8 (PP). in which v is the volume at 0° C. and 760 mm. pressure of the vapor that escapes per second per unit area of the cross-section of the tube, P the total pressure, a constant, a, the vapor v= pressure gradient along the tube at and normal to the cross- section at which the partial pressure due to the vapor is p, and k the coefficient of diffusion, whose value depends upon the nature of the vapor and the gas through which it is passing, and their temperature. But as a steady state is assumed, it follows that both the rate of flow and the coefficient of diffusion k are independent of the distance 1 along the tube above the liquid surface. Hence, kA P—p" Vay log Boe in which V is the rate of total evaporation, A the area of the cross-section of the tube, / its height, or the distance of its top (tube supposed vertical) above the liquid, p” and p’ the partial pressures of the vapor at the free end and evaporating surface, respectively. All the terms in this equation except k may easily be measured, and thus Fk itself evaluated. But with k known, the rate of evaporation of the same liquid (water, sav) from a circular tube or well of any given cross-section and length. provided the length is equal to or greater than the diameter. mav be computed from ® Sitsungsberichte der K. Akad. der Wis. Wien. 68 (1873), 385-423. EVAPORATION AND CONDENSATION 243 the total gas pressure and the vapor pressures at the surface of the liquid and top of the tube. Evaporation into Still Air (b) from Flush Circular Areas.— The rate of evaporation into still air from a circular tank or pond filled flush with a relatively extensive plane which itself neither absorbs nor gives off any vapor has also been found by Stefan ®® susceptible of complete analysis. From the general equation it follows that d P—ho v=—k me By in which po is the constant partial pressure of the vapor, during a steady state, at a given point. Hence if es P=? u=log P=p du TE But this is identical with the flow of heat when me is the nH temperature gradient and k the thermal conductivity. Similarly it represents the flow of electricity, and also the field of force in the presence of a charged plate. If o is the density of the surface charge on a plate, then Oe ae Further, if E is the total charge, E=Cu in which C is the capacity of the plate and w, its potential. Hence the total diffusion, confined to one side, is given by the expression V=2nkCuy But P—bo P-h uy =log in which fo is the vapor pressure of the free air at a great distance from the evaporating surface and /, its pressure at the surface, or saturation pressure at the surface temperature. © Sitzungsberichte der K. Akad. der Wis. Wien, 73 (1881), 943-954. 244 PHYSICS OF THE AIR The capacity of a circular disk of radius a is Nv c=2 Hence P—bo P-p V =4ak log If po and p, are both small in comparison to P, V =4ak so ) " nearly. The real importance of this equation is its proof that evapora- tion, under the restricted conditions assumed, is proportional to the diameter (or other linear dimension) of the evaporating sur- face and not, as one might suppose, to its area. Obviously, there- fore, evaporation in the open under ordinary conditions cannot be directly proportional, as often assumed, to the area involved. Evaporation into Still ir (c) from Elliptical Areas.—Evap- oration from an elliptical surface is slightly faster than from a circular one of equal area, but the difference is small until the major axis of the ellipse becomes several times longer than the minor; being only 1.11 as fast when the ratio of the axes is I to 4. Hence, when the axes do not greatly differ, a close approximation to the rate of evaporation from an elliptical surface is given by the equation na P—h V=4//a0 k log P or, when fo and p,are small with reference to P, pit to P V=4) “abk No exact mathematical expression has yet been obtained for the rate of evaporation into still air from surfaces of any other outline than the above—circle and ellipse. Evaporation into a Steady Horizontal IVind—Significant progress towards the complete solution of this difficult problem has been made by Jeffreys,°°* whose discussion of it is substan- tially as follows: Let p be the density of the atmosphere at any point and D the fraction of this density due to water vapor; let the wind be in the direction + parallel to the evaporating surface, and let its velocity at some distance above this surface be u. The a Phil. Mag., 35, Pp. 273, 1918. EVAPORATION AND CONDENSATION 245 components v and w of the wind velocity in the directions y and z, respectively (z being normal to the surface and y at right angles to both * and z) are, therefore, both zero. For moderate winds the velocity of the air may be assumed to increase rapidly through a thin shearing layer from zero at the surface to perhaps half value, u/2, a millimetre or so above it. Through this same layer the vapor density will rapidly decrease, if the general air is com- paratively dry, from saturation at the surface, where D=D,, say, to some decidedly less value. Beyond this layer the transfer of water vapor, of heat, and of momentum, are all owing essen- tially to turbulence, as fully explained by Taylor,® and the co- efficient k of this “eddy diffusion” is practically independent of position. Therefore, in analogy to heat conduction, molecular diffu- sion, etc. dD a (,0D af, SD\, 8 4.80 Tax (Foe) + stan) tashas) Also dD. 8D! ap. ap. ap oP ar Fae ay oe Hence, as the density gradient changes only with elevation (v= w=o), and as k is constant, it follows that, when a steady state has been attained, An integral of this equation is °° “q 2 = 253 eu qg D Dy ( I he if e da) 0 1 shy x in which > Phil. Trans. Roy. Soc. A., 215, p. 1, 1915. ®c Van Orstrand and Dewey, Professional Paper 95-G, U. S. Geological Survey, 1915. 17 246 PHYSICS OF THE AUR On taking the origin at the windward edge of the liquid surface, D=o0, when x is negative. Hence, at the surface, where z= 0, aD__Dy 02 yrx Therefore, the rate of evaporation is aD “Bu kp —— =pDo | ku per unit area. ds Nx and, for a strip of width dy, extending from r=0 to r=4¥ rE Ru\% Rux\3 va f° (e)hanaen.) 0 If, now, the length of the strip from margin to margin be /, neglecting end corrections due to sidewise diffusion, the rate of total evaporation is (RuN3 3 2p Do \— )*l*dy, taken over the whole area. In the case, therefore, of free, unruffled liquid surfaces of medium dimensions, roughly, 20 centimetres to 500 metres across," it appears, in the case of “ eddy diffusion ”’ : 1. That the rate of evaporation is proportional to the square root of the wind velocity. 2. That the rates of total evaporation from surfaces of the same shape and same orientation to the wind are to each other as the three-quarter powers of their re- spective areas. If, for instance, the surface is a circle of radius a, the rate of evaporation from it is at 2.44 Do (kua®) ; which accords with the observations of Thomas and Ferguson.*” The equation, therefore, that expresses the rate of total evaporation from a given surface by “eddy diffusion” is very different from the corresponding equation when the diffusion is wholly molecular, nor are they reducible the one to the other. %d Jeffries, Loc. cit. %e Phil. Mag. 34, p. 308, 1917. EVAPORATION AND CONDENSATION 247 The first applies, approximately, at least, when there is an appre- ciable wind of the kind specified, namely, steady and strictly hori- zontal; the second, only when the air is absolutely quiet. The problem, however, of evaporation into imperceptible to very light winds is more difficult, and, as yet, unsolved. Evaporation in the Open.—Several hundred papers,’° many of them giving the results of elaborate investigations, have been published on the evaporation of water from free surfaces, vege- tation, and soil, and, while no equation has been found that expresses in terms of easily measurable quantities the rates of evaporation in the open, nevertheless several factors that control these rates have been discovered and more or less approximately evaluated. In the case of free, clean surfaces the principal factors are: (a) Salinity.—It has repeatedly been observed that the evap- oration of salt solutions decreases with increase of concentration, and that sea-water evaporates approximately 5 per cent. less rapidly than fresh water under the same conditions. (b) Dryness of the Air—Many observations have shown that, to at least a first approximation, the rate of evaporation is directly proportional, other things being equal, to the difference in tem- perature indicated by the wet and dry bulb thermometers of a whirled psychrometer. According to the psychrometric formula developed by Apjohn, Maxwell, Stefan, and others, : Pi—po=AB(to—h) in which fo is the temperature and fo the vapor pressure of the free air, ¢; the temperature of the wet bulb (and surface of evaporating liquid), p, the saturation vapor pressure at tempera- ture t,, B the barometric pressure, and A a constant, provided ventilation is sufficient. But evaporation is proportional to the ratio of vapor pressure gradient to total pressure; that is, _ 2, Piro Veer Ss Hence, other things being equal, V=C (to—h), approximately. But to-t,increases with the dryness, and hence so does evaporation. * Livingston, “An Annotated Bibliography of Evaporation,’ M. W. R., June, September, and November, 1908, and February, March, April, May, and June, 1909. 248 PHYSICS OF THE AIR (c) Velocity of the Wind.—All observers agree that evapora- tion increases with wind velocity, presumably through increase, by the action of eddy diffusion, of the vapor pressure gradient near the surface. As above explained, it is now known that in the case of a strictly horizontal and steady wind evaporation from an area of medium size is proportional to the square root of the wind velocity. But, in general, these conditions are not ful- filled in nature. The wind usually has a variable vertical com- ponent, and, besides, is irregular in strength and direction. There ig not, therefore, any constant relation of evaporation to the average horizontal component of wind velocity—the value usually measured. (d) Barometric Pressure.—Since the presence of any gas retards the diffusion of other gas molecules, whether of the same or different nature, it follows that when the vapor tension is comparatively small, evaporation must vary inversely, nearly, as the total barometric pressure, if temperature is constant. (e) Area of Surface —Obviously the total amount of water evaporated must increase with the area of the evaporating sur- face, but not necessarily at the same rate. In fact, as already explained, if the evaporation is from a circular area into still air, it increases as the square root of the area; and as the 34 power of the area in the case of a strictly horizontal wind. Under out- door conditions, however, it is much more nearly, though prob- ‘ably by no means exactly, proportional to the first power of the surface. (f) Temperature of the Water—Evaporation increases rapidly with the temperature of the water, roughly in proportion to the saturation pressure at that temperature, provided the gen- eral humidity of the air is low. When, however, the water surface is colder than the dew-point temperature of the air the evaporation becomes negative; that is, condensation occurs. When the air is colder than the water surface, evaporation may continue into it after saturation has been reached and thereby produce fog, the process being one of distillation and condensation. Even when the water is frozen, it still continues slowly to evaporate (sublime) whenever the air is sufficiently dry, but the laws governing this sublimation are not well known. Empirical Evaporation Equations.—Various equations, each at least partially empirical, have been devised to fit evaporation EVAPORATION AND CONDENSATION 249 data obtained under special conditions. But the “ constants” of these equations generally are not constant under other circum- stances. Indeed, it may be that no simple equation of this kind, applicable to a wide range of conditions, is possible, and that therefore the most expeditious way to obtain useful evaporation data would be to note the daily, monthly, annual, etc., loss from standard exposures in each climatic region, and, wherever prac- tical, to supplement such data by similar observations on lakes, ponds, and reservoirs. Controlled wind-tunnel experiments would also be interesting and useful. One of the earliest experimenters to make a careful study of evaporation was John Dalton,"? who says: 1. “ Some fluids evaporate much more quickly than others.” 2. “The quantity evaporated is in direct proportion to the surface exposed, all other circumstances alike.” 3. “ An increase of temperature in the liquid is attended with an increase of evaporation, not directly proportionable.” 4. “ Evaporation is greater where there is a stream of air than where the.air is stagnant.” 5. “ Evaporation from water is greater the less the humidity previously existing in the atmosphere, all other circumstances the same.” All these are important observations, but they do not fully justify the so-called Dalton equation which Dalton himself appar- ently never wrote. ‘ Weilenmann and Stelling, working independently and at dif- ferent places, obtained evaporation equations of the general form 7? = (cb-+bw) (bs— bo) in which c and k are constants, b the barometric pressure, w the wind velocity, p, the saturation vapor pressure at the temperature of the water surface, and po the actual vapor pressure in the free air at some distance from the water. Fitzgerald7® finds the rate of evaporation, E, in inches per hour, given approximately by the equation gu (be bo) (1-41 /2w) 60 ™% Mem. Manchester Lit. and Phil. Soc., 5, 574, read October, 1801. ™ Hann, “Lehrbuch der Meteorologie,” 3d edition, p. 214. *® Trans. Amer. Soc. Civ. Eng., 15 (1886), 581-645. 250 PHYSICS OF THE AIR in which ps and po have the meanings, respectively, given above, and w.is the average wind velocity in miles per hour. Various other equations have been found or proposed, but they either contain unevaluated functions or else were constructed to fit a special set of observations. The multiplicity of such equa- tions, each of but limited use, emphasizes the difficulty of the evaporation problem, if not even the impossibility of finding for it a practical, universal equation. CONDENSATION. Condensation, the process by which a vapor is reduced to a liquid or solid, is induced by: (a) reduction of temperature, volume remaining constant; (b) reduction of volume, tempera- ture remaining constant; (c) a combination of temperature and volume changes that jointly reduce the total vapor capacity. In the open, water vapor is condensed: (1) by contact cooling; (2) by radiational cooling; (3) by the mixture of masses of air of unequal temperatures; (4) by expansional or dynamic cooling due to vertical convection, or, occasionally, other causes, espe- cially rotation, as in tornado and waterspout funnels. Condensation Due to Contact Cooling.—During clear nights the surface of the earth, including vegetation and other. objects. loses much heat by radiation, and thus both it and the air in contact with it are reduced to lower temperatures, obviously more pronounced the gentler the winds. After the dew-point has been reached all further loss of heat, producing now a much smaller proportionate decrease of temperature, results in the deposition, respectively, of dew and hoar-frost at temperatures above and below freezing. Similarly, relatively warm, moist air moving over a snow bank, for instance, may deposit some of its moisture. In any typical case of surface cooling the deposition of dew, say, is caused partly by temperature reduction and partly by decrease of volume. Let the air, saturated at the absolute tem- perature To, be cooled, without change of volume, to T,, and let the water vapor per unit saturated volume at these temperatures be wo and w,, respectively. Then the quantity of water, wo—w, will be deposited per unit volume as a result of cooling alone, EVAPORATION .AND CONDENSATION 251 while if the pressure remains constant; as it does, approximately, the volume will be reduced in the proportion Vo _To Vi im T and an additional quantity of water To—Ti To Fic. 63. W TEMPERATURE CENT. w ° 20° 259 30° Pre Grammes of water vapor per saturated cubic metre, at different temperatures. Bases of shaded Portions proportional to precipitations per 5° C. cooling from the temperatures indicated. deposited per unit volume at temperature To. Hence the quantity q of water deposited per original unit volume due to both proc- esses combined, decrease of temperature and decrease of volume, is given by the equation Ti q =Wo— U1 T, 252 PHYSICS OF THE AIR Condensation Due to “Mixing.—Since the amount of water vapor per saturated unit volume decreases with temperature more rapidly than the absolute temperature itself, at least through the range of atmospheric temperatures (see Fig. 63), it follows that the mixture of two saturated masses of air of unequal tem- peratures must produce some precipitation. The amount of pre- cipitation induced in this manner, however, is surprisingly small; indeed, it seldom can be sufficient to produce more than a light cloud or fog. If the resulting temperature were the proportionate mean of the known temperatures of the quantities of air mixed, the amount of precipitation could easily be computed from the Fic. 64. GRAMS. a tw a « oO < - a bs =< S n k 24 a a oO TEMPERATURE C.. Precipitation due to the mixing of saturated equal masses of warm and cold air initial humidities. But the latent heat of the condensation pre- vents this simple relation from obtaining, so that the actual amount of precipitation can better be determined graphically than by direct calculation.** To this end use a humidity temperature curve, such as Fig. 64, drawn to scale. For example, let equal masses of saturated air at o° C. and 20° C. be mixed at normal pressure—certainly an extreme case. As a first approximation it may be assumed that the final temperature is 10% C., and, since there are 3.75, 7.52, and 14.34 grammes of water vapor per 1000 grammes of saturated air at normal pressure and 0° C., 10° C., “Hann, “Lehrbuch der Meteorologie,” 3d edition, p. 249. EVAPORATION AND CONDENSATION 253 and 20° C., respectively, the precipitation per 1000 grammes of the mixed air would seem to be 3-75 $14.34 a —7.52 =1.53 grammes, represented by AD in the figure. But the latent heat of condensation causes the final tempera- ture to be above the average, and the amount of precipitated water, therefore, less than that just computed. But since the latent heat of vaporization at 10° C. is approximately 591 calories per gramme, and the specific heat of the air at constant pressure about 0.24, it follows that the warming of the air will be at the rate of 2.5° C., nearly, per gramme of water vapor condensed per 1000 grammes of air. Hence a second approximation to the final tem- perature and condensation is found by drawing from A a line in such direction that it shall indicate a change of 2.5° C. per gramme of condensate, and prolonging it until it meets the humidity tem- perature curve in B. This second approximation gives 11.5° C. very closely, instead of 10° C., as the temperature of the mixture, and 0.6 gramme, instead of 1.53 grammes, as the amount of con- densation per 1000 grammes of air, a quantity which, as the figure shows, would be condensed by a temperature decrease of less than 1° C. Obviously similar graphical solutions may easily be made for mixtures of unequal masses of air, for unsaturated air, for other pressures, and for other temperatures; though for temperatures slightly below 0° C. a greater latent heat of vaporization, approxi- mately 680, must be used. Since 1000 grammes of saturated air at 10° C. and normal i i 25 ic metre, it pressure occupies very approximately i of a cubic metre, follows that the condensation above described is about 0.74 gramme per cubic metre, a quantity capable of producing only a light cloud through which objects would be visible to a distance of about 70 metres.7®> Further, assuming the diameter of each cloud particle to be 0.033 mm., Wagner’s average value, it follows that the condensation in question could produce only about 39 such fog particles per cubic centimetre. Even if such a cloud were 1 kilometre thick and all its droplets should be brought down, they would produce a water layer only ™ Wagner, Site. der K. Akad. der Wis. Wien, 117 (1908), p. 1290. 254 PHYSICS OF THE AIK 0.074 cm. deep. Obviously, therefore, the mere mixing of masses of humid air at different temperatures cannot produce any appreciable precipitation in the form of rain or snow. Condensation Due to Dynamic Cooling—Dynamic cooling incident to vertical convection is by far the most effective method of inducing precipitation, but even when the convection is adia- batic it is not immediately obvious, from the initial temperature, humidity, and pressure, just how much water will be precipitated as the result of a given increase of altitude, nor even for a given decrease of temperature. This is because the rate of cooling with elevation is affected by the latent heat of vaporization, and the amount of condensation in turn decreased by the increase of volume, which itself is a function of the temperature and pressure. The problem is further complicated, on passing to temperatures below 0° C., by the latent heat of fusion and by the abrupt con- siderable change in the heat of vaporization. It therefore will be convenient to consider independently four possible stages in the dynamic cooling of a quantity of moist air: (a) the unsaturated; (b) the saturated at temperatures above o° C.; (c) the freezing; and (d) the saturated at temperatures below 0° C, This subject has been studied by several investigators, espe- cially Hann,7¢ Guldberg and Mohn,"* Hertz,‘ and Neuhoff.” Of these Neuhoff’s paper appears to be the most explicit, and it therefore will be used as the basis of the following brief discussion. Dry (Unsaturated) Stage.—Let the humidity be such that the mass ratio of dry air to water vapor is 1:w. Then the number of calories, dQ, necessary to change the temperature of 1 +w grammes of this atmosphere by dT and its volume by dV is given by the equation dQ=(Cy+wC'r)dT+A pd V, in which C» and C’y are the specific heats at constant volume, respectively, of dry air and unsaturated water vapor, A the ™ Met. Zeit., 9 (1874), 321, 337. 7“ Btudes sur les Mouvements de l’Atmosphére,” part 1, Christiania, 1876, revised 1883; translation by Abbe, “ Mechanics of the Earth’s Atmosphere,” Smithsonian Institution, 1910. % Met. Zeit., 1 (1884), p. 421; translation by Abbe, “ Mechanics of the Earth’s Atmosphere,” Smithsonian Institution, 1891. ” K. Prus. Meteor. Inst., 1 (1900), p. 271; translated by Abbe, “ Mechanics of the Earth’s Atmosphere,” Smithsonian Institution, rgto. EVAPORATION AND CONDENSATION 255 reciprocal of the mechanical equivalent of heat, and p the pressure. But, for 7 grammes, pV=nRT, in which R is the well-known gas constant and T the absolute temperature, numerically, 273 + reading of centigrade thermom- eter. Hence, dQ=(Cu+wC'r)dT+(R+wR)A rey Since pressures in the open air are easily measured, while volumes are not, it will be more convenient to have this equation expressed in terms of the former. This may be done by substitu- tions from the equations pdV + Vip =RdT and Cv=Cp—AR in which C> is the specific heat at constant pressure. If the convection is adiabatic—that is, if dQ=0 these substitutions give the equation (Co+wC'p) F =A(R+ URE: or, by integration, (Co-bw0'p) log rn (R-+4wR’) log e or, more simply, ’ 0 log o aK log - K =a constant, in which fo and To are, respectively, the initial surface pressure and temperature. Obviously this equation is applicable only until saturation is attained. Let éo and e be, respectively, the initial and saturation vapor pressures corresponding to the total pressures fp, and p, and abso- lute temperatures To and T. Then G T lo ak log rR and log e—K log T=log es—K log To =C, a constant. If ¢o and Ts are both known, C is also known, and since satu- ration vapor pressure depends upon temperature alone, and is known through a wide temperature range, it is obvious that both log e and K log T may be tabulated for many values of T, and 256 PHYSICS OF THE AIR that with such a table it is easy to pick out that value of T which gives the equation log e—K log T=C, the equation that determines the limit of the non-saturated or dry stage. If the convection has been adiabatic it is obvious that the height 4 of the dry stage is given by the equation h=100 (T,—T) metres, approximately. A crude estimate of the saturation, or cloud, height may also be made from the current temperature To and dew point Ta. Thus, when owing to convection Ty. P= 1" Cs the new volume is, roughly, one part in 80 larger than it would be under the initial pressure. But this increase in volume lowers the dew point 0.2° C., roughly, for average temperatures, as shown by vapor-saturation tables. Hence Ty =T,= = (7 = 1), any, and h = 125 (T, — Tz) meters, roughly. It should be distinctly noted that in general vertical convec- tion does not follow a fixed plumb-line. In cyclonic areas, for instance, the horizontal travel of the air doubtless often is hun- dreds of times the vertical. Hence in the quadrant of such a region where the clouds are from lower latitudes the vertical temperature gradient at any given place is likely to indicate a greater departure from adiabatic expansion than actually has occurred. This, as explained, is because the proper po and To to use in the above equations are those that obtained when and where the mass of air in question started to rise, and not those at the surface beneath its position at the time for which the equations are given. Under such circumstances the true values of po and To are not accurately known, but that does not affect the validity of the above discussion ; it only emphasizes the complexity of the problem as frequently presented in Nature. EVAPORATION AND CONDENSATION 257 Rain (Saturated, Unfrozen) Stage-—After saturation has been attained any further convectional cooling leads to precipita- tion. It will be assumed that this water is carried along with the ascending current (never strictly true and less nearly so as the drops grow in size), thus leaving the process adiabatic and re- versible, and that the volume of the liquid water is negligible in comparison to the space from which it was condensed. Let p be the total pressure, made up of the two partial pres- sures, air pressure p’ and saturated water vapor pressure e, a function of the temperature alone, and let the mass ratio of air to total water, condensed and uncondensed, be 1: w. Then p=pte= aT te. As before, the quantity of heat necessary to change the tem- perature of 1 gramme of air by an amount dT and its volume by dV is dQ = (CAT +ART Let w’ be the grammes of uncondensed water vapor per gramme of dry air. Then w-—w’ is the corresponding number of grammes of liquid water. Hence the heat necessary to bring about the temperature change dT and the vapor change dw’ is dQ” =w's.dT + (w—w’) dT +Ldw’ in which s, is the specific heat of saturated water vapor (that is, its specific heat when the volume so changes with the temperature as to maintain saturation and avoid condensation—a negative quantity), s, the specific heat of water, and L the latent heat of vaporization. With T constant, db L dQ” =L dw'=Tdd, or, (3,) TF & being entropy. With w/ constant, dQ” =w'sdT+ (w—w') dT =Tdd, or, (ar) _si(w—w') +50! aT } wy T But dQ is a perfect differential, therefore d (u@o=w!)-tow ) a (z.) dw’ Er “aT \T wor e(B) and 258 PHYSICS OF THE AIR Hence os d Lw’ aT, 40” =wsdT +7 ea ‘i ) and d= (car+aRry ) +7 & rr ) iP eae dp! d = (Cpa? ART a ae ( iz ) ar +usd?. Hence, since the process is adiabatic. (Co+wsi) T+ +5(4 )aramar “2 - By integration, using the subscript o for initial conditions, po _Cptus, tne f+ ar a) \ "oa, OAR , ts in which M is the modulus of the system of logarithms used. But »_ Re w= R'p’ Therefore Cotwsi 1, eL eoLo _ a@ a log 2 = Gory Ee 0. \ og FOE woe tae (pt pa) ~2 eat Fa): in which b, a, and do obviously are determinable numerical quan- tities for given values of w, T, and To. Hence log ar — blog T=log p’o ae —b log To=a constant. oO From this equation a table may be constructed giving the relation between p’ and T, and also, since e is known through a wide range of temperatures, between p and T. The value of w’, or grammes of water per gramme of dry air, is given for any temperature by the equation, 1_ Re_ Ww y R’p’ and the condensed water, w”’, per gramme of dry air by the equation, Re R'p’ wv =w—- EVAPORATION AND CONDENSATION 259 Hail (Freezing) Stage—Further lowering of the pressure beyond that at which the temperature reaches 0° C. causes, so long as there is any liquid water present, both freezing and evaporation. ‘The latent heat of fusion keeps the temperature constant, while the increase of volume under the reduced pressure increases the vapor capacity and thus leads to evaporation. To each gramme of dry air let there be w, w’, and w” grammes, respectively, of water, vapor, and ice. Then, as there is no change of temperature through this stage, dQ=ARTo oy + Law’ — Fdw" in which F is the latent heat of fusion, and To the absolute tem- perature at o° C. The negative sign is used because the heat : of fusion is added, or becomes sensitive with freezing; that is, with decrease of pressure and increase of volume. Assuming the process adiabatic, dividing by T, as before, and integrating, the above equation reduces to AR tog p+ (w’, — w'o) -F 0" —w"'o) =0. Let the subscript o indicate the condition when the tempera- ture reaches 0° C. with no ice, and subscript 1 the condition when all the water is just frozen. As the temperature is constant, ¢ will be the same at the beginning and end of the freezing process. At the end of the freezing w’} = w- w’,. Also, Ee SE ne Ve oy? meee Bae ee o=6, Hence e M(L+F) _ e ML MF Ee og Ae Pe ae "Ae This equation gives, in terms of known quantities, the rela- tion between the partial pressures of the air at the beginning and end of the “hail stage,” and therefore the depth of this stage, obviously determined by the amount of water to be frozen, which in turn depends on the original temperature and humidity. Snow (Frozen) Stage-—At temperatures below o° C. there will be present in the air only ice and enough water vapor to produce saturation. Hence the discussion applicable to this stage is identical with that for the “rain stage,” though two of the constants, specific heat and latent heat, will be different. The specific heat is now of ice, roughly one-half that of water, while 260 PHYSICS OF THE ALR the total latent heat is due to two distinct processes, fusion and vaporization. The equation, therefore, applicable to the snow stage is, log pb! _Cotwsi M (etP tll + fal) a log fk 7 7 = , Po AR tT, AR \ oT Pols in whiclr si is the specific heat of ice, and the other terms have the meanings previously given. It will be interesting to note that the form of the adiabatic equation is: 1. For the dry stage, log p—a log T=C, a constant. 2. For a condensation stage, log a log T=K, a constant, in which a and b are numerical coefficients, p the total pressure, and ’ the partial air pressure. The short hail or freezing stage is distinct from either of the others, though it may be represented approximately by an equation of the second or condensation type. “ Pseudoadiabatic’”’ Convection.—Adiabatic expansion of the atmosphere obviously implies that all cloud particles, rain drops, and snowflakes are carried along with the identical mass of air out of which they were condensed. This condition cannot rigorously obtain in Nature at any level; neither do all the products of condensation, especially the smaller droplets, rapidly fall away immediately they are formed. Hence the actual process, if con- duction, radiation, and absorption were negligible, would lie some- where between the adiabatic, with all condensation products re- tained, and that special type of the nonadiabatic which Neuhoft and others have called pseudoadiabatic, where all such products are immediately removed, probably much nearer the latter than the former. To reduce adiabatic to “pseudoadiabatic” equations it evi- dently is only necessary to drop the water and ice terms. This of course, automatically excludes the hail stage—it eliminates all water and therefore renders freezing impossible. Nevertheless the differences between the temperatures and pressures given by the two processes generally are small. For convenience of inter-comparison the two sets of equa- tions, adiabatic and “pseudoadiabatic,” are here grouped together. EVAPORATION AND CONDENSATION 261 : . P_ CptwC'p Tr Adiabatic, log bo A(R+WR’) log TF, “Pseudoadiabatic,’’ Does not exist, there having been no condensa- tion. p Cotwsr dis M eL eoLo Adiabatic, log ra log = + AR \p'T p'oTo t AR T Rain stage G ak ak, ‘a “rT CF s. Pins ss é. €o Pseudoadiabatic,”’ log Pe ak =? log T, ive a iver IT pl a) Dry stage “Pseudoadiabatic,’’ Does not exist, there being no water and there- fore no freezing. Cyp+wsi joe T +H ae @o(Lo + Fy) AR’ Adiabatic, log Hail stage , Adiabatic, log 2 = b') AR Snow stage fi tian Po fey 2 e(L+F) _ o(Lo+Fo) Pseudoadiabatic,” log an AR log Tr, +75 oe 0 lle Fe) p' T : p's To It will also be convenient to have listed the several constants of these equations and their numerical values. If the unitof heat is 1 calorie, the heat necessary to raise the temperature of 1 gramme of water from 0° C. to 1° C., the values of these constants are: eee X 10’ ergs, nearly. F =80o calories, about. L=600 calories, approximately. M —0.434209448, for base Io. T =273 +reading of centigrade thermometer. R=28.71 x 10° ergs per gramme 1° C., nearly. R’ = 46.42 x 10° ergs per gramme I° C., closely. C, =0.241, about. C’, =0.46, roughly. si=1, closely. 5; = 0.5, approximately. With these values various tables may be constructed for con- venient use of the formule, as has been done by Neuhoff.8° Proper hypsometric formule give the elevations above sea level corresponding to different conditions of the atmosphere with respect to temperature, pressure, and humidity. Hence it is possible to construct diagrams more or less accurately embodying all such calculations. Fig. 65, copied from Neuhoff’s paper, is an especially good adiabatic diagram of this kind. © Loe. cit. 18 262 PHYSICS OF THE AIR As is obvious from inspection, this diagram applies to all altitudes from o (sea level) to 7000 metres, and from —30° C. to +30° C. The temperature and altitude differences are equally spaced, and the pressure differences, therefore, unequally in respect to both the other terms. It is assumed that the adiabatic cooling Fic. 65. -30°_ -25° -20° -15° -10° -5° +5° 410° 415° +20° + PRESSURE re) a ID i) nn Ww a a o o MILLIMETERS MILLIMETERS ~ 760 -25° -2 4 -10° - O° +5° +10° +15° +20° +25° +30° TEMPERATURE C. — DRY ADIABATS | ——SATURATION CURVES -—-—SATURATION ADIABATS Adiabatic diagram (Neuhoff). of non-saturated air is at the rate of 1° C. per 100 metres increase of elevation, an approximately correct value, hence the dry adia- bats, given in full lines for intervals of 10° C., are straight diagonals, while the saturation adiabats, represented by dot and dash, are considerably curved. The saturation moisture content, in terms of grammes of water vapor per kilogramme of dry air, is given by the broken lines. EVAPORATION AND CONDENSATION 263 Interpolations are readily made on the diagram and approxi- mate values easily obtained by always starting from the intersec- tion of the given temperature and pressure codrdinates. For example, let the temperature be 20° C., the barometer reading 760 mm., and the relative humidity 55 per cent. Since, as the diagram shows, saturation at the given temperature and pressure would require about 14.6 grammes of water vapor per 1000 grammes of dry air, it follows that under the assumed conditions only about 8 grammes would be present. Hence the temperature, pressure, and altitude of such a mass of air rising adiabatically are given, through the first convective stage, by that dry adiabat that starts at the intersection of the initial temperature and pres- sure ordinates, 20° C. and 760 mm. The first stage terminates when saturation is attained, and therefore, in the present case, at the intersection of the given adiabat with the 8-gramme humidity curve at an elevation, as inspection shows, of rather more than 1100 metres and where the pressure corresponds to a barometric reading of about 625 mm. From this level up the conditions of the rising mass of air are given by a saturation adiabat, according to which the temperature will have fallen to o° C. and the humidity to about 5.25 grammes at an elevation of approximately 2700 metres. The humidity decrease, 2.75 grammes per 1000 grammes of dry air, is the amount precipi- tated as water in the form of cloud particles and rain drops. If all this water is carried along, its latent heat of fusion will main- tain the temperature at 0° C. through an additional rise of about 80 metres, but, as much of this water obviously must drop out, it follows that the actual conditions presumably are rather better represented by omitting the “hail stage,” or by a continuous rather than a broken adiabat. While this diagram gives approximately the relations between temperature, pressure, humidity, and altitude that obtain in regions of strong vertical convection, it does not closely represent them as they normally exist at other places. This is due partly to the horizontal component of air movement, as above explained, and partly to that constant emission and absorption of radiation that always precludes the existence in the atmosphere of strictly adiabatic conditions. Principal Forms of Condensation.—Condensation assumes many forms, of which the chief are: (a) free drops, varying in 264 PHYSICS OF THE. AIR size all the way from the fog or cloud particle up to the largest rain drop, or from .03 mm., roughly, to about 5 mm. in diameter ; (b) dew, water that has condensed on objects that by any process have attained a temperature below the current dew-point of the air immediately in contact with the bedewed objects. The cool- ing necessary to the formation of dew usually results from loss of heat by radiation; (c) frost, a light feathery deposit of ice caused by the same process that produces dew, but occurring when the temperatures of the objects on which it forms are below freezing ; (d) rime, a frost-like deposit of ice, often several inches deep on the windward sides of exposed objects. It is formed from impinging undercooled fog particles, and hence grows straight into the wind; (e) glaze (ice storm), a coating of clear, smooth ice on the ground, trees, etc. It generally is caused by the falling of rain on cold (below freezing) surfaces; (f) snow, tabu- lar, and columnar particles of ice formed in the free air at tem- peratures below freezing. All are hexagonal in type but of endless variety in detail—many exquisitely beautiful; (g) sleet, ice pellets, mere frozen rain drops (or largely melted snow- flakes refrozen)—frozen during the fall of the precipitation through a cold layer of air near the surface of the earth—that rattle when they strike a window, for instance; (/:) hail, lumps of ice more or less irregular in outline and generally consisting of concentric layers of clearish ice and compact snow. It occurs only in connection with thunderstorms and may be of any size up to that, at least, of a baseball or large orange such as fell in considerable quantities at Annapolis and other points in Mary- land on June 22, 1915.° Indeed, much larger stones have occa- sionally been reported and presumably have occurred. At any rate, in some instances stock in the fields have been killed by blows from hailstones of unusual size. Other forms of precipitation that should, perhaps, be men- tioned are: graupel soft snow pellets; mist, a thin fog of relatively large particles; and drizzle, a light rain of very small drops. How Raindrops Are Formed.—As already explained, the amount of condensation resulting from given temperature and pressure changes can easily be computed, but this is not sufficient to account for the formation of ordinary raindrops. The difficulty lies in the fact. that the number of nuclei per unit volume of the 5a Fassig, Monthly Weather Revicw, September, Ig15. EVAPORATION AND CONDENSATION 265 air (hundreds, or thousands, usually, per cubic centimetre) is so great that the condensation of even all the water vapor present would produce nothing larger than minute fog particles. It is natural, of course, to suppose that some of the droplets in any cloud are relatively large, and that all of this kind that happen to be in the upper portion will, on falling, grow by col- lision into full-sized raindrops. But this simple assumption is beset with several difficulties. In the first place, nothing of the kind occurs, at least not to any appreciable extent, in a fog, nor even in the average cloud. In fact, clouds may continuously cover the sky for days without yielding any rain whatever. Secondly, it is far from obvious that the droplets will coalesce, as assumed, on collision. Indeed, if they are not electrified, it is highly probable that, on the contrary, they will rebound from each other, as do the drops of a spraying jet of water,5°” due, presumably, to the air film between them. Finally, whether one considers a dense sea fog, diameter of particle 1o#, 1200 par- ticles per c.c.,8°° or a cloud, diameter of particle 33, 120 particles per c.c.,°°, a little calculation shows that not enough water could, on the average, be accumulated by simple collisions, in the manner assumed, to produce medium-sized raindrops. However, this latter difficulty is more apparent than real, as will be ex- plained presently. A factor in the growth of drops that needs to be examined is the relation of the saturation vapor pressure to their size, by virtue of which the larger tend to increase at the expense of the smaller. From the equation (see page 12) 2T p, R (Pw rs p-.) AP = it appears that the excess pressure above that of normal saturation about fog droplets of diameter 10 is 2.76 dynes per square centi- metre. Now, at 10° C. saturation pressure balances a column of mercury 9.14 centimetres high; hence at 10° C. the ratio of the excess pressure about droplets of 10m diameter to normal satu- ration pressure is, approximately, I to 44,000; nor is this ratio greatly different at other ordinary temperatures. b Lord Rayleigh: Proc. Roy. Soc., 38, p. 406, 1879. "e Wells and Thuras: U S. Coast Guard, Bulletin 5, 1916. "4d Wagner: Sits. der k. Akad. der Wiss., Wien., 117, p. 1281, 1908. 266 PHYSICS OF THE AIR Obviously, therefore, the growth of the larger drops at the expense of the smaller, as a result of the difference between their saturation pressures, is entirely negligible. Another factor is the difference between the temperature of the relatively cool falling drop and that of the adjacent atmos- phere. But the amount of condensation thus induced is very small owing to the large value of the latent heat of vaporization. The difficulties, then, that have to be considered in an attempt to explain the formation of raindrops, seem to be as follows: a. Drops large enough to fall at an appreciable rate—drops upon which any subsequent coalescence and resulting rain must depend—do not form in the average cloud. : This merely amounts to saying that such formation occurs only in rain clouds—that is, in clouds formed essentially by vertical convection. But how can convection produce drops of the necessary drizzle size in view of the hundreds, or, usually, thousands of nuclei per cubic centimetre? This seemingly in- superable difficulty is overcome (for it does rain), presumably in the following manner: All droplets of whatever size are actually falling in respect to the air in which they happen to be. Hence the rising air leaves more and more of its own nuclei behind as the droplets are abandoned—passes on as progressively filtered air—and thus contributes its subsequent condensation to only the fewer and fewer particles that exist along its upward path. Not only do the droplets fall out of the air in which they were formed, but they also aid in filtering the next portions of the rising column; and so on continuously. In this way the droplets well up within a cloud that is formed by vertical convection even- tually become relatively very few, and therefore grow compara- tively large as a result of the continuous condensation onto them. b. Water drops commonly do not unite on collision, but re- bound, as shown by the scattering of a jet. This difficulty is met by the fact that, when slightly electrified, drops do unite on collision,’ together with the further fact that rain is always more more or less electrified. c. A cloud particle in passing straight down through a cloud from top to bottom would not, on the average, touch enough other particles to form by union with them a medium-sized drop. But this is not important since rains are caused by rising air ®%e Lord Rayleigh: 1. c. EVAPORATION AND CONDENSATION 267 through which drops can not approach the earth until they have grown beyond a certain size which increases with the upward velocity. Besides, the variations in this velocity produce repeated rises and falls of drops of the appropriate sizes until growth through coalescence, or condensation, or both, sufficient for their final fall does occur. The rain process may, therefore, conveniently be divided into the following stages: 1. Vertical convection and the consequent formation of innu- merable cloud particles about the condensation nuclei immediately after the dew-point is passed, or, in the case of the more hygro- scopic nuclei, slightly before it is reached. 2. The continued rise of the saturated air, but now in a pro- gressively filtered condition as more and more cloud particles are abandoned. 3. Continuous condensation on the fewer and fewer droplets that remain in the “ filtered” air, and their consequent growth to appreciable size, accelerated, presumably by coalescence, though at what stage this phenomenon becomes important is not known. 4. The growth of the small drops by further condensation and, especially, by coalescence with other drops (all, on the aver- age, being more or less electrified) during their fall through the cloud and to the earth. In short, the rising air automatically filters itself immediately it passes the dew-point; the remaining water vapor condenses on relatively few nuclei (transported cloud particles) and thus produces droplets of appreciable or drizzle size; these, being elec- trified, unite on collision and form raindrops. Persistent vertical convection does not occur in fogs, nor in the average cloud. Hence they exhibit neither progressive filter- ing nor continuous condensation. Drops of appreciable size do not, therefore, form within them, nor rain fall from them. Velocity of Fall of Raindrops —If the diameter of the drop is very small, 0.1 mm. or less, its approximate steady, or terminal, velocity of fall can be computed by Stokes’s well-known equation,®°* eae to =p) V= =>¢ 9 ML € Phys. and Math. Papers, Vol. iii, p. 59. 268 PHYSICS OF THE AIR in which V is the velocity in centimetres per second, g the value, in C.G.S. units, of gravity acceleration, 7 the radius of the drop in centimetres, o the density of the drop, p the density of the air, and p» its viscosity. The equations of fall in the case of raindrops of average and larger sizes, I mm. to 5 mm. diameter, are, however, very differ- ent, and but little more than empirical.8°* Several of the more important velocities, and sufficient for approximate interpolations, are given in the table below of Precipitation Values. The maxi- mum velocity in air of normal density (velocity proportional, nearly, to square root of density), at which the larger drops break up, is about 8 metres per second. Intensity of Precipitation—The intensity, or rate, of rainfall vartes from zero up to several inches per hour, and, like the strength of the wind, has been popularly divided into several more or less definite grades. Most of these, together with other roughly average values they imply, are given in the accompany- ing table. PRECIPITATION VALUES (Air density as at 0° C. and 740 mm. pressure.) Precipitation] Djameter | Velocity of aia Height of Papulaihatnd, pg of drop, fall, metres | water per | cloud above Re mm. per second. | giutic metre surface, of air. metres. CT CAI di brenie B Stet torte 0.00 asst itplte 0.00 apttes OB in, cine gy a ait gina Trace 0.01 0.003, 6.0 oO SS Te ead crc 0.05 0.1 0.25 55-5 100 Diz Zen. «ses He lnese 0.25 0.2 0.75 92.6 200 Light taitcs«¢22 aye 1.00 0.45 2.00 138.9 600 Moderate rain...... 4.00 1.0 4.00 277.8 600 Heavy rain......... 15.00 1.5 5.00 833.3 1000 Excessive rain...... 40.00 1 6.00 1851.9 1200 Cloudburst. 5 en. n0s 100.00 3.0 7.00 5401.4 1200 5.0 8.00 IVhy the Atmosphere Generally is Unsatwrated.—It may, perhaps, seem strange that, in spite of the continuous and rapid evaporation from nearly all parts of the earth’s surface, the atmosphere as a whole never becomes even approximately satu- rated. This condition, however, is a necessary result of vertical convection. Obviously whatever the temperature and relative “gs Liznar: Met. Zcit., Vol. xxxi, p. 339, 1914. EVAPORATION AND CONDENSATION 269 humidity of a given mass of air at any point of its convectional route, its absolute humidity is less then, in general, than when its ascent began, by the amount of rain or snow already abandoned by it. That is, on the average, air in a convection circuit descends to the earth drier than when it previously ascended from it. In short, convection, because it induces abundant precipitation, is therefore a.most efficient drying process; and because compara- tively little precipitation is produced in any other way, convection alone prevents the atmosphere from becoming and remaining intolerably humid. Summer and IVinter Precipitation.—Vertical convection, essential, as above explained, to all considerable condensation, results from three distinct causes: (a) superadiabatic tempera- ture gradients, due often to surface heating; (b) converging winds, as in the front half of cyclones; and (c) forced rise from (1) flow over land elevations and barriers of cold air, (2) underrunning of cooler winds. The first, or thunderstorm, type of convection causes much of the summer precipitation of temperate regions, as also nearly all the rain of the tropics, while the second, or cyclonic, convection produces by far the greater part of winter precipitation, except, perhaps, that which occurs along the wind- ward sides of the most favorably situated barriers. Also, during the colder season precipitation usually occurs lower down the barrier slope and may be induced by feebler cyclones or other storms than in the warmer. This is owing in part to the fact that generally there is less difference between the actual and dew- point temperatures during winter than during summer (a condi- tion determined by the great seasonal temperature changes of continents with reference to the ocean), and therefore a less con- vection required in the first case than in the second to induce condensation, and partly to the greater rate of decrease of tem- perature with increase of latitude while the days are short than while they are long, a condition that favors winter precipitation by causing a greater fall of temperature during the winter season than any other for a given travel of the wind on the front or rainy side of acyclone. That is, usually a less vertical convection and a less horizontal travel of the air—a feebler storm—suffices to induce precipitation during winter than during summer. The contrasts, then, between summer and winter precipitation 270 PHYSICS OF THE AIR are manifold. The more important differences are listed in the following table: Contrast Between Summer and Winter Precipitation. | Summer Winter Rainecesec de ouawls tews we Usually. Often. DONO Weatis'ea alin 25.5 eee kt Never. Frequent. Hail (ice lumps)........... Occasionally. Never. Sleet (frozen rain)......... Never. Occasionally. On barrier.............00. High. Low, and up. Type of storm............. Thunderstorm frequently Cyclone. Strength of convection..... Strong,generally essential Feebler, often sufficient. Intensity of cyclone........] Decided,usually essential Slight, often sufficient. CHAPTER XIV. FOGS AND CLOUDS. THE deposition of dew, the forming of hoar-frost, and the sweating of ice pitchers, all examples of surface condensation, show that atmospheric moisture promptly condenses upon any object whose temperature is below the dew-point. Similarly, volume condensation takes place in the form of a fog or cloud of innumerable droplets, or ice spicules, throughout the body of ordinary air whenever by expansion or otherwise it is sufficiently cooled. But this is not equally true of all air. Thus, while the first considerable rapid expansion, and therefore decided volume cooling, of humid air in a receiver, if recently admitted unfiltered, is quite certain to produce a miniature cloud, subsequent expan- sions of the same air produce fewer and fewer fog particles. If the old air is removed and unfiltered fresh air admitted, the con- densations again occur as before; but if the fresh air enters through an efficient filter, such as a plug of cotton wool a few centimetres long, condensation remains as difficult as in the exhausted air. The admission, however, of a little smoke restores to the ex- hausted, and confers upon the filtered, air full powers of condensation. Obviously, then, cloud droplets form about nuclei that cannot easily pass through mechanical filters of fine texture, and micro- scopic examinations of the residue left on the evaporation of these droplets have shown the nuclei to consist in large measure of dust particles, both mineral and organic. Hygroscopic gases, such as the oxides of sulphur and of nitrogen, may also act as condensa- tion nuclei, but ordinarily there is abundant dust in the atmos- phere (thousands of particles per cubic centimetre) to provide for all precipitation. It is often urged that free electrons in the air also act as nuclei about which water vapor condenses, but, as this type of condensation requires about a fourfold supersaturation, its occurrence in the open seems extremely improbable. As stated, volume condensation may be induced in the atmos- phere by any cooling process: whether by radiation, as on clear nights; mixing warmer with colder masses of air; movement of relatively warm air over cold surfaces, as in the case of winter 271 272 PHYSICS OF THE AIR south winds (northern hemisphere) ; or expansion, owing either to convection or barometric depression. But the cooling process has much to do with determining the extent of the condensation, the kind and amount of precipitation from it, and its general appearance, according to which, chiefly, it is classified. Distinction Between Fog and Cloud.—Volume condensation is divided primarily into fog and cloud, but a sharp distinction between them that would enable one always to say which is which is not possible. In general, however, a fog differs from a cloud only in its location. Both are owing, as explained, to the cooling of the atmosphere to a temperature below its dew-point, but in the case of the cloud this cooling usually results from vertical convection, and hence the cloud is nearly always separated from the earth, except on mountain tops. Fog, on the other hand, is induced by relatively low temperatures at and near the surface, and commonly itself extends quite to the surface, at least during the stage of its development. In short, fog consists of water droplets or ice spicules condensed from and floating in the air near the surface; cloud, of water droplets or ice spicules condensed from and floating in the air well above the surface. Fog is a cloud on the earth; cloud a fog in the sky. FOGS. According to the conditions under which they are formed, fogs may be divided into two general classes—radiation fogs and advection fogs. Radiation Fog.—Fog is likely to form along rivers and creeks and even in cleared mountain valleys during any still, cloudless night of summer and, especially, autumn. In the course of a calm warm day and earlier portion, at least, of the night much water is evaporated into the lower atmosphere of such regions, where in large part it remains as long as there are no winds. Hence this air, because it is humid, and the adjacent sur- face of the earth lose heat rapidly during the night by radiation to the clear sky. In many cases they cool in the end to a tempera- ture below the dew-point, and thus induce a greater or less volume condensation, on the always-present dust motes, that results in a correspondingly dense fog (Fig. 66). Such fog, however, is not likely to occur during cloudy nights, because the air seldom then cools sufficiently, nor during high winds, since they dissipate the 273 FOGS AND CLOUDS (-oyoyd ‘paam “Lf *¥) ‘eA ‘AQTIVA UNOpNoy ‘Boj UoryeIpEey 274 PHYSICS OF THE ATK moisture and also through turbulence prevent the formation of excessively cold aerial lakes. The distinctive factor in the formation of this type of fog is the free radiation of the ground and the lower air by which the latter is sufficiently cooled to induce condensation. Hence fogs formed in this manner are properly termed “ radiation fogs,” sometimes also called “ land fogs ” and “‘ summer fogs.” A frequent incidental phenomenon in connection with fogs of this class is their accelerated growth well after daybreak, which occasionally continues until after sun-up when radiation gain ex- ceeds the corresponding loss.. It has been suggested that this phenomenon is due to hygroscopic compounds formed in the air by insolation, either direct or diffused, but there is as yet no proof that these compounds are more than a contributing factor, perhaps an entirely negligible one, to the observed result. An- other factor, that at times and places may be of some importance, is the soot and hygroscopic compounds discharged into the foggy air from numerous breakfast fires. Usually, however, the sole appreciable cause is the gradual onset of convectional disturb- ances in the quiescent valley air incident to the insolational warm- ing of the mountain tops and sides. This mixes the cool sur- face layer with that next above and thereby often increases the fog depth. Furthermore, it drags the river of fog up the valley walls, and thus also increases its width. However, before either process has gone very far evaporation becomes manifest, and generally within an hour or two the fog has totally vanished. Advection Fog.—Whenever warm, humid air drifts over a cold surface its temperature is reduced throughout the lower turbulent layers by conduction to that surface and by mixture with remaining portions of the previous cold air and a corre- spondingly dense fog produced. Hence fog often occurs, during -winter, in the front portion of a weak cyclone; also whenever ‘air drifts from warm water to cold—from the Gulf Stream, for instance, to the Labrador Current; and wherever gentle ocean winds blow over snow-covered land—circumstances that justify the terms “ winter fog” and “sea fog” (drifting on shore in places, and even some distance inland, Fig. 67). Similarly, a cold wind drifting or spreading under and through a body of warm, humid air also produces a fog, though usually a compara- tively light one. This explains the fog that frequently forms, DEPT, OF hizi cUBO FOGS AND CLOUDS 275 276 PHYSICS OF THE AIR during winter, along the front of a “ high,” and the thin fog that occasionally is seen over lakes on frosty autumn mornings, when the water appears to be steaming—actually evaporating into air already saturated and thus inducing condensation. It also explains the frequent occurrence of “ frost smoke”’ on polar seas. If the wind is strong the turbulence extends through a com- paratively deep layer. Hence in the case of warm air drifting over a cold surface if the movement is rapid the total duration of contact between any portion of the air and that surface is likely to be so brief that but little cooling can take place and no fog be formed. Similarly, it usually also happens that fog does not form when the cold wind blowing over a warm, humid region is even moderately strong. Here the turbulence mixes the ex- cessive moisture near the surface through so large a volume that saturation commonly is not produced, nor, therefore, any trace of fog. From the above, it appears that all fogs that result from the drifting of warm, humid air over cold surfaces, as also those that are produced by the flow of cold air over warm, humid regions, are but effects of temperature changes induced by the horizontal transportation of air; hence the proposed general name, “ advec- tion fog.” The term advection is preferred to convection because the latter is practically restricted, in meteorological usage, to a change of level, whereas in the case under consideration only horizontal movements are concerned. The contradistinction, therefore, between “advection fog”’ and “convection cloud ” is obvious, and, presumably, worth while. CLOUDS. The cooling of the atmosphere by which cloud condensation is induced is, perhaps, most frequently produced by vertical con- vection, either thermal or forced ; often, presumably, by the mixing of winds of different temperatures; occasionally by pressure changes, elevation remaining the same; occasionally, also, by radiation ; and rarely, in the case of very thin clouds, by diffusion and conduction. Radiation, though productive of many fogs, is excluded from the list of principal cloud-forming processes for the reason that, as explained elsewhere, any mass of free air that cools in position, as it must whenever its radiation exceeds its absorption, imme- FOGS AND CLOUDS 277 diately gains in density and falls to a lower level where, when equilibrium is reached, it actually is warmer than it was before the cooling began, and its relative humidity, therefore, lower. Hence it seems that radiation could produce clouds only when equally active, or nearly so, over an extensive layer of practically saturated air. If radiation is unequally distributed it tends to evaporate clouds rather than to produce them. Classification —lIt is not practicable, however desirable, to classify clouds according to their causes, as in the case of fogs, for it often happens that the exact cause is not obvious. Hence other bases of classification have been adopted, especially form or appearance, activity, and position. Most, but not all, clouds belong to one or other of the four distinct types, cirrus, stratus, cumulus, nimbus, including their alto-, fracto-, and combination forms; alto-stratus, alto-cumulus; fracto-stratus, fracto-cumulus, fracto-nimbus; cirro-stratus, cirro-cumulus, strato-cumulus, cumulo-nimbus. Cirrus (Ci.).—The name cirrus, literally a curl or ringlet, has been given to those fibrous white clouds that resemble great wisps of hair (mares’ tails), giant curling plumes (feather clouds), tangled skeins, and various other things (Figs. 68 and 69). These are the highest, often 10 to 12 kilometres above the earth in middle latitudes and still higher in tropical regions, the most tenuous, and among the most familiar of all clouds. Since cirri usually run far ahead of the rainy portions of a cyclonic area, often even well into the preceding anticyclone, and grow denser as the storm approaches, it is obvious that they frequently result from cyclonic convections that extend nearly or quite to the stratosphere, where, and for some distance | below which, the rising air is carried forward much faster than the storm centre. But they also are fairly common as isolated clouds in the midst of ‘“ highs,” due, presumably, to a mechanical or bodily lifting of the upper air of these regions, or overrunning . of air in the general circulation, and, consequently, dynamical cool- ing not only of the stratosphere, as abundantly shown by the records of sounding balloons, but also of the topmost portion of the troposphere where cirri usually form. It has been suggested that cirri often are caused by cooling in place by radiation, but, as already explained, this appears to be improbable for clouds so broken and discontinuous. On the 19 278 PHYSICS OF THE AIK cS Coyoyd ‘uvurley[g "y) ‘snis) 279 FOGS AND CLOUDS 280 PHYSICS OF THE AIR contrary, however, it seems likely that through free radiation and cooling at night they often sink to lower levels, get warmer, and evaporate. Thermal and mechanical convection, therefore, the first prevailing in tropical regions, the second, presumably, in extratropical, appear to be the only abundant causes of cirri. The excessively low temperatures at which cirri are formed, generally —30° C. to -50°C., necessitate their being tenuous (at such temperatures there is but little water vapor to condense) and practically insure (exceptions have been reported **) that they shall consist of ice needles, or, in some cases, of small snow- flakes. The fibrous and feathery structures of the highest cirri may perhaps be explained as follows: Since diffusion is a very slow process, it is clear that moisture is carried into the upper atmosphere mainly by vertical convection, and, as this often occurs sporadically, it appears that through the increase of winds with elevation, the rising and generally humid air is likely to be drawn out into long threads and bands, and to ficat away in filaments at the convective limit, just as during the early hours of calm autumn mornings chimney smoke in mountain valleys often is drawn out into streaks and ribbons at or near the inversion level. Any cloud, therefore, produced in this fibrously humid air obviously itself must have the same general structure—a com- mon structure of cirrus clouds. Through local convection, how- ever, and abrupt changes in velocity at the upper surface of these clouds the air currents to which they are due presumably often are deflected into curves of changing radii. Hence, perhaps, the curved or plumed cirrus. Mare’s tails are streaks of snow fall- ing from and generally trailing behind small alto- or cirro-cumuli. They often are curved by changes with level of wind direction. Cirro-stratus (Ci.-St.).—When cirrus clouds thicken, as they usually do on the approach of a cyclonic storm, they gradually merge into a broad cloud layer, having the appearance of a more or less continuous white veil of uneven and often fibrous texture (Fig. 70), to which the name cirro-status has been given. Its altitude is nearly that of the cirrus, of which indeed it is only a “dense and extensive form, though its under surface is not so. high. Like its forerunner, the thinner cirrus, it also consists = Simpson, Qr. Jr. Roy. Meteorol. Soc., 38 (1912), p. 291. 281 S AND CLOUDS a: FOC PHYSICS OF THE AIR N N FOGS AND CLOUDS 283 of ice crystals, as is evident from the various types of halos it forms about the sun and moon. The origin of these clouds is substantially the same as that of the cirrus; that is, convection, which in turn may be caused by general expansion of the air below or by convergence of winds, such as occurs in the cyclone. Frequently, as explained above, the cirro-stratus is only the higher and swifter portion of the cyclonic cloud system, the result of forced convection to great altitudes. Cirro-cumulus (Ci.-Cu.).—Cirro-cumuli are small, fleecy cumulus clouds, generally 6 to 7 kilometres above the surface; that is, in the lower cirrus region. They usually occur in large numbers, producing an effect sometimes described as ‘“ curdled sky ”; frequently, also, in groups and rows that remind one of the patterns (not the scales) on the backs of mackerel. Hence the expression “ mackerel-back sky,” commonly abbreviated to “mackerel sky ” (Fig. 71). Their origin obviously is due chiefly to a single cause—local vertical convection, induced by an overrunning, cold layer of air, when the cumuli are in rows, or by unequal local heating of a layer of varied humidity. To each convective rise of the air there evidently must be an equivalent descent, and if the heating maxima are numerous the minima between must also be numer- ous, thus producing many rising currents, each with its small cumulus, surrounded by descending air and relatively clear sky. Through precipitation and turbulence the cirro-cumulus often develops into a cirro-stratus, or alto-stratus. Alto-stratus (A.-St.).—The alto-stratus is a thick, grayish cloud veil (Fig. 72), at times compact and fibrous in structure, and again thinner, like a heavy cirro-stratus, through which the sun or moon may dimly be seen. Its average elevation (under surface) is about 4 kilometres. It may result from the forward running of air forced up by the convergence of winds in the storm area of a cyclone, from the spreading tops of cumuli, from the flow of warmer over colder air, from falling precipitation out of alto- and cirro-cumuli, or from the mere radiational cool- ing in place, of a layer of relatively humid air—humid from the evaporation of alto-cumuli, perhaps. Alto-cumulus (A. Cu).—The name alto-cumulus has been given to those detached, fleecy clouds, with shaded portions PHYSICS OF THE AIR 284 285 FOGS AND CLOUDS OF THE AIR N FOGS AND CLOUDS 287 (Fig. 73), often occurring in closely packed groups and rows, that resemble enlarged cirro-cumuli, and doubtless are formed in much the same way. The moisture involved, especially during fair weather, seems often to be furnished by previously evapo- rated cumuli. Their average altitude is approximately that of the alto-stratus, that is, 4 kilometres. Indeed, detached portions of forming or evaporating alto-stratus also are generally called alto-cumuli, the more exact term, fracto-alto-stratus, not being in use. Strato-cumulus (St.-Cu).—Strato-cumuli are large rolls of dark cloud more or less connected with thinner clouds which together cover nearly or quite the entire sky (Fig. 74). Their bases are flat and at about the same height, generally 1.5 to 2 kilometres. They are formed by vertical convection, as is obvious from their rounded tops and flat bases at approximately the same level—the common saturation level. Their shallow depth and broad expanse are due, presumably, to an overlying layer of small, or even inverted, temperature gradient through which ris- ing air cannot easily penetrate. This name is also given to a stratus of irregular density, and thus to all that entire range of clouds between the uniform stratus and the discrete cumuli. Nimbus (Nb.).—The nimbus is any thick, extensive layer of formless cloud from which rain or snow is falling. The average altitude of its under-surface is of the order of 1 kilo- metre. It is produced chiefly by some type of forced convection: the converging of wind currents as occurs especially in front of cyclonic centres, the upward deflection of winds by either land or cold atmospheric barriers, and the under-running of warmer by colder air. In part, however, the cooling and consequent condensation often is owing to the mixing of cold air with warm, and to the transfer of warm air to a colder region, where it is cooled bv contact. by mixing with cooler air, and by excess of radiation loss over radiation gain. Fracto-nimbus (¥Fr.-Nb.).—The fracto-nimbus, popularlv known as scud, is that low, detached cloud fragment, too thin and fog-like to produce rain, that occasionally is seen drifting rapidly beneath a heavy nimbus at an average elevation of prob- ably not more than 100 to 300 metres. It may rise, like steam, during or following rainfall on a warm surface, especially in valleys and on the sides of mountains (where it is often called PHYSICS OF THE AIR 288 FOGS AND CLOUDS 289 fog) which it ascends. It is also caused by forced convection over cliffs or other obstacles. Cumulus (Cu).—The cumulus (Fig. 75), often called Fic. 76. Cumulus cloud formed by convection over fire on Sister Elsie Peak, Calif. September 13, 1913. (O. H. Lawrence, photo.) ‘ ‘woolpack,’”’ is a dense, detached cloud with a rapidly changing cauliflower head and flat base at the saturation level of rising air. Its illuminated portions are snow white, while the shaded parts PHYSICS OF THE AIR 290 FOGS AND CLOUDS 291 are unusually dark. Its border is sharply defined and, when near the sun, very bright. The average altitude of the base is about 1.5 kilometres, and of the top rather more than 2 kilometres. Cumuli are produced entirely by vertical convection induced by temperature differences—even fires sometimes cause them (Fig. 76). Hence they are always frequent in tropical regions, and also over continents at higher latitudes during summer. For the same reason, they occur over land most numerously of afternoons, and at sea late in the night. At times rather low cumuli form a sort of coastal fringe along the locus of upward convection—that is, a short way out over the sea at night, and a few miles inland during the day—that might, perhaps, be called coast cumuli—attendants of the land breeze and the sea breeze, respectively. They often occur over reefs and islands (Fig. 77), whose presence frequently is thus revealed while they them- selves are still below the horizon. Occasionally they even parallel a large river on either side where there is rising air over the hills and bottoms and sinking over the cooler water. Further, since vertical convection depends only on the establishment of a proper vertical temperature gradient, it follows that cumuli may also form at high latitudes over the warmer portions of the ocean, or, indeed, wherever there is a sufficient temperature contrast between the surface and overlying air to induce marked upward currents. Fracto-cumulus (Fr.-Cu.).—During the initial stages, espe- cially, of their development cumuli often are small, and appear tattered and torn like detached and dissolving masses of fog (Fig. 78). While in this condition stich clouds are often called fracto-cumuli. Cumulo-nimbus (Cu.-Nb.).—The cumulo-nimbus (Fig. 79), a necessary accompaniment of every thunderstorm, is, as its name implies, a cumulus cloud from which rain is falling. It is very turbulent and much the deepest of all clouds, being usually anywhere from I to 4 or § kilometres thick—occasionally even 10 or more, especially in the tropics. Its times and places of occurrence and mode of formation are all the same as those of the cumulus. Stratus (St.).—The stratus is a low, fog-like cloud of wide extent, often merging into a nimbus and again clearing away like lifted fog. Its average altitude is between 0.5 and 1 kilometre. It seems often to result from forced convection due to the under- 292 PHYSICS OF THE AIR 293 FOGS AND CLOUDS PHYSICS OF THE AIR 294 FOGS AND CLOUDS bo \o on 296 PHYSICS OF THE AIR running of cold air, and also, perhaps, to the mixing of humid layers of different temperatures. In some cases, that of the “velo” cloud, for instance, in southern California, it is only sea fog drifting over relatively warm land. SPECIAL CLOUD FORMS. Although it might seem that the above cloud types, including their numerous gradations and transitions, are exhaustive, there nevertheless are several occasional forms sufficiently distinct to justify individual names and special descriptions. Billow Cloud.—Billow clouds (Figs. 80 and 81), also called windrow clouds and wave clouds, occur in series of approxi- mately regularly spaced bands, generally with intervening strips of clear sky. They usually form in the lower cirrus region—that is, at elevations of 6 to 8 kilometres—but may occur at any level from the surface—fogs are occasionally billowed—up to that of the highest cirrus. They are caused by the flow of one air stratum over another of different temperature and density and usually of different humidity. It has been shown ®? that when two strata of air of different densities or vapor content flow over each other billows of great wave-length and often of large amplitude are generated in the same manner that winds produce ocean billows. As the series of waves progress the atmosphere involved obviously rises and falls, and therefore is subjected to alternate dynamical heating and cooling, with the maxima and minima temperatures corre- sponding to the troughs and crests respectively. Hence when the under layer is wholly or nearly saturated the wave crests are cloudy and the troughs clear. If, however, the humidity is not high, it is obvious that wind billows may exist without the incidental clouds. It is interesting to note that, although the billow cloud appears to consist continuously of the same mass, nevertheless, it is rapidly evaporating on the rear or descending portion of the wave and as speedily forming on the front or ascending portion. ” Helmholtz, Sitz. d. Akad. d. Wiss., Berlin, 1888, i, p. 646; 1889, ii, p. 761. W. Wien, Sits. d. Akad. d. Wiss., Berlin, 1894, ii, p. 509; 18095, i, p. 361. A. Wegener, Beitrige Phys. d. fr. Atmos., 2 (1906), p. 55; 4 (1911), p. 23. 297 FOGS AND CLOUDS oyd ‘tu Osiay Uy d ‘O) JaUILY JUNOTY J3A0 ‘pnojo rejnoyUsT ‘Oly err ror PEO PEL Pci .| Sn EO MT eee PHYSICS OF THE AIR 298 FOGS AND CLOUDS 299 Lenticular Cloud.—The lenticular cloud (Figs. 82 and 83) is formed by the upward deflection of the wind over mountain peaks, the cloud often appearing some distance away at the crest of a billow; and, perhaps, by similar deflections and other disturb- ances due to rising air currents. In some cases, doubtless, the cooling is accentuated by the low temperature of the peak itself. In either case the cloud particles are rapidly evaporated as they are carried away, and the thickness of the whole mass reduced to zero at no great distance. Fic. 84. Crest cloud, Windward side, seen from the Pali, near Honolulu. (A. M. Hamrick photo.) Crest Cloud.—The crest cloud (Figs. 84 and 85) is formed by the upward deflection of the wind by a long mountain ridge. It usually covers the higher slopes as well as the top, and, though called cloud by people in the valleys below, is likely to be desig- nated fog by any one actually in it. Occasionally condensation occurs only along the upper reaches of the deflected winds, in which case the cloud belt is above and to the leeward of the mountain ridge. In either case the individual droplets are quickly evaporated and the cloud form preserved only through continuous conden- sation from renewed air. It is permanent in the same sense 300 PHYSICS OF THE AIR that a cataract is permanent through the continuous supply of water by the stream above. Banner Cloud-—The banner cloud (Fig. 86), as its name implies, resembles a great white flag floating from a high moun- tain peak. In strong winds the pressure to the immediate lee- ward of such a peak is more or less reduced, and the resulting low temperature, intensified, perhaps. by the mountain surface. appears to be the cause of this singular cloud that, though con- Fic. 85. Crest cloud, lee side, seen from Honolulu. (A. M. Hamrick, photo.) tinuously evaporating, as constantly re-forms in the turbulent wake. Scarf Cloud.—It occasionally happens that as a cumulus rises rapidly and to great heights a thin, cirrus-like cloud, convex upward, forms above the cumulus head and, at first, entirely detached from it. As the cumulus continues to rise the flossy cloud becomes more extensive and rests on the thunder head or heads. A little later it mantles the shoulders, the heads being free (Fig. 87), and may even drape the sides of the cumulus. In all stages it resembles a great silken scarf, hence the above- suggested name. It often is called false cirrus, but that name FOGS AND CLOUDS 301 Tic. 86. Banner cloud, Mount Assiniboine, near Banff, Canada. (C. D. Walcott, photo.) PHYSICS OF THE AIR 302 FOGS AND CLOUDS 303 is now and better applied to a different formation. It has also been called cap cloud, but this is confusing, because the same term has long been applied loosely to any cloud that hovers above, or, especially, rests upon a mountain peak, and, besides, the cap analogy applies to only the early stages. It is caused by the elevation and consequent expansion and cooling of the air immediately and to some distance above the rising mass of the cumulus. Generally ‘this expansion of the superincumbent atmosphere produces no visible effect, but occa- sionally there exists a thin stratum of nearly saturated air in which an alto-stratus might form, or, indeed, later does form, and when this is lifted by the rising cumulus it immediately develops a local cirrus-like cloud. But if the saturated layer is thin, as it often is, the cumulus head may easily rise quite above it into drier air, leaving the filmy cloud at practically its original level, the level of the humid stratum, or completely absorbing it. False Cirrus.—The name “ false cirrus” formerly was applied indifferently to the scarf cloud, just described, and to those gray locks, to speak figuratively, combed out from old thunder heads by the upper winds. At present, however, the term usually is restricted to the latter phenomenon. Although the lower atmosphere, up to at least 3 or 4 kilo- metres, generally is comparatively calm whenever cumuli are most conspicuous, it nevertheless occasionally happens that the highest thunder heads reach into a stratum of much greater velocity in which, therefore, the topmost portions of the cloud are drawn out into wispy bands and fibres of snow crystals—a truly cirrus cloud whose peculiar origin is, perhaps, its only claim to the special name “ false cirrus.” The same name is also ap- plied to the thinner edges of the anvil cloud, or spreading top of a cumulo-nimbus. Mammato-cumulus—The mammato-cumulus, sometimes called pocky-cloud, festoon-cloud, “rain balls,” sack-cloud, or cther similar name, is essentially a reversed cumulus (Fig. 88). It generally occurs in an alto-stratus or cumulo-stratus cloud, and seldom except in connection with a severe thunderstorm. As is well known, ice in the form of hail and snow often occurs in the upper portions of large cumuli. If, now, this snow, say, is drifted out just above a stratus cloud, it is obvious that the cooled layer will descend at many different places, and that at 304 PHYSICS OF THE AIR 395 FOGS AND CLOUDS Cojoyd ‘130394 “EE M) “Ae ‘N ‘1o[}UW ‘pnop opeusoy 306 PHYSICS Ob THE AIR each such place there will be produced a sag or pendulous bulge in the cloud base and, of course, a lift or rise wherever the counter-current obtains, thus producing the festooned appear- ance characteristic of this rather unusual cloud. Tornado or Funnel Cloud.—The tornado cloud (Fig. 89) is only a funnel-shaped extension of, generally, if not quite always, a cumulo-nimbus. It is produced by the expansional cooling inci- dent to the rapid rotation of the atmosphere in which it appears. CLOUD HEIGHTS. Relation to Humidity—The heights of clouds have been measured by several obvious methods of triangulation, and from Average Cloud Heights in Kilometres. | , : Cu.- : . Ci.- | Ci.- A.- | St.- oY Gay. \sCas.| Pre Station Ci. | SE | Cu. A.St Cu. | Cu. Nb. pe Top | Base | Cu. St. I, SUMMER, CHIEFLY APRIL TO SEPTEMBER. Bossekop, 70°N ....| 8.32) 6.01] 5.35) 4.05 | 3.42 | 1.34 | 0.08 | 3.90 | 2.10 | 1.32] .... [0.06 Pavlovsk, 60° N....| 8.81] 8.00] 4.60] .... | 3.05 | 1.85 | .... | 4.68 | 2.41 | 1.64 | 2.15 [0.84 Upsala, 60° N...... 8.18] 6.36] 6.45] 2.77 | 3-95 | 1.77 | 1.20 | 3.97 | 2.00] 1.45 | 1.83 |.... Potsdam, 5214°N ..| 9.05] 8.08] 5.89] 3.29 | 3.63 | 2.16 | 1.79 | 3.99 | 2.10 | 1.44 | 1.71 }0.68 Trappes, 40°N..... 8.94| 7.85) 5.83] 3.79 | 3-68 | 1.82 | 1.08 | 5.48 | 2.16] .... | 1.40 |0.94 Toronto, 4314° N...| 10.90] 8.94] 8.88] 4.24 | 3.52 | 2.06/] ....] .... 1.70 : as Blue Hill, 42°N.....| 9.52/ 10.10] 6.67] 6.25 | 3.76 | 1.16 | 1.19 | 9.03 | 2.90 | 1.78 | .... |o.51 Washington, 39° N..| 10.36| 10.62} 8.83] 5.77 | 5.03 | 2.87 | 1.93 | 4.96 |(2.45)/ 1.18 | .... |0.84 Allahabad, 251%4°N .| 10.76] .....] 11.28] .... | 4.50] .... | 0.84] .... 1.76 mati orgies Manila, 144%4° N....| 11.13) 12.97| 6.82] 4.30 | 5.71 | 1.90 | 1.38 | 6.45 1.84 wee. [T.06 Batavia, (year), 6°S.| 11.49| 10.59] 6.30] .... | 5.40] .... nas: || a nege 1.74 waive [0.70 2. WINTER, CHIEFLY OCTOBER TO MARCH. Pavlovsk........-.| 8.74 7-09; 5.98) .... | 3.17 | 1.50] .... | .... | 1.60 | I.12 / .... [1.00 Upsala... 6.98; 5.46] 6.13] 4.09 | 4.15 | 1.96 | 0.99 | 5.18 | 1.52 | 0.71 | 1.22 0.51 Potsdam 8.07' 7.65] 5.41] 2.09 | 3.35 | 1.42 | 1.28 | 4.74 | 1.74 | 0.99 | 1.02 |0.61 Trappes .. wee{ 8.51 5.85] 5.63] 3.82 | 4.27 | 1.61 | 1.05 | 3.85 | 2.37] .... | 1.43 |...- TOrOnto ser seve svsonscns 9.98) 8.53| 8.25) 4.18 | 2.50 | 1.54 eis 1.33 ainesa || ages Bitte: Aibbee vce gcicdes 8.61; 8.80] 6.16] 4.57 | 3.66 | 1.60 | 0.65 | .... | 1.62 | 1.54 | .... |0.61 Washington........ 9.51] 9.53] 7-41] 4.80 | 3.82 | 2.40 | 1.80 | 3.73 | 2.28 | 1.20] .... [1.13 Manila vsscs4600} 2230 | 430 metres | Minimum..] 105 50 50 160 340 go 70 Number of observa- HONS wee wees ser 6 18 18 16 aT 22 26 310 PHYSICS (OF THE AIR Cloud Velocities—The velocity of a cloud is usually the velocity of the air in which it floats, except in the case of a sta- tionary type—crest cloud, banner cloud, et cetera—or a billow cloud. With these exceptions, it therefore is approximately the gradient velocity at the cloud level, which varies with altitude, latitude, temperature, and pressure distribution. Average values, observed at certain places, are given in the following table, also copied from Hann’s ‘“‘ Lehrbuch der Meteor- ologie’’: Average Wind Velocity in Metres per Second. . : Cu.- : Ci.- | Ci.- A.- | St.- Cu. | Cu. | Fr.- Ci. St. | Cu. A-St. Cu. | Cu. Nb. | Nb. Top | Base | Cu. St. Top I, SUMMER, CHIEFLY APRIL TO SEPTEMBER. Bossekop, 70° N....] 18 18 Il 13 Ir 35 6 ee 7 7 7 Upsala, 60° N...... 20 | (30) | 17 5 12 7 7 os 7 6 Bell sce Potsdam, 5214° N...| 22 24 13 II Io 9 Il 9 8 6 7 7 Trappes, 40° N..... 23 23 23 15 13 9 10 14 10 9 8 | 10 Blue Hill, 42° N....] 30 30 18 25 13 10 14 22 13 9 6 Washington, 39° N..} 30 27 23 18 16 10 8 Is a Be 6 Manila, 144° N....] 13 16 3 See II 4 sa Le es o xi oe Batavia (year),6°S.| 12 19 3 ar 6 6 or i 4 ts ee I 2. WINTER, CHIEFLY OCTOBER TO MARCH. Upsala... sc. cee sod 23 13 18 ve 13 12 6 18 I2 ae I2 ae Potsdam cx} 28 20 24 16 16 12 13 28 Io | (14) | 12 | 10 Trappes.. sai] 2S 19 27 18 14 Ir 16 oe 12 12 Ir Io Blue Hill........... 37 41 36 25 24 13 13 bs te Is i 10 Washington........ 35 30 33 2r 21 15 12 2r Il ms eg Io Manila ...... ..... 13 16 3 19 4 8 6 te ar CHAPTER XV THE THUNDERSTORM. Introduction.—A thunderstorm, as its name implies, is a storm characterized by thunder and lightning, just as a dust storm is characterized by a great quantity of flying dust. But the dust is never in any sense the cause of the storm that carries it along, nor, so far as is known, does either thunder or lightning have any influence on the course—genesis, development, and termination— of even those storms of which they form, in some respects, the most important features. No matter how impressive or how terrifying these phenomena may be, they never are anything more than mere incidents to, or products of, the peculiar storms they accompany, as will be made clear by what follows. In short, they are never in any sense either storm-originating or storm-con- trolling factors. Origin of Thunderstorm Electricity—Many have supposed that, whatever the genesis of the thunderstorm, the lightning, at least, is a product or manifestation of the free electricity always present in the atmosphere—normal atmospheric electricity. Ob- servations, however (discussed later), seem definitely to exclude this assumption. Thus, while the difference in electrical potential between the surface of the earth and a point at constant elevation is, roughly, the same at all parts of the world, the number and intensity of thunderstorms vary greatly from place to place. Further, while the potential gradient at any given place is greatest in winter, the number of thunderstorms is most frequent in summer, and while the gradient in the lower layer of the atmos- phere, at many places, usually is greatest from 8 to 10 o’clock, both morning and evening, and least at 2 to 3 o’clock p.m. and 3 to 4 o'clock a.m., no closely analogous relations hold for the thunderstorm. But how, then, is the great amount of electricity incident to a thunderstorm generated? Fortunately an answer to this question based on careful experiments and numerous observations, and that greatly aids our understanding of the interrelations between the various thunderstorm phenomena, has been given by Dr. G. C. Simpson,®? of the Indian Meteorological Department. “ Memoirs, Indian Meteorl. Dept., Simla, 1910, 20, pt. 8; Phil. Mag., 30, T, 1915. 311 312 PHYSICS OF THE AIR Doctor Simpson’s observations, just referred to, were made at Simla, India, at an elevation of about 7000 feet above sea-level, and covered all of the monsoon seasons, roughly, April 15 to September 15, of 1908 and 1909. He also made observations of the electrical conditions of the snow at Simla during the winter of 1908-9. A tipping bucket rain gauge gave an automatic, continuous record of the rate and time of rainfall, while a Benndorf * self- registering electrometer marked the sign and potential of the charge acquired during each two-minute interval. A second Benndorf electrometer recorded the potential gradients near the earth, and a coherer of the type used in radiotelegraphy registered the occurrence of each lightning discharge. All obvious sources of error were examined and carefully guarded against. Hence it would seem that the conclusions drawn from the thousands of observations given in the memoir are fully justified; and especially so since several independent series of similar observations made at different times, by different people, and at places widely separated, have given confirmatory results in every case. Simpson’s records show that— (1) The electricity brought down by the rain was sometimes positive and sometimes negative. (2) The total quantity of positive electricity brought down by the rain was 3.2 times greater than the total quantity of negative electricity. (3) The period during which positively charged rain fell was 2.5 times longer than the period during which negatively charged rain fell. (4) Treating charged rain as equivalent to a vertical current of electricity, the current densities were generally smaller than 4 x 107° amperes per square centimetre; but on a few occasions greater current densities, both positive and negative, were recorded. (5) Negative currents occurred less frequently than positive currents, and the greater the current density the greater the preponderance of the positive currents. * Physikal. Ztschr., Leipzig, 1906, 7, 08. THE THUNDERSTORM 313 _ (6) The charge carried by the rain was generally less than 6 electrostatic units per cubic centimetre of water, but larger charges were occasionally recorded, and in one exceptional storm (May 13, 1908) the negative charge exceeded 19 electrostatic units per cubic centimetre. (7) As stated in paragraph (3) above, positive elec- tricity was recorded more frequently than negative, but the excess was the less marked the higher the charge on the rain. (8) With all rates of rainfall positively charged rain occurred more frequently than negatively charged rain, and the relative frequency of positively charged rain increased rapidly with increased rate of rainfall. With rainfall of less than about I millimetre in two minutes, positively charged rain occurred twice as often as negatively charged rain, while with greater intensities it occurred 14 times as often. (9) When the rain was falling at a less rate than about 0.6 millimetre in two minutes, the charge per cubic centimetre of water decreased as the intensity of the rain increased. (10) With rainfall of greater intensity than about 0.6 millimetre in two minutes the positive charge carried per cubic centimetre of water was inde- pendent of the rate of rainfall, while the nega- tive charge carried decreased as the rate of rainfall increased. (11) During periods of rainfall the potential gradient was more often negative than positive, but there were no clear indications of a relationship be- tween the sign of the charge and the sign of the potential gradient. (12) The data do not suggest that the negative elec- tricity occurs more frequently during any par- ticular period of a storm than during any other. Concerning his observations on the electrification of snow Doctor Simpson says: 314 PHYSICS OF THE AIR So far as can be judged from the few measurements made during the winter of 1908-9, it would appear that— (1) More positive than negative electricity is brought down by snow in the proportion of about 3.6 to I. (2) Positively charged snow falls more often than negatively charged. (3) The vertical electric currents during snowstorms are, on the average, larger than during rainfall. While these observations were being secured a number of well-devised experiments were made to determine the electrical effects of each obvious process that takes place in the thunder- storm. Freezing and thawing, air friction, and other things were tried, but none produced any electrification. Finally, on allowing drops of distilled water to fall through a vertical blast of air of sufficient strength to produce some spray, positive and important results were found, showing: (1) That breaking of drops of water is accompanied by the production of both positive and negative ions. (2) That three times as many negative ions as posi- tive ions are released [thus leaving the drops charged positively ]. Now, a strong upward current of air is one of the most con- spicuous features of the thunderstorm. It is always evident in the turbulent cauliflower heads of the cumulus cloud—the parent, presumably, of all thunderstorms. Besides, its inference is com- pelled by the occurrence of hail, a frequent thunderstorm phe- nomenon, whose formation requires the carrying of raindrops and the growing hailstones repeatedly to cold and therefore high altitudes. And from the existence of hail it is further inferred that an updraft of at least 8 metres per second must often occur within the body of the storm, since, as experiment shows,®> air of normal density must have approximately this upward velocity to support the larger drops, those of 4 mm. or more in diameter, *P. Lenard, Met. Zeit., vol. 21, p. 249, 1904. THE THUNDERSTORM 315 and, because of its greater weight, even a stronger updraft to support the average hailstone. Experiment also shows ®° that raindrops of whatever size can not fall through air of normal density whose upward velocity is greater than about 8 metres per second, nor themselves fall with greater velocity through still air; that drops large enough, 4.5 mm. in diameter and up, if kept intact, to attain through the action of gravity a greater velocity than 8 metres per second with reference to the air, whether still or in motion, are so blown to pieces that the increased ratio of supporting area to total mass causes the resulting spray to be carried aloft or, at least, left behind, together with, of course, all original smaller drops. Above sea-level this limiting velocity is greater. It is given approx- imately by equating the weight of the drop, 4/3 7 r°g (p — *), to the supporting force, 7 7? « v?, roughly, in which r is the radius of the drop, p its density, «the density of the air, v the velocity in question, and g the gravitational acceleration. Hence the limiting velocity increases in practically the same ratio that the square-root of the density decreases. Thus at an elevation of 3 kilometres above sea-level, where the barometric pressure is about 520 mm. and the temperature, say, 15° C. lower than at the surface, the limiting velocity is approximately 9.4 metres per second, instead of 8, the value for normal density, or density at o° C. and 760 mm. pressure. Clearly, then, the updrafts within a cumulus cloud frequently must be strong and therefore break up at about the same level, that of maximum rain accumulation, innumerable drops which, through coalescence, have grown beyond the critical size, and thereby, according to Simpson’s experiments, produce electrical separation within the cloud itself. Obviously, under the turmoil of a thunderstorm, such drops may be forced through the cycle of union (facilitated by any charges they may carry) and division, of coalescence and disruption, from one to many times, with the formation on each at every disruption, again according to experiment, of a correspondingly increased electrical charge. The turmoil compels mechanical contact between the drops, whereupon the disruptive equalization of their electrical potential breaks down their surface tensions and insures coales- cence. Hence, once started, the electricity of a thunderstorm rapidly grows to a considerable maximum, *°P. Lenard, Met Zeit., vol. 21, p. 249, 1904. ‘316 PHYSICS OF THE AIR After a time the larger drops reach, here and there, places below which the updraft is small—the air cannot be rushing up everywhere—and then fall as positively charged rain, because of the processes just explained. The negative electrons, in the meantime, are carried up into the higher portions of the cumulus, where they unite with the cloud particles and thereby facilitate their coalescence into negatively charged drops. Hence the heavy rain of a thunderstorm should be positively charged, as it almost always is, and the gentler portions negatively charged, which also very frequently is the case. Such in brief is Doctor Simpson’s theory of the origin of the electricity in thunderstorms, a theory that fully accounts for the facts of observation and in turn is itself abundantly supported by laboratory tests and imitative experiments. If this theory is correct—and it seems well founded—it must follow that the one essential to the formation of the giant cumulus cloud—namely, the rapid uprush of moist air—is also the one essential to the generation of the electricity of thunderstorms. Hence the reason why lightning seldom occurs except in con- nection with a cumulus cloud is understandable and obvious. It is simply because the electrifying process of splashing is vigor- ously active in this cloud and nearly absent in others. The occasional lightning in connection with snowstorms, dust storms, and volcanic eruptions may in each case be due to the fact that the collision of solid particles produces electrification.*” The Violent Motions of Cumulus Clouds——From observa- tions, and from the graphic descriptions of the few balloonists and aviators who have experienced the trying ordeal of passing through the heart of a thunderstorm, it is known that there is violent vertical motion and much turbulence in the middle of a large cumulus cloud, a fact which, so far as it relates to the theory alone of the thunderstorm, it would be sufficient to accept without inquiring into its cause. However, to render the dis- cussion more nearly complete, it perhaps is worth while, since it is a mooted question, to inquire what the probable cause of the violent motions in large cumulus clouds really is—motions which, in the magnitude of their vertical components and degree of tur- moil, are never exhibited by clouds of any other type nor met "Rudge, Proc. Roy. Soc., A, 90, 256, 1914. THE THUNDERSTORM 317 with elsewhere by either kites or balloons of any kind, manned, sounding, or pilot. It has been shown by von Bezold ®* that sudden condensation from a state of supersaturation, and also sudden congelation of undercooled cloud droplets, would, as a result of the heat thus liberated, cause an equally sudden expansion of the atmosphere, and thereby turbulent motions analogous to those observed in large cumuli. However, as von Bezold himself points out, it is not evident how either the condensation or the freezing could suddenly take place throughout a cloud volume great enough to produce the observed effects. Besides, these eruptive turmoils, whatever their genesis, undoubtedly originate and run their course in regions already filled with cloud particles in the presence of which no appreciable degree of supersaturation can occur. Hence the rapid uprush and the violent turbulence in question obviously must have some other cause, which indeed is provided by the difference between the actual temperature gradient of the sur- rounding atmosphere and the adiabatic temperature gradient of the saturated air within the cloud itself. Consider a warm summer afternoon, temperature 30° C., and assume the dew-point to be 18° C. Now, the adiabatic decrease of temperature of non-saturated air is about 1° C. per roo metres increase in elevation, and therefore, under the assumed conditions, vertical convection of the surface air causes condensation to begin at an elevation of approximately 1.5 kilometres—allowing for the increase of volume per unit mass of vapor. From this level, however, so long as the cloud particles are carried up with the rising air, the rate of temperature decrease for at least a couple of kilometres is much less—at first about one-half the previous rate, and appreciably less than that of the surrounding clear air. After a considerable rise above the level of initial condensation, half a kilometre, say, the raindrops have so in- creased in size as to lag behind the upward current and even to drop out, while at the same time the amount of moisture con- densed per degree fall of temperature grows rapidly less, as shown by the saturation adiabats of Fig. 65. Hence for both reasons—because the heat of the water is no longer available to the air from which it was condensed, the drops having been left behind, and because a decreasing amount of latent heat is to be 8 Sitzber. K..Preuss. Akad. d. Wiss., Berlin, 1892, 8, 279-309. 318 PHYSICS OF THE AIR had from further condensation, there being less and less precipi- tation per degree cooling—the rate of temperature decrease again approaches the adiabatic gradient of dry air, or 1° C. per 100 metres change of elevation. Obviously, then, for some distance above the level at which condensation begins to set free its latent heat the temperature of the rising mass of moist air departs farther and farther from the temperature of the surrounding atmosphere at the same level, and therefore its buoyancy for a time as steadily increases. But, of course, as explained above, this increase of buoyancy does not continue to any great altitude. In the lower atmosphere continuous and progressive convec- tion builds up the adiabatic gradient so gradually that no great difference between the temperature of the rising column and that of the adjacent atmosphere is anywhere possible. Hence, under ordinary conditions, the uprush in this region is never violent. But whenever the vertical movement of the air brings about a considerable condensation it follows, as above explained, that there is likely to be an increase in its buoyancy, and hence a more or less rapid upward movement of the central portion, like air up a heated chimney, and for the same reason, together with, because of viscosity, a rolling and turbulent motion of the sides, of the type so often seen in towering cumulus clouds. Obviously, too, the uprushing column of air must continue to gain in velocity so long as its temperature is greater, or density less, than that of the surrounding atmosphere, except as modified by viscosity, and therefore have its greatest velocity near the level at which these two temperatures are the same. Hence the rising column must ascend somewhat beyond its point of equilibrium, and then, be- cause slightly undercooled, correspondingly drop back. Fig. 90, based upon approximately average conditions, illus- trates the points just explained. The elevation is in kilometres and the temperature in degrees Centigrade. AB is the adiabatic temperature gradient for non-saturated air, about 1° C. per 100 metres change in elevation. GCKDEF is the supposed temperature gradient before convection begins, or a decrease, in accordance with observations, of 6° C., about, per kilometre increase in elevation, except near the surface, where the temperature decrease, before convection has begun, ordinarily THE THUNDERSTORM 319 is less rapid, and at elevations between 5 kilometres, roughly, and the isothermal level, where it is more rapid. As convection sets in, the temperature decrease near the sur- face soon approximates the adiabatic gradient for dry air, and this condition extends gradually to greater altitudes, till, in the given case, condensation begins at the level C, or where the tem- Fic. 90. km. \ \G A -40° -30° -20° -10° 0° 10° 20° Temperature gradients within (CLD) and without (CKD) cumulus clouds. perature is 15°C. Here the temperature decrease, under the assumed conditions, suddenly changes from 10° C. per kilometre increase of elevation to rather less than half that amount, but slowly increases with increase of altitude and consequent decrease of temperature. At some level, as L, the temperature difference between the rising and the adjacent air is a maximum. At D the temperature of the rising air is the same as that of the air 320 PHYSICS OF THE AIR adjacent, but its momentum presumably carries it on to some such level as H. Within the rising column, then, the temperature. gradient is given approximately by the curve ACLDHE, while that of the surrounding air is substantially as shown by the curve ACKDEF. The cause, therefore, of the violent uprush and turbulent con- dition within large cumulus clouds is the difference between the temperature of the inner or warmer portions of the cloud itself and that of the surrounding atmosphere at the same level as indicated by their respective temperature gradients CLD and CKD. Clearly, too, while some air must flow into the condensa- tion column all along its length, the greatest pressure difference, and therefore the greatest inflow, obviously is at its base. After the rain has set in, however, this basal inflow is from immediately in front of the storm, and necessarily so, as will be explained later. The approximate difference in level between D and H, or the height to which the momentum of the ascending column will force it to rise after it has cooled to the temperature of the surrounding air, may easily be computed in terms of the vertical velocity at D and the difference between the temperature gradients of the rising and the non-rising masses of air. Let the vertical velocity of the rising column be V centimetres per second at D; let the average absolute temperature between D and H be T; and let the differ- ence between the temperature of the rising air and the surround- ing air change uniformly at the rate 8 T per centimetre change of elevation. Obviously the kinetic energy of the rising air at D will be used up in lifting it to some greater elevation. But the weight of a mass m of this air is not mg (g being gravity acceleration), which it would be in vacuo, but mg ( <), in which p is the density of the air in question and ¢ the density of the surrounding air. Thus 3 6 T, : at h centimetres above D, p—o= = , approximately, and there- fore the weight of the mass m at this level is mg aat approx- imately. Hence the work in lifting the mass m through this altitude h is its average weight, — multiplied by the distance h. THE THUNDERSTORM 321 Hence 4% mV? = mgxrot or = a in which x, directly proportional to V, is the height in centimetres to which the air will rise above D. Let T = 265° C. absolute, corresponding to the conditions shown in Fig. 90; let the temperature gradient be 6° C. per kilometre in the free air and 8° C. per kilometre in the rising air, and T the temperature change between the two per centimetre change of elevation, therefore 1/50000; and let V = 12 metres per second, then =! 5 X 104 X 265 __ : x == 1200 J gio 1.395 kilometres. Since the height of the barometer at an elevation of 5 kilometres above sea-level is, roughly, 400 mm., and since the supporting force of an updraft is proportional to the product of its density by the square of its velocity, it follows that the vertical velocity in metres per second necessary to support the largest drops at this elevation is given by the equation, V=uv 760 V 400’ in which v is the required velocity at normal density. But, as above explained, v = 8 metres per second, about, and therefore V = 11 metres per second, approximately. Hence the above assumption that the vertical velocity at D is 12 metres per second appears to be conservative. Viscosity between the rising and the adjacent air prevents the actual height attained from being quite equal to the above theo- retical value ; nevertheless, the maximum elevation, or what might be called the “‘ momentum level ” often, especially in the case of the largest and most active cumulus clouds, is much greater than the equilibrium level. Convectional Instability.—Rapid vertical convection of humid air, as we have seen, is essential to the production of the cumulus cloud and, therefore, to the generation of the thunderstorm. Hence it is essential to consider the conditions under which the vertical temperature gradient necessary to this convection can be established. These are: 1. Strong surface heating, especially in regions of light winds; a frequent occurrence. The condition that the winds be light is not essential, 322 PHYSICS OF THE AIR or perhaps even favorable, to the genesis of all thunder- storms, but only to the local or heat variety, and favor- able to these simply because winds, by thoroughly mixing the air, prevent the formation of isolated rising columns, the progenitors of this particular type of storm. 2. The overrunning of one layer of air by another at a temperature sufficiently lower to induce convection. This apparently is the cause of practically all ocean thunderstorms. It seems also to be the chief cause of those that so frequently occur on land in connection with cyclones. 3. The underrunning and consequent uplift of a saturated layer of air by a denser layer; a frequent occurrence to a greater or less extent and presumably, therefore, occasionally, at least, one of sufficient mag- nitude to produce a thunderstorm. Here the underrunning air lifts both the saturated layer and the superincumbent unsaturated layer, and thereby forces each to cool adiabatically. But as both layers are lifted equally, while, because of the latent heat of condensation, the saturated layer cools much slower than the dry, it follows that a sufficient mechanical lift of a saturated layer of air would establish between it and the non-saturated layer above a superadiabatic temperature gradient and thereby produce local convection, cumulus clouds, and perhaps a thunderstorm. Periodic Recurrence of Thunderstorms.—While thunder- storms may develop at any hour of any day, they nevertheless have three distinct periods of maximum occurrence: (a) Daily, (b) yearly, and (c) irregularly cyclic. Each maximum depends upon the simple facts that the more humid the air and the more rapid the local vertical convections the more frequent and also the more intense the thunderstorms, for the obvious reason that it is rapid vertical convection of humid air that produces them. Daily Land Period —Vertical convection of the atmosphere over land areas reaches its greatest altitudes and thereby produces the heaviest condensation and largest cumulus clouds when the surface is most heated; that is, during afternoons. Hence the hours of maximum frequency of inland or continental thunder- storms are, in most places, 2 to 4 P.M. THE THUNDERSTORM 323 Daily Ocean Period.—Because of the great amount of heat rendered latent by evaporation, because of the considerable depth to which the sea is penetrated by solar radiation, and because of the high specific heat of water, the surface temperature of the ocean increases but little during the day, and because of convec- tion or the sinking of any surface water that has appreciably cooled and the bringing of the warmest water always to the top, it decreases but slightly.at night. Indeed, the diurnal tempera- ture range of the ocean surface usually is but a small fraction of one degree C., while that of the atmosphere at from 500 to 1000 metres elevation is several fold as great.2® Hence those tem- perature gradients over the ocean that are favorable to rapid vertical convection are most frequent during the early morning hours, and therefore the maximum of ocean thunderstorms usually occurs between midnight and 4 a.m. Yearly Land Period.—Just as inland thunderstorms are most frequent during the hottest hours of the day, so, too, and for the same reason, they are, in general, most frequent over the land during the hottest months of the year, or rather during those months when the amount of surface heating, and therefore the vertical temperature gradient, is a maximum. This will be better understood by reference to the winter and summer temperatures of Fig. 16, determined, as previously explained, by averaging 185 and 231 records, respectively, obtained by sounding balloons sent up from Munich, Strassburg, Trappes, and Uccle, places of about the same latitude and having generally similar climates. It will be seen that the temperature of the air not only is much higher at all levels during summer than during winter, but also decreases through the first three kilometres much more rapidly. That this important difference between the temperature gradi- ents of winter and summer is general and not peculiar to the above localities is obvious from the fact that during summer the surface of the earth gradually grows warmer and therefore in- duces correspondingly frequent and vigorous convection, while during winter it as steadily becomes colder and therefore only occasionally, at the times of temporary warming, induces con- vections strong enough to form large and well-defined cumulus clouds. From these several considerations it is evident that: ” Braak, Beitr. z. Physik d. fr. Atmosph., Leipzig, 1914, 6, 141. 324 PHYSICS OF THE AIR a. Winter convections cannot, in general, rise to nearly so great altitudes nor with such velocity as those of summer. b. The absolute humidity of summer air may at times be greatly in excess of that of winter. c. The winter snow level usually is much below that of summet. Hence thunderstorms, since they depend, as explained, upon the action of strong vertical convection on an abundance of rain drops, necessarily occur most frequently during the warmer seasons, and only occasionally during the colder months. In middle latitudes, where there are no late spring snows to hold back the temperatures, the month of maximum frequency is June. In higher latitudes, where strong surface heating is more or less delayed, the maximum occurs in July or even August. Yearly Ocean Period.—Over the oceans, on the other hand, temperature gradients favorable to the genesis of thunderstorms, and therefore the storms themselves, occur most frequently dur- ing winter and least frequently during summer. This is because the temperature of the air at some distance above the surface, being largely what it was when it left the windward continent, greatly changes from season to season, while that of the water, and, of course, the air in contact with it, changes relatively but little through the year. That is, over the oceans the average decrease of temperature with increase of elevation obviously is least and, therefore, thunderstorms fewest in summer, and great- est, with such storms most numerous, in winter. Cyclic Land Period —Since thunderstorms are accompanied by rain and since over land they are most numerous during sum- mer, it would appear that they must occur most frequently either in warm or in wet years and least frequently in cold or in dry years. Further, if it should happen, as it actually does, that, for the earth as a whole, warm years are also wet years and dry years cold years, it would appear logically certain that, for the entire world, the maxima numbers of thunderstorms must belong to the years that are wet and warm and the minima to those that are cold and dry. - A complete statistical examination of these statements is not possible, owing to the fact that meteorological data are available for only portions of the earth’s surface and not for the whole of it.” Nevertheless, well-nigh conclusive data do exist. The annual THE THUNDERSTORM 325 rainfall, for instance, to the leeward of a large body of water obviously must bear the same relation to the annual average wind- ward temperature that the total annual precipitation over the entire world does to the annual average world temperature. In each case the amount of evaporation or amount of water vapor taken into the atmosphere, and therefore the amount of subse- quent precipitation, clearly must increase and decrease with the temperature. An excellent test and complete support of this de- duction is furnished by Fig. 91, in which the full line represents the smoothed annual European precipitation,®® and the dotted line smoothed annual average temperatures over the eastern United States. Obviously, as supported by the data graphically represented in Fig. 91, the warmer the air as it leaves America Fic. 91. 83 64 85 8687 92 93 94 95 96 97 98 99190001 02 05 06 07 08 EUROPEAN RAINFALL EASTERN U.S TE Relation of European rainfall to eastern United States temperature. the greater the moisture it must take up in its passage across the Atlantic, and therefore the greater its supply of humidity on reaching Europe and the heavier the subsequent precipitation. Clearly, too, the same relatioris must apply to the entire earth that so obviously should and so demonstrably do hold for the North Atlantic and its adjacent continents. Beyond a reasonable doubt, therefore, for the world as a whole, warm years are wet and cold ones are dry. Hence, as above stated, it is practically certain that the maxima of thunder- storms occur during years that are wet, or warm—for the two are identical—and the minima during years that are dry or cold. A partial and, so far as it goes, a confirmatory statistical test of this conclusion is given by Fig. 92. The lower group of curves is based on an exhaustive study by Dr. van Gulik ®! of thunder- “Hellmann, “Die Niederschlage in den Norddeutschen Stromge- bieten,” Berlin, 1906, vol. 1, pp. 336-337, and elsewhere. " Meteorologische Zeitschrift, Braunschweig, 1908, 25th Jhrg., 108. 22 326 PHYSICS OF ‘THE AIR. storms and lightning injuries in Holland. The continuous zigzag line gives the actual number of thunderstorm days, and the con- tinuous curved line the same numbers smoothed. The broken lines give, respectively, the actual and the smoothed values of the annual average precipitation. The upper curve represents the variations in the smoothed number of destructive thunderstorms °? (number of thunderstorm days not readily available) in Germany. The original data on which this last curve is based indicate a continuous and rapid increase of thunderstorm destructiveness throughout the period studied, 1854-1901. Presumably, how- ever, this increase is real only to the extent that the country has Fic. 92. 84 85 86 87 88 89 189091 92 93 94 95 96 97 98 99 1900 01 02 03 04 05 HOLLAND Relation of annual number of thunderstorm days to total annual precipitation—Holland. The uppermost wavy curve shows the variation in the smoothed number of destructive thunder- storms in Germany. become more densely populated and more thickly studded with destructible property. Since thunderstorms are caused by rapid vertical convection and heavy condensation, and since the tem- perature of the air upon which these in turn depend has not, on the decade average, measurably changed since reliable records began, at least a hundred years ago, there clearly is no logical reason for believing that the decade average either of the fre- quency or the intensity of the storms themselves has materially changed during that time. At any rate, this element—that is, the rapid increase suggested by insurance data—has been omitted from the curve and only the fluctuation factor retained. It will be noticed that the curve of thunderstorm frequency "Otto Steffens, Ztschr. f. d. gesamte Versicherungswiss., Berlin, 1904, 4, pt. 4. (Also Diss.-Berlin, 1904.) THE THUNDERSTORM 327 for all Holland closely parallels the curve of thunderstorm injury in all Germany. Hence it seems safe to infer that the frequency of thunderstorm varies pretty much the same way over both countries, and presumably also over many other portions of Europe; that is, roughly as the rainfall varies, or, considering the world as a whole, roughly as the temperature varies. Additional statistical evidence of the relation between the annual number of thunderstorm days and the total annual pre- cipitation, kindly furnished by P. C. Day, in charge of the Fic. 93. ” 1904 5 6 7 & 9 10 " 12 13 = » = ft a a i i 2 i a a e a 4 LIN 840 ud z \ z. ~ 820 BE / a Pa P «MN 4) NX 800 Jenne, | LA 780 xX zw A4 A 760 SO : Relation of annual number of thunderstorm days, T, to total precipitation, P—United States 38 Climatological Division of the Weather Bureau, is shown by Fig. 93, in which the upper line gives, in millimetres, the smoothed annual precipitation of 127 stations scattered over the whole of the United States, and the lower line the smoothed average annual number of thunderstorm days at these same stations. It was thought at first that this relation might differ greatly for those portions of the United States whose climates are radically dis- similar, and for this reason the stations east of the one hundredth meridian provisionally were classed separately from those west of it; but the results for the two sections, being substantially alike, show that for this purpose their division is entirely unnecessary. 328 PHYSICS OF THE AIR As will be seen from the figure, the earliest statistics used are those of 1904. This is because the annual number of such days reported rapidly decreases from 1904 back to about 1890. In- deed, the annual number of thunderstorm days reported per station since 1903 is almost double the annual number per station (practically the same stations) from 1880 to 1890. The transition from the smaller to the larger number was due in great measure, doubtless, to an alteration in station regulations equivalent to changing the official definition of a thunderstorm from “ thunder with rain” to “ thunder with or without rain.” This, however, does not account for the fact that from 1890 to 1904 the average annual number of thunderstorm days reported per station in- creased, at a nearly constant rate, almost 100 per cent. Either the storms did so increase, which from the fact that there have been no corresponding temperature changes seems incredible, or else there was, on the average, an increase of attention given to this particular phenomenon. At any rate, so continuous and so great an increase in the average number of thunderstorm days cannot be accepted without abundant confirmation, and for this reason the earlier thunderstorm records provisionally have been rejected. Obviously a much closer relation between the number of thunderstorm days and total precipitation would hold for some months and seasons than for others, but no such sub-grouping of the data has been made, though, presumably, it would give in- teresting results. The whole purpose of this portion of the study was to arrive at some definite idea in regard to the cyclic change of thunderstorm frequency, to see with what other meteorological phenomena this change is associated, and, if possible, to determine its cause. Now, it is well known that the average temperature of the world as a whole follows in general the sun-spot changes, in the sense that the greater the number of spots the lower the tempera- ture, and the smaller the number of spots the higher the tem- perature. This regular relation, however, often is greatly modi- fied 98 by the presence in the high atmosphere of volcanic dust, one invariable effect of which is a lower average temperature. Hence the warm and the cold periods are irregularly cyclic, and ° Humphreys, W. J., Bull. Mount Weather Observatory, Washington, 1913, 6, 1. Also in Part IV of this book. THE THUNDERSTORM 329 also irregular in intensity. Hence, also, the annual amount of precipitation, the frequency of thunderstorms, and many other phenomena must perforce undergo exactly the same irregular cyclic variation. As already stated, the statistical evidence bearing on these conclusions neither is nor can be complete, but the deductions are so obvious and the statistical data already examined so con- firmatory that but little doubt can exist of their general accuracy. Cyclic Ocean Period.—The record of thunderstorms over the ocean is not sufficiently full to justify any conclusions in regard to their cyclic changes. Possibly, as in the yearly and the daily periods, the ocean cyclic period may be just the reverse of that of the land, but this is not certain. Geographic Distribution—The geographic distribution of the thunderstorm may safely be inferred from the fact that it is caused by the strong vertical convection of humid air. From the nature of its formation one would assume—and the assump= tion is supported by observation—that the thunderstorm must be rare beyond either polar circle, especially over Greenland and over the Antarctic continent, rare over great desert regions wherever situated, rare over the trade belts of the oceans, and, on the other hand, increasingly abundant with increase of temperature and humidity, and therefore, in general, most abundant in the more rainy portions of the equatorial regions. The east coast of South America, from Pernambuco to Bahia, is said to be an exception. An interesting and instructive example of the annual geo- graphic distribution of thunderstorms is given by Fig. 94, copied from a statistical study of this subject by W. H. Alexander.** Although this example, based on a ten-year (1904-1913) average, refers to only the United States and southern Canada, it never- theless shows the great influence of humidity, latitude, and topography on thunderstorm frequency. One of the most striking facts shown by this map is the rela- tively unusual occurrence of this phenomenon along the Pacific Coast. This exceptional condition is explained by the fact that during the summer time, or season of strong vertical convection, the temperature of the on-shore winds of that region is too low and their humidity too small to permit of the ready formation * Monthly Weather Review, 43, Pp. 322, 1915. PHYSICS OF THE ATK 330 : (iepuexey) ‘eAtsnyour €161-P061 ‘sivak us} ay} Bulinp sajzejg pau sy} ul sAep uLI0}s1opuNnyy jo Joquinu [ej0], se x = a a ci ———— oy we Oktay He Om enums: 002 099 og Y “no be tena ee zs SZ oun ! Fravaf!cohae89P) THE THUNDERSTORM 331 over the heated interior of abundant cumuli, without which, as already explained, thunderstorms do not occur. Pressure and Temperature Distribution —lIn illustrating the occurrence of thunderstorms with reference to the disposition of isobars and isotherms, or the distribution of atmospheric pressure and temperature, typical weather maps of the United States,?® Figs. 95 to 109, have been used, not because the thunderstorms of this country are different in any essential particular from those of other countries, but chiefly as a matter of convenience in mak- ing the drawings. To facilitate their study, each of the several types discussed is illustrated with three consecutive maps. The first shows the 12-hour antecedent conditions, the second the particular pressure-temperature distribution in question, and the third the 12-hour subsequent conditions. In these figures the isobars, in corrected inches of mercury as read on the barometer and reduced to sea-level, and the isotherms in Fahrenheit degrees, are marked by full and dotted lines respectively. The legend “ LOW ” is written over a region from which, for some distance in every horizontal direction, the pressure increases. Similarly, the legend “ HIGH ” applies to a region from which, in every horizontal direction, the pressure decreases. The arrows, as is customary on such maps, fly with the wind, while the state of the weather is indicated by the usual U.S. Weather Bureau symbols. All refer to the time of observa- tion, except that of the thunderstorm, which covers the previous 12 hours. Obviously, the key to the geographic distribution of thunder- storms—that is, the distribution of conditions likely to induce strong vertical convection of humid air—is also the key to their probable location with reference to any given system of isotherms and isobars, or distribution of atmospheric temperature and | pressure. From this standpoint the places of their most frequent occurrence are: a. Regions of high temperature and widely extended nearly uniform pressure (see Figs. 95, 96, and 97). The conditions are still more favorable to the genesis of thunderstorms when the air is humid and the pressure, partly * The author wishes to acknowledge the kind codperation of the official forecasters of the U. S. Weather Bureau in selecting: maps typical of thunderstorm conditions in the United States. “uloysrepuny} ‘Mf tures ‘yy fApnojo '@ !Apnoyo Apyied ‘© !1vayo ‘O iSULIOJSIOPUNY} ,,}9Y,, JO Suruutsaq ye suot}Ipuod [eoIdAy ‘6061 ‘Lz aun[ ‘wv g ‘deur 1ayzeaM = 7 a : | WY ‘606T ‘22 ANNE hag —S ei ha onus PHYSICS OF THE AIR 332 333 THE THUNDERSTORM Apqied ‘© ‘1e9]9 ‘O ‘woyssapuny} “YY furer ‘y !Apnojo '‘@ ‘!Apnojo isWIOYsapUNny}y ,,Feay,, JO [VdIdAz ‘6061 ‘Lz aun “W'd g ‘deur JayzEOM pose w y Bs Fr sone oOL, Wd ‘606T ‘22 ANNE oS ae itl ae meant et PHYSICS OF THE AIR 334 ‘wioysropuny} ‘VY ‘ures ‘yy !Apnopo ‘@ ‘Apnoya Ayjied '© t1vajo ‘oO *SUIIOPSIOPUNY} ,,}V9Y,, JO DUT[IIP 4B SUOIZIPUOD jo [eoId A} ‘6OGI ‘gz auNf[ “WV g ‘deur 19ayyBIM aL = ey QL “UW ‘VW ‘606F ‘82 ANN || 63 "mogog gk oem Aer snuns 339 THE THUNDERSTORM “UILOJsIJapuNyy ‘NY ‘ures ‘y !Apnojo ‘@ ‘Apoyo Ayysed ‘© ‘1eapo ‘OQ :sms04s -Japung} ,, omopoAd,, Jo BuruutBeq 4e suOIyIPUOD jo [eIId Ay ‘LOGI ‘PY auNf “Wy g ‘deur JaqyeaM OL. roggrraetieg 308 cae a ee drongagull ! t tony => \ WV y x ih ‘LO6T ea nf] —_ RAI ous PHYSICS OF THE AIR 336 Ayqysied '© ‘1vajo ‘O “wmdIOYsIapUNnyy “VY Surely HApnoys '@ !Apnoyo :SUIO4SIOPUNY} ,, TUOTOAD,, JO [word Ay ‘LOGI ‘PY auNf ‘wd g ‘duu J3ay,vOM 7 . 6 ‘Asi 0 8°6Z 7m aE \ 20a 1°68 os, ~~ . ‘ | 0 ey ops 4'8%,0809'6z NY Ayer. 0 SS LINDE Moghae OY 0'6e — } ¢ > mui Vi >ia= a 9 Ey = = \ i r’ ~~ * aa \\es = ‘ phd / N ‘a =F ITSP / otk = Ose sae \ me Ea \ NS Ss = aN | 1 gies \\ .08 tome / "IW ‘d ‘L061 * ANNI ne at on weet sen enumn Ba THE THUNDERSTORM “ulJOysJopunYyY “Yf Sures ‘y SApnops ‘@ ‘Apnoyjo Ajysed ‘© tseapo © ISUIIO}SIJAPUNY} ,, NUO[IAD,, JO aUI[Op Je SUOI}IPUOD Jo [POIGAY ‘LOGI ‘S ouNf[ “W'y g ‘deur sayyEaM a = = = = o'oe a eT : ' “WV ‘L06T ‘S ANNE, 208 epee Ces . ee oroe — “s : a 5 a i oot e6z of — HDIH - BEA. Boatey is ; Oi | _ aR o 9 0 aw TA—-—H4 | ; J 6. IEF 4 | « a aferesihanniy t : ; Q ‘I a ‘oe hey a 1 : eS : cae | sy38T) tee Se ‘ -'1607 g en y < LN rips SD, ets as wager < cae ae Kee oe 3 AO ase Pee Lage SE NS weae’ rr af z reg bie 1% oe oOL, ee atepie Riso —- sy et : an A , s Sie of 9 OLS, | DSpogp NY ar *. 7 t sgh a Fie \ H ee a ” ee 4 only oa Rory “OOI ‘OL PHYSICS OF THE AIR 338 “WIOYSJapuNnYy ‘NT ‘ures ‘Y SApnopo ‘@ ‘Apnojo Apyred ‘© tivajo'OQ :sus03s -Jepuny} ,, oIpeuso},, jo Buraurseq 42 SUOIJIPUOD jo [eoTd 4 ‘LOGI ‘I qorey;w “Nv g ‘deur 1ayyeo yy Wl Vv ‘L06T J VIN] “IOI ‘OY 339 “uLOYsJOpUNYy "VY ‘ures ‘y :Apnojo ‘@ !Apnojpo Apjied ‘Q@ freayo ‘OC :surioysiepuny} ,,oIpeusoz,, jo yeordAy ‘LoGI ‘I qorey “Wd g ‘deus Jayqyvo My THE THUNDERSTORM t t r : PT Tas aL =F - Wd LO6F F HOUVWN eo a 4 9 Seance po NX ! woe \ 4, je, t oOL NM ! (fT ; : ; : A 1oro8| | Aron On ‘ ! = see = I» = = ON s - s G 3 fA -— re 9 ~ 200. a ~kS ms a oye 7 Ks SOS mA Ast Ro? vo 4 a NO 5 L be Fr Sgro j 7 F091 P< = JI ogy? ta'de me! ~ = 5 i 4 Qj 7 we Kae TP oe eae fe _wata} 3 = -~ =\s (eet PC, angie” enon ar fowl, + vee ~4 T= xy~ - (00 semen Gj je yor NSS -—~, oP ' i o'oe ‘ \ ~ ‘ Qf: a fo ae | S q . INN , a a os SN < " (, A AY; \ ay ne . ‘ \ . 7 =o aa —f / NY = a Ss ‘ : = aii Je Re Ae og! PB 1 = ( ~- Aba 9 RTH { PPS Ee SENT Ned o08-~ = ‘0; \ fering | Pig hee b pS , 0 ; Keay od) PP RR ee fer So ts, < = > lm *§ rt opp a ; o a i ay / = J : 8 - x 2A& : | ~ % ‘ Z Xe! fe imho \ Pe ? k ZO aaa Sf : Wh ea S\~—- SHS ‘ 100 3 i 0L'6 ‘“ 0 J ope? oP 08 Aaa WA Fook Ve 10 e = mar, 4 ' “i a 0G be soe {USO —0 iv osgz 09 6S 0'Oe f\ = ! 7! ioe f ‘zol ‘DIY Fic. 103. 340 PHYSICS OF THE AIR [MAR. 2, 1907, A. M. Soa —_ onditions at decline of ‘‘tornadic'’ thunder- rain; K, thunderstorm. storms: O, clear; , partly cloudy; @, cloudy; R, Weather map, 8 A.M., March 2, 1907, typical of c 341 THE THUNDERSTORM “wsoyssepunyy “VY ‘ules ‘yl tApnopo ‘@ :Apnoyo Aqyed ‘© svajo'O :surs0}3s -Japuny} ,, Y3n01},, JO Buruurseq ye suolIpuod jo [eordAy ‘go6x ‘z1 aun[{ “wa g ‘dew sayzVaM : ys ‘ - W ‘d ‘8067 ‘ct ANNE Co So i ' 008 eT i 86s. eae 206 oe A 1 eat 6s 008 soy -n0 ( “ 1406 sa i o' 7 eGOl 1008 = 1h bg = pn iewt Tampa aay \ 9°6 dag f WOO? : a1\! Y \ ; Ge whet \ \ on w PY! Lanes Ve AQT Mad HPS Nh | * : o7 |: -76a7> ey Tot 2 Col | % pot] OF hs \a ao it Bet fy a0 IT = ot bay 1 =< we seta e 2, Best Fe ate oOL- aN ays jogtors | so, 2 ‘ Bo ae E . 8 Caen) a /d a ae YY OS. vos H x PX / 4 ra. es C NY te NS Ja MR ka oA AR AEST WN ol aa t | 3 , ! Ne fWerstonbl acct sf -- ae NN NF ON Gerd et | - Le the AV 7 ao f[.\-—+ . 7 L eh 4 "1 sas a LN p Pimen i i Dy: . i ~ Mos 7 ~ a | 2 os iN aa pr ‘ i’ ) 1H dex 1 x hy \ Sau ss “a PG a Sao ouster { - E ‘ . SLs J “tT nt a \y ie \ - ' i “ PP een) AV 5 is / O84 Ne ” 3 I\e° ao if # ‘ s “He \ ode “PON = ce au 2 (-.09 2 ae = oO VV ee Yes 1 wily 17 PO <= SBE ? t Rey, --,.09 rt wT LG R ' : a Al i 00) ea / 1 \e™ 0Q9L Mh log: vt ‘ toe ~», JAD, 0 HOIW 209 erez¥, \r decd bg 46'6s 6 Ws or 7 = 7 or a a= cI a ~~ 23 342 PHYSICS OF THE AIR Si i yo St Ee Be an oo Zo EN p- 1k DS oh DY Pr Ry as | aN eo en A JUNE 13, 1908 M. & Fic. 106. THE THUNDERSTORM 343 I JUNE 13, 1908, P. M. ——— Weather map, 8 P.M., June 13, 1908, typical of conditions at decline of “ trough"’ thunderstorms: O, clear; @, partly cloudy; @, cloudy; R, rain; K.. thunderstorm. PHYSICS OF THE. ALR 344 “uIdOSJapuNnyy “VY tures ‘yy SApnojo '@ !Apnoys Apzied '@ ‘1vajo 'O iSWIIOJSIOpUNYY ,, Jopsoq,, Jo Auruutsaq 7e SuOoTzIpuUoOd jo [wold Ay ‘LOGI ‘2 aunf[ ‘wd g ‘deur 19y}e9 MM as ci : , XY NS i “ simone aeenrp to] ana OL \_ Wd ‘L061 ‘2a NAL 345 THE THUNDERSTORM “UILOJSIapUNY} ‘Vy ‘ures ‘yy +Apnoyjo '@® ‘Apnojo Ayqied ‘© ‘reajo ‘OQ :surroysiapuny} ,,Japiog,, jo [eardAy 'Lo61 ‘g aunf “wy g ‘deur Joyzea yy — : : [== z = ‘WV ‘L067 ‘8 ANNES oe oer vot uot tt OoTK sus HOIH si oer Fic. 109. PHYSICS OF THE AIK "' thunderstorms: K, thunderstorm. “‘border clear; o x= a ul a Yn wW a z= WIND VELOCITY RAINFALL NW. NW. N. oN NN NW WNSNNEESSWW Course of meteorological elements on a thunderstorm day. (Washington, D.C., July 30, r913.) sumably is established over a wide area, roughly up to the base level of the cumulus clouds, all of which, because of a practically common temperature and common humidity over the whole region, must have substantially the same base level and therefore often appear en échelon, as shown in Fig. 111. But while the upris- ing branches of the existing convection currents, due to super- Copoyd ‘yeayeg “gd “a “FA ‘AQT[VA UOpnoy) “wojayrg ua TTNUIND 350 b g @ THE THUNDERSTORM ‘III ‘OIg 354 PHYSICS OF THE AIR adiabatic gradients, may be localized and here and there rather rapid, the return or compensating down-flow is relatively wide- spread and correspondingly gentle. The condition essential to a local and rapid down-flow, that is, a local decided cooling at a high altitude, does not exist, and therefore the counterpart to the upward current is nowhere conspicuous. Second.—The convections in the cumuli are accelerated by virtue of the latent heat of vaporization set free in them, and thus FIG. I12. Towering cumulus. (West end of Java, E. E. Barnard, photo.) one or more of them rapidly developed. In some cases great size and remarkable altitudes are attained, as illustrated by Fig. 112. Third.—After a time, as a result of the abundant condensation induced by the convectional cooling, rain is formed at a consider- able altitude where, of course, the air is quite cold, in fact so cold that often hail is produced. Now this cold rain, or rain and hail, as it falls, and as long as it falls, chills the air from the level of its formation all the way to the earth, partly as a result of its THE THUNDERSTORM gas initial low temperature and partly because of the evaporation that takes place during its fall, Hence this continuously chilled col- umn of air, because, partly, of the frictional drag of the rain, but mainly because of the increase, due to this chilling, of its own density, immediately and necessarily becomes a concentrated and vigorous return branch of the vertical circulation. In fact, it (or gravity acting through it) becomes the sustaining cause of the storm’s circulation. At the same time, because of the down- ward blow and because of the retardation of the winds by surface friction, the barometric pressure is abruptly increased, as will be explained later. It will be worth while to consider some of these statements a little more closely, and to test them with possible numerical values. Omitting, as one may, the effects of radiation, there seem to be but three possible ways by which the cooling of a thunder- storm may be obtained: (a) by the descent of originally poten- tially cold air; (b) by chilling the air with the cold rain; (c) by evaporation. Each of these will be considered separately. (a) Obviously no portion of the upper air could maintain its position if potentially even slightly colder than that near the sur- face, that is, so cold that even after warming up adiabatically in a fall to the surface it still would be colder than the air displaced. If at all potentially colder it would fall until it itself became the surface air. Hence the great decrease in temperature that comes with a thunderstorm is not the result of the descent of a layer of air originally potentially cold for, as explained, an upper layer sufficiently cold to give, after its descent, the actual cooling could not exist. Again, any descending air must come from either below the under surface of the cloud or from above this level. If from below, then, because of adiabatic heating during its descent through air which, as above explained, has practically the adia- batic temperature gradient, it must reach the earth at substantially the original surface temperature. If from above it would, as is obvious from Fig. 90, reach the earth even warmer than the original surface temperature. Hence, looked at in any way, case a clearly is inadmissible. Possibly the above statements may seem to contravene the explanation that many thunderstorms originate in the establish- ment by cross currents of superadiabatic temperature gradients. 356 PHYSICS OF THE AIR In reality, however, they are in harmony with that explanation which is based on the fact that such gradients can not be main- tained, but must at once cause vertical convection. Besides, such mechanically established gradients merely initiate but do not, as we shall see, maintain the storm. (b) Let the under surface of the thunderstorm cloud be 1500 metres above the earth, and the column of air cooled by the cold rain and its evaporation, 2000 metres high. Let the surface tem- perature be 30° C., and the temperature gradient before the storm begins adiabatic up to the under-cloud level, and let there be a 2-centimetre rainfall. Now at the temperature assumed, a column of air 2000 metres high whose cross section is I square centimetre, and whose base is at sea level, weighs, roughly, 210 grams, and its heat capacity, therefore, is approximately that of 50 grams of water. At the top of this column the temperature can be, at most, only about 20° C. lower than at the bottom, corresponding to the adiabatic or maximum temperature gradient, and if the rain leaves the top at this temperature but reaches the earth 7° C. colder than the surface air before the storm (temperatures that seem at least to be of the correct order), it will have been warmed 13° C. during its fall and the a.r column, at the expense of whose heat this warm- ing was produced, cooled, on the average, about 0.5° C. But, as a matter of fact, the air usually is cooled 5° C. to 10° C. Hence, while the temperature of the air necessarily is reduced to some extent by mere heat conduction to the cold rain, much the greater portion of the cooling clearly must have some other origin. Further, since @ is inadmissible and b only a minor contributing factor, it follows by exclusion that of the three obvious causes only evaporation is left to account for much the greater portion of the cooling. Consider, then, whether evaporation really can produce the effects observed. (c) It is a common thing in semiarid regions to see a heavy shower, even a thunder shower, leave the base of a cloud and yet fail utterly to reach the surface of the earth. Hence, it appears quite certain that in the average thunderstorm a considerable por- tion of the rain that leaves the cloud may evaporate before it reaches the ground, and therefore that the temperature decrease of the atmosphere may largely be owing to this fact. But if so, THE THUNDERSTORM 357 why then, one properly might ask, does not an equally great tem- perature drop accompany all heavy rains? The answer is obvious: It is because, as a rule, the tempera- ture is higher, the relative humidity lower, and the temperature gradient more nearly adiabatic during a thunderstorm than at the time of an ordinary rain. Other rains, those that are accompanied by long horizontal and slow, rather than rapid upward movements of the air, begin only when the humidity is so high that but little evaporation and therefore but little cooling from this source can take place. In such rains there is nothing that can greatly increase the density of the air and consequently there is no rapidly descend- ing current or wind. Thunderstorms, on the other hand, are developed by strong vertical convection which establishes a nearly adiabatic gradient and when the relative humidity, in the case of the heat thunderstorm, at least, is low, 50 per cent., say. Evapora- tion into this air, as soon as the rain has begun, obviously must be rapid, with the consequent cooling and increase of density corre- spondingly great. Hence, since the temperature gradient was already nearly adiabatic, a strong downward current necessarily is established in the midst of the falling and evaporating rain. Further, whatever the type of thunderstorm, the descending air, which can be no more than saturated at the base of the cloud, dynamically warms so rapidly that evaporation into it can not keep pace with its water capacity. That is, evaporation which takes place all the way from cloud to earth, by rendering the air locally cool and dense, causes it to fall, while this fall, in turn, through dynamical heating, maintains the evaporation. Hence the down- rush of the air must continue so long as there is an abundant sup- ply of local rain, and cease when the rain becomes light. It will be instructive now to return to the numerical values and compute a probable magnitude of the cooling due to evaporation. As before, let a 2-centimetre rain leave the cloud, but let one- fourth of the rain that started, or half a centimetre, be evaporated. This would consume 303 heat units from an air column 2000 metres high whose heat capacity is that of only 50 cubic centi- metres of water. Hence, as a result of evaporation alone, the temperature of the air column would be lowered on the average by about 6° C. Evaporation, therefore, appears to be both neces- sary and sufficient to produce all or nearly all the cooling of a thunderstorm. 24 358 PHYSICS OF THE AIR But what is the effect of this evaporation on the density of the atmosphere? Since the molecular weight of water is 18 while the average molecular weight of air is approximately 28.9, it fol- lows that the amount of evaporation above assumed would de- crease the density of the atmosphere by, roughly, one part in a thousand. On the other hand, a decrease in temperature of 6° C., that would be produced by the evaporation assumed, would in- crease it by about one part in fifty. Hence the resultant of these two opposing effects is substantially that of the second alone; that is, a distinct increase in density, and a consequent downrush of cold air. Doubtless, as already implied, the evaporation of thunderstorm rain, and therefore the drop in temperature and the consequent fractional gain in density, all increase with decrease of elevation. In some measure, however, this effect is counteracted by the higher temperatures of the lower layers—the higher the absolute tem- perature the less, proportionately, the change of density per degree change of temperature. But no matter how nor to what extent the details may vary, it seems quite certain that the cold rain of a thunderstorm and its evaporation together must establish a local downrush of cold air, an observed important and characteristic phenomenon, really the immediate cause of the vigorous circula- tion, whose rational explanation has been attempted in the past few paragraphs. As the column or sheet of cold air flows down it maintains in great measure its original horizontal velocity and, therefore, on reaching the earth rushes forward in the direction of the storm movement, underrunning and buoying up the adjacent warm air. And this condition, largely due, as explained, to con- densation and evaporation, once established necessarily is self- perpetuating, so long as the general temperature gradient, humid- ity, and wind direction are favorable. It must be remembered. however, that thunderstorm convection, rising air just in front of, and descending air with, the rain, does not occur in a closed cir- cuit, for the air that goes up does not return nor does the air that comes down immediately go up again, there simply is an interchange between the surface air in front of the storm and the upper air in its rear. The travel of the storm, by keeping up with the under-running cold current, just as effectually maintains the temperature contrasts essential to this open-circuit convection THE THUNDERSTORM 359 as does continuous heating on one side and cooling on the other maintain the temperature contrast essential to a closed circuit convection. The movements of the warm air in front of the rain, the lull, the inflow, and the updraft, resemble somewhat those of a horizontal cylinder resting on the earth where the air is quiet and rolling forward with the speed of the storm. Similarly, the cold air in its descent and forward rush, together with the updraft of warm air, also resembles a horizontal cylinder, but one sliding on the earth and turning in the opposite direction from that of the forward-rolling or all-warm cylinder. In neither case, however, is the analogy complete, for, as above explained, the air that goes up Fic. 113. > 7 i ae Principal air movements in the development of a cumulus cloud. remains aloft, while the cold air that comes down is kept by its greater density to the lower levels. The condition of flow per- sists, as do cataracts and crestclouds (clouds along mountain crests), but here, too, as in their case, the material involved is ever renewed. The Squall Cloud.—Between the uprising sheet of warm air and the adjacent descending sheet of cold air horizontal vor- tices are sure to be formed in which the two currents are more or less mixed. The lower of these vortices can only be inferred as a necessary consequence of the opposite directions of flow of the adjacent sheets of warm and cold air, for there is nothing to render them visible. Neither can any vortices that may exist within the cloud be seen. Near the front lower edge of the cumulo-nimbus system, however, and immediately in front of the sheet of rain, or rain and hail, the rising air has so nearly reached its dew point that the somewhat lower temperature pro- 360 PHYSICS OF THE AIR duced by the admixture of the descending cold air is sufficient to produce in it a light fog-like condensation which, of course, renders any detached vortex at this position quite visible. This squall cloud, in which the direction of motion on top is against the storm, may be regarded as a third horizontal thun- derstorm cylinder much smaller but more complete than either of the others. Schematic Illustrations—The above conceptions of the mechanism of a thunderstorm can, perhaps, be made a little clearer with the aid of illustrations. Fig. 113, a schematic representation of a thunderstorm in the making, gives the boundary of a large FIG. 114. r ) : 1 ‘i it I! | Duis hy Li Mbit di j ills lf aN I i I fat i! it ili i ye 1 I 1 qn mH 25 oye ‘ ih ee i il nh Mie HM) if r 1 i || i ! M1 a il! L fin lt a val } rh | ; ry I i) i ! i i } | 1 i Hat Hy Ideal cross-section of a typical thunderstorm, A, ascending air; D, descending air; C, storm collar; S, roll scud; D’, wind gust; H, hail; T, thunderheads; R, primary rain; R’, secondary rain. cumulus cloud from which rain ‘has not yet begun to fall, and the stream lines of atmospheric flow into it. When the cloud is sta- tionary and there is no surface wind the updraft obviously will be more or less symmetrical about a vertical through its centre, but when it has an appreciable velocity, as indicated in the figure, it is equally obvious that most, often nearly all, of the air enter- ing the cloud will do so through its front under-surface. At this stage there will be no concentrated or local down current, only counter settling of the air round about, because, as previously explained, the air cataract requires strong local cooling, and this, in turn, calls for local rain. Fig. 114 schematically represents a well-developed thunder- storm in progress. The rain, often mixed with hail, cools the air through which it falls, both by conduction and evaporation, the THE THUNDERSTORM 361 hail also by fusion, and as the temperature gradient over a con- siderable area already was closely adiabatic it follows that the actual temperatures within the rain column must be lower than those of the surrounding air at corresponding levels all the way from the surface of the earth to within the cloud, that is, through- out and a little beyond the nonsaturated or evaporating region. As soon, then, as this column or sheet of air is sufficiently cooled it flows down and forward and all the atmospheric movements peculiar to the thunderstorm are established substantially as represented. Referring to the figure: The warm ascending air is in the region A; the cold descending air at D; the dust cloud (in dry weather) at D’; the squall cloud at S; the storm collar at C; the thunder heads at 7; the hail at H; the primary rain, due to ini- tial convection, at R; and the secondary rain at R’. This latter phenomenon, the secondary rain, is a thing of frequent occurrence and often is due, as indicated in the figure, to the coalescence and quiet settling of drops from an abandoned portion of the cumulus in which and below which winds and convection are no longer active. The thunderstorm is also frequently accompanied by false cirri, occasionally by scarf clouds and even, though rarely, by mamato-cumuli; but, as none of these is essential to it, all, there- fore, are omitted from the above schematic illustration. Thunderstorm Pressures Before the onset of a thunder- storm there usually if not always is a distinct fall in the barometer. At times this fall is extended over several hours, but whether the period be long or short the rate of fall usually is greatest at the near approach of the storm. Just as the storm breaks, however, the pressure rises very rapidly, usually from 1 to 2 millimetres, fluctuates irregularly, and finally, as the storm passes, again be- comes rather steady but usually at a somewhat higher pressure than prevailed before the rain began. The cause of these pressure changes is rather complex. The decrease in the absolute water vapor of the air as a whole, meas- ured by the condensation, and the decrease in the temperature of the lower air—perhaps more than offset by the latent heat set free in the upper—both tend to increase the atmospheric pres- sure, and each contributes its share to the final result. Both these effects, however, are comparatively permanent, and while they 362 PHYSICS OF THE AIR may be mainly responsible for the increase of pressure after the storm has gone by, they probably are not the chief factors in the production of the initial and quickly produced pressure maximum. Here at least two factors, one obvious, the other inconspicuous, are involved. These are: (a) the rapid downrush of air, and (b) the interference to horizontal flow caused by the vertical circulation. The downrush of air clearly produces a vertically directed pressure on the surface of the earth, in the same manner that a horizontal flow produces a horizontally directed pressure against the side of a house. But a pressure equal to that given by 2 mm. of mercury, a pressure increase frequently reached in a thunder- storm, would mean about 2.72 grams per square centimetre, or 27.2 kilograms per square metre, and require a wind velocity of, roughly, 50 kilometres per hour or 14 metres per second. Now, the velocity of the downrush of air in a thunderstorm is not at all accurately known, but while at times probably very consider- able, the above value of 14 metres per second seems to be exces- sive; in fact, its average value may not be even half so great. If in reality it is not, then, since the pressure of a wind varies as the square of its velocity, it follows that less than one-fourth of the actual pressure increase can be caused in this way. Hence it would seem that there probably is at least one other pressure fac- tor, and, indeed, such a factor obviously exists in the check to the horizontal flow caused by vertical convection. To make this point clear: Assume two layers of air, an upper and a lower, flowing parallel to each other. Let their respective masses per unit length in the direction of their horizontal move- ment be M and m, and their velocities VY andwv. Now, if, through convection, say, the whole or any portion of the lower layer is car- ried aloft, it must be replaced below by an equal amount of the upper air. Let the whole of the lower layer be carried up. To produce the rainfall above assumed, 2 centimetres, this layer would have to be at least 1 kilometre deep; but no matter what its depth if it should merely change places with the upper air, there obviously could be no effect on the flow nor on the height of the barometer: Even if the different layers should mingle and assume a common velocity ’’, the rate of flow would still remain unchanged, in ac- THE THUNDERSTORM 363 .cordance with the law of the conservation of linear momentum, and the barometer reading unaltered. . In symbols we would have the equation MV + mv = (M+ ™m) V’. Hence, neither interchange nor mingling of the two air cur- rents, upper and lower, can change the vertical mass of the atmos- phere, nor, therefore, the surface pressure. But, then, in the case of atmospheric convection there is something more than simple mingling of two air currents, and the linear momentum does not, in general, remain constant. The increased surface velocity fol- lowing convection, a phenomenon very marked in the case of a thunderstorm, causes an increased frictional drag and therefore a greater or less decrease in the total flow. Suppose this amounts to the equivalent of reducing the velocity of a layer of air only 25 metres thick from V tov, and let 7 =5v. That is, the equiv- alent of the one-three-hundred-and-twentieth part of the atmos- phere having its flow reduced to one-fifth its former value. This would reduce the total flow of the atmosphere by about 1 part in 400, and thereby increase the barometric reading by nearly 2 millimetres. It would seem, then, that the friction of the thunderstorm gust on the surface of the earth, through the consequent decrease in the total linear momentum of the atmosphere and, therefore, its total flow, must be an important contributing cause of the rapid and marked increase of the barometric pressure that accom- panies the onset of a heavy thunderstorm. To sum up: The chief factors contributing to the increase of the barometric pressure during a thunderstorm appear to be, pos- sibly in the order of their magnitude: (a) decrease of horizontal flow, due to surface friction; (b) vertical wind pressure, due to descending air; (c) decrease in total humidity, due to precipita- tion; (d) lower temperature, due largely to evaporation—prob- ably more than offset by the heat of condensation. Thunderstorm Temperatures.—Before the onset of the storm the temperature commonly is high, but it begins rapidly to fall with the first outward gust and soon drops often as much as 5° C. to 10° C., because, as already explained, this gust is a portion of the descending air cooled by the cold rain and by its evaporation. 364 PHYSICS OF THE AIR As the storm passes the temperature generally recovers somewhat, though it-seldom regains its original value. Thunderstorm Humidity—As previously explained, heavy rain, at least up in the clouds, and therefore much humidity, and a temperature contrast sufficient to produce rapid vertical convec- tion, are essential to the genesis of athunderstorm. Hence during the early forenoon of a day favorable to the development of heat thunderstorms both the absolute and relative humidity are likely to be high. Just before the storm, however, when the tempera- ture has greatly increased, though the absolute humidity still is high, the relative humidity is likely to be rather low. On the other hand, during and immediately after the storm, the relative humidity is high, owing to both evaporation and decrease of temperature, and a little later, at least, the absolute humidity, because of the removal of a large amount of moisture from the atmosphere, often, presumably, comparatively low. “Rain-gush.”—It has frequently been noted that the rainfall is greatest after heavy claps of thunder, a fact that appears to have given much comfort and great encouragement to those who main- tain the efficacy of mere noise to produce precipitation—to jostle cloud particles together into raindrops. The correct explanation, however, of this phenomenon seems obvious: The violent turmoil and spasmodic movements within a large cumulus or thunder- storm cloud cause similar irregularities in the condensation and resulting number of raindrops at any given level. These in turn, as broken by the air currents, give local excess of electrification and of electric discharge or lightning flash. We have, then, start- ing toward the earth at the same time and from practically the same level, mass, sound, and light. The light travels with the greatest velocity, about 300,000 kilometres per second, and there- fore the lightning flash is seen before the thunder is heard—its velocity being, roughly, only 330 metres per second—while the rain, with a maximum velocity of & to 10 metres per second with reference to the air, reaches the earth still later. In fact, it is the excessive condensation or rain formation up in the cumulus cloud that causes the vivid lightning and the heavy thunder. Ac- cording only to the order in which their several velocities cause them to reach the surface of the earth it might appear, and has often been so interpreted, that lightning, the first perceived. is the cause of thunder, which, indeed, it is, and that heavy thunder, THE THUNDERSTORM 365 the next in order, is the cause of excessive rain, which most cer- tainly it is not. Thunderstorm V elocity.—The velocity of the thunderstorm is nearly the velocity of the atmosphere in which the bulk of the cumulus cloud happens to be located. Hence, as the wind at this level is faster by night than by day and faster over the ocean than over land, it follows that exactly the same relations hold for the thunderstorm, namely, that it travels faster over water than over land and faster by night than by day. The actual velocity of the thunderstorm, of course, varies greatly, but its average velocity in Europe is 30 to 50 kilometres per hour; in the United States, 50 to 65 kilometres per hour. Hail.—Hail, consisting of lumps of roughly concentric layers of compact snow and solid ice, is a conspicuous and well-known phenomenon that occurs during the early portion of most severe extratropical thunderstorms. But in what portion of the cloud it is formed and by what process the layers of ice and snow are built up are facts that, far from being obvious, become clear only when the mechanism of the storm itself is understood. As before, let the surface temperature be 30° C. and the rela- tive humidity 50 per cent., or the dew-point 18° C., nearly. Under these conditions saturation will obtain, and, therefore, cloud formation begin when the surface air has risen to an elevation of approximately 1.5 kilometres. Immediately above this level the latent heat of condensation reduces the rate of temperature de- crease with elevation to about half its former value, nor does this rate rapidly increase with further gain of height. Hence in mid- latitudes, where the above assumptions correspond in general to average thunderstorm conditions, it is only beyond the 4-kilo- metre level that freezing temperatures are reached, and where hail, therefore, can form. In the tropics and, after mid-summer, in the warmer portions of the temperate regions, where the freezing level is very high, hail seldom occurs. Generally, either it is not formed at all, owing to insufficient cloud height, or, if formed, is melted before reaching the ground from its initial great altitude. The process by which the nucleus of the hailstone is formed and its layer upon layer of snow and ice built up seems to be as follows: Such drops of rain as the strong updraft within the cloud blows into the region of freezing temperatures quickly con- 366 PHYSICS OF THE AIR geal and also gather coatings of snow and frost. After a time each incipient hailstone gets into a weaker updraft, for this is always irregular and puffy, or else tumbles to the edge of the ascending column. In either case it then falls back into the region of liquid drops where it gathers a layer of water, a portion of which is at once frozen by the low temperature of the kernel. But again it meets an upward gust, or falls back where the ascend- ing draft is stronger, and again the cyclic journey from realm of rain to region of snow is begun; and each time—there may be sev- eral—the journey is completed a new layer of ice and fresh layer of snow are added. In general the size of the hailstones will be roughly proportional to the strength of the convection current, but since their weights vary approximately (they are not homogen- eous) as the cubes of their diameters, while the supporting force of the upward air current varies, also approximately, as only the square of their diameters, it follows that a limiting size is quickly reached. It is also evident, from the fact that a strong convection current is essential to the formation of hail, that it can occur only where this convection exists; that is, in the front portion of a heavy to violent thunderstorm. Some meteorologists hold that the roll scud between the ascending warm and descending cold air is the seat of hail forma- tion, but this is a mistaken assumption. Centrifugal force would throw a solid object, like a hailstone, out of this roll probably before a single turn had been completed. Besides, and this ob- jection is, perhaps, more obviously fatal than the one just given, the temperature of the roll scud, because of its position, the lowest of the whole storm cloud, clearly must be many degrees above the freezing po’nt. Indeed, as the above calculation shows, tempera- tures low enough for the formation of hail can not often obtain at levels much less than three times that of the scud, and therefore it evidentlv is in the higher levels of the cumulus and not in the low scud that hail must heve its genes's and make its growth. CHAPTER XVI LIGHTNING. INTRODUCTION. Axsout the middle of the eighteenth century Franklin and others clearly demonstrated that the lightning of a thunder- storm and the discharge of an ordinary electric machine are identical in nature, and thereby established the fact that many of the properties of the former may logically be inferred from laboratory experiments with the latter. There is, however, one important difference between the two phenomena that does not seem always to be kept in mind, namely, the distribution of the charge. In the one case, that of the laboratory experiment, the charge commonly exists almost wholly on the surface of the ap- paratus used, while in the other, that of the thunderstorm, it is irregularly distributed throughout the great cloud volume. Hence the two discharges, lightning and laboratory sparks, necessarily differ from each other in important details. Nevertheless, in each case the atmosphere must be ionized before the discharge can take place freely, and this condition seems, at times at least, to establish itself progresso-spasmodically. That is, a small initial discharge, losing itself in a terminal brush, is rapidly followed by another and another, each losing itself in a manner similar to the first, until a path from pole to pole is sufficiently ionized to permit of a free electric flow and quick exhaustion of the remaining charge. Fig. 115, copied from a photograph by Walker,®* taken on a rapidly. moving plate, shows how a laboratory spark spasmodically (doubtless influenced by the period of electrical oscillation) ion- izes the air from either pole and thus progressively extends and: finally closes the conducting path of complete discharge. There appears also to be good evidence that the lightning discharge often hehaves in a manner generally similiar, though, perhaps, radicallv different, in certain details. Thus the free period of electrical oscillation that belongs to ordinary laboratory apparatus pre- sumably affects the process of discharge building as well as the nature of the discharge after it is fully established; while, on the other hand, if, as seems practically certain, lightning is not oscil- * Annalen der Physik u. Chemic, Leipzig, 1899, 68, 776. 367 368 PHYSICS OF THE AIR latory, it follows that its growth into a full flash must be acquired by some process independent of a periodic surge. Lightning, however, usually is pulsatory, as is obvious from the flicker of sheet lightning, described below, discharge after dis- charge taking place in the same direction and along the same path. Occasionally these sequent discharges extend to unequal distances, the latter especially becoming feebler and shorter, as shown in Fig. 116, thereby in their decay inversely simulating the growth or progressive development of a freely oscillating lab- oratory discharge. However, being pulsatory, or consisting of a group of unidirectional discharges, is an entirely different thing from being oscillatory, that is, consisting of an equally spaced series the units of which are alternately in opposite directions. Fic. 115. Growth of an electric spark discharge. (Walter.) It will be convenient, in discussing the facts about lightning, to classify the discharges according to their general appearance. Streak Lightning—When the storm is close by, the light- ning discharge invariably appears to the unaided eye as one or more sinuous lines or streaks of vivid white or pink—invariably sinuous, because electrically the atmosphere is always heterogen- eous or unequally ionized and the directive force constantly changing during, and because of, the discharge itself. Often there is one main trunk with a number of branches, all occurring at the same time and apparently instantaneously, while at other times there are two or more simultaneous though locally discon- nected streaks. Frequently the discharge continues flickeringly (on rare occasions even steady, like a white-hot wire) during a perceptible time—occasionally a full second. But all these phenomena are best studied by means of the camera, and have been so studied by several persons, among whom Walter, of Hamburg; Larsen, of Chicago; and Stead- LIGHTNING 369 worthy, of Toronto, are among the most persistent and success- ful. Stationary cameras, revolving cameras, stereoscopic cam- eras, cameras with revolving plates, and cameras with spectro- graphic attachments have all been used, separately and jointly, and the results have abundantly justified the time and the labor devoted: to the work. Fig. 117, copied by permission from one of Walter’s nega- tives, shows the ordinary tracery of a lightning discharge when photographed with a stationary camera. It is only a permanent Fic. 116. Streak lightning (sequent discharges), rotating camera. (Larsen.) record of the appearance of the lightning to the unaided eye. Fig. 118, however, also copied by Walter’s kind permission from one of his photographs, is a record of the same discharge obtained with a rotating camera. It will be noted that the more nearly vertical discharge occurred but once or was single; that this discharge was quickly followed by a second along the same path to about one-fourth of the way to the earth, where it branched off on a new course; that the second discharge was followed in turn at short but irregular intervals by a whole series of sequent discharges; that most of the discharges ap- peared as narrow intensely luminous streaks, and that one of the 379 PHYSICS OF THE AIR LIGHTNING 371 sequent discharges appeared, not to the eye, but on the plate of the rotating camera, as a broad band or ribbon. On close inspec- tion it will be obvious that the plaid-like ribbon effect is due, the warp to irregularities in the more or less continuous discharge, Fic. 118. Streak lightning (sequent discharges), rotating camera; companion to Fig. 117. (Walter.) and the woof to roughly end-on and therefore brighter portions of the streak. Another point particularly worthy of attention is the fact that while the first and second discharges have several side branches the following ones remain entire from end to end and are nowhere subdivided. Fig. 116, taken from a photograph obtained by Mr. Larsen, of Chicago, and kindly lent for use here by the Smithsonian 372 PHYSICS OF THE AIR Institution, shows another series of sequent discharges similar to those of Fig. 118, except that in this case there was no ribbon discharge. The time of the whole discharge, as calculated by Mr. Larsen, was 0.315 second. Here, too, side branches occur with the first but only the first discharge. This, however, is not an invariable rule for occasionally, as illustrated by Fig. 119, Fic. 119. Streak lightning (sequent discharges), rotating camera. (Walter.) copied from a published photograph by Walter, the side branches persist through two or three of the first successive discharges, but not through all. In such case each tributary when repeated fol- lows, as does the main stream, its own original channel. The phenomenon of sequent discharges, all along the same path, and the disappearance of the side branches with or quickly after the first discharge both seem reasonably clear. The first discharge, however produced, obviously takes place against very great resistance, and therefore under conditions the most favor- able for the occurrence of side branches, or ramifications. But the LIGHTNING 373 discharge itself leaves the air along its path temporarily highly ionized, puts a temporary line conductor with here and there a poorer conducting branch, in the atmosphere. This conductor is not only temporary (half the ions are reunited in about 0.15 sec- ond, the air being dusty”) but also so extremely fragile as to be liable to rupture by the violent disturbances, both explosive and of other types to be discussed later, it itself creates in the atmos- phere. Because partly, perhaps, of just such interruptions, and because also of the volume distribution of the electricity which prevents a sudden and complete discharge, the actual discharge is divided into a number of partials that occur sequently. Obvi- ously the breaks in the conducting (ionized) path, if they exist, are only here and there and but little more than sufficient to inter- rupt the flow. Hence the next discharge, if it occurs quickly, must follow the conducting and, therefore, original discharge path. Besides, in the subsequent discharges the original side branches will be quickly abandoned because of their greater resistance, or, what comes to the same thing, because of the more abundant ionization and consequent higher conductivity of the path of heaviest discharge. This leaves to be explained the genesis of the initial discharge, the least understood perhaps of all the many thunderstorm phe- nomena. Judging from the voltages required to produce labora- tory sparks, roughly 30,000 volts per centimetre, it is not obvious how such tremendous potential differences can be established between clouds or between a cloud and the earth as would seem to be necessary to produce a discharge kilometres in length, as often occurs. Indeed, a fatal objection to the assumption of such high voltage is the effect it would have on the velocity of fall and consequent size of the electrified raindrops. According to Simpson”, thunderstorm rain often carries as much as 6 electro- static units of electricity per c.c., and occasionally even more. Hence 30,000 volts per centimetre would produce an electric force on such rain roughly six-tenths that due to gravity and therefore either retard its fall, if directed upward, or, if directed downward, give it a velocity that would quickly break it into smaller drops. But thunderstorm rain does not consist essentially of smaller drops. On the contrary, as casual observation leads one to believe * Rutherford, Philosophical Magazine 44, p. 430, 1897. * Loc. cit., pp. 149-150. 25 374 PHYSICS OF THE AIR and as measurements have shown®®, raindrops average larger (1 to 6 mm. in diameter) during a thunderstorm than at any other time. Their velocity of fall therefore can not be excessive, nor indeed does it ever appear to be greatly different from that of ordinary rain. Flence electrical gradients of the order above assumed do not exist between clouds and the earth. Obviously the potential of individual drops may grow in either of two ways: (a) by the union of similarly charged smaller drops into larger ones. In this case, since capacity is directly proportioned to the radius, and the charge, after coalescence, to the volume (if droplets had equal size and charges), the poten- tials of the resultant drops, that is, their charges divided by their capacities, must be proportional to the squares of their radii, and therefore rapidly increase with coalescence and growth of size; (b) by evaporation of however charged drops. Here the charges remain constant and therefore the potential of each individual drop, being inversely proportional to its radius, obviously must become larger as the drop itself evaporates and gets smaller. In each case the tendency of the separate drops to discharge is in- creased, and the general ionization perhaps somewhat corre- spondingly increased, but the potential difference between the earth and the cloud as a whole unchanged. At present, therefore, one can do but little more than speculate on the subject of the primary lightning discharge, but even that much may be worth while since it helps one to remember the facts. As already explained the electrical separation within a thun- derstorm cloud is such as to place a heavily charged positive layer (lower portion of the cloud) between the earth and a much higher, also heavily charged, negative laver (upper portion of the cloud). Hence the discharges, or lightning, from the intermedi- ate or positively charged layer may be to either the negative por- tion above, in some cases even an entirely different cloud, or the earth below. Further, through the sustaining influence and tur- bulence of the uprushing air there must be formed at times and places practically continuous sheets and streams of water, of course heavily charged and at high potential, and also layers and streaks of highly ionized air. That is, electrically speaking, heavily charged conducting sheets and rods, whether of coalesced drops or of ionized air, are over and over, so long as the storm ™ Bentley, Monthly Weather Review, 32, p. 453, 1904. LIGHTNING 375 lasts, momentarily placed here and there within the positively charged mass of the storm cloud. Consider, then, what might be expected as the result of this peculiar disposition of charges and conductors, the result, namely, of the existence of a heavily surface-charged vertical conductor in a strongly volume-charged horizontal layer or region above and below which there are steep potential gradients to negatively charged parallel surfaces. The conductor will be at the same potential throughout, and therefore the maxima of potential gradients normal to it will be at its ends, where, if these gradients are steep enough, and the longer the conductor the steeper the gradients, brush discharges will take place. Assume, then, that a brush discharge does take place and that there is a supply of electricity Howing into the con- ductor to make good the loss. The brush and the line of its most vigorous ionization, other things being equal, necessarily will be directed along the steepest potential gradient or directly toward the surface of opposite charge. But this very ionization auto- matically increases the length of the conductor, for a path of highly ionized air is a conductor, and as the length of the con- ductor grows so, too, does the steepness of the potential gradient at its forward or terminal end, and as the steepness of this gradi- ent increases the more vigorous the discharge, always assuming an abundant electrical supply. Hence, an electric spark once started within a thunderstorm cloud has a good chance, by making its own conductor as it goes, of geometrically growing into a light- ning flash of large dimensions. Of course, when the electrical supply is small the lightning is feeble and soon dissipated. Whether the discharge actually does burrow its way through the atmosphere in some such manner as that indicated probably would be difficult, though not necessarily impossible, of observa- tion. The gradual lengthening of the streak, if the discharge takes place in this manner, might be detected by photographing it on oppositely directed rapidly moving films. A phenomenon roughly analogous to the burrowing progress suggested’°° can in-~ deed be produced on a photographic plate by bringing in contact with the film, some distance apart, two conducting points attached to the opposite poles of an influence machine. Brush discharges Leduc, Comptes rendus, Paris, 1899, 129, 37. 376 - PHYSICS OF THE AIR develop about each point, but the glow at the negative pole de- taches itself and slowly meanders across the plate toward the posi- tive point. As it goes it continually builds for itself, with the sil- ver of the emulsion, a highly conducting path. Rocket Lightning—Many persons have observed what at least seemed to be a progressive growth in the length of a streak of lightning. In some cases’! this growth or progression has appeared so slow as actually to suggest the flight of a rocket, hence the name. At first one might well feel disposed to regard the phenome- non in question as illusory, but it has been too definitely described and too frequently observed to justify such summary dismissal. Naturally, in the course of thousands of lightning discharges, many degrees of ionization, availability of electric charge, and slopes of potential gradient are encountered. Ordinarily the growth of the discharge, doubtless, is in a geometric ratio and the progress of its end exceedingly swift, but it seems possible for the conditions to be such that the discharge can barely more than sustain itself, in which case the movement of the flash ter- minal may, possibly, be relatively slow, and the appearance of a rocket therefore roughly imitated. Ball Lightning—Curious luminous balls or masses, of which C. de Jans 1°? probably has given the fullest account, have time and again been reported among the phenomena observed during a thunderstorm. Most of them appear to have lasted only a sec- ond or two and to have been seen at close range, some even pass- ing through a house, but they have also seemed to fall, as would a stone,’°? like a meteor, from the storm cloud, and along the ap- proximate path of both previous and subsequent lightning flashes. Others appeared to start from a cloud and then quickly return, and so on through an endless variety of places and conditions. Doubtless many reported cases of ball lightning, probably the great majority, are entirely spurious, being either fixed or wandering brush discharges or else nothing other than optical illusions, due, presumably, to persistence of vision. But here, too, as in the case of rocket lightning, the amount and excellence of observational evidence forbid the assumption that all such 1 Everett, Nature, London, 1903, 68, 599. Ciel et terre, Bruxelles, 1910, 31, 499. 8 Violle, Comptes rendus, Paris, 1901, 132, 1537. LIGHTNING 277 phenomena are merely subjective. Possibly in some instances, especially those in which it is seen to fall from the clouds, ball lightning may be only extreme cases of rocket lightning, cases in which the discharge for a time just sustains itself. A closely similar idea has been developed in detail by Toepler.°* It might either disappear wholly and noiselessly, as often reported, or it could, perhaps, suddenly gain in strength and instantly dis- appear as sometimes observed, with a sharp, abrupt clap of thunder. To say that all genuine cases of ball lightning, those that are neither brush discharges nor mere optical illusions, are stalled thunderbolts, certainly may sound very strange. But that, in- deed, is just what they are, according to the above speculation, a speculation that recognizes no difference in kind between streak, rocket, and ball lightning; only differences in the amounts of ionization, quantities of available electricity and steepness of po- tential gradients. Sheet Lightning—When a distant thundercloud is observed at night one is quite certain to see in it beautiful illuminations, appearing like great sheets of flame, that usually wander, flicker and glow in exactly the same manner as does streak lightning, often for well-nigh a whole second, and occasionally even longer. In the daytime and in full sunlight the phenomenon when seen at all appears like a sudden sheen that travels and spreads here and there over the surface of the cloud.. Certainly in most cases, so far as definitely known in all cases, this is only reflection from the body of the cloud of streak lightning in other and invisible portions. Often a blurred, yellowish streak is seen through the thinner portions of the intervening cloud. Occasionally, too, the cloud is wholly cleared in places where, of course, the dis- charge is white and dazzling. Conceivably a brush or coronal discharge may take place from the upper surface of a thunder- storm cloud, but one would expect this to be either a faint con- tinuous glow or else a momentary flash coincident with a dis- charge from the lower portion of the cloud to earth or to some other cloud. But, as already stated, only reflection is definitely known to be the cause of sheet lightning. Coronal effects seem occasionally possible, but that they ever are the cause of the phenomenon in question has never clearly been established and ™ Annalen d. Physik, Leipzig, 1900, 2, 623. 378 PHYSICS UF THE. ATR appears very doubtful. It has often been asserted, too, that there is a radical difference between the spectra of streak and sheet lightning, but even this appears never to have been photograph- ically, or otherwise definitely established. Beaded Lightning—Many photographs showing streaks of light broken into more or less evenly spaced dashes have been obtained and reported as records of beaded lightning, Without exception, however, these seem certainly to be nothing other than photographs of alternating-current electric lights, taken with the camera in motion. On the other hand, it occasionally happens that a reliable observer reports that he has actually seen a discontinuous or beaded streak of lightning. Thus Professor O. J. Ferguson, of the University of Nebraska (Department of Electric Engineer- ing), says :'°° “In the spring of 1914 a violent thunderstorm swept over Lincoln at about nine o’clock at night. There were numerous vivid lightning displays. One of these discharges occurring in the storm front originated at an elevation of about 45 degrees from my viewpoint and struck almost vertically downward. I was watching the storm from the window of a dark room, and the flash occurred directly in front of me. It was a direct stroke of chain or streak lightning. “ However, in dying away, it took probably a full second to disappear; it broke up seemingly into detached ‘portions, short and numerous. In fact, it gave a bead-like effect, and it would be very easy for one to have retained the latter impression and to have called the stroke bead lightning. “Tn explanation of this phenomenon I would suggest that each bead probably represents the ‘end-on’ view of the irregu- lar portions of the lightning path, and that they remained lumin- ous during the subsequent lesser discharges, while the inter- mediate sections became non-luminous, because viewed from the side.” The explanation offered by Professor Ferguson and _illus- trated by Fig. 118 doubtless is entirely correct. Hence beaded or pearl lightning must be accepted as a real though unusual phenomenon, which probably would be more often seen if def- initely watched for. Indeed, by close observation, the author has several times had that pleasure. 5 JOURNAL OF THE FRANKLIN INSTITUTE, V. 179, p. 253, IQIS. LIGHTNING 379 Return Lightning.—This is commonly referred to as the re- turn shock, and is only that relatively small electrical discharge that takes place here and there from objects on the surface of the earth coincidently with lightning flashes, and as a result of the suddenly changed electrical strain. This discharge is always small in comparison with the main lightning flash, but at times is sufficient to induce explosions, to start fires and even to take life. FIG. 120. Dark lightning. (F. Ellerman, photo.) Dark Lightning—When a photographic plate is exposed to a succession of lightning flashes it occasionally happens that one or more of the earlier streak images, on development, exhibits the “ Clayden effect ’’—that is, appears completely reversed— while the others show no such tendency. Obviously, then, on prints from such a negative the reversed streaks must appear as dark lines (Fig. 120), and for that reason the lightning flashes that produced them have been called “ dark lightning.” There is, of course, no such thing as dark lightning, since the only invisible radiation to which the ordinary photographic plate is sensitive is the ultra-violet, which cannot be excited by electric discharges 380 PHYSICS OF THE AIK in the atmosphere without at the same time producing visible radiation. Nevertheless, the photographic phenomenon that gives rise to the name “ dark lightning,” is real, interesting, and reproducible at will in the laboratory.’ Duration.—The duration of the lightning discharge is ex- ceedingly variable, ranging from measured intervals of 0.0002 second,’ and probably less, for a single flash to even a full second or more for a multiple flash consisting of a series of sequent discharges. On rare occasions a discharge of long dura- tion appears to the eye to be steady like a glowing solid. Prob- ably the best measurements of the shorter intervals were made by De Blois 7°° with the aid of a high-frequency oscillograph. He found the durations of 38 single peaks, averaging 0.00065 second, to range from 0.0002 second to 0.0016 second. Flashes that last as long as a few tenths or even a few hundredths of a second are almost certainly multiple, consisting of a succession of appar- ently individual discharges occurring at unequal intervals. Oc- casionally a practically continuous discharge of varying intensity, but all the time strong enough to produce luminosity, will last a few hundredths of a second. It must be remembered that the duration of even a single dis- charge and the length of time to complete the circuit, or ionize a path, from cloud to earth, say, are entirely different things. The latter seems usually (rocket and ball lightning may furnish ex- ceptions) to be of exceedingly short duration, while the former depends upon the supply of electricity and the ohmic resistance directly, and upon the potential difference inversely. _ Length of Streak.—The total length of a streak of lightning varies greatly. Indeed the brush discharge so gradually merges into the spark and the spark into an unmistakable thunderbolt that it is not possible sharply to distinguish between them, nor, there- fore, to set a minimum limit to the length of a lightning path. When the discharge is from cloud to earth the length of the path is seldom more than 2 to 3 kilometres; in the case of low-lying clouds even much less, especially when they envelop a mountain peak. On the other hand, when the discharge is from cloud to cloud *§ Wood, Science, New York (N.S.), 1899, 10, 717. *"De Blois. “8 Toc. cit. LIGHTNING 381 the path generally is far more tortuous and its total length much greater, amounting at times to Io, 15, and even 20 kilometres. Discharge, Where to Where?—As already explained, light- ning discharges may be between cloud and earth, between one part and another of the same cloud, or between cloud and cloud. But since the great amount of electrical separation, without which the lightning could not occur, takes place within the rain cloud, it follows that this is also likely to be the seat of the steepest potential gradients. Hence it would appear that lightning must occur most frequently between the lower and the upper portions of the same cloud, and this is fully supported by observations. The next in frequency, especially in mountainous regions, is the discharge between cloud (lower portion) and earth and the least frequent of all, ordinarily, those that take place between one and another entirely independent or disconnected clouds. Since the electricity of the thunderstorm obviously is gen- erated within the cumulus cloud and there mechanically separated into upper and lower layers it may not at first be clear how dis- charges can take place to earth at all. Of course, there will be some lines of force between the earth and each cloud charge, but these must ‘be relatively few so long as the charges are equal and approximately superimposed and the resulting dielectric strain correspondingly feeble. However, as the upper charge is car- ried higher, and especially as it is drifted away from the lower by the winds into which it projects, the lines of force between cloud and earth become more and more numerous, and the strain progressively greater until suddenly relieved by the lightning’s disruptive flash. It would seem, therefore, that a marked difference between the wind velocities at the upper and lower storm levels would be especially favorable to frequency of cloud-to-earth discharges. Hence one would infer that heat thunderstorms, since they occur only when the general winds are light, are less dangerous—less likely to be accompanied by cloud-to-earth lightning—than those (presumably every other type) in which the wind velocity in- creases more rapidly with elevation. And from this one would further infer that tropical thunderstorms, since they commonly belong to the heat variety, are less dangerous than storms of equal electrical intensity of middle and higher latitudes, where the other or cross-current varieties prevail. 382 PHYSICS OF THE AIR Unfortunately data are not at hand by which these deduc- tions may be tested statistically. They are, however, in accord with the general impression '°° that thunderstorms are more dan- gerous in England than in India. Discharges Direct, not Alternating.—Y ears ago some one for sotue reason or other, or for no reason, made the statement that the lightning flash is alternating and of high frequency, like the discharge of a Leyden jar, and forthwith, despite the fact that all evidence is to the contrary, it became a favorite dogma of the textbook, passed on unquestioned from author to author and handed down inviolate from edition to edition. True, there often are a number of successive discharges in a fraction of a second, as shown by photographs taken with a revolving camera, but these not only are along the same path but also in the same di- rection. This is obvious from the fact that side branches, whose trend with reference to the main trunk gives the direction of discharge, persisting as in Fig, 119, through two or more par- tial or sequent discharges, always follow the same paths. It is also proved by the direct evidence of the oscillograph.4° In the case of each separate discharge also the direction seems constant; it may vary in strength, or pulsate, but, apparently, it does not alternate. There are several reasons for concluding that lightning dis- charges, both single and multiple, are direct and not alternating, of which the following cover a wide range and probably are the best: (a) Lightning operates telegraph instruments. If the dis- charge were alternating it would not do so, unless very heavily damped. (b) At times it reverses the polarity of dynamos. This re- quires either a direct current or an alternating one so damped as to be quasidirect. (c) The oscillograph'’? shows each surge or pulsation, as well as the whole flash, to be unidirectional. (d)The relative values of the ohmic resistance, the self-in- duction, and the capacity, in pte case of a lightning discharge, am Symons, Metrl. Masasiie, 49, p. 114 and p. 164, 1914. *° De Blois, loc. cit. ™ De Blois, loc. cit. LIGHTNING 383 appear usually, if not always, to be such as to forbid the possi- bility of oscillations. From the equation of a condenser discharge, fe ip eee ee L qe +R a ++ co O it may be shown'!? that whenever the product of the capacity by the square of the resistance is greater than four times the self-induction, or, in symbols, that whenever CR’>4L oscillations are impossible. Undoubtedly all these terms vary greatly in the case of lightning discharges, but I, presumably, is always sufficiently large to maintain the above inequality and therefore absolutely to prevent oscillations. To illustrate with perhaps a typical case, assume a cloud whose under surface is circular with a radius of 3 kilometres, and whose height above the ground is 1 kilometre, and let there be a discharge from the centre of the cloud base straight to the earth: Find a probable value for the self-induction and capacity, and from these the limiting value of the resistance to prevent oscillations, or the value of R in the equation CR? — 4L. To find L we have the fact that the coefficient of self-in- duction is numerically equal to twice the energy in the mag- netic field per unit current in the circuit, and the further fact that per unit volume this energy is numerically equal to »H?/8z, in which H is the magnetic force and » the magnetic permeabil- ity of the medium. Let a be the radius of the lightning path and assume the current density in it to be uniform. Let b be the equivalent radius of the cylinder, concentric with the lightning path, along which the return or displacement current flows, In this case, » being unity, the energy JV of the magnetic field per unit current and per centimetre length of the discharge is given by the equation W = log > + 4. J. J. Thomson, “Elements of Electricity and Magnetism,” § Dis- charge of a Leyden Jar. 384 PHYSICS OF THE AIR Let b=2 kilometres and a=5 centimetres. Then IW =log, 4x10! +14 =11, approximately. Hence the energy of the mag- netic field per unit current for the whole length, 1 kilometre of the flash is represented by the equation Wio® — 11 X 10°, and the self-induction = 22 x 10° = 10% henry. To find C, assume a uniform field between the cloud and the earth. Asa matter of fact, this field is not uniform, and the cal- culated value of C, based upon the above assumption, is some- what less than its actual value, but not greatly less. Assuming, then, a uniform field we have = " = 225 X 10° = 25 X 10° farad, about. Hence, by substitution in the equation GR" = AL, it appears that R—rs190 ohms per kilometre, approximately. Neither a, the radius of the lightning path, nor J, the equiv- alent radius of the return current, is accurately known, but from the obviously large amount of suddenly expanded air necessary to produce the atmospheric disturbances incident to thunder it would seem that I centimetre would be the minimum value for a. Also, from the size of thunder clouds, it appears that 10 kilo- metres would be the maximum value for b. The substitution of these extreme values in the above equa- tion gives == 200 ohms per kilometre, roughly. From the fact that C varies inversely and L directly as the altitude of the cloud it follows that, other things remaining equal, the height of the cloud has no effect on the value of R per unit length. If the altitude is kept constant and the size of the cloud varied C’ will increase directly as the area, and L will increase directly as the natural logarithm of the equivalent radius of the cylinder of return current. Assuming the area of the cloud base LIGHTNING 385 to be 1 square kilometre, which certainly is far less than the or- dinary size, and computing as above it is found that R= 850 ohms per kilometre, roughly. Again, assuming the base area to be 1000 square kilometres, an area far in excess of that of the base of an ordinary thunder- storm cloud, the result is A == 35 ohms per kilometre, roughly. It would seem, therefore, that a resistance along the light- ning path of the order of 200 ohms per kilometre, or 0.002 ohm per centimetre, would suffice, in most cases, absolutely to prevent electrical oscillations between cloud and earth. In reality the total resistance includes, in addition to that upon which the above calculations are based, the resistance in parallel of the numerous feeders or branches within the cloud itself. In other words, the assumption that the resistance of the condenser plates is negligible may not be strictly true in the case of a cloud. Nor is this the only uncertainty, for no one knows what the resistance along the path of even the main discharge actually is; though, judging from the resistance of an oscillatory electric spark,'12 it, presumably, is many times greater than the calculated limit- ing value; and if so, then lightning flashes, as we have seen, must be unidirectional and not alternating. Temperature.—What the temperature along the path of a lightning discharge is no one knows, but it obviously is high, since it frequently sets fire to buildings, trees, and many other objects struck. In an ordinary electrical conductor the amount of heat generated in a given time by an electric current is proportional to the product C?RT, in which C is the strength of the current, R the ohmic resistance, and T the time in question during which C and R are supposed to remain constant. In a spark discharge of the nature of lightning some of the energy produces effects, such as decomposition and ionization, other than mere local heating, but as experiment shows, a great deal of heat is gen- erated, according, so far as we know, to the same laws that ob- tain for ordinary conductors. Hence extra heavy discharges, like extra large currents, produce excessive heating, and therefore “8 Fleming, “The Principles of Electric Wave Telegraphy and Telephony,” 2d ed. 1910, 80, p. 228-237. 386 PHYSICS OF THE AIR are far more liable than are light ones to set on fire any objects that they may hit. Visibility.—Just how a lightning discharge renders the at- mosphere through which it passes luminous is not definitely known. It must and does make the air path very hot, but no one has yet succeeded, by any amount of ordinary heating, in ren- dering either oxygen or nitrogen luminous. Hence it seems well-nigh certain that the light of lightning flashes owes its origin to something other than high temperature, probably to Fic. 121. LIGHTNING AIR Spectrum of lightning. (Fox.) internal atomic disturbances induced by the swiftly moving elec- trons of the discharge, and to ionic recombination. Spectrum.—Lightning flashes are of two colors, white, and pink or rose. The rose-colored flashes, when examined in the spectroscope, show several lines due to hydrogen which, of course, is furnished by the decomposition of some of the water along the lightning path. The white flashes, on the other hand, show no hydrogen lines or at most but faint ones. As one might sus- pect, the spectrum of a lightning flash and that of an ordinary electric spark in air are practically identical. This is well shown by Fig. 121, copied from an article on the spectrum of lightning by Fox,14 in which the upper or wavy portion is due to the light- ™ Astrophysical Jr., 1913, 18, p. 293. LIGHTNING 387 ning and the lower or straight portion to a laboratory spark in air. Fig. 122 is from an exceptionally fine photograph by Mr. Steadworthy of the Dominion Observatory, Ottawa, Canada. The heavy streak across the spectrum is not the parent, but an accidental stray that got in beside the prism. Fic. 122. Spectrum of lightning; and stray streak. (Steadworthy.) It is often asserted that the spectrum of streak lightning con- sists wholly of bright lines, and that sheet lightning gives only nitrogen bands; and from this it is argued that the latter is not a mere reflection of the first. This assertion is not supported by Figs, 121-122, the brightest portions of which, the portions that would the longest be seen as reflection grew steadily feebler, co- incide with strong nitrogen bands. Thunder.—For a long while no one had even a remotely sat- isfactory idea in regard to the cause of thunder, and it is not a 388 PHYSICS OF THE AIR rare thing even yet to hear such a childish explanation as that it is the noise caused by the bumping or rubbing of one cloud against another. Nor are all the learned explanations wholly free from error. Thus it has been suggested that thunder is due to the mutual repulsion of electrons along the path of discharge, though there are several objections to this pleasing hypothesis. If such repul- sion really occurred to the extent indicated, one might therefore expect a thread or rod of mercury carrying a current to spread out. Instead, however, it actually draws together, and, with a strong enough current, even pinches itself in two. Again, if mutual repulsion actually drove the electrons violently asunder one would expect the discharge instantly to dissipate, producing some kind of a brush effect, instead of concentrating along the familiar streak. Electronic repulsion, therefore, though it must exist to some extent, does not seem adequate, nor, as we shall see presently, is it necessary, to the production of heavy peals of thunder, Another plausible but erroneous hypothesis in regard to the origin of thunder insists that it is caused by the collapse of the partial vacuum produced by the heat generated by the lightning. Obviously cooling in this case must be rapid, especially at the instant the discharge ceases, but probably not nearly rapid enough to create sound, nor, therefore, ever to produce any of the crashes and rumbling that always follow heavy lightning. On the other hand, the heating of the atmosphere, the molec- ular agitation due to ionization, along the discharge path is so great and the resulting expansion so sudden-as to simulate a violent explosion and therefore to send out a steep compression wave. Indeed, compression waves generated by electric sparks are so sharply defined that not only they themselves but even their reflections may be clearly photographed.14* A compression wave, therefore, generated in the manner just explained, appar- ently is an adequate cause of thunder, and hence, presumably, its only cause. Rumbling.—Probably the most distinctive characteristic of thunder is its long-continued rumbling and great variation in intensity. Several factors contribute to this peculiarity, among them : ™® Wood, Philosophical Magazine, 48, 218, 1809. LIGHTNING 380 (a) Inequalities in the distances from the observer to the various portions of the lightning’s path. Hence the sound, which ordinarily travels about 330 metres per second in the air, will not all reach him simultaneously, but continuously over an ap- preciable interval of time. (b) Crookedness of path. Because of this condition it often happens that sections of the path here and there are, each through its length, at nearly the same distance from the observer or follow roughly the circumferences of circles of which he is the centre, while other portions are directed more or less radially from him. This would account for, and doubtless in a measure is the cor- rect explanation of, some of the loud booming effects or crashes that accompany thunder. (c) Succession of discharges. When, as often happens, sev- eral discharges follow each other in rapid succession there is every opportunity for all sorts of irregular mutual interference and reinforcement of the compression waves or sound impulses they send out. Occasionally they may even give rise to a musical note of short duration. (d) Reflection. Under favorable conditions, especially when the lightning is at a considerable distance, the echo from clouds, hills, and other reflecting objects certainly is effective in ac- centuating and prolonging the noise and rumble of thunder. But the importance of this factor generally is overestimated, for ordinarily the rumble is substantially the same whether over the ocean, on a prairie, or among the mountains. Distance Heard.—The distance to which thunder can be heard seldom exceeds 25 kilometres, while ordinarily, perhaps, it is not heard more than half so far. To most persons, familiar with the great distances to which the firing of large cannon is still perceptible, the relatively small distances to which thunder is audi- ble is quite a surprise. It should be remembered, however, that both the origin of the sound and often the air itself as a sound conductor are radically different in the two cases. The firing of cannon or any other surface disturbance is heard farthest when the air is still and when, through temperature inversion or other- wise, it is so stratified as in a measure to conserve the sound energy between horizontal planes. Conversely, sound is heard to the least distance when the atmosphere is irregular in respect to either its temperature or moisture distribution, or both, for 26 390 PHYSICS OF THE AIR these conditions favor the production of internal sound reflections and the dissipation of energy. Now the former or favorable conditions occasionally obtain during the production of ordinary noises, including the firing of cannon, but never during a thun- derstorm. In fact, the thunderstorm is especially likely to estab- lish the second set of the above conditions, or those least favor- able to the far carrying of sound. Then, too, when a cannon, say, is fired the noise all starts from the same place, the energy is concentrated, while in the case of thunder it is stretched out over the entire length of the light- ning path. In the first case the energy is confined to a single shell; in the second it is diffused through an extensive volume. It is these differences in the concentration and the conservation of the energy that cause the cannon to be heard much farther than the heaviest thunder, even though the latter almost certainly produces much the greater total atmospheric disturbance. The Ceraunograph—vVarious instruments, based upon the principles of ‘“‘ wireless ” receivers and known as ceraunographs, have been devised for recording the occurrence of lightning dis- charges, whether close by or so far away as to be invisible and their thunder unheard. Of course, the sensitiveness of the in- strument, the distance, and the magnitude of the discharge, all are factors that affect the record, but by keeping the sensitiveness constant, or nearly so, it is possible with an instrument of this kind to estimate the approximate distance, progress, and to some extent even the direction and intensity of the storm. Neverthe- less, there does not appear to be much demand for this informa- tion, and therefore at present the ceraunograph is but sparingly used. Chemical Effects —As is well known, oxides of nitrogen and even what might be termed the oxide of oxygen, or ozone, are produced along the path of an electric spark in the laboratory. Therefore, one might expect an abundant formation during a thunderstorm of these same compounds. And this is exactly what does occur, as observation conclusively shows. It seems prob- able, too, that some ammonia must also be formed in this way, the hydrogen being supplied by the decomposition of raindrops and water vapor. In the presence of water or water vapor these several com- pounds undergo important changes or combinations. The nitro- LIGHTNING 391 gen peroxide (most stable of the oxides of nitrogen) combines with water to produce both nitric and nitrous acids; the ozone with water gives hydrogen peroxide and sets free oxygen; and the ammonia in the main merely dissolves, but probably also to some extent forms caustic ammonia. Symbolically the reactions seem to be as follows: 2NO, + H,O = HNO, + HNO,. O; + H,0 = HO, + 02. NH, + H,O = NH,OH. The ammonia and also both the acids through the production of soluble salts are valuable fertilizers. Hence, wherever the thunderstorm is frequent and severe, especially, therefore, within the tropics, the chemical actions of the lightning may materially add, as has recently been shown,!!® to the fertility of the soil and the growth of crops. Explosive Effects—As already explained, the excessive and abrupt heating caused by the lightning current explosively and greatly expands the column of air through which it passes, thereby shattering chimneys, ripping off shingles, and producing many other similar and surprising results. It also explosively vaporizes such volatile objects as it may hit that have not sufficient con- ductivity to carry it off. Hence trees are stripped by it of their bark or utterly slivered and demolished through the sudden vola- tilization of sap and other substances; wire fused and vaporized; holes melted through steeple bells and other large pieces of metal, and a thousand other seeming freaks and vagaries wrought. Many of the effects of lightning appear at first difficult to explain, but, except the physiological, which, indeed, are but lit- tle understood, and probably some of the chemical, nearly all depend upon the sudden and intense heating along its path. Crushing Effects —One of the more surprising phenomena of the lightning discharge is the crushing of hollow conductors. an effect that gives some idea of the strength of current and quantity of electricity involved, and therefore deserves a full discussion. Pollock and Barraclough’ have described and explained this phenomenon in connection with a hollow copper cylinder: outside *° Capus, Guillaume, Annales de géographie, 1914, 23, p. 109. “Tr, and Proc. Roy. Soc. N. S. Wales, 39, p. 131, 1905. 392 PHYSICS OF THE AIR diameter 18 mm., inside 16 mm., lap join 4 mm. wide, 2 mm. thick. In what follows, however, reference will be had to a re- markable and even more instructive product of the same phenom- enon kindly lent by Mr. West Dodd, of Des Moines, Iowa. Fig. 123 shows two originally duplicate (so reported), hollow, copper lightning rods, one uninjured (never in use), the other crushed by a discharge. The uninjured rod consists of two parts, shown assembled in Fig. 123, and separate in Fig. 124. The conical cap, nickel plated to avoid corrosion, telescopes snugly over the top of the cylindrical section, and when in place, where it is left loose or unsoldered, becomes the ordinary discharge point. The dimensions are: Section Outside Diameter Inside Diameter Gylindér sicscusesserda 16.0 MMs cenieusecs cede 14.65 mm. Cone shank ............ 17:4 MM, ccceavcwedes 16.0 mm. Length of conical cap, cylindrical portion, 7 cm., total 1g cm. Both the cylindrical and the conical portions of the rod are securely brazed along square joints. The general effects of the discharge, most of which are obvi- ous from the illustrations, were: 1. One or two centimetres of the point were melted off. 2. The conical portion of the top piece and all the cylindrical rod except the upper 2 centimetres, roughly, within the cap, were opened along the brazed joint. 3. The brazing solder appears to have been fused and nearly all volatilized—only patches of it remain here and there along the edges. 4. The upper end of the cylindrical rod was fused to the cap just below its conical portion. 5. The rod was fused off where it passed through a staple. Whether a bend in the conductor occurred at the place of fusion is not stated. 6. The collapse of the cylindrical rod extended up about 5 centimetres into the cap. 7. The cylindrical portion of the cap, about 7 centimetres in length, was uninjured, even the brazing was left in place. What force or forces caused this collapse? Possibly it might occur to many that it was produced by the reaction pressure from LIGHTNING 303 an explosion-like wave in the atmosphere due to sudden and intense heating. But however plausible this assumption may seem at first there, nevertheless, are serious objections to it, some of which are: (a) While explosions with their consequent pressures may be obtained by passing a powerful current along a conductor they Fic. 123. Originally duplicate hollow copper lightning rods; one never used, the other crushed by a lightning discharge. seem to occur only with the sudden volatilization of the con- ductor itself, which in this case did not take place. (b) The heating of the enclosed air should have produced a pressure from within more or less nearly equal to the pressure simultaneously caused from without, and thereby have either prevented or at least greatly reduced the collapse. 304 PHYSICS OF THE AIR (c) The assumption that the crushing of the conductor was due to mass inertia of the suddenly heated air offers no solution whatever of the collapse of the rod up into the shank of the cap. For these reasons it seems that the idea that the collapse of the conductor may have been caused by the reaction pressure of Fic. 124. Same as Fig. 114, except unused rod is not assembled, an explosion wave in the atmosphere due to sudden heating, is untenable. Probably the correct explanation of the collapse, as already offered by Pollock and Barraclough,’'® an explanation that at least must involve an important factor, is as follows: Each longitudinal fiber. as it were. of the conductor attracted "8 Toc. cit. LIGHTNING 305 every other such fibre through the interaction of the magnetic fields due to their respective currents, and the resulting magnetic squeeze on the hollow rod, whose walls were weakened by the heating of the current, caused it to collapse in the manner shown. As is well known the force, f, in dynes per centimetre length, with which a straight wire carrying a current of J amperes is Fic. 125. sar | ae al | Section of a hollow tubular conductor, inner radius, u, outer radius, b. urged at right angles to the direction of the lines of force of a uniform magnetic field of intensity H is given by the equation Also, the value of H, r centimetres from a relatively very long straight conductor carrying J amperes, is given by the relation al oS lor Now, as developed by Northrup!’ in the theory of his heavy- current ammeters, let a, Fig. 125, be the outer, and b the inner radius of a tubular conductor, and let 7 be the radius of any in- termediate tube of infinitesimal thickness, dr. Also let the con- ductor as a whole carry a uniformly distributed current of J am- ™ Trans. Amer. Electrochem. Soc. 15, p. 303, 1909. 306 PHYSICS OF THE AIR péres. Then the value of the magnetic force, at the end of the radius r, is given by the equation He = 250?) 10 r (a*—b?) which depends upon the fact that only those portions of the cur- rent less than r distant from the axis are effective—the forces due to the outer portions neutralizing each other. Also the strength of the current, d/, carried by the cylinder of radius r and infinitesimal thickness, dr, is given by the relation 2Irdr (e—#) dI= Hence, under the assumed conditions, the normal pressure, dP, per unit area on the cylinder of radius r and thickness, dr, may be determined by the equation 2Irdr 2 I (r—b?) eS 27 1 10 (a?—b?) x Tor (a’—b?) Hence the total normal pressure, P, per square centimetre of the inner surface is given by integrating the above expression be- tween the limits b anda. That is, pe 2F rary dr 100 + (a2—b?)? 20 258 , “tow aeae pe +B loge 2 LP 2D? b “Too m (ab?) (+3 ep kes ~) Substituting for a and b their numerical values, 0.8 cm. and 0.7325 cm. respectively, it is found that [2 ; ~ 379.1 If we assume P, the pressure in dynes per square centimetre of the inner surface, to be 10°, approximately one atmosphere, then I= 109,470 ampéres, approximately. If the lightning discharge were alternating the current density would be greatest in the outer portions of the conductor, and therefore the total current would have to be still heavier than the above computed value to produce the assumed pressure. How- LIGHTNING 307 ever, from reasons already given, it seems extremely probable that the discharge is unidirectional and not alternating, and there- fore that the computed strength of current, though of minimum value, is substantially correct. Quantity of Electricity in Discharge—To determine the amount of electricity involved in a lightning discharge it is neces- sary to know both its duration and the average strength of cur- rent. Both factors and, therefore, the total charge are known to vary greatly, though actual measurements have been compara- tively few and even these as a rule only crudely approximate. It has often been stated that the duration of a single dis- charge, or single component of a multiple discharge, is not more than one one-millionth of a second. Some have computed a dura- tion of roughly one one-hundred thousandth of a second, while others have estimated that it can not be greater than one forty thousandth or, at most, one thirty-five thousandth of a second. Possibly many discharges are as brief as some of these estimates would indicate, but there is ample reason to believe that others are much longer. Thus one oceasionally sees a streak of light- ning that lasts fully half a second without apparent flicker, while more or less continuous or ribbon discharges are often photo- graphed by moving cameras. But in addition to these evidences we have also a number of time-measurements made by Rood??° with a rotating disk, ranging from less than 1/1600 second up to 1/20 second, and others, 38 in all, by De Blois?*? with an oscil- lograph, ranging from 0.0002 second to 0.0016 second. In one case De Blois found the durations of 5 sequent discharges to be 0.0005, 0.0015, 0.0016, 0.0014 and 0.0012 second respectively, or 0.0062 second as the summation time of these principal com- ponents of the total discharge. Hence it seems probable that the actual time of a complete discharge, that is, the sum of the times of the several components, may occasionalby amount to at least 0.01 second. The second factor mentioned above, the strength of discharge, is even more difficult to determine, and but few estimates of it have been made. Pockels,!22 adopting the ingenious method of measuring the ” Amer. Jr. Sci., vol. 5, p. 163, 1873. ™ Proceedings Am. Inst. Elec. Eng., vol. 33, p- 568, 1914. ™ Annalen d. Phys., 63, p. 195, 1897; 65, p. 458, 1898; Met. Zeit., 15, D. 41, 1898; Phys. Zeit., 2, p. 306, I9OI. 398 PHYSICS OF THE AIR residual magnetism in basalt near a place struck by lightning and comparing these quantities with those similarly obtained in the laboratory, concluded that the maximum strength of current in such discharges amounted occasionally to at least 10,000 am- péres. However, the loss of magnetism before the measurements were made, and other unavoidable sources of error, indicate that the actual current strength probably was much greater than the estimated value—that the maximum strength of a heavy lightning discharge certainly amounts to many thousands of amperes, oc- casionally perhaps to even one hundred thousand. Since the above estimates are very rough it would be well to check them, even though the check itself be equally crude. Hence it may be worth while further to consider the crushed lightning rod with this particular object in view. From the dimensions already given of this rod, outside diam- eter 1.6 centimetres, inside diameter 1.465 centimetres, it follows that its cross-sectional area is about .325 square centimetre, and its weight, therefore, approximately 2.9 grams per centimetre length. Further, from the fact that the brazed joint was opened and most of the solder removed, apparently volatilized, and the further fact that the rod itself, in several places, indicates in- cipient fusion, it would seem that the final temperature may have been roughly 1050° C. If so the rod must have been heated about 1023° C., since its temperature just before being struck probably was approximately 25° C. But the average specific heat of cop- per over this temperature range is roughly o.11 and therefore the calories generated per centimetre length about 327. Now one ampére against one ohm generates 0.24 calories per second. Hence, since the resistance of the uninjured or check rod, as kindly measured by the Bureau of Standards, is practically that of pure copper, the average resistance of the crushed con- ductor over the assumed temperature range probably was about 17 microhms per centimetre length,’?* we have the equation 3 LP = b 327. in which J is the average strength of current, and ¢ the actual time of discharge. Assuming that t=.01 sec. we get, roughly, [ =90,000 amperes. 2 Northrup, JOURNAL FRANKLIN INSTITUTE, I914, 177, Dp. 15. LIGHTNING 399 A current of this average value would indicate a maximum value of perhaps 100,000 amperes. It was computed above that a current of 19.470 ampéres in the given hollow conductor would produce on it a radial pres- sure of 10° dynes per square centimetre, or about one atmosphere. Hence 100,000 ampéres would give a pressure of 2638 x10! dynes per square centimetre, or approximately 400 pounds per square inch; enough, presumably, to produce the crushing that actually occurred. A current of 90,000 ampéres for .o1 second would mean goo coulombs or 27 x10"* electrostatic units of electricity; certainly an enormous charge in comparison with laboratory quantities, but after all a surprisingly small amount of electricity, since it would electrolyze only .084 of a gram of water. It must be distinctly remembered, however, that these estimates are exceedingly rough, and further that this particular discharge presumably was excep- tionally heavy since it produced an exceptional effect. An interesting method of measuring the resultant electric. exchange between earth and cloud incident to a lightning dis- charge recently has been used by C. T. R. Wilson.12# Values up to about 50 coulombs were found, but it is not stated whether the discharges were single or mutliple, nor are their durations given. From the above various observations and experiments, there- fore, it appears that in some cases the strength of current in a lightning discharge probably amounts to many thousands of am- peres, and that the total duration of the individual or partial discharges may be several thousandths of a second. Danger.—It is impossible to say much of value about dan- ger from lightning. Generally, it is safer to be indoors than out during a thunderstorm, and greatly so if the house has a well- grounded metallic roof or properly installed system of lightning rods. If outdoors it is far better to be in a valley than on the ridge of a hill, and it is always dangerous to take shelter under an isolated tree—the taller the tree, other things being equal, the greater the danger. An exceptionally tall tree is dangerous even ina forest. Some varieties of trees appear to be more frequently struck, in proportion to their numbers and exposure, than others, but no tree is immune, In general, however, the trees most ™ Proc, Roy. Soc. A., 92, p. 555, 1916. 400 PHYSICS OF THE AIR likely to be struck are those that have either an extensive root system, like the locust, or deep tap roots, like the pine, and this for the very obvious reason that they are the best grounded and therefore offer, on the whole, the least electrical resistance. If one has to be outdoors and exposed to a violent thunder- storm, it is advisable, so far as danger from the lightning is con- cerned, to get soaking wet, because wet clothes are much better conductors, and dry ones poorer, than the human body. In extreme cases it might even be advisable to lie flat on the .vet ground. In case of severe shock, resuscitation should be at- tempted through persistent (hour or more, if necessary) arti- ficial respiration and prevention from chill. As just implied, the contour of the land is an important fac- tor in determining the relative danger from lightning because. obviously, the chance of a discharge between cloud and earth, the only kind that is dangerous, varies somewhat inversely as the distance between them. Hence thunderstorms are more dan- gerous in mountainous regions, at least in the higher portions, than over a level country. For this same reason, also (inverse relation between distance from cloud to earth and frequency of discharge between them), there exists on high peaks a level or belt of maximum danger, the level, approximately, of the base of the average cumulus cloud. The tops of the highest peaks are sel- dom struck, simply because the storm generally forms and runs its course at a lower level. Clearly, too, for any given region the lower the cloud the greater the danger. Hence a high degree of humidity is favor- able to a dangerous storm, partly because the clouds will form at a low level and partly because the precipitation, and probably therefore the electricity generated will be abundant, Hence, too, a winter thunderstorm, because of its generally lower clouds, is likely to be more dangerous than an equally heavy summer one. Finally, as already explained, cyclonic or other cross-current thunderstorms presumably are more dangerous, than those due to local heating, and therefore the thunderstorm of middle lati- tudes generally more dangerous than one of equal severity in the tropics. It may also be interesting to note that the front edge of a thunderstorm probably is more dangerous than any other por- tion; more dangerous because it is immediately beneath the re- LIGHTNING 4o1 gion of most active electrical generation, and because objects here often still are dry and therefore if struck more likely to be penetrated and fired than later when wet and thus partially shielded by conducting surfaces. LIGHTNING PROTECTION. If, as seems quite certain, the lightning discharge follows, or tends closely to follow, the instantaneous lines of electric force, then it is obvious that whatever changes the direction of this force must correspondingly alter the path the flash shall take. To the extent then that the direction of electric force near the surface of the earth can be changed, but in general to only this extent, lightning protection is possible. If also the strength of the field could materially be reduced, clearly, the discharges might be rendered less violent and even less fre- quent, but, as will be explained presently, there is no evidence that the strength of the field can greatly be altered by any practicable means. Hence it appears that protection from lightning must be sought through directional control, which is both possible and practical,??® rather than through prevention. Assume, in accordance with observation, that over an ex- tended horizontal surface, a prairie for instance, the lines of elec- tric force are vertical; determine how the field of force will be modified by the presence of a given structure. Obviously if the structure itself consists of such non-conducting materials as wood and stone there will be but little directional change of the electric force. If, however, it is made of a conducting substance the direction of the force will be changed, but to an extent and over an area that depend upon the size and shape of the struc- ture in question. In general this effect is not calculable, but for- tunately it may be definitely computed in the special case of a conducting semi-ellipsoid with vertical axis and standing, as would a right cone, on the conducting surface—the actual surface, if wet, somewhat below, if dry. The ground and all parts of the conductor, unless actively discharging, will have the same poten- tial. Hence by varying the values of the three diameters of the semi-ellipsoid a fair approximation may be made to many ordi- *5OQ. S. Peters, “ Protection of Life and Property Against Lightning.” Technologic Paper, 56, Bureau of Standards, Washington, D. C., 1915. Also R. N. Covert, “ Modern Methods of Protection Against Lightning,” Farmers’ Bulletin 842, Department of Agriculture, Washington, D. C., 1917. 402 PHYSICS OF THE AIR nary structures and their effects on the electric field estimated, in some cases roughly, in others with even a high degree of ac- curacy. Thus, by making each of the horizontal diameters small and the vertical one relatively very large, the modification of the field by a single upright metallic rod may be computed very closely, and its efficiency as a protection against lightning approxi- mately determined. This has recently been done by Sir J. Larmor and Mr. J. S. B. Larmor,!*° who say that “In fact, if the undisturbed vertical atmospheric field is F, the modified potential V=—F4+ 4. Seo a ‘ (BHA + AA + AM will be null over the ground, and also null over the ellipsoid (a, b, c), provided FL dz A 9 (a2 + A) (b2 + AN (2 + 2)%8 ‘For our special case of a thin symmetrical semi-ellipsoid of height c, this gives ‘ da. J = —F, + Aa i if A (+ A)K “The value of this integral, however, increases indefinitely towards its lower limit as ¢ falls to zero, when a and B are null. Thus as the semi-ellipsoid becomes thinner the value of A dimin- ishes without limit; that is, the modification of the field of force by a very thin rod is negligible along its sides unless close to it. A thin isolated rod thus draws the discharge hardly at all unless in the region around its summit.” This is not to be taken as a condemnation of lightning rods in general, It only shows that a single vertical rod affords but little protection to things in its neighborhood, and thus explains why kite wires, for instance,are so seldom struck. When, however, the horizontal diameters of the semi-ellipsoid are of appreciable length the directions of the otherwise vertical lines of force are greatly changed for some distance on all sides, as illustrated by Fig. 126, adapted from the paper quoted above. Hence one method, and so far as known the only method, of at least partially ”* Proceedings Roy. Soc. London, A 90, p. 314, 1914. LIGHTNING 403 protecting an object from lightning consists in surrounding it by a hollow conductor, or by a well-grounded conducting cage. Perfect protection ordinarily is not practical, if even possible. By this method the lightning that otherwise would hit at ran- dom is guided to the conducting system and through it, if all goes well, harmlessly to the ground. It must be clearly remem- bered, however, that this discharge, though in all probability unidirectional, is extremely abrupt and of great amperage and therefore possesses the dangerous voltage and inductive prop- erties of alternating currents of high frequency and large vol- ume. It should also be remembered that although the successive Fic. 126. Vertical field of electric force disturbed by a conducting, semi-ellipsoidal column. partial discharges that make up the usual lightning flash follow the same ionized path, this path itself, shifted by the winds, prob- ably often guides one or more of the secondary or sequent dis- charges to an entirely different object from that hit by the first. From these fundamental principles it is easy to formulate general rules (details: may be varied indefinitely) for the con- struction of an efficient system of lightning protection. CONDUCTORS. Since lightning discharges occasionally involve very heavy currents, it is necessary that the conductors of the protective sys- tem be sufficiently large to prevent fusion. Probably copper is the best material to use, mainly because non-corrosive, or prac- 404 PHYSICS OF THE AIR tically so, in the atmosphere and therefore very durable, though aluminum and ‘galvanized iron are also good. If copper, a weight of 370 grams per metre (4 ounces per foot) might suffice, but a greater weight possibly would be better. The shape of the cross section appears to be of comparatively small importance. TERMINALS. Because of the distortion of the electric field due to the object to be protected, house for instance, and to the system of con- ductors, each ridge, peak, chimney and other highest point should be capped or surmounted by a conductor that is well grounded. It would be better if the conductor extended 2 metres or so above each of these salients, though the protection is still fair to good with much shorter projections, or even none at all. Whether or not each projection in turn is provided with the customary sharp points probably is of small importance—rather a matter of taste or sentiment than a necessity. To be sure, it often is asserted that sharp points discharge so freely that they thereby largely prevent lightning. But this assumption has little support from observation or experiment. Lodge,’*’ for instance, says: “T find that points do not discharge much till they begin to fizz and audibly spit; and when the tension is high enough for this, blunt and rough terminals are nearly as efficient as the finest needle points. The latter, indeed, begin to act at comparatively low po- tentials, but the amount of electricity they can get rid of at such potentials is surprisingly trivial, and of no moment whatever when dealing with a thundercloud.” SYSTEM. Because a single rod modifies the electric field only in its near neighborhood, and because the wind shifts the ionized or conducting path during the interval between successive partial discharges, it is obvious that the smaller the spaces left bare by the conductive covering the more effective the protection. A steel frame building with the framing well grounded from its lower portions and connected at all upper corners, and other places of near approach, to a metallic roof from which in turn conductors extended above the chimney tops and other protrusions, would, therefore, appear to be especially well protected from lightning damage. vt“ Tightning Conductors and Lightning Guards,” London, 1802, p. 370. LIGHTNING 405 A stone or wooden building should have electrically continu- ous rods up each corner to the eave, thence to and along the ridge, with such side branches and elevated projections as the size and shape of the building, and other considerations, may require. In general, no place on the roof should be more than 3 metres (10 feet) from some portion of the protective system. Further, the principal and secondary conductors must be so placed that from any point the ground may be reached by a continuous downward course. Protection would also be increased by surmounting each cor- ner with a conducting rod 3 to 4 metres tall, properly connected to the rest of the system. Architectural considerations, however, might often forbid this additional precaution. JOINTS. To facilitate the discharge as far as possible the conductors should be as nearly as practicable continuous. Hence all neces- sary joints should be electrically good and mechanically secure. Well-made screw joints turned up tight appear to be the best. BENDS. Since electric surges tend to arc across sharp angles lightning rods must have no short bends. Changes in direction must be avoided as far as possible and wherever necessary be made gradu- ally along a curve of 30 centimetres (one foot) radius, or more,— self induction must be kept at a minimum. ATTACHMENT. The rods should be attached to the building with holders of the same material as the rod itself. This prevents corrosion, and also secures electrical connection to the roof and sides which usu- ally are wet and conducting during a thunderstorm, GROUND CONNECTIONS. Because of the considerable resistance of even very damp earth, ground connections should be as good and as many as practicable. Every descending rod, and there would better be one at each corner, and on large buildings even more, should be sunk straight down to perpetually damp earth, if convenient con- nected also to underground water pipes, and of course protected 27 406 PHYSICS OF THe, AIR from injury a couple of metres above ground. Generally copper is best for this purpose. If iron is used it should not be packed in coke or charcoal, since either would cause the iron more rapidly to corrode. CONNECTION TO NEIGHBORING CONDUCTORS. The high potential and strong induction of the lightning dis- charge require that not only gutters, waterspouts, and the like, on the outside, but also all internal conductors of large size or considerable length be connected with the outer system at their upper ends and wherever they come within even two or three metres of it, cross connected with each other at points of close approach, and, finally, well grounded, from their lower ends, either directly or by proper attachment to the main conductors. It is often stated that leaky gas pipes should be excepted from such connections. Possibly so, but in the first place gas pipes should not be allowed to leak. SPECIAL DANGERS. Overland wires, telephone, telegraph, light and power, neces- sarily are sources of danger unless provided with proper lightning arresters. However, appropriate devices of this nature com- monly are installed, and therefore danger from electric wires usually is negligible. Nevertheless, it must be remembered that this distinctly is a case where the price of protection is proper forethought and adequate precaution. A much greater source of danger, because seldom if ever provided with an efficient lightning arrester, is the harmless-look- ing wire clothes line running from some part of the house to a convenient tree. The obvious remedy in this important case is either to use a cotton or other fibre rope, or else to avoid con- nection with the house altogether. Still another common source of danger, especially to stock, is the ordinary wire fence. But here, too, approximate safety is easy of attainment. It is only necessary that good ground con- nections be made at intervals of every 100 metres (20 rods), or less—the shorter the better, so far as safety is concerned. Finally the question of shade trees is of some importance. None is safe, but in general the danger they imply increases both with their own height and with the elevation of the ground above adjacent regions. PART II. ATMOSPHERIC ELECTRICITY AND AURORAS CHAPTER [| ATMOSPHERIC ELECTRICITY, THREE manifestations of atmospheric electricity, lightning (discussed in connection with the thunderstorm), the aurora po- laris, and St. Elmo’s fire—a “brush” discharge from elevated objects—have long been known; the first two, of course, from the beginning of human existence, and the last, as an object of the sailor’s superstition, certainly since the days of ancient Greece and Rome.'*§ Their identification, however, as electrical phe- nomena is very modern. The following list of contributions to the science of at- mospheric electricity, though fragmentary, will, perhaps, give some idea of its slow but accelerated course of development : (a) The suspicion of the electrical nature of lightning by Hawksbee, who says,!*° “‘ Sometimes I have observed the light to break from the agitated [electrified] glass in as strange a form as lightning.” And also,'®° “I likewise observed that... it was but approaching my hand near the surface of the outer glass [a rotated open receiver containing an exhausted vessel] to pro- duce flashes of light like lightning in the inner one’; by Wall,!* “by holding a finger a little distance from the [electrified ] amber, a crackling is produced, with a great flash of light suc- ceeding it . . . and it seems, in some degree, to represent thun- der and lightning”; by Gray’? . . . “this electric fire, which, by several of these experiments, seems to be of the same nature with that of thunder and lightning ”; and by many others. (b) The devising by Franklin,'#° in 1749, of a simple means “to determine the question, whether the clouds that contain light- ning are electrified or not.” (c) The proof, May 10, 1752, by Dalibard?%* (following “ Brand’s “ Antiquities,’ Castor and Pollux. ™ Phil. Trans., 1705. * Phil. Trans., 1707. *! Phil. Trans., 1708. ™ Phil. Trans., 1735. “Experiments on Electricity,” edition 1769, p. 66. ™ Franklin, “Experiments on Electricity,” edition 1769, p. 107. 407 408 PHYSICS OF THE AIR: Franklin’s suggestion), that clouds in which lightning appears are electrified. (d) The proof, July, 1752, by Le Monnier!®® that a tall, in- sulated metallic conductor becomes electrified even when the sky is absolutely clear. (ce) The inauguration in 1757 by Beccaria’®® of system- atic and long continued (15 years) observations of atmospheric electricity. (f) The invention by Thomson1#? (Lord Kelvin) of the quadrant electrometer in 1855, and the ‘‘ water-dropper,” about the same time, that greatly increased the delicacy and accuracy of the measurements of atmospheric electricity. (g) The discovery by Linss!#8 in 1887 that even the most perfectly insulated conductors lose their charges, when exposed to the air, in a manner that shows the atmsophere itself to be a conductor of electricity. (h) The discovery in 1900 by C. T. R. Wilson’®® and also by H. Geitel'?? of spontaneous ionization in the atmosphere. (1) The discovery in 1902 independently by Rutherford and Cooke,‘ and McLennon and Burton,'*” of a penetrating radia- tion in the lower atmosphere, presumably from radioactive sub- stances near the surface of the earth. (j) The discovery in 1905 by Langevin'*® of slow moving or large ions in the atmosphere. (k) The discovery by Simpson'** in 1908 and 1909 that the electric charge on thunderstorm rain, and precipitation generally, is prevailingly positive. (1) The discovery by Kolhorster?#* that an extremely hard or penetrating radiation exists in the atmosphere that comes from the outside—chiefly, apparently, from the sun. % Acad. Roy. des. Sciences, 1752, p. 233. 9 Tell’ Elettricita Terrestre Atmospherica a Cielo Sereno,” Torino, 1775. 8B A. Rept., 1855 (2), p. 22. “8 Met. Zeit., 4, Pp. 345, 1887. * Proc. Cambr. Phil. Soc., 2, p. 52, 1900. © Phys. Zeitsch., 2, p. 116, 1900. 1 Phys, Rev., 16, p. 183, 1903. ™? Phys. Rev., 16, p. 184, 1903. *°C. R., 140, p. 232, 1905. ™ Memoirs Indian Meteorl. Dept., Simla, 1910, 20, pt. 8. ™ Deutsche Phys. Gesel., July 30, 1914. ATMOSPHERIC ELECTRICITY 409 ELECTRICAL FIELD OF THE EARTH. The experiments of Franklin and others with kites and in- sulated vertical rods revealed a persistent difference of electric ‘potential between the earth and the atmosphere, that soon be- came, and still is, the object of innumerable measurements. Instruments.—The instruments essential for accurate meas- urements of the difference of potential between the earth and any point in the atmosphere are a “collector”? and an electroscope. The “collector ” is merely an insulated conductor provided with an adequate means of electric discharge—sharp point, flame, ionizing salt, or “ dropper ’—that brings it and.all other conduc- tors with which it is electrically connected to the potential in the air at the point of discharge. The electrometer, one element of which is connected to the “collector” and thus brought to its potential while the other is grounded, or connected to a “ collector ” at a different level, may be any one of several types. Those generally used at present are the Thomson quadrant, Bendorf registering (adaptation of the Thomson quadrant). Wulf bifilar, and Einthoven single-fibre. The quadrant type must be kept stationary, but the others are not so restricted and give good results even on shipboard and in balloons. Potential Gradient Near the Surface.-—The vertical potential gradient near the surface of the earth varies greatly, with loca- tion, season, hour, and weather conditions—occasionally even re- versing sign during storms—but the general average over level areas and during fine weather appears to be of the order of 100 volts per metre, in response to a negative surface charge. Location Effect—Since the earth is a conductor it is obvious that the distribution on its surface and the resulting vertical po- tential gradient will be so modified by topography as to be smaller in narrow valleys than on the neighboring ridges. Over level regions of the same elevation the gradient appears to be largest in the interior of continents of the temperate zones and least within the tropics, and also, perhaps, in very high latitudes. Annual Variation.—The annual variation of the vertical po- tential gradient near the surface of the earth differs greatly from place to place. In general it is comparatively small in tropical re- gions, and also anywhere on mountain tops, but large, as much in some cases as twice the annual average value, in the temperate 410 PHYSICS OF THE AIR zones where the gradient changes are roughly as follows: An increase during the fall and early winter to a maximum of per- haps 250 volts per metre followed by a rapid decrease during spring to a moderately constant summer minimum of roughly 100 volts per metre. Diurnal Variation—The diurnal variation of the potential gradient, in some places fully equal to the average gradient, changes with place, season, and altitude. Its amplitude is greater along middle latitudes in the interior of continents than along low latitudes, or anywhere over the ocean; greater during winter, when it is. single-crested, than summer, when double-crested. At moderate elevations, half a kilometre or less, the gradient has only a single daily maximum and minimum, whatever its sur- face periods. Jn all cases a minimum gradient occurs about 4 o’clock in the morning. If the variation is double diurnal the second, but less pronounced minimum, occurs about mid-afternoon; the first max- imum at 9 o'clock, roughly, in the forenoon, and the second at about 8 to 9 o’clock in the evening. If the variation is only diur- nal, as in the winter, the maximum is attained during the after- noon. Typical examples of such curves are given in Fig. 127 after Bauer and Swann.** From the above facts it appears that the single daily varia- tion of the potential gradient is fundamental, and that the sum- mer afternon minimum that develops a double diurnal variation is only a shallow disturbance due, presumably, in part at least, to dust, since any material caught up from the earth obviously must carry along some of the negative surface charge and thereby de- crease the gradient in the lower air. Potential Gradient and Meteorological Elements.——Many ef- forts have been made to find what relations obtain between the potential gradient and the various meteorological elements, but the results in most cases are inconclusive, especially in respect to temperature, humidity, and pressure changes. Strength and di- rection of wind both are important through their effect on the amount of smoke, dust, factory fumes, et cetera, in the air at the place of measurement. Fog, rain, and other forms of pre- cipitation are nearly always electrically charged and therefore “6 Publication No. 175 (Vol. III) of the Carnegie Institution of Wash- ington. ATMOSPHERIC ELECTRICITY 4II often greatly modify and occasionally even reverse the potential gradient as do also heavily charged or thunderstorm clouds. Cir- rus and other types of high, fair-weather clouds produce little or no effect. Potential Gradient and Elevation.—Measurements of the po- tential gradient from free balloons have shown that it varies greatly and irregularly through the low dust-laden stratum, and that above this layer it decreases less and less rapidly to a com- Fic. 127. 280 240 POTSDAM 200 160 KEW OCEAN 120 MUNICH KREMS- MUNSTER © oO TRIEST SAMOA mS oO POTENTIAL-GRADIENT-VOLTS PER METER- = 2 HOURS Diurnal variation of potential gradient | 24 paratively small value at an altitude of only a few kilometres. If the surface gradient is 100 volts per metre, it may be 25 volts per metre at an elevation of 1.5 kilometres, Io at an elevation of 4 kilometres, 8 at 6 kilometres elevation, with similar decreases for greater heights. Surface and Volume Charges, et cetera.—From the simple equation, dV _ 100 volts dn metre = bane, giving the electric force, f, or rate of change of potential normal to the surface, in terms of the surface charge o per unit area, it 412 PHYSICS OF THE ALR follows that when the potential gradient at the surface of the earth is 100 volts per metre the charge is 2.65 x 10° negative electro- static units per square centimetre, or 4.5 x 10° coulombs, roughly, for the total surface charge of the earth. Similarly, from the equation, @V df _ dn dn 4 between the volume charge p and the ratio of change of the electric force to change of elevation, it appears that near the surface of the earth the net charge of the air is roughly 0.1 electrostatic unit of positive electricity per cubic metre. ELECTRICAL CONDUCTIVITY OF THE ATMOSPHERE It is well known that an electrified conductor exposed to the air gradually loses its charge, however carefully it may be insu- lated. This phenomenon was first investigated by Coulomb,?** who found the important law that the rate of loss of charge is proportional to the existing charge, or rate of drop of potential proportional to the existing potential. In symbols, dQ _ a Ss gy ae ry or Qu= Qoe** and y= lhe where Q. and Jo are the charge and potential, respectively, at any given instant, Q: and /”: the corresponding values ¢ seconds, or other units of time, later, e the base of the natural logarithms, and aa constant. The loss of charge was explained by Coulomb, and his ex- planation was accepted for more than a century, as due to the charging by contact of neutral molecules of air and their subse- quent repulsion. From the work begun by Linss'#8 and extended by others it is now known, however, that the discharge coefficient a varies more or less from hour to hour and from season to season, and, further, that generally it is not the same for charges of opposite “1 Mém., de V'Acad. de Paris, 1785, p. 616. “8 Met. Zeit., 4, 345 ,1887. ATMOSPHERIC ELECTRICITY 413 sign. Hence the loss of charge in addition to that which may be accounted for by imperfect insulation, is due to neutralization by numerous minute charges of the opposite sign normally present in the atmosphere—charges that render it conductive. It is also known that the values of these charges are either that of the electron or multiples thereof. Swann'*® has shown that whatever the shape of the charged body the rate of its loss of charge is given by the equation, dQ 2a 47Qnev where Q is the charge on the object, m the number of ions per cubic centimetre of sign opposite to that of Q, w the specific ve- locity of these ions and e the ionic charge. In other words, the rate of supply of electricity by the ions to the charged body is 4m C V, in which C is the capacity of the charged object and \ the conductivity of the air for electricity of sign opposite to that of the charge. The conductivity, therefore, of the atmosphere may be con- veniently measured by noting the rate of potential drop of a charged cylinder concentrically surrounded by a relatively large tube through which a good circulation of fresh air is maintained. Fig. 128 indicates the equipment used for this purpose on the Carnegie during the cruises of 1915-1916.1°° As explained in the publication referred to, if C, is the capacity of the whole ap- paratus, including the electroscope, and C, the measured capacitv of the concentric cylinders, including that portion of the support- ing rod A that is exposed to the air current, then Or gre QV and 6 Vi 47 2 C= F loge re in which T is the time required for the potential to fall from V, to V,. Hence both conductivities, A;and A_, corresponding respectively to the positive and negative ions, are easily determinable. © Terr. Mag. and Atmos. Elec., 19, p. 81, 1914. ™ Bauer and Swann, Publication 175 (Vol. III) of the Carnegie Institu- tion of Washington, p. 385. 414 PHYSICS. OF THE ALK The average value of the conductivities found during the above-mentioned cruise of the Carnegie were 4+ = 1.44 x Io+ and A-=1.19x 10%. These are also approximately the values found over land during clear weather. Annual Variation—In general the conductivity is greater during the summer than during winter—the reverse of the poten- tial gradient. Fic. 128. H —— Conductivity apparatus. Diurnal Variation —vThe diurnal variation of the conductiv- ity is quite irregular, but is more or less the reverse of the poten- tial gradient, that is, high in the early morning and low in the evening. Relation to Weather.—The conductivity of the atmosphere is very small when the air is either dusty or foggy; nearly all the ions being then attached to masses so large that the velocity factor, v7, in the current equation, and consequently the current itself, is quite small. On the other hand, when the air is clean and dry, the conductivity is relatively large. Conductivity and Elevation —Through the first kilometre the ATMOSPHERIC ELECTRICITY 415 conductivity of the atmosphere varies irregularly, owing, pre- sumably, at least in part, to corresponding variations in the dust content. Beyond about that level it generally increases rather rapidly, so that at the elevation of 6 kilometres it may have roughly 20 times the surface value. IONIC CONTENT OF THE AIR Iomc Density —The number of ions of either sign per unit volume of the atmosphere may be found by passing a known vol- ume of air through a cylindrical condenser, sufficiently charged to catch all the ions of opposite sign, and noting the drop in potential. Let m+ and n— be the number of positive and negative ions respectively per cubic centimetre of the air examined, ¢ the ionic charge, V the initial potential, and 8/ the drop in potential on passage of 4 cubic centimetres of air through the condenser, then, neglecting, or allowing for the leakage, C8Y n+ eA The value of m varies greatly, being very small during foggy and dusty weather, and relatively large when the air is clear. In general it is larger during summer than winter, larger during the day time than at night, and larger when the temperature is high than when it is low. It also increases with elevation through at least the first few kilometres, but to what maximum value, and where, is not known. Through the lower atmosphere the fair-weather values of n+ and n— generally are of the order of 800 and 680, respectively, per cubic centimetre. Ionic Velocity—The velocities v, and v2, of the positive and negative ions respectively, may be computed from the corre- sponding values of the current, +ev, and ionic density n4, since the value of e is a known constant. The average value of v+ in cm/sec cm/sec volt/cm volt/cm * Both values increase with decrease of pressure—at half the pres- sure the velocity is double, approximately—and therefore with increase of elevation. Large, or Langevin Ions.—After the atmosphere is deprived of all its ions of molecular size it still is slightly conductive, be- the lower air is of the order of 1 , and of v_, 1.2 416 PHYSICS OF THE ALR cause, as discovered by Langevin,*! of the presence of relatively slow moving and therefore comparatively massive ions. The number of such ions per cubic centimetre varies greatly. In the open country this number appears to be comparatively small, but it is very great over large cities, perhaps many times that of the ordinary or molecular ions. ELECTRIC CURRENTS IN THE ATMOSPHERE At least four different electric currents exist in the atmosphere —two always and everywhere, or nearly so, and two sporadically in time and place. These are: (a) The lightning discharge, of very brief duration, but often rising to a strength of many thousand amperes. (b) Precipitation currents, or currents due to the falling of charged rain, snow, hail, et cetera. The average strength of such current may be found from the rate of precipitation and charge, usually positive, per cubic centimetre, say, of the rain, or its equivalent in the case of snow or hail. During non-thunder- storm rains this current often averages about 107° ampere per square centimetre of surface. During violent thunderstorms, however, it is far greater, even as much as 10? ampere per square centimetre for brief intervals has been reported. (c) Convection currents, due to the mechanical transfer of the ions in the atmosphere from one place to another by winds, including vertical convection. The strength of such current per unit area at right angles to the direction of the wind is obtained by multiplying the wind velocity by the net density of the charge. This density may be found either by multiplying the ionic charge by the difference between the numbers of ions of opposite sign per cubic centimetre, or from the equation, _1@YV : 4m dh? in which p is the density required, and dl’ /dh the vertical poten- tial gradient. The value of p varies greatly, but through much of the at- mosphere the convection current is of the order 107° ampere per square centimetre cross section of the wind, per metre/second velocity. p= *1C_ R., 140, p. 232. 1905. ATMOSPHERIC ELECTRICITY 417 (d) Conduction current, due to the downward flow of one set of ions, usually the positive, and the simultaneous upward flow of the other in response to the vertical potential gradient. The density of this current, or strength per square centimetre cross section, may be computed from the potential gradient and the conductivity, or, with suitable apparatus, may be measured directly. The average value of this conduction current is of the order of 3x 107° ampére per square centimetre of, apparently, the entire surface of the earth. It generally is less during the day than at night, and less in summer than winter ; but always of such value that the sum total of the current for the entire earth is roughly 1500 ampéres. How this constant current, always, on the whole, in the same direction, is maintained is one of the greatest problems of atmospheric electricity. RADIOACTIVE CONTENT OF THE ATMOSPHERE The first evidence that the atmosphere normally contains one or more radioactive substances was obtained in 1900 when Geitel *? and C. T. R. Wilson *** independently found that an in- sulated electrified conductor gradually loses its charge even when inside a closed vessel. Later Elster and Geitel'®*! showed that a bare wire exposed to the air and charged negatively to a high voltage gradually becomes coated with radioactive material. In 1904 Bumstead’*> showed that the radioactive substance of the atmosphere consists essentially of radium and thorium emana- tions, which, it is now known, occur in widely varying propor- tions. On the average, however, they appear to produce about the same amount of ionization, that is, near the surface and over land, roughly 2 ions each, of each sign, per cubic centimetre per second. The emanations, which are heavy, radioactive gases, are sev- eral fold more abundant in mines and cellars than in the open and obviously get into the atmosphere by diffusion from the earth where they are generated by the spontaneous decomposi- tion of radium and thorium. They may be absorbed from a known volume of air by cocoanut charcoal, liquified by low tem- ™ Phys. Zeit., 2, p. 116, 1900. *8 Proc. Camb. Phil. Soc., 2, p. 52, 1900. ™ Phys. Zeit., 2, p. 590, 190I. * Amer. Jr. Sci., 18, p. 1, 1904. 418 PHYSICS OF THE AIR peratures (-150° C. or lower), or caught up by a conductor charged to a high negative potential. In any case the nature of the deposit can be determined from the decay curve, from which, together with the saturation current and the volume of air used, the amount of active material per unit volume may be deter- mined. In this way it has been found’*® that the radioactive emanations in the atmosphere over the Pacific Ocean, Sub-Ant- arctic Ocean, and land (average) amount to 3.3 x 107%, 0.4.x I07?”, and 88 x 107!” curie per cubic metre, respectively. Or, since the volume of one curie of emanation at standard tempera- ture and pressure is 0.59 cubic millimetre, 1°" the emanation gases constitute, in these several regions, 1.95 x 10°'®, 0.24 x 10719, and 51.9 x 107° of the atmosphere, respectively. The amount of these emanations appears to be sufficient to account for the measured ionization (ions of molecular size) on the land, but quite insufficient over the oceans to maintain the ionization of these regions. Perhaps, as the slow ions are so very numerous over land areas, it may account for only a small part of the ionization in either case. PENETRATING RADIATION It has been found that the air within a closed metallic vessel remains fully conductive, even when deprived of all emanations and when the inner walls of the vessel have been cleaned, as far as possible, of radioactive materials. By surrounding this vessel with thick screens, or sinking it in water, the conductivity of the enclosed air is more or less reduced.'®8 It is, therefore, inferred that the conductivity in question is produced by penetrating radia- tion of the y type from the outside. One obvious source of such radiation is the radium and thorium, and their decomposition products, that seem to be more or less prevalent everywhere near the surface of the earth, especially over land. That a portion, at least, of the ionization giving this conductiv- ity is produced by the y rays of ordinary radioactive substances *° Bauer and Swann, Publication 175 (Vol. III) Carnegie Institution of Washington, p. 422. *' Rutherford, “Radioactive Substances and Their Radiations,’ Cam- bridge University Press, 1913, p. 480. *8 Rutherford and Cook, Phys. Rev., 16, p. 183, 1903; McLennan and Burton, Phys. Rev. 16, p. 184, 1903. ATMOSPHERIC ELECTRICITY 419 in the earth and lower atmosphere is evident from the fact that it decreases with elevation up to about 1.5 kilometres above the surface. From this level, however, up to the greatest elevation at which it has been reported, 9 kilometres, the ionization in- creases very rapidly, and to several fold its surface value. Hence there appears also to be a y radiation of extremely high penetrating power that enters the lower atmosphere from some- where above it. ORIGIN AND MAINTENANCE OF THE EARTH'S CHARGE Numerous hypotheses have been made to account for the negative charge of the earth and to explain how that charge is maintained in spite of the conductivity of the atmosphere, but no satisfactory explanation of either has yet been found. As Simpson!®° has explained, since the vertical current is constant up to at least 1800 metres, the greatest altitude at which it has been determined, it follows that the negative charge of the earth can not be supplied from the air below that level. Neither can it be supplied by electrical separation within the earth, as that would quickly lead to a positive instead of the prevailing nega- tive surface charge. Simpson'*! suggests that the negative charge of the earth may be maintained by a bombardment from the upper atmo- sphere, or even cosmical space, of negative ions of much greater penetrating power than any now known. But, it is stated, this is only a suggestion and not a solution of the greatest, perhaps, of the problems of atmospheric electricity. The latest and most satisfactory explanation of the origin of the earth’s charge is the following, by Swann’® : “Measurements of the variation of the penetrating radiation, with altitude, point to the upper atmosphere as the origin of a part-of this radiation. The whole of the penetrating radiation is probably of the y-ray type, but the part which reaches the earth’s surface from the outer atmosphere is naturally the most penetrating part. Indeed, it is so penetrating that it passes through a thickness of air which would be equivalent, in absorp- * Kolhorster, Deutsch. Phys. Gesell., 16, p. 719, 1914. »7@ MLW. R., 44, p. 115, 1916. ~ “™ Loc. cit. @ Phys. Rev... 9, P. 555, 1917. 420 PHYSICS OF THE AIR tive action, to a column of mercury 76 cm. high, if absorption coefficients were simply proportional to density and were inde- pendent of material. The y-ray radiation from the outer layers of the atmosphere will consequently be very ‘hard,’ and, in ac- cordance with the known results of laboratory experiments, we must conclude that the negative corpuscles which it emits from the air molecules are emitted almost entirely in the direction of the radiation, and further, that they can have a range in air at least equal to that of the swiftest 8-rays from radium products, a range, for example, of 8 metres. The emission of corpuscles by these y-rays will consequently result, at each point of the atmosphere, in a downward current of negative electricity, which we shall call the corpuscular current. This corpuscular current will charge the earth until the return conduction-current balances the corpuscular current at each point of the atmosphere. “Taking, for the purpose of this abstract, a simplified case where the penetrating radiation considered is all directed ver- tically downwards, if gq is the number of corpuscles liberated per c.c. per second by the penetrating radiation and /; the average distance which a corpuscle travels from its point of origin, the corpuscular current density will be 1 = geh, where e¢ is the electronic charge. “Tf q be taken as 2, which is probably about equal to the num- ber of pairs of ions produced per c.c. per second in a closed vessel as a result of the part of the penetrating radiation in question, and if /) be taken as 8 metres, we have i= 2x 48x 10” x 800 = about 8 x 107 E. S. U./em2, which is just of the order of magnitude of the air-earth current density, so that on this view, the penetrating radiation from the outer layers of the atmosphere provides a sufficient basis for the explanation of the maintenance of the earth’s charge. “The corpuscular current-density, and consequently the con- duction current-density, will not necessarily be independent of the altitude, for the factors upon which i depends, viz., the intensity and quality of the penetrating radiation, the number of molecules per c.c. available for possible ionization by the radiation, and the range of the corpuscles set free all alter with the altitude. ATMOSPHERIC ELECTRICITY 421 “ A few minor difficulties present themselves if the above view be adopted. Thus, for example, near the surface of the earth, a considerable portion of the whole penetrating radiation comes from the soil, and is directed upwards, but this difficulty disappears when it is remembered that the average ‘ hardness’ of the radiation from the soil is very much less than that of the radiation which reaches the earth from the outer layers of the atmosphere. Again, it might appear that the corpuscles set free by the penetrating radiation should, on account of their great energy, produce in the atmosphere many more ions per second than are actually found to be produced. This difficulty, and others of allied nature become greatly reduced in magnitude, however, when considered in the light of our present knowledge of the action of very swift B-rays when passing through a gas.” 28 CuHapTerR II AURORA POLARIS THE aurora polaris is a well-known but imperfectly under- stood luminous phenomenon of the upper atmosphere, of which Figs. 129 and 130, from Stormer’s numerous photographs, are good examples. Types.—While no two auroras are exactly alike, several types have been recognized, such as arcs, bands, rays, curtains or drap- eries, coronas, luminous patches, and diffuse glows. The arcs normal to the magnetic meridian, often, but not always, reach the horizon. Their under edge is rather sharply defined, so that by contrast the adjacent portion of the sky appears exceptionally dark. The rays, sometimes extending upward from an arch, at other times isolated, are parallel to the lines of magnetic force. Many auroras are quiescent, others exceedingly changeable, flit- ting from side to side like wandering searchlights, and in some cases even waving like giant tongues of flame. Latitude Variation The aurora of the northern hemisphere occurs most frequently, about 100 per year, at the latitudes 60° (over the North Atlantic and North America) to 70° (off the coast of Siberia). Its frequency appears to be less within this boundary, while with decrease of latitude it falls off so rapidly that even in southern Europe it is a rare phenomenon. At the same latitude it is distinctly more frequent in North America than in either Europe or Asia. The distribution of auroras in the southern hemisphere is not so well known, but it appears to be similar, in general, to that of the northern. Periodicity.—It is well established that on the average auroras are more numerous during years of sun spot maxima than during years of spot minima. They also appear to be more numerous before midnight than after. Relations of frequency to phase of the moon, season, et cetera, have also been discussed, but with no conclusive results. Color—Many auroras are practically white. Red, yellow and green are also common auroral colors. Some streaks and bands are reddish through their lower (northern) portion, then yellowish, and finally greenish through the higher portions. 422 § AURORA POLARIS 423 Fic. 129. Aurora, February 28, 1910. (Stérmer.) Aurora, March 3 1910. (Stérmer.) 424 PHYSICS OF THE AIR Much of the light is due to nitrogen bands, but the source of the most prominent line of the auroral spectrum, » .5578 » (green), is not known. It has often been attributed to krypton, but other conspicuous krypton lines are absent; besides krypton is too heavy to exist at auroral heights in sufficient abundance to pro- duce a spectrum of such brilliance. There is good evidence that this green light, the light that produces the “ auroral line,” is always present in the sky, though whether wholly of auroral origin, or due in part to bombardment by meteoric dust, or to some other cause, is not known FIG. 131. Parallactic auroral photographs for determining altitude. (Stormer.) Height.—The problem of the height of auroras has often been investigated, but only recently solved. By simultaneously photo- graphing the same aurora from two stations against a common background of stars, Fig. 131, and measuring the parallax ob- tained, Stormer,*®* and Vegard and Kioenesatl have secured many excellent height measurements. The upper limits of the auroral light vary from about 100 kilometres to over 300 kilo- metres; and the lower limits from perhaps 85 kilometres to 170 kilometres, with two well-defined maxima, one at 100 kilometres, the other at 106 kilometres. Cause.—The fact that brilliant shifting auroras are accom- panied by magnetic storms renders it t practical ly certain that they, Ae OER: ieee and Atmos. Elec., 21, p. 157, 1916. ™ Terr, Magnet. and Atmos. Elec., 21, p. 169, 1916. AURORA POLARIS | 425 and presumably therefore all auroras, are due to electric dis- charges; and the further fact that they vary in frequency with the sunspot period indicates that this current either comes from or is induced by the sun. For some time it was thought prob- able that auroras are caused by negative particles shot off from the sun, and entrapped by the magnetic field of the earth. On the other hand, Vegard '°* has given strong arguments in favor of the @ particle which is positively charged, and Stormer’®* has found at least one case that required the positive charge to ac- count for the observed magnetic disturbance. The evidence, then, while not conclusive, indicates that auroras are due to streams of a particles in the upper atmos- phere shot off by radioactive substances in the sun. The seeming convergence of the auroral rays on a point far short of the magnetic pole, towards which they actually do con- verge, is due to perspective. Similarly, their apparent divergence from the magnetic zenith, thus forming a corona, is also a phenom- enon of perspective, for here one is looking out along a bundle, or tube, of rays that, following the lines of magnetic force, surround him in every direction. The rapid, upward pulses of light along these rays, however, are quite real, and due, pre- sumably, to progressive electric discharges. "5 Phil, Mag., 23. p. 211, 1912; Ann. der Phrys., 50, p. 853, 1916. *° Terr, Magnet. and Atmos. Elec., 20, p. 1, 1915. PART ITI. ATMOSPHERIC OPTICS INTRODUCTION—CLASSIFICATION. Many curious and beautiful phenomena, of which the mirage, the rainbow, the halo, the azured sky, and the twilight glow, are some of the more conspicuous, are due to the optical properties of the air and the foreign substances suspended in or falling through it. All, or nearly all, of them have been the objects of innumerable observations and many careful studies, the results of which, fortunately, have been summarized and discussed by various authors. The most extensive discussion, however, of this subject is by Pernter and Exner, whose work, “ Meteoro- logische Optik,” therefore, will be largely, but by no means ex- clusively, drawn upon for the material of this section. When one’s chief or only purpose in discussing the optics of the air is to describe the phenomena seen, it is convenient to divide them into such general classes as mirages, rainbows, halos, cor- onas, etc. For explanatory purposes it is more convenient, per- haps, to group them according to (a) their objective or material causes, namely: atmosphere, raindrops, water droplets, ice crys- tals, etc.; or (b) their physical causes, such as reflection, refrac- tion, diffraction, etc. Each of the above classifications has its advantages and dis- advantages. On the whole, however, the division according to physical causes seems best suited to the needs of an explanatory discussion and therefore is here adopted. 426 CHAPTER I. PERSPECTIVE PHENOMENA. Apparent Stair-step Ascent of Clouds——The stair-step ap- pearance of the echelon cloud (Fig. 132) is, perhaps, the simplest sky phenomenon due to perspective. The exact manner by which the stair-step or terrace illusion is brought about is shown by Fig. 132, in which O is the position of the observer, H his hori- zon, I, 2, 3, etc., evenly spaced flat-bottomed cumuli of the same base elevation—flat-bottomed and of constant level because of the approximately uniform horizontal distribution of moisture. Since the clouds are at a higher level than the observer, each successive cumulus, as the distance increases, is seen at a lower angle than its predecessor; and the dark bases of any two adja- cent clouds appear to be connected with each other by the lighter side of the farther one. Besides, their general resemblance to stair-steps often leads one into the error of “seeing” the con- nection between any two adjacent bases to be at right angles to both. That is, starting with base a, the light side of cloud 3 appears as a vertical surface at b, and its base as a dark horizontal surface at c; the side and base of cloud 4 appear as the next vertical and horizontal surfaces, d and e, respectively, and so on for the other clouds; the whole effect merging into the appear- ance of a great stairway, consisting of the horizontal treads, a,c, e, etc., connected by the seemingly vertical risers, b, d, f, ete. Apparent Arching of Cloud Bands.—Occasionally a narrow cloud band is seen to stretch almost, if not entirely, from horizon to horizon, but although its course is practically horizontal and its direction often nearly straight, it usually appears arched. If even the nearest portion of the cloud still is far away, the apparent arching is slight. On the other hand, when the cloud is near the arching is great. The apparent curve is neither circular nor elliptical, but resembles rather a conchoid whose origin is at the observer and whose asymptote is his horizon. The angle of elevation at which different segments of the cloud are seen clearly varies from a minimum for the more dis- tant portions to a maximum for the nearest. Hence, the phe- nomenon in question, the apparent arching of the band along its nearest portions, is only an optical illusion, due entirely to the 427 428 PHYSICS OF THE AIR projection of the cloud (above the observer’s level) onto the sky. When several such bands or streaks occur in parallel, they appear to start from a common point at or beyond the horizon, to terminate, if long enough, in a similar opposite point, and pro- gressively to arch and spread apart as they approach the ob- server's zenith. They thus form the perspective effect often called “ Noah’s Ark ” or polar bands. Apparent Divergence and Convergence of Crepuscular Rays (Sunbeams).—Everyone is familiar with the beautiful phe- nomenon of the “sun drawing water ’’—sunbeams that, finding their way through rifts in the clouds, are rendered luminous by the dust in their courses. Equally familiar and equally beautiful are also those streaks and bands of pearly lights (where the lower atmosphere is illuminated) and azure shadows (where only the Fic. 132. Cloud echelon effect. upper atmosphere is illuminated) that often at twilight and occa- sionally at dawn radiate far out from the region of the sun, and at times even converge towards the opposite point of the horizon. These, too, are only beams of sunlight and shadow caused by broken clouds or irregular horizon. All such crepuscular rays, whether their common origin, the sun, be below or above the horizon, seem first to diverge, while the few that cross the sky appear also to arch on the way and finally to converge towards the antisolar point. Here, again, the facts are not as they seem, for the rays, all coming, as they do, from the sun, some 93,000,000 miles away, necessarily are practically parallel. Their apparent divergence, convergence, and arching are all illusions due to perspective, just as are the apparent divergence, convergence, and arching of the rails on a long straight track. Apparent Divergence of Auroral Streamers—Anyone at all familiar with the appearance of auroral streamers will recall that PERSPECTIVE PHENOMENA 429 at most localities they seem to radiate from some place far below the horizon. In reality they do diverge (or converge, if one pre- fers) slightly since they follow, approximately, the terrestrial lines of magnetic force. Indeed, their rate of convergence is -about the same, on the average, as that of the geographic merid- ians at the same latitudes, and therefore far less than one would infer from their apparent courses. That is, their seeming rapid convergence is only another illusion due to perspective, just as is the apparent divergence of the crepuscular rays, as above explained. Apparent Shape (Flat Vault) of the Sky.—To everyone the sky looks like a great blue dome, low and flattish, whose circular rim rests on the horizon and whose apex is directly overhead. So flat, indeed, does this dome appear to be that points on it estimated to lie half-way between the rim and apex generally have an eleva- tion of but little more than 20°, instead of 45°, as they would if it seemed spherical. That the rim of the sky dome should appear circular is ob- vious enough. It is simply because the horizon, where land and sky come together, itself is circular, except when conspicuously broken by hills or mountains. To understand the other and more important feature, that is, why the dome looks so flat, consider (1) a sky filled from horizon to horizon with high cirrus clouds. These seem nearest over- head for the simple reason that that is just where they are nearest. As the horizon is approached, the clouds merge, through perspective, into a uniform gray cover that appears to rest on the land at the limit of vision, whether this limit be fixed by the curvature of the earth or by haze, and the whole cloud canopy may seem arched just as and for the same reason that cloud streaks and crepuscular rays seem arched, as above explained. But (2) even a thin cirro-stratus veil whose parts are well-nigh indistinguishable produces a similar effect, the nearest portions appearing nearest, largely because they are the most clearly seen. Similarly, when there are no clouds the sky overhead also appears nearest because it is clearest; and that unconscious inference, based on endless experience, is correct—it is clearest because nearest. As the eye approaches the horizon, the increasing haze produces the impression of greater distance; and this impression is entirely correct, for the blue sky seen in any such direction is 430 PHYSICS: OF ‘THE ALK ‘farther away than the sky overhead. In short, the spring of a cloudless sky dome is ‘‘ seen”’ to rest on the distant horizon and its ceiling to come closer and closer, in proportion to increasing clearness, as the zenith is approached. The shape, then, of this dome should not always appear the same, and it does not—not the same on a clear night, for instance, as on a clear day. Impressions, therefore, of the “shape” of the sky are, per- haps, not so erroneous as sometimes they are said to be. Indeed, they usually conform surprisingly well to the actual facts. Change, with Elevation, of Apparent Size of Sun and Moon. —One of the most familiar, as also one of the most puzzling, of optical illusions is the change between the apparent sizes of the full moon, say, or of the sun, at rising or setting, and at or near culmination. It is, however, only a phenomenon of perspective. Since the solid angle subtended at any place on the earth by the moon, as also that subtended by the sun, is sensibly constant throughout its course from rising to setting, it follows that its projection, and, therefore, its apparent size, must be relatively large, or small, as the place of projection (sky dome) is com- paratively far away or nearby. But, as already explained, the sky dome, against which all celestial objects are projected and along which they therefore appear to move, seems to be farther away, and is farther away, near the horizon than at places of con- siderable elevation. Hence the moon and the sun must look much larger when near the horizon than when far up in the heavens, and the fact that they do so look, is, as stated, merely a phe- nomenon of perspective. The familiar fact that the moon appears of one size to one person and a different size to another clearly is also due to per- spective. The one who judges it large imagines his comparison object to be at a greater distance than does the one who judges it small. But such estimates usually are very erroneous; the moon may seem a foot in diameter, for instance, and three miles away, whereas at that distance a 144-foot circle would just cover it. Change, with Elevation, of Apparent Distance Between Neighboring Stars.—The generally recognized fact that the dis- tance between neighboring stars appears much greater when they are near the horizon than when well up is also a phenomenon of perspective. Its explanation is identical with that of the change, under similar circumstances, of the apparent diameter of the moon, and therefore need not be given in further detail. CHAPTER II. REFRACTION PHENOMENA: ATMOSPHERIC REFRACTION Astronomical Refraction.—It is well known that because of astronomical refraction the zenith distance of a star, or other celestial object, is greater than it seems, except when zero, to an extent that increases with that distance. To understand this im- portant phenomenon, it is necessary to recall two experimental facts: (a) that in any homogeneous medium light travels in sen- sibly straight lines, and (0) that its velocity (velocity pertaining to any given wave frequency) differs from medium to medium. Let, then, the parallel lines 4B and DE (Fig. 133) be the intersections of the boundaries between three homogeneous media, I, 2, 3, by a plane normal thereto and to the wave front, BC. Let the velocities in these media of a given monochromatic light be Vy, Vg, and vz, respectively. Hence, when the light disturbance at C has travelled the distance CA in the first medium, that at B will have gone the distance BE in the second, where CA/BE = V/V, and AE will be the new wave front. Similarly, DF will be the wave front in the third medium, and so on for any addi- tional media that may be traversed. If 7 is the angle between the normal to the interface, 4B, and the direction of the light, both in medium 1, and r the corre- sponding angle in medium 2, then, as is obvious from the figure, sin 7 Vy ey. 8 V1 : - = -—,orsinz = — sin r. sin 7 V2 V2 . 5 . v é ‘. : VY . ‘ Similarly, sin r = — sine’. Hence, sini=— sinr’ That V3 U3 is, the total change in direction of the light depends solely on its velocities in the first and final media, respectively, and the initial angle of incidence. The optical densities of the intermediate layers may abruptly change by large amounts, as indicated, and thus cause the light to follow a perceptibly broken course, as from air to water, for instance; or they may change so gradually that the path is a smooth curve, even to the closest observation. Since the ratio of the velocity of light in space to its velocity 431 432, PHYSICS OF THE AIR in any given gas, or definite mixture of gases (the refractive index of that medium), increases directly with density, it follows that all rays of light that cross the atmospheric shell, except those that enter it normally, must follow continuously curved paths, somewhat as shown to an exaggerated extent in Fig. 134. To determine the shape of such a curve through the at- mosphere, let ¢ (Fig. 134) be the angle between the radii from the Fic. 133. Refraction of light on change of media. centre of the earth at the place of observation and any other point along the course of a refracted ray. As before, f2 sin m1 = /y sin a1 in which p, and p, are the refractive indices (with reference to space) of media, or layers, 1 and 2, respectively, 7, the angle of incidence and 7, the angle of refraction at the interface between these media or layers. But, corresponding to the radii R, and Ro, Sint, _ Ri sin 7 Re Hence, Ri Hy sin 11 = Rs He sin de, or, in general, Rwsin i = C, a constant. REFRACTION PHENOMENA 433 Further, ms Sas . cost _ I— sintz _ eR But cot 1= sini NV sin? 7 ~ ee Hence, an aaa 2 R ag a Ge and Path of light through the atmosphere. Clearly, then, the value of ¢ corresponding to a definite value of R, or the value of R appropriate to a definite value of ¢, de- pends upon the relation of » to R, or, very nearly, the relation of the density of the atmosphere at any point to the altitude of that point. Hence, refraction curves may be drawn for different angles of incidence, or, if preferred, for different apparent alti- 434 PHYSICS OF THE AIR tudes, according to any assumed distribution of atmospheric density—a distribution fairly well known. The approximate value of astronomical refraction, that is, its value generally to within one second of arc, through all zenith distances up to at least 60°, may easily be obtained as follows: Assume the atmosphere to be flat, as it nearly is, over the restricted area through which stars may be seen whose zenith distances are within 60°, or thereabouts. Let O (Fig. 135) be the position of the observer, S the true position of a star and S” its apparent position. Fic. 135. Approximate astronomical refraction. As explained above, sini = » sin r in which p is the refractive index of the air at the point of observa- tion, 7 the actual and r the apparent zenith distance. But tT=r+oa in which:8 is the angle of deviation. Hence, sin (X¥ + 6) = sin rcosd + cosry sind = mw sin r When the angle of incidence is 60°, or less, 8 is always very small, and sin 6 = (u — 1) tan ¢, nearly. Expressed in seconds of arc this gives oO” = 206265” (u — 1) tan r in which the numerical coefficient is the approximate number of seconds in a radian. REFRACTION PHENOMENA 435 For dry air at o° C. and 760 mm. pressure, the average value of » is about 1.000293. Hence, also ov = 60.4 tan r. But for gases 4-1= Kp, very closely, in which K is a con- stant and p the density. Hence, finally, 21.7 B on = i tan 1, T in which B is the height of the barometer in millimetres, and T the absolute temperature in degrees C. Fic. 136. Astronomical refraction (Lord Rayleigh). As a matter of fact, the atmospheric shell is not plane, even over small areas, but slightly curved, and therefore the complete formula for astronomical refraction, such as is needed for the construction of tables to be used in the most accurate measure- ments of star positions, is rather complicated. Probably the briefest and simplest derivation of a formula adequate for all zenith distances to at least 75° is due to Lord Rayleigh,’® and is essentially as follows: Let Po, Pi, Po, etc., be the normals from the centre of the earth onto the tangents of a ray path through the atmosphere at the *” Phil. Mag., 36, p. 141, 1803. 436 PHYSICS OF THE AIR points where the refractive indices are po, #41, M2, etc., respectively. Let ig, 71, i, etc., be the angles of incidence, and 7, 72, etc., the corresponding angles of refraction. Then (see Fig. 136), My sin r2 _ po ay sin 1) Pr » ete, Hence, “ p = constant. Let the tangent to the ray path, where it enters the atmosphere, meet the vertical at the distance, C, above the point of observa- tion, .4; let »s be the refractive index at A; 6 the apparent zenith distance; 8@ the total refraction; and R the radius of the earth. Then, since the refractive index of space is I, Hs po = po, or Ws Rsin 9 = (R + C) sin (6 + 66)... (A) Obviously, the refraction, 58, could be determined from this equation directly if the value of C were known. But 9 sdpbndeurar in ; (B) in which u, the total linear deviation of the ray, may be substituted by known terms. Hence, C and, therefore, 8@ are determinable. To determine u, let a be the angle which the ray makes with the direction of most rapid increase of index of refraction (at the surface a equals 4); z the vertical codrdinate; and w the velocity of light. Now consider a wave front moving through the at- mosphere in any direction except vertical. The portion in the higher or thinner air will move faster than that in the denser air and the path will be curved. If is the radius of curvature and dp is regarded as positive when measured towards the centre, then, as is obvious from Fig. 137, dp _ dv p v Also, since the refractive index, », is inversely proportional to the velocity, wv, sIS Ie REFRACTION PHENOMENA 437 Hence, calling the path s, and since du = du. dp a sin a, I dloge _ d loge. _ d logy _ au me ae de — sina = ds ae ae To a close approximation, “ =ftana d loge = tana (u — 1) +4, in which a is the constant of integration and »—1 is substituted for loge#, “ being but little greater than 1, and u = tanaf(u — 1) ds + as + 3, sina = oe aa fu - 1)dz+as+b..... (C) Fic. 137. Vv dp dv pP Curvature of a light path in the air. But »—1 is directly proportional to the density. Hence, if the height, 4, in ‘‘ the homogeneous atmosphere ” be such that air below it is the same as below 2 in the actual atmosphere, and if the origin be taken at the surface where a =9, and p= be sin? (h sin @ v= SS (4 — 1) dz = ey (le — Dh 29 438 PHYS. OF THE ALK For the limit of the atmosphere, and any point beyond, =H, the height of the homogeneous atmosphere, or about 7.990x 10° cm. For stars, therefore, viewed from the surface of the earth, sin 6 = Age ap ge 8 oe & ie Substituting this value of u in (B) we get We — 1) A, cos? 4 Cs Hence, substituting in (4), us R sin @ -{r¢"ou*t ; a+ dale cos? 6 With this equation it is only a matter of arithmetic to com- pute a table of corrections, that is, values of 80 for every value of 6 and ps; 6 being the apparent or observed zenith distance, and js the current refraction at the surface, given by the equation — 2730 B oe 760 T in which B is the height of the barometer in millimetres, T the absolute temperature in degrees C., and », atmospheric refraction at o° C. and 760 mm. pressure. Since 86 is small, we have from (4), to a close approximation, 4 60: Sst P= a tan 4 cos 00 = tan @ (is _ V I — sin? ‘o) i = tan@ ee = pels wo Us C = tan@ 4 bs — a = 1+ 1% (06)? - nearly. But, from the laws of refraction, ; Hs sin@ = sin (6+06) from which 66 = (us — 1) tan 6, nearly. Hence, UsC dg = (us — 1) tan of 1 — Me : (4s — 1) R +14 (us — 1) tan? @ ; , approximately. REFRACTION PHENOMENA 439 Substituting for C its value and noting that I jeeianee! GES 2 cos? 8 I + tan’?6@ this equation reduces to 00 = (Us — nt - ) tan — (Hs — 1) (“3 - a Ss “= ') tan? 6 = (He — I) (: - 2) tané — (Hs — I) (= - =) tan?6, nearly. If H=7.990 x 10° cm.; R=6.3709 x 108 cm.; and pse—1 = .0002927, all closely approximate values, then, 68 = 60’.29 tan@ — 0.06688 tan¢. This is Lord Rayleigh’s final equation, and it appears to be exceedingly accurate for all values of @ up to at least 75°, or as far, perhaps, as irregular surface densities generally allow any refraction formula to be used with confidence. Since the index of refraction varies from color to color, it follows that star images are drawn out into vertical spectra. The amount of this effect, however, is small. Thus the difference between the refractions of red and blue-green is only about one one-hundredth of the total refraction of yellow (D) light. Hence, the approximate angular' distance between the red and blue-green images of a star at the zenith distances, 30°, 45°, 60° and 75° are 0.35, 0.60, 1.04, and 2.24, respectively. Possibly this may account, in part at least, for the fact that stellar declinations, as determined from the northern and southern hemispheres, re- spectively, are not quite the same. Scintillation or Twinkling and Unsteadiness of Stars—The scintillation or twinkling of stars, that is, their rapid changes in brightness and occasionally also in color, especially when near the eastern or western horizon, is a well-known, and now well- understood, phenomenon that for many centuries, certainly since the days of Aristotle (384-322 B.C.), who noted the fact that the fixed stars twinkle while the planets shine with comparatively steady lights, has been observed, investigated, and discussed. The most systematic and complete observations, however, of scintillation are those made by Respighi 1° with a spectroscope 8 Assoc. Francaise pour l’Avancement des Sciences, I, 1872, p. 148. 440 PHYSICS OF “THE AUR during the years 1868-1869, and which he summed up sub- stantially as follows: (1) In the spectra of stars near the horizon more or less broad and distinct dark and bright bands sweep with greater or less velocity from the red to the violet and from the violet to the red or oscillate from the one to the other; and this whatever the direction of the spectra from the horizontal to the vertical. (2) When the conditions of the atmosphere are nor- mal the dark and bright bands of western stars travel regularly from the red to the violet, and of eastern from the violet to the red; while in the neighborhood of the meridian they usually oscillate from the one color to the other, or even are limited to a portion of the spectrum. (3) On examining the horizontal spectrum of a Star sensibly parallel dark and bright bands more or less inclined to the axis (transverse) of the spectrum are seen passing from the red to the violet or reversely, according as the star is in the west or east. (4) The inclination of the bands, or angle between them and the axis (transverse) of the spec- trum, depends upon the altitude of the star; increasing rapidly from o° at the horizon to go° at an elevation of 30° to 40°, where they, therefore, are longitudinal. (5) The inclination of the bands, reckoned from above, is towards the violet end of the spectrum. (6) The bands, most distinct at the horizon, become less conspicuous with increase of elevation. Above 40° the longitudinal bands reduce to mere shaded streaks and often can be seen in the spectrum only as slight general changes of brightness. (7) With increase of elevation the movement of the bands becomes more rapid and less regular. REFRACTION PHENOMENA 441 (8) On turning the spectrum from the horizontal the inclination of the bands to the transversal con- tinuously diminishes until it becomes zero, when the spectrum is nearly vertical. They also be- come less distinct, but continue always to move in the same direction. (9) The bright bands are less frequent and more irregular than the dark, and are well-defined only in the spectra of stars near the horizon. (10) In the midst of this general and violent move- ment of light and shade over the spectra of stars, the Fraunhofer lines peculiar to the light of each star remain quiescent or are subject to only very slight oscillations. (11) When the atmospheric conditions are abnormal, the bands are fainter and more irregular in form and movement. (12) When the wind is strong, the bands usually are quite faint and ill-defined; the spectra even of stars near the horizon showing mere changes of brightness. (13) Good definition and regular movement of the bands appear to indicate the continuance of fair weather, while varying definition and irregular motion seem to imply a probable change. These observations show that the dark bands are due to tem- porary deflection of light from the object glass by irregularities in the density of the atmosphere. For stars near the horizon, the linear separation of the rays of different color is so great as they pass through the atmosphere to the observer that successive por- tions of the spectrum may be deflected from or concentrated onto (light deficiencies in a transparent medium must be balanced by light concentrations, and wice versa) the telescope or eye. Hence, the progression of bright and dark bands along the spectra of low altitude stars, and their rapid change of color to the un- aided eye. Further, since the path of the more refrangible light neces- sarily lies above that of the less refrangible (Montigny’s prin- ciple) it follows that an atmospheric irregularity travelling or 442 PHYSICS OF THE AIR rotating with the earth would affect the different-colored rays from stars in the west in the order of red, green, blue, violet, and rays from stars in the east in the reverse order. If, then, the separation of the extreme rays is large in comparison to the effective dimension of the air irregularity, the resulting band will, at any given instant, cover only a portion of the spectrum. But the approximate amount of this separation is readily obtained from equation (D), page 438. Thus, for the limit of the atmosphere, sin 0 ai ae ae. cos? Hence, at the zenith distance, 80°, the red and violet rays simultaneously received by the observer from the same star will be separated at the limit of the atmosphere (assuming the dis- persion between these rays to be one-fiftieth the refraction of yellow light) by about 156 centimetres, and proportionately for levels below which definite fractions of the total mass of the atmosphere lie. For the zenith distance, 40°, however, the cor- responding separation at the limit of the atmosphere is only about 5 centimetres, and for 20° about 2 centimetres. Inequalities in the atmosphere may, therefore, interfere with only a portion at a time of the spectrum of a star near the horizon and thus pro- duce the phenomenon of a travelling band, while in the case of a star whose zenith distance is 40°, or less, the interference will include nearly or quite the entire spectrum, and thus produce mere changes of brightness. . It is generally stated that the direction of travel of the bands during fine weather, red to violet for stars in the west, violet to red for stars in the east, and irregularly or simultaneously over the entire spectrum for stars near the meridian, is directly de- pendent upon the west to east rotation of the earth. It is cor- rectly stated (on assumption of a stationary atmosphere) that this rotation would cause an atmospheric irregularity to affect the red rays first and the violet last, violet first and red last, and all rays more or less simultaneously, of stars in the west, east, and near the meridian, respectively. But the order would be the same if the earth were at rest and the air travelling from west to east. As a matter of fact, over most of the earth outside the tropics the west to east angular velocity of the general winds. as seen by the observer, is several times that of the earth. Hence, REFRACTION PHENOMENA 443 the rate at which the disturbance drifts across the line of sight presumably depends much more on the direction of the prevail- ing winds than upon the rotation of the earth. Indeed, in tropi- cal regions, where the prevailing winds are from easterly points, the usual direction of travel of the bands probably (if the above reasoning is correct) is reversed. The disappearance of distinct bands with high winds is due, of course, to the more complete mixing of the atmosphere at such times. In the same general way, atmospheric inequalities produce “unsteadiness,” or rapid changes in the apparent positions of stars as seen in a telescope. In reality, this is a telescopic form of scintillation which, because never amounting to more than a very few seconds of arc, the unaided eye cannot detect. On the other hand, the great changes in brightness and color so con- spicuous to the naked eye are scarcely if at all noticeable in a large telescope. This is because the object glass is so large that, in general, light deflected from one portion of it is caught in another. Scintillation of the Planets, Sun, and Moon.—It is commonly stated that the planets do not scintillate—that the light from the several portions of their disks follow such different paths through the atmosphere that not all nor even any large portion of it can be affected at any one time. It is true that because of their sensible disks the scintillation of planets is much less than that of fixed stars, but under favorable circumstances their scin- tillation is quite perceptible. Even the rims of ‘the sun and the moon boil or “ scintillate ” while, of course, any fine marking on either or on a planet is quite as unsteady as the image of a fixed star. Nature of Irregularities——It is well known that the at- mosphere, generally, is so stratified that with increase of elevation many more or less abrupt changes occur in temperature, com- position, density, and, therefore, refrangibility. As such layers glide over each other, billows are formed, and the adjacent layers thereby corrugated. The several layers frequently also heat unequally, largely because of disproportionate vapor contents, and thereby develop, both day and night, and at various levels, innumerable vertical convections; each moving mass differing, of course, in density from the surrounding air, and by the chang- 444 PHYSICS OF THE AIR ing velocity being drawn out into dissolving filaments. Optically, therefore, the atmosphere is so heterogeneous that a sufficiently bright star shining through it would produce on the earth a some- what streaky pattern of light and shade. Shadow Bands.—A striking proof of the optical streakiness of the atmosphere is seen in the well-known shadow bands that at the time of a total solar eclipse appear immediately before the second, and after the third, contact. Terrestrial Scintillation —A bright terrestrial light of small size, such as an open electric arc, scintillates when seen at a great distance, quite as distinctly as do the stars and for substantially the same reason, that is, optical inequalities due to constant and innumerable vertical convections and conflicting winds. Shimmering—The tremulous appearance of objects, the common phenomenon of shimmering, seen through the atmos- phere immediately over any heated surface, is another manifesta- tion of atmospheric refraction, and is due to the innumerable fibrous convections that always occur over such an area. Optical Haze-—The frequent indistinctness of distant objects on warm days when the atmosphere is comparatively free from dust, and ascribed to optical haze, is due to the same thing, namely, optical heterogeneity of the atmosphere, that causes that un- steadiness or dancing of star images that so often interferes with the positional and other exact work of the astronomer. Both are but provoking manifestations of atmospheric refraction. Times of Rising and Setting of Sun, Moon, and Stars —An interesting and important result of astronomical refraction is the fact that the sun, moon, and stars rise earlier and set later than they otherwise would. For places at sea level the amount of elevation of celestial objects on the horizon averages about 35’, and therefore the entire solar and lunar disks may be seen before (on rising) and after (on setting) even their upper levels would have appeared, in the first case, or disappeared, in the second, if there had been no refraction. This difference in time of rising, or setting, depends on the angle or inclination, a, of the path to the horizon. In general, it is given by the equation, t = 140° csca, about. The minimum time, therefore, occurs when the path is nor- mal to the horizon and is about 2” 20°, while the maximum, which REFRACTION PHENOMENA 445 obviously occurs at the poles, is infinite in the case of stars that just clear the horizon, and, for the sun, about a day and a half, the time required near equinox for the solar declination to change by 35. Green Flash—dAs the upper limb of the sun disappears in a clear sky below a distant horizon its last star-like point often is seen to change rapidly from pale yellow or orange to green and finally blue, or, at least, a bluish-green. The vividness of the green, when the sky is exceptionally clear, together with its almost instant appearance, has given rise to the name “ green flash” for this phenomenon. The same gamut of colors, only in reverse order, occasionally is seen at sunrise. The entire phenomenon has been described by some as merely a complementary after-image effect, that is, the sensation of its complementary color that frequently follows the sudden removal of a bright light. This explanation, however, cannot account for the reverse order of the colors as seen at sunrise. Neither does it account for the twinkling of the ‘‘ flash ” close observation now ‘and then reveals, nor for the fact that when the sun is especially red the “ flash ” is never seen. It is not, indeed, a physiological effect, but only the inevitable result of atmospheric refraction, by virtue of which as a celes- tial object sinks below the horizon its light must disappear in the order of refrangibility ; the red first, being least refrangible, then the green, and finally the blue or most refrangible. Violet need not be considered, since only a comparatively small portion of it can penetrate so far through the atmosphere. It may properly be asked, then, why these color changes do not apply to the whole solar disk. The answer is, because the angular dispersion, due to the refraction of the atmosphere, be- tween the several colors is very small—between red and green, for instance, only about 20”, even when the object is on the horizon, so that any color from a given point on the sun is rein- forced by its complementary color, thus giving white, from a closely neighboring point. Hence, color phenomena can appear only when there are no such neighboring points, or when only a minute portion of the disk is above the horizon. It must further be noted that color effects, due to the general refraction of the atmosphere, occur only when the source (brilliant point) is on the horizon. Stars above the horizon are not permanently drawn out 446 PHYSICS OF THE ATK into rainbow bands, and that for. the simple reason that the red light by one route is supplemented by the green, blue, etc., by others and the whole blended into white, yellow, or whatever the real color of the star may be. This multiplicity of routes and consequent blending of color, is not possible for rays of light from objects just sinking below or rising above the horizon, and, therefore, under such circumstances, they pass through a series of color changes. Terrestrial Refraction—The curving of rays of light is not confined to those that come from some celestial object, but ap- plies also to those that pass between any points within the at- mosphere, whether at the same or different levels. This latter Fic. 138. Approximate terrestrial refraction. phenomenon, known as terrestrial refraction, causes all objects on the earth or in the atmosphere to appear to be at greater alti- tudes than they actually are, except when the surface air is so strongly heated as to cause an increase of density with elevation and thus produce the inferior mirage, described below. Terrestrial refraction is also a matter of great importance, especially to the geodesist, and its complete analysis, from which practical tables may be constructed, essentially the same as that of astronomical refraction.1°** It will be instructive, however, to consider a few graphical corrections of apparent elevations. Let ON (Fig. 138) be normal to the surface, OD, of the earth, and let P be observed from O. Obviously P, whose horizontal distance, OD, may be supposed known, will seem to be at P’ and thus its apparent altitude greater than the actual by the distance 4a McLeod, Phil. Mag. 38, p. 546, 1910. REFRACTION PHENOMENA 447 PP’. From the angle 7, the density of the air at the observer’s position, O, and the approximate density at P (known from the approximate height of P) it is easy to draw OP” parallel to the tangent at P to the refraction curve, SPO. This gives P”, neces- sarily below P. Hence P lies somewhere between P’ and P”. A more exact determination could be had by drawing the curve of refraction, OPS, corresponding to the angle v and noting its intersection with the normal at D. If the observer happens to be at P, the point O will appear elevated to O’. Clearly, however, from a knowledge of the angle PO’N, and the approximate air densities at P and O, one may draw PO” parallel to P’O, and thus locate O somewhere between the two determined points O’ and O”. Here, too, it would be more accurate to use the refraction curve, SPO. Even initially horizontal rays normally curve down towards the surface of the earth, so that objects at the observer’s own level, as well as those above and below it, appear elevated. To understand this phenomenon, consider a wave front normal to the surface of the earth and, consequently, moving horizontally. If, now, the density of the air at the place in question decreases with increase of elevation, as it nearly always does, the upper por- tion of the wave front will travel faster than the lower, and the path will be bent down towards the earth along a curve whose radius depends upon the rate of this density decrease. For ex- ample, let the corrected height of the barometer be 760 mm., the temperature 17° C., and the rate of temperature decrease with elevation 5° C. per kilometre; conditions that not infrequently obtain at sea level. On substituting these values in the density- elevation equation, it appears that the density gradient would be such that if continuous the limit of the atmosphere would be reached at an elevation of about 10 kilometres. Hence, under these circumstances, the velocity of light at an elevation of 10 kilometres would be to its velocity at the surface in the ratio of 1,000,276 to 1,000,000, approximately, since the re- fractive index of the lower air would be 1.000,276, about. The radius of curvature, 7, therefore, is closely given in kilometres by the equation, r ___ 1,000,000 r+ 10 1,000,276 448 PHYSICS OF THE AIR Hence, 7 = 36,232 kilometres, or approximately 5.7 times the radius of the earth. It is conceivable, therefore, that the size of a planet and the vertical density gradient of its atmosphere might be such that one’s horizon on it would include the entire surface—that he could look all the way round and, as some one has said, see his own back. The distance to the horizon, corresponding to a given altitude, obviously depends upon the rate of vertical density decrease in such manner that when the latter is known the approximate value of the former can easily be computed. Thus, let the density decrease be such that the radius of curvature of a ray tangent to the surface shall be 5.7 R, R = 6366 kilometres, being the radius of the earth; let a@ be the angle between the radii from the centre of the earth to the observer and a point on his unobstructed hori- zon respectively ; let , be the observer’s height in metres above the level of his horizon; and let r be the distance, in kilometres, measured over the surface from the horizon to a point on the same level below the observer; then, by trigonometry, to a close approximation ; h = 6366000 (sec a — 1) — 36286200 (sec oe — 1) seca and r = 6366 a, @ in radians A few values of the distance to the horizon from different elevations, computed by the above formula, are given in the following table: Distance to Horizon. Distance in Kilometres. 20 I 2 is | 10 50 | 100 25.901 Elevation in metres. .061 | .263 | 1.613 | 6.856 161.918 | 647.604 Looming.—Since the extension of the actual beyond the geometrical horizon depends, as just explained, upon the density decrease of the atmosphere with increase of elevation, it follows that any change in the latter must produce a corresponding varia- tion of the former. An increase, for instance, in the normal rate of decrease, such as often happens over water in middle to high latitudes, produces the phenomenon of looming, or the coming into sight of objects normally below the horizon, a classical in- REFRACTION PHENOMENA 449 stance of which was described by Latham.’®® Similar changes in the rate of density decrease with increase of elevation also are common in valleys, but here looming, in the above sense, is ren- dered impossible by the surrounding hills or mountains. Towering.—The condition of the atmosphere that produces looming, in the sense here used, or would produce it if the region were level, often gives rise to two other phenomena, namely, unwonted towering, also usually called looming, and the conse- quent apparent approach of surrounding objects. The more rapid the downward curvature of the ray paths at the observer the more elevated, clearly, will objects appear to be, and such curvature may, indeed, be very considerable. Thus, a temperature inversion near the surface of the earth of 1° C. per metre change of elevation bends down a ray along an arc whose radius is about 0.16 that of the earth, while an inversion of 10° C. per metre—a possible condition through a shallow stratum-— gives a radius of only about 0.016 that of the earth, or, say, 100 kilometres. If now, as occasionally happens, the inversion layer is so located that rays to the observer from the top of an object are more curved than those from the bottom, it will appear not only elevated but also verticaliy magnified—it will tower and seem to draw nearer. Sinking.—Instead of increasing the curvature of rays the temperature distribution may be such as, on the contrary, to de- crease it and thereby cause objects normally on the horizon to sink quite beyond it. Such phenomena, exactly the reverse of looming, are also most frequently observed at sea. Stooping.—Occasionally rays from the base of an object may be curved down much more rapidly than those from the top, with the obvious result of apparent vertical contraction, and the pro- duction of effects quite as odd and grotesque as those due to towering. Indeed, since the refraction of the atmosphere in- creases, in general, with the zenith distance, it is obvious that the bases of objects nearly always apparently are elevated more than their tops, and themselves, therefore vertically shortened. The normal effect. however, is small and seldom noticed except, per- haps, in connection with the slightly flattened shape of the sun and moon when on the horizon. *™ Phil. Trans., v. 88, 1798; abridged, v. 18, p. 337. See also Everett, “Nature,” v. 11, p. 49, 1874. 450 PHYSICs OF “THE ALR Superior Mirage.—It occasionally happens that one or more images of a distant object, a ship for instance, are seen directly Fic. 139. Examples of superior mirage (Vince). above it, as shown in Fig. 139, copied from Vince’s 17° well-known description of exceptionally fine displays of this phenomenon. *° Phil. Trans., 89 (8, abridged, p. 436), 1790. REFRACTION PHENOMENA 451 The image nearest the object always is inverted and there- fore appears as though reflected from an overhead plane mirror— hence the name “superior mirage ”—and, indeed, many seem to assume that this image really is due to a certain kind of re- flection, that is, total reflection, such as occurs at the undersur- face of water. It is obvious, however, that this assumption is entirely erroneous, since the atmosphere can never be sufficiently stratified in nature to produce the discontinuity in density (adja- cent layers are always interdiffusible) this explanation of the origin of the proximate inverted image presupposes. Another apparently simple explanation of mirage phenomena is furnished by drawing imaginary rays from the object along arbitrary paths tothe observer. But, in reality, this is no explanation at all, unless it is first demonstrated that the rays must follow the paths as- sumed. It is allowable, of course, to assume any possible distri- bution of atmospheric density and to trace the rays from an ob- ject accordingly. If the assumed distribution follows a simple law, the rays may be traced mathematically, as by Mascart,?"! though such discussions, when at all thorough, necessarily are long. A simple explanation of mirage that admirably accounts for the phenomena observed has been given by Hastings,!*? in swh- stance as follows: Let the air be calm and let there be a strong temperature in- version some distance, 10 metres, say, above the surface—condi- tions that occasionally obtain, especially over quiet water. Ob- viously the ratio of decrease of density to increase of elevation is irregular in such an atmosphere, and therefore the velocity of light travelling horizontally through it must increase also ir- regularly with increase of elevation. Thus, beginning with the under surface of the inversion layer, the rate of velocity increase with elevation must first grow to a maximum and then diminish to something like its normal small value at and beyond the upper surface of this layer. Hence, that portion of an originally ver- tical, or approximately vertical, wave front that lies within the inversion layer must soon become doubly deflected, substantially as indicated in Fig. 140. ™ “ Traité ¢’Optique,” v. 3, pp. 305-308. 2 “Tight,” Chapter 7, New York, Chas. Saibaete Sons, 1902. J 452 PHYSICS OF THE AIR Let AB (Fig. 140) be the surface of water, say, CD the under _and EF the upper surface of a strong inversion layer, and let GHIKL be the distorted wave front of light, travelling in the direction indicated, from a distant source. The future approxi- mate positions of the wave front, of which G’H’I'K’L’ is one, are readily located from the fact that its progress is always normal to itself, and the appearance of the distant object from which these wave fronts are proceeding easily determined. At 1, for instance, the object seems upright and at its proper level, no images are seen and the whole appearance is normal; at 2 confused elevated images appear, in addition to the object itself; at 3 the Fic. 140. L L | E 6 KK’ E* Fe 5 | Cc 4H H D 3 i i ge 1 A G’ G B Wave fronts giving a superior mirage (Hastings). object and two distinct images are seen, the lower produced by the segment H/ of the wave front inverted, the other erect; at 4, the under surface of the inversion layer, the inverted image blends with the object and disappears; at 5 only the erect image can be seen, and, indeed, may be seen even when the object itself nor- mally would be below the horizon; at 6, the upper surface of the inversion layer, the vertical image merges with the object and disappears; while everywhere beyond the upper surface only the object itself is visible, as at 1, with no evidence whatever of abnormal refraction and mirage. An additional inversion layer obviously might produce other images, while more or less confused layers might produce multiple and distorted images, such as shown in Fig. 141, copied from REFRACTION PHENOMENA 453 Scoresby’s account 17° of a certain telescopic view of the east coast of Greenland. Inferior Mirage.—It is a very common thing in flat desert regions, especially during the warmer hours of the day, to see below distant objects and somewhat separated from them their apparently mirrored images—the inferior image. The phenom- enon closely simulates, even to the quivering of the images, the reflection by a quiet body of water of objects on the distant shore, the “‘ water” being the image of the distant low sky, and there- fore frequently leads to the false assumption that a lake or bay Fic. 141. Telescopic appearance of the coast of Greenland, at the distance of 35 miles, when under the influence of an extraordinary refraction. July 18, 1820. Lat. 71° 20’, Long. 17° 30’ W. isclose by. This type of mirage is very common on the west coast of Great Salt Lake. Indeed, on approaching this lake from the west one can often see the railway over which he has just passed apparently disappearing beneath a shimmering surface. It is also common over smooth-paved streets provided one’s eyes are just above the street level. An under-grade crossing in a level town, for instance, offers an excellent opportunity almost any warm day of seeing well-defined small images that are apt to arouse one’s surprise at the careless way his fellow-citizens wade through pools of water! ** Trans. Roy. Soc. Edinburgh, v. 9, p. 290, 1823. 30 454 PHYSICS OF THE AIR Since the inferior mirage occurs only over approximately level places and there only when they are so strongly heated that for a short distance the density of the atmosphere increases with elevation it follows that its explanation is essentially the same as that of the superior mirage. Of course, the surface air is in unstable equilibrium and rising in innumerable filaments, but its rarefied state is maintained so long as there is an abundant sup- ply of insolation. A wave front, therefore, from an object slightly above-the general level soon becomes distorted through the greater speed of its lower portion, as schematically indicated in Fig. 142. Let AB of this figure be the surface of the earth and CD the upper level of the superheated stratum. Let EFG be the posi- tion of a wave front travelling as indicated, the lower portion curved forward as a result of its greater speed in the rarefied Fic. 142. 5 oe G6 3 C 2 = ae) A | JE B Wave fronts giving an inferior mirage (Hastings). layer. One of the consequent later positions of the wave front is shown at E’F’G’, from which it follows that at 1 neither the object in question nor any image of it can be seen; at 2 the object and its inverted image are glimpsed, superimposed; at 3 both the object and its inverted image, well below it, are plainly visible; at 4 the image is just disappearing; while at 5 there is no evidence of a mirage, unless of objects more distant than the one under consideration. Great uncertainty may exist, therefore, in regard to the exact positions of objects seen in (or perhaps hidden by) a mirage. Thus, in his official report of the battle of April 11, 1917, between the English and the Turks in Mesopotamia, General Maude, the British commander, says: “ The fighting had to be temporarily suspended owing to a mirage.” Lateral Mirage.—Vertical sheets of abnormally dense or ab- normally rare atmosphere obviously would produce lateral mirages in every way like those due to similar horizontal layers, REFRACTION PHENOMENA 455 and indeed such mirages are occasionally seen along walls and cliffs whose temperatures differ widely from that of the air a few metres from them. Fata Morgana.—Morgana (Breton equivalent of sea woman), according to Celtic legend and Arthurian romance, was a fairy, half-sister of King Arthur, who exhibited her powers by the mirage. Italian poets represent her as dwelling in a crystal palace beneath the waves. Hence, presumably, the name Fata Morgana (Italian for Morgan le Fay, or Morgan the fairy) was given, centuries ago, to those complicated mirages that occasionally appear over the strait of Messina moulding the bluffs and houses of the opposite shore into wondrous castles that alike tower into the sky and sink beneath the surface; nor is it strange that this poetical name should have become generic, as it has, for all such multiple mirages wherever they occur. According to Forel,1"4 this phenomenon, to which he has given much attention, results from the coexistence of the tem- perature disturbances peculiar to both the inferior and superior mirages, such as might be produced by a strong inversion over a relatively warm sea. This, of course, implies a marked increase of density with elevation to a maximum a short distance above the surface, followed by a rapid density decrease-—an unstable condition and therefore liable to quick and multiform changes. Obviously, too, such a cold intermediate layer in addition to pro- ducing a double mirage acts also as a sort of cylindrical lens that vertically magnifies distant objects seen through it. No wonder, then, that under such circumstances the most com- monplace cliffs and cottages are converted, through their multiple, distorted, and magnified images, into magic castles, or the mar- vellous crystal palaces of Morgan le Fay! ™ Archives des Sciences Phys. et Nat., v. 32, p. 471, JOII. CHAPTER III. REFRACTION PHENOMENA: REFRACTION BY WATER DROPS— RAINBOW. Principal Bows.—It may seem entirely supertiuous to describe so common a phenomenon as the rainbow, or to offer more than the simple explanation of it that may be found in innumerable text-books. But rainbows differ among themselves as one tree from another, and besides some oi their most interesting tea- tures usually are not even mentioned—and naturally so, for the “explanations” generally given of the rainbow may well be said to explain beautifully that which does not occur and to leave unexplained that which does. The ordinary rainbow, seen on a sheet of water drops—rain or spray—is a group of circular or nearly circular arcs of colors “whose common centre is on the line connecting the observer's eye with the exciting light (sun, moon, electric arc, etc.) or rather, except rarely, on that line extended in the direction of the ob- server's shadow. A very great number of rainbows are theoreti- cally possible, as will be explained later, and doubtless all that are possible actually occur, though only three (not counting super- numeraries) certainly have been seen on sheets of rain. The most brilliant bow, known as the primary, with red outer border of about 42° radius and blue to violet inner border, appears oppo- site the sun (or other adequate light) ; the next brightest, or the secondary bow, is on the same side of the observer, but the order of its colors is reversed and its radius, about 50° to the redl, is larger; the third or tertiary bow, having about the same radius as that of the primary and colors in the same order, lies between the observer and the sun, but is so faint that it is rarely seen in nature. Obviously the common centre of the primary and sec- ondary bows is angularly as far below the observer as the source (sun generally) is above, so that usually less than a semicircle of these spectral arcs is visible, and never more, except from an eminence. The records of close observations of rainbows soon show that not even the colors are always the same; neither is the band of any color of constant angular width; nor the total breadth of the several colors at all uniform; similarly the purity and brightness of the different colors are subject to large variations. The great- 456 REFRACTION PHENOMENA 457 est contrast, perhaps, is between the sharply-defined brilliant rainbow of the retreating thunderstorm and that illy-defined faintly tinged bow that sometimes appears in a mist—the “ white bow ” or “ fog bow.” All these differences depend, as will be explained later, essen-~ ~ tially upon the size of the drops, and therefore inequalities often exist between even the several portions, especially top and bot- toms, of the same bow, or develop as the rain progresses. Ad- ditional complications occasionally result from the reflection of bows and from bows produced by reflected images of the sun, but though unusual and thus likely to excite wonder and com- ment such phenomena are easily explained. Supernumerary Bows.—Rather narrow bands of color, essen- tially red, or red and green, often appear parallel to both the primary and the secondary bows, along the inner side of the first and outer of the second. These also differ greatly in purity and color, number visible, width, etc., not only between individual bows but also between the several parts of the same bow. No such colored arcs, however, occur between the principal bows; indeed, on the contrary, the general illumination here is per- ceptibly at a minimum. Deviation in Direction of Emerging from Entering Ray.— Since a raindrop is spherical, its action on an enveloping wave front may be obtained by determining first the effects in the plane of a great circle containing an entering ray, and then revolving this plane about that line in it that bisects the angle between the incident and emerged paths of any given ray in the same plane. Let, then, ABC (Fig. 143) be the plane of a great circle of an enlarged raindrop and let S A B C E be the path of a ray in this plane, entering the drop at A and emerging at C. The changes in direction at 4 and C are each i—r, in which 7 is the angle of incidence and ¢ the angle of refraction, and the change at B, as also at every other place of an internal reflection, when there are more than one, is r—2r. Hence, the total deviation, D, is given by the equation, D=2(i-—7r)+niw-—ar... a8 . (1) in which » is the number of internal reflections. Minimum Deviation.—The above general expression for the deviation shows that it varies with the angle of incidence. There is also a minimum deviation, corresponding to a particular angle 458 PHYSICS OF THE AIR of incidence, as may be shown in the usual way. Thus by equation (1), dD = 2di — 2 (n +1) ar which, on putting dD =o, the condition of stationary (maximum or minimum) deviation, gives, di = (n +1) dr . (2) FIG. 143. Change in light direction by raindrop. But sini=p sin r, in which p» is the refractive index of water with reference to air, and, therefore, cos 4 di = “cos r dr. Hence, by (2) ecosr = (n + 1) cos and cos i = jw Srl. V n? + 2n This value of the angle of incidence corresponds, as stated, to a stationary deviation, but whether of maximum or minimum value may be determined by noting the sign of the second differ- ential, which gives: 2 z etn But dr _ cost ui cos? and dr (1 — #) sini di* uw cos’ r REFRACTION PHENOMENA 459 Hence, as » is greater than unity, this latter value is negative and therefore the second differential of D with respect to 7 is posi- tive, and the corresponding value of D is a minimum. The following table gives these values for the primary, sec- n=1 n=2 n=3 n=4 n=5 Violet, H | 7 58° 48" 71° 30" 76° 36’ 79° 27’ 81° 17’ 14=3968.5 | 7 39° 33 44° 54 46° 23’ 47° 2’ 47° 22’ p=1.3435 | D |r—40° 36’ |2r—126° 24'\27 —37° 52’ |3m—131° 26/137 —45° 50’ weley i 59° 23’ 71" 50’ 76° 50’ 79° 38’ 81° 26’ te out] #| 40° 12" 45°27'| 46° 55’ a? ga'| gg? ga" p=4 D \w—42° 2’ = Jam —129° 2’ |am—4I° 40’ [37 —136° 4’ 1307-51" 32’ Red, Ha 1 59° 31’ 71 54’ 76° 53’ 79° 40’ 81° 28/ 4=6562.9 | r 40° 21’ 5° 34’ 47° 2" 47° 39° 47° 59’ w=1.3311 | D |r—42° 22’ |2r—129° 36’]2m —42° 30’ (347 —137° 10'}3m—52° 52" ondary, tertiary, quaternary, and quinary rainbows correspond- ing to I, 2, 3, 4, and 5 internal reflections, respectively, as shown in Figs. 144, 145, 146, 147, and 148. Entering and Emerging Rays.—Since a raindrop is spherical, it is obvious that its effect on incident radiation from the sun, Fic. 144. ’ w Change of light direction in primary rainbow. or other spherical or point source, is symmetrical about an axis through the centre of the drop and the luminous object. Hence, in the study of the rainbow, it is sufficient to use only a single plane containing this axis, tracing the rays incident over one 460 PHYSICS OF THE ATR Fic. 145. Change of light direction in secondary rainbow. Fic. 146. Change of light direction in tertiary rainbow. quadrant of the intersection circle and noting the resulting phe- nomena. It is also obvious that, neglecting sky light, solar rays are parallel to within the angular diameter of the sun, 0.5° about, and that as a first approximation they may be regarded as REFRACTION PHENOMENA 461 strictly parallel. Let, then, the plane of Fig. 149 pass through the centres of a raindrop and the sun, and let AB be the wave front of parallel rays incident, as shown, above the normal or axial ray (ray passing through centre of drop). An equal amount of light Fic. 147. S SS Ro) z2 SA aoe Change of light direction in quaternary rainbow. Fic. 148. y Change of light direction in quinary rainbow. clearly enters below the normal ray, but for simplicity this is omitted. Similarly that portion reflected from the outer surface is ignored, as is also all that is internally reflected more than once. This reduces the problem of the rainbow to its simplest 462 PHYSICS OF THE AIR terms, but loses none of its generality, since additional internal reflections merely change angular dimensions and brightness. The heavy line shows the course of the Descartes ray, or ray of minimum deviation for light of air-water refractive index, 4/3. ~~ The courses of other rays are, very approximately, as indicated. Since the deviations of the rays incident between the axial and the Descartes rays are greater than that of the Descartes, it follows Fic. 149. Ss Sx ok Course of light through a raindrop and the corresponding wave fronts. that their exits are, as shown, between those of the same two rays. Similarly, all rays that enter beyond the Descartes ray are likewise more deviated, and, therefore, while they leave the drop beyond this ray, they do so in such direction as sooner or later also to come between it and the axial ray, substantially as shown. Clearly, then, the once reflected light is diffuse and feeble except near the path of minimum deviation, and confined, as indicated, to the region between this path and the axial ray. Formation of the Bow.—From the course, just given, of light through raindrops, it is clear that maximum brightness will be REFRACTION PHENOMENA 463 produced by all illuminated drops along the elements of a right circular cone whose vertex is at the eye, whose axis passes through the sun, and whose angular opening, corresponding to a given number of internal reflections, is determined by the wave- length. Hence, the rainbow exhibits a number of concentric circular arcs of different colors whose centres are angularly as far below the observer as the sun is above him. Minimum Brightness Between Primary and Secondary Bows. —Careful observers often note the fact that the region between the primary and secondary bows is slightly darker than any other in the same general direction. The explanation of this phenom- enon is very simple. As the deviation of no ray can be less than Fic. 150. Q Minimum light between primary and secondary rainbows. that of the Descartes, it is clear that all light pertaining to any given number of internal reflections must leave a drop within a cone formed by the rotation of a corresponding Descartes ray about the axial ray, keeping the angle between them constant as shown in Fig, 150 for light of 1, and 2 internal reflections, re- spectively. Hence, once reflected light reaches an observer from drops along and within his primary bow, but none from those without, while twice reflected light reaches him from along and without the secondary bow, but none from within it. The region between the two bows, therefore, and it alone, is devoid of both the once and the twice reflected rays and in consequence is com- paratively dark. Origin of Supernumerary Bows.—Since wave fronts are 464 PHYSICS OF THE AIR normal to the corresponding rays, it is clear that the incident front, AB (Fig. 140), will, at the moment of complete emergence, appear as ACB”—exactly as though it had come from the virtual front, 4’B’, the locus of the terminus of a line of constant length, AA’, as it travels normally over the emerging wave front, ACB”. Further, since the rays here lie on both sides of the one of mini- mum deviation, it is obvious that this ray divides A’B’ into two portions curved in opposite directions. That portion of the front that is convex forward will, of course, remain convex, but with increasing radii of curvature, while the part that is concave for- ward will later become convex, and although neither portion is Fic. I51. MAX. Interference giving supernumerary rainbows. strictly the arc of a circle, the results they produce at a consid- erable distance, at the position of the observer, for instance, are qualitatively as though they were. Let AJB, then (Fig. 151), be such a wave front, J being the point of inflection where the front is normal to the ray of mini- mum deviation. Let the full and dotted curves be opposite phase positions of the resulting cusped wave front. By inspection, it is obvious that soon after leaving the drop all the light must lie on one side of the ray of minimum deviation, thus making the observed angular radius of an arc of any given color slightly less than that of the Descartes ray. It is also obvious that with in- creasing angular distance from the Descartes ray the two branches of the cusped front are alternately, and with increasing REFRACTION PHENOMENA 465 frequency, in opposite and like phases, thus producing alternate arcs of minimum and maximum brightness, within and without the circle of the primary and the secondary bow, respectively. These additional maxima, of which several frequently are visible, constitute the familiar supernumerary bows. Clearly, from Fig. 151, the widths of all the color bands, Fic. 152. Y Effect of raindrop on shape of wave front. and the spacing of the maxima, vary inversely with the distance between the centres of the interfering waves, or size of the drop. Equation of Portion of Outgoing Wave Front Near Ray of Minimum Deviation.—In deriving this equation, originally due to Airy,!"® the more direct and elementary method of Wirt- *® Cambridge Phil. Trans., vi, 380. 466 PHYSICS OF THE AIR inger 1° will be followed with only such modifications as appear to make for clearness. Let AB (Fig. 152) be an incident wave front tangent to a raindrop of radius a; let w be a small section of the emitted front near the minimum deviation ray—more distant portions of the front need not be considered as they are formed by rays too divergent to produce anything more than a slight general illum- ination; let 7, be the velocity in air of the light under exam- ination and v,p its velocity in water. Clearly, then, from the constancy of the time interval between corresponding points on the wave fronts, I- . sr Ss BAS es) AE EOS FB oe oats V1 UL Vy in which s is the distance between the drop and the corresponding point on w; 7, and +, the angles of incidence and refraction, respectively. Let the completely emitted front be also tangent to the drop, as shown in Fig. 149. Then 4ue a Cy T= and s = a 44u (1 = cos 7) — (1 — cos iif Let the centre of the drop be the intersection of codrdinates as indicated. Then, if D is the angle of deflection, a point on w is given by the values, x = acos (D — 1) + s cos D, and y = — asin (D — 1) —s sin D. By turning the coordinates clockwise through the angle D,-7/2, in which D, is the change in direction of the ray of minimum deviation, the projection angles are correspondingly reduced and the new y axis brought parallel to the emerged Descartes ray. Hence, in terms of the new coordinates, writing dforD-D,, x = — asin (d — 7) — s sind ' — wv = acos (d — i) + s cos d. ** Rerichte des naturw. medicin. Vereines an der Universitat Innsbruck, xxi Jahrg., 1896-97. See also Pernter-Exner, Meteorologische Optik. REFRACTION PHENOMENA 467 But as only rays very near that of minimum deviation need be considered, d is so small that to a sufficiently close approximation, cos d = I, and sind = d. Hence, x’ = — adcosi +asini — sd, and —-y =acosi+adsini+s. From Fig. 149 it is obvious that the small section, w (Fig. 152), of the emerged wave front is very nearly parallel to the +’ axis, and that the x’ coordinate, therefore, is extremely sensitive to changes in y’. while the y’ codrdinate is relatively but little affected by the changes in x’. Hence, as d is very small, points on w are sufficiently closely given by the expressions, x’ = asini and -y' =ucosi + ad sini +u } 4 (1 — cos r) — (I — cos at. Let J and R be the angles of incidence and refraction, re- spectively, corresponding to the minimum deviation, D,, and let i=I+a,andr=R+68 in which « and 8 are quite small, since only rays near that of mini- mum deviation are considered. Further, to make the problem entirely general, let 2 be the number of internal reflections. Then, x =asin (I +a) = asin +aacosl -y =acosi tatsini +a fou (n +1) (1 = cos 7) = (1 = cos a) = 20 cos i +$ sini — mn + 1) cos r + (n+ 1) ~ 36h. Treating d and 8 as functions of a and developing we get, neglecting powers of a higher than the third, 2 3 cost = cos (J +a) =cosI — a sin I rk Ee ae ee vie =~ D-D) = (I+) ~(R+—) +2 fr—2R+Ht-{1-R +2@-2~} 2 + =a —(n +1) B =a — (n + 1) (E)2-m+y (5). = - m+ (S5), 2 Z 2 \ da’ ]0 6 468 PHYSICS OF THE AIR Since ad ad *) iS, coil 27 e ~ M+R, d> = de (w +1) d8,and (FE), = 4, and, since = I+a,orsini = sin I +a cos ZI, therefore, ae 2 B3\ 2 , Sani - men (SS o), sin — w + (F oa) sin I — ) a (mn + 1) (s ie cos J ---- Finally, dcosr a d? cosr a3 cos = cos |R+f (a) } = cosR +a ag ee de? oe d@ cos r da’ aoe But dcosr _ gp _ _ sin ¢ dB da = aT = Bw da’ @cosr _ _ cosi dB _ sini d?® B dee HB dae “do? @oosr _ sini d3 cost @3} cosi@B _ sini d’ B dai nde KL da? Bde? EL dod At the limits dB , @ B ’ a B ’ f= (3), (5), (SS), wae t= - —“#(n +1) cosr = =p es cos Row (Se), [ - «sar oe oe F d? B oe, a — eos Fe sin r|- (m7 + »(S),[- © sin 1 — © cos 1] a Bp a, +4 (G5). [4 97] Hence, by addition of the above terms, remembering that, # cos R = (n + 1) cos I Ca heree -—y =2udr —(n+ rytboos F = w (n+ 1) (=),= a and that cos I + afouin+n) — tt REFRACTION PHENOMENA 469 Since sinz =p sin? cost = # cosr ae da and ae k af a? B - sini = — asin (4 + p cos r (<4) or boc Des a B\? a2 —sinJ = —psinR (S), + # cos R (F4). = BR ng (he = ae Hit # cos R (FS), ‘But # sin R = sin J, and x cos R = (n + 1) cos J. Therefore, @B\ _ _ sin I nm + 2n do? Jo cos I (n + 1)8 and —y = 2a [ —(n?*+2n)cosI+e(n+1)-% | +aa} We sin J a 3 (n + 1)? Ps v= [asin r | + aacos I. The first terms in the equations for 2’ and y’ are the codrdi- nates of the point of inflection on the curve w. Taking this point as the origin and calling the coordinates +, and y, we have for points on w, x =uacosl n> +2n = a a ———, sin I. mm 3 (n + 1)? But S$ oti ~ @ cos I hence, I n? + 2n ee ce ee 3 1 1 3a (in + 1)? cos 7 SP fi wat cos I = n> + 2n sy Se (n? + 2n)? [@ +12 — 2 3 @m +1? 1) ea As previously shown, hence, xP. 31 470 PHYSICS OF THE AIK Putting (w? + 2n)? (+ = My (w + 1)? (@ — 1) et yi = 3a xy". This equation, then, represents a curve very nearly coincident with that portion of the wave front to which the rainbow phe- nomena are due, and since the effects computed from it substan- tially agree with those observed, as will be seen presently, it is clear that the approximation thus obtained is sufficient for most, if not all, practical uses; indeed, the assumption that raindrops are perfectly spherical involves, perhaps, a greater error. Fic. 153. Y A ae T 0 L x R B 8 Variation of intensity with angular distance from ray of minimum deviation. Intensity and Its Variation with Angular Distance froi the Ray of Minimum Deviation —This, too, was first determined by Airy.1%* The following discussion, however, is essentially that of Mascart “8 and Pernter-Exner.!*° wee SG: “8 Tyaité d'Optique, i. ™ Meteorologische Optik. REFRACTION PHENOMENA 471 Let O (Fig. 153) be the point of inflection of an emitted wave front near a drop; let P be a distant point in the direction 6 from the ray of minimum deviation. Then the difference in phase, 4F, between the light vibrations at P, due respectively to an element, ds, of the front at O and an equal element at VM is given by the equation, OR- MT _ , ,* sind — y cose AF = 2 z T in which A is the wave-length. Hence, substituting for y its value, = , and dx for ds, which -is allowable over the effective portion of the wave front, the vibration at P is given by the equation, l hx? ; V =kfsin 27 = 308 cos@é — x sing i a in which T is the period and k the amplitude per unit length of front. Or, putting 3 Z (5 se - x sing) = 3 a Pek in (are - 8 d => sin "FF ) ax = bf cos 8 dx sin an 4 — bf sind dx cos 27 F. Since cos 8d and sin 6d appear in this equation as amplitudes it follows, if b [cos 0 dx b fsin # ax that the resultant amplitude C = yt? + B But to find A and B it is necessary to integrate the given ex- pressions over the effective portion of the wave front, or through limits that produce essentially the same results. Such limits may be determined as follows: A and B 472 PHYSICS OF THE AIR Let + and +, be so situated that the difference between their ‘ Bay ie a 3 7 distances from P is 5, and their combined result at that point, therefore, zero. That is, let + (x3; — x3) cos@ — (x1 — x) sind = vl» or a 3a? 2 cosd h (xm? + x m + x) — tané Mi - x = Considering the primary bow in which h has its least value, 4.89, nearly, for pot ; assuming the radius, a, of a drop to be I mm., and writing 6x for x, — 4, it follows, since 4 is small, that xx = .0002 mm, roughly, for yellow light. Hence, 8% decreases rapidly with increase of x (even when *#=.Imm., 'r=.02 mm.), and the successive portions of the curve beyond a very short distance from the inversion point, O (Fig. 153), completely neutralize each other, and, therefore, no error will be introduced by integrating between infinity limits in- stead of between the unknown limits of the effective portion of the wave front. +o A=k ‘a cos 6 dx J—o Hence, +o Be=k sin 6 dx —o But as the sign of B reverses with that of x, while that of A remains unchanged, and B=0O foo} ar fh ; A= af — — cos@é — « sind ) as. A 3a? Oo Putting «> cosd = > and 2h 3a 4 REFRACTION PHENOMENA 473 from which a (Se hyn la (355) at and = sing = = 2 2A A= 1 f (Gitta) = Ww — su) du, which is Airy’s rainbow integral, in which (u3 — gu) du = 34, N| =I the difference in phase. Putting ts = (u3 — gu) du = f(z) - 2 (Ge Ae “f@) = M fle), say, and the intensity, A? = M? f? (z), The evaluation of f(z) is not simple, but it has been accom- plished through mechanical quadrature by Airy 8° and through development in series by both Airy 18! and Stokes. !82 Fic. 154. i Pippnogos 0 Z Periodic changes of intensity of monochromatic light. The following table and its graph (Fig. 154), both from Pern- ter-Exner’s “‘ Meteorologische Optik,” give certain values of z and 7 (2), corresponding to fnpaocheatietie light of a particular wave-length and drops of a definite size. *° Cambridge Phil. Trans., vi, Pp. 379. ™ Cambridge Phil. Trans., viii, p. 595. ™ Cambridge Phil. Trans., ix, part i. 474 PHYSICS OF THE AIR Values of f?(z) for Different Values of z. Z fa) zZ Pz) zZ fz) —2.0 0.006 3.4 0.609 8.8 0.189 —1.8 0.011 3.6 0.586 9.0 0.373 —1.6 0.018 3.8 0.436 9.2 0.320 1.4 0.030 4.0 0.225 9-4 0.100 —1.2 0.048 4.2 0.051 9.6 0.001 —1.0 0.074 4.4 0.003 9.8 0.054 —0.8 0.113 4.6 0.104 10.0 0.240 —0.6 0.168 4.8 0.297 10.2 0.360 —0.4 0.239 5.0 0.465 10.4 0.220 —0.2 0.331 5.2 0.501 10.6 0.022 0.0 0.443 5.4 0.379 10.8 0.013 0.2 0.571 5.6 0.172 11.0 0.170 0.4 0.706 5.8 0.014 11.2 0.338 0.6 0.836 6.0 0.022 Il.4 0.270 0.8 0.941 6.2 0.174 11.6 0.050 1.0 1.001 6.4 0.370 11.8 0.004. 12 0.996 6.6 0.450 12.0 0.140 1A 0.914 6.8 0.353 12:2 0.320 1.6 0.758 7.0 0.141 12.4 0.256 1.8 0.547 7:2 0.010 12.6 0.045 20 0.319 74 0.046 12.8 0.006 2.2 0.125 7.6 0.230 13.0 0.136 2:4 0.014 7:8 0.394 13.2 0.314 2.6 0.016 8.0 0.363 13.4 0.202 2.8 0.131 8.2 0.150 13.6 0.013 3.0 0.317 8.4 0.010 ee ia heal 3.2 0.502 8.6 0.038 Afaxima and Minima. Maxima zZ f(z) Minima zZ i 1.0845 I.005 I. 2.4955 2h: 3-4669 0.615 2s 4.3631 3: 5-1446 0.510 2 5.8922 4. 6.5782 0.450 ay 7.2436 5: 7.8685 0.412 5. 8.4788 6. 9.0599 0.384 6. 9.6300 7% 10.1774 0.362 7. 10.7161 8. 11.2364 0.345 8. 11.7496 9- 12.2475 0.330 9. 1 12.7395 10. 13.2185 0.318 10. 13.6924 It will be noticed that the first maximum does not coincide with s=0, nor, therefore, with 6=0, the direction of the ray of minimum deviation; that the intensity of the first maximum, cor- responding to a principal bow, is much the greatest; and that the succeeding maxima, corresponding to the supernumerary REFRACTION PHENOMENA 475 bows, and also the angular intervals between successive maxima, continuously decrease, at a decreasing rate, with the increase of 0. Distribution of Colors in the Rainbow.—The above discus- sion of the distribution of light intensity applies, as stated, to monochromatic light. When the source of light simultaneously emits radiations of various wave-lengths, as does the sun, a cor- responding number of bows, each consisting of a sequence of maxima and minima, are partially superimposed on each other. In this way different colors are mixed, and thus the familiar polychromatic rainbow produced. The particular mixing of colors that obtains is the result of several codperating causes. Thus the distribution of intensity, as illustrated by Fig. 154, depends on phase difference, as given by the expression, he 2 cosé — x sin@ an 2S... 2 The angular intervals between maxima, say, increase, therefore, with A, and, consequently, coincident distribution of the intensities of any two colors is impossible. Again, since the direction of the ray of minimum deviation varies with the refractive index, as already explained, and that in turn with the wave-length or color, it follows that the direction of the zero point on the intensity curve, near which the first maximum lies, correspondingly varies. Obviously, then, these two causes together produce all sorts of color mixings that in turn arouse widely varied sensations. To determine, however, just what color mixtures are induced by drops of any given size, it obviously is necessary to express the values of the abscissa, z, of the intensity curve (Fig. 154) in terms of angular deviation from the corresponding principal ray, since the direction of each such ray fixes the position of origin of its particular curve. Let, then, as before, Zu Bags — = > sing 2 2 or 4 sing x\? 2 = |—— = aA 4 Also, as before, let ae a G ) = 4 h cos8 476 PHYSICS OF THE AIR hence, 48 a? re sin?@ tané. 2 = But whatever the value of 9 from 0° to 30° in2 weet = I, to within .0055. Hence, approximately, 8 a = + 7s 03, or i se, ()% "2a 6 From this equation it appears that the angular distance be- tween any two successive intensity maxima varies directly as the cube root of the square of the wave-length and inversely as the cube root of the square of the diameter, or other linear dimen- sion of the parent drop. That is, this interval is greater for red light than for blue, and greater for small drops than for large ones. The following table, copied with slight changes, from Pernter- Exner’s “ Meteorologische Optik,” gives the values of 6 in minutes of arc per 0.2 2, for lights of different wave-length and drops of different size. Angle in Minutes per 0.2 2, Primary Bow. iaesoné 5 to | 15 | 20 | 25 | 30 | 40 | so | 100 | rs0 | 250 | 500 | 1000 ai | Angle in minutes .687 85.8] 54.0] 41.2] 34.0] 29.3} 26.0] 21.4] 18.5] 11.7] 8.9 | 6.32] 3.98] 2.51 656 83.0] 52.3] 39-9] 32.9] 28.4] 25.1] 20.7] 18.0] 11.0} 8.6 | 6.10] 3.84] 2.43 -589 77.0] 48.5] 37-0] 30.5] 26.4] 23.3] 19.3] 16.6] 10.5] 7.9 | 5.67] 3.57] 2-26 527 71.2] 44.9] 34.2| 28.2] 24.4) 21.6] 17.8] 15.4] 9.6] 7.4 | 5.25] 3.31] 2-10 -494 68.1) 42.8] 32.6] 27.0] 23.1] 20.6] 17.0] 14.7] 9.3] 7.1 | 5.02] 3.15] 2.03 .486 67.2| 42.3] 32.3] 26.7] 22.8] 20.3] 16.8) 14.5] 9.1] 7-0 | 4.94] 3.12] 1.99 -449 63.4] 40.0] 30.5] 25.2] 21.7| 19.2) 15.9] 13.7} 8.6] 6.6 | 4.67] 2.93] 1 88 -431 51.5] 38.8] 29.6] 24.4] 21.0) 18.6] 15.4] 13.3] 8.3] 6.4 | 4.53] 2.87) 1.82 By the aid of this table; a table of intensity distribution, M*f?(z), along the coordinate z; and the following relative intensities, 687 656 589 527 494 486 449 431 I 20 86 250 152 121 134 163 74 REFRACTION PHENOMENA 477 Pernter has constructed Figs. 155 and 156 that show the intensity distributions of these several colors due to drops of .5 mm. and .05 mm. radius, respectively. It still remains to determine the color at any particular point at which the relative intensities of the several colors are known. This can be done by the aid of Maxwell’s 183 color triangle, as explained in detail by Pernter.*84 Relation of size of Drop and Wave-length to Intensity — Since the Airy expression for the amplitude of the vibration produced at a distant point by the effective portion of the emitted wave front involves the factor, (Aa?)”, it is evident that the cor- ~ DARK RED. RED. ORANGE, LIGHT GREEN, DARK GREEN, Distributions of colors by drops of 0.5 mm. radius. responding intensity, which is proportional to the square of the amplitude, will be proportional to (Aa?) *. This, however, is based on the assumption that the effective light from the drop comes strictly from the line of a great circle. Asa matter of fact, it actually comes from a narrow belt whose effective angular width, as measured from the centre of the drop, is inversely pro- portional to the curvature, or directly to the radius a, and in- versely proportional to the wave-length.18° Hence, the actual . . . . ot a intensity is proportional to » Pail *8 Trans. Roy. Soc., p. 57, 1860. ™ Meteorologische Optik. “ Mascart, C. R., V. 115, p. 453, 1892. 478 PHYSICS OF THE AIR A larger fraction of the short wave-length light is effective, therefore, than of the long. Further, the rainbow bands pro- duced by very small droplets are not only broad, as previously explained, but also feeble, and as their colors necessarily are faint they frequently are not distinguished—the bow appearing as a mere white band. Popular Questions About the Rainbow.—A few popular questions about the rainbow need perhaps to be answered. ‘What is the rainbow’s distance?’ In the sense of its proximate origin, the drops that produce it, it is nearby or far away, according to their respective distances, and thus extends from the closest to the farthest illuminated drops along the elements of the rainbow cone. Indeed, the rainbow may be regarded as consisting of coaxial, hollow conical beams of light of different colors seen edgewise from the vertex, and thus having great depth or extent in the line of sight. Fic. 156. Distributions of colors by drops of 0.05 mm. radius. ‘Why is the rainbow so frequently seen during summer and so seldom during winter?” Its formation requires the coexist- ence of rain and sunshine, a condition that often occurs during local convectional showers but rarely during a general cyclonic storm, and as the former are characteristic of summer and the latter of winter, it follows that the occurrence of the rainbow correspondingly varies with the seasons. “Why are rainbows so rarely seen at noon?” As above explained, the centre of the rainbow’s circle is angularly as far below the level of the observer as the sun is above it, hence no portion of the bow can he seen (except from an elevation) when its angular radius is less than the elevation of the sun above the horizon. Now, during summer, the rainbow season, the elevation of the sun at noon is nearly everywhere greater than 42°, the angular radius of the primary bow, or even 51°, the radius of the REFRACTION PHENOMENA 479 secondary bow. A rainbow at noon, therefore, is, except for very high latitudes, an impossible summer phenomenon, and, of course, a rare winter one, for reasons given above, even where possible. .. “Do two people ever see the same rainbow?” Theory teaches, and ordinary experience shows, that as the observer re- mains stationary or moves, so also, other things being equal, does his rainbow. If then, two observers initially close together should move in opposite directions, each would find his rainbow re- sponding in the same sense as his shadow, and presently the Fic. 157. Reflected rainbow. positions and, therefore, the identity of the two bows would become unquestionably different, from which it follows that as the eyes of two observers must always be separated by a greater or less distance their bows must also be correspondingly sep- arated and different—different in the sense that they have differ- ent positions and are produced by different drops. In short, since the rainbow is a special distribution of colors (produced in a particular way) with reference to a definite point—the eye of the observer—and as no single distribution (other than uniform and infinite) can be the same for two separate points, it follows that two observers do not and cannot see the same rainbow. 480 PHYSICS OF THE AIR “Can one see the same rainbow by reflection that he sees directly?” An object seen by reflection in a plane surface is seen by the same rays that but for the mirror would have focussed to a point on a line normal to it from the eye and as far back of it as the eye is in front. But, as just explained, the bows appropriate to two different points are produced by different drops; hence, a bow seen by reflection is not the same as the one seen directly. Reflected Rainbows.—Since rainbows occasionally are seen reflected in smooth bodies of water they deserve, perhaps, a somewhat fuller explanation than that just given. Let an observer be at O (Fig. 157). Under proper conditions of rain and sunshine he will see directly a primary bow due to drops on the surface of a cone formed by rotating OP about Fic. 158. Ww Reflection rainbow. OX, parallel to SP, keeping the angle, POX, roughly 42°, con- stant; and by reflection in the surface of the water, I”, another primary bow due to drops on the surface of a different cone, one formed by rotating O’P’ about O’X’, also parallel to SP, keeping the angle P’O’X’ constant. The bow seen by reflection neces- sarily will appear upside down, P’ at P’, etc. The arc of the bow seen by reflection obviously (from the figure) will be less than that of the bow seen directly, and for that reason is likely to appear flatter. Reflection Rainbows.—A reflection rainbow is here defined as one due to reflection of the light source, the sun, usually, but itself seen directly. Let the observer be at O (Fig. 158) with the sun and a smooth surface of water, WV, at his back and illuminated rain in front. The direct sunshine will give a primary and a secondary bow REFRACTION PHENOMENA 481 along the elements of cones formed by rotating OP and OS, respectively, about the common axis, OX, parallel to the incident rays, keeping the angles POX and SOX constant; while the re- flected light will give a primary bow along the elements of a cone formed by the rotation of OP, about the axis OX, (OXr parallel to RP,), keeping the angle P-OX; constant, and equal to POX. Reflection bows of higher orders than that of the primary are likely to be too faint to be seen. The angular elevation of the centre (axis really) of the re- flection bows clearly is equal to the angular depression of the Fic. 159. REFLECTION SECONDARY REFLECTION PRIMARY CONDAR PRIMARY 20 Direct and reflection rainbows. centre of the direct bows. Hence, the direct and the reflection bows of the same order intersect on the observer’s level, as shown in Fig. 159. Horizontal Rainbow.—A rainbow is occasionally formed by a sheet of drops resting on a smooth water surface, probably oily. Juday '®°*, for instance, reports the simultaneous observ- ance, October 23, 1914, of the primary bow, its first two super- numeraries, and also the secondary, in such a sheet on Lake Men- dota, Wisconsin. The peculiar appearance of such bows is due entirely to the unusual distribution of the parent drops—there is nothing new in the theory of their formation. “a Monthly Weather Review, 44, p. 65, 1916. 482 PHYSICS OF THE AIR Why There is No Visible Rainbow without Internal Reflec- tion.—Since more light passes through the raindrop at the place of first internal reflection than anywhere else, it is reasonable to ask why this light, which is refracted as much as any other, instead of giving the brightest of all rainbows, shows none at all. Clearly, and as is obvious from inspection of Fig. 149, the deviation of this non-reflected light varies from zero, in the case of that which is normal to the drop, to a maximum for the tan- gential. Its brightness, however, as seen by the observer, grad- ually decreases, with increase of deviation, to zero at 2(90°—arc sin I/#) from the sun— being the air-water refractive index for the wave-length under consideration. Hence, owing to super- position of the several colors, all this refracted but non-reflected light is white, except a violet to bluish circular border about 84° from the sun, or other source, and far too faint ever to be seen. CuapTer IV. REFRACTION PHENOMENA: REFRACTION BY ICE CRYSTALS. Introduction—The cirrus clouds and others formed at tem- peratures considerably below o” C. usually consist of small but relatively thick snowflakes with flat bases, or ice spicules with flat or, rarely, pyramidal bases, always hexagonal in pattern and detail, as shown by Fig. 160 from Bentley’s remarkable collec- tion of photomicrographs of snow crystals. Light from the sun, for instance, obviously takes many paths through such crystals and produces in each case a corresponding and peculiar optical phenomenon. Several of these phenomena, the halo of 22° radius, the halo of 46° radius, the circumzenithal arc, parhelia, etc., are quite familiar and their explanations defi- nitely known. Others, however, have so rarely been seen and measured that the theories of their formation are still somewhat in doubt. Finally, many phenomena, theoretically possible, as results of refraction by ice crystals, appear so far to have escaped notice. Prismatic Refraction—Since the phenomena caused by the passage of light through ice crystals are numerous, it will be most convenient, in discussing them, first to obtain general equa- tions for prismatic refraction, and then to substitute in these eyuations the numerical constants applicable to each particu- lar case. Deviation.—Let A (Fig. 161) be the angle between two ad- jacent faces of a prism; let CE be the path of a ray of light ina plane normal to their intersection (direction of -travel imma- terial) : let i and 7’ be the angles of incidence and r and 7’ the cor- responding angles of refraction. Then the change in direction, D, of the ray is given by the equation, Deeg ae a) St SS Aes ste ongncs (1) Minimum Deviation—Minimum deviation occurs when da 2 wD _ Oand#?> 9 But when di div? : 483 PHYSICS OF THE AIR 484 160. Fic. Snow crystals (Bentley). REFRACTION PHENOMENA 485 and as r+tr =A. dr = — dr’, Also, from the law of refraction, snit =p sin r. sin 7’ = p» sin r’ Hence, directly, snit sin 7 . * = + ’ sin 7’ sin 7’ or sin 7 sin r’ = sin 72’ sin 7 Fic. 161. Deviation by refraction. and, by differentiation, if di=— di’ and dr=- dr’, cosi — cos? cos 1’ cos r’ or cos 7 cos 7’ = cos 7’ cos 7. By addition, cos (i-r’)=cos (i’-7), ori-r = 7. By subtraction, cos (i+ 17’) =cos (i +7), oritr =v +7, Hence, if, as assumed, e Say 4 =v,andr=fr = 32 486 PHYSICS OF THE AIR From cos 7’ dr’ dD di’ i! cos 2 cos r’ me ST SE erg i OOS Sp di di cos r dr cos 2’ cos 7’ cos 7 it follows, by a little reduction, that when ab =o 1 @D _ 2 “cos? r sin i — 2 cos’ 7 Sin r. di #203 1 COs? © But H>0, cos? r>cos? 4, sin i>sin r, and w cos i cos? r>0. Hence, when dD aD ae that is, when r = 7’, gee and the deviation has its minimum value. Writing D, for the minimum deviation, it follows that De =e? — A, (2) Hence, from sini=ypsin 7, and r= a we get sin ——— = pt sin 4 - (3) Maximum deviation, Dn, obviously occurs when t = 90°, or, for ice for which »= 1.31, when r= 49° 46’. Since Dae py aa Dm = 90° +7 —A and sin (Dm + A — 90°) = mw sin r = # sin (A — 49° 46’), for ice, or cos [(180° — 4) — Dm] =/ sin (A — 49° 46’) - - (4) The above equations apply only to refraction in a plane nor- mal to the intersection of the faces of the prism. When the inci- dent ray is inclined to this plane, the effective angle of refraction is increased, and as such inclination usually occurs in the case of floating ice crystals it is necessary, in the study of halos, to evaluate its effect on the deviation. REFRACTION PHENOMENA 487 Let the ray, CE (Fig. 162), enter a prism at O and leave it at O’. Let ON be the normal to the prism face at O, and let OP be the projection of CO onto a plane through O normal to the intersection of the refracting faces. Let P be the projection of C, and let the plane CNP be normal to ON. Similarly, let P’ be the projection of C’ on the principal plane, PON, and let the plane C’P'N’ be perpendicular to the normal ON extended; then, since Fic. 162. Refraction of rays inclined to principal plane. the refracted ray OC” lies in the plane OCN, it follows that the triangles CNP and C’N'P’ are similar. Therefore, sinh _ sin a sin k sin r and sin h = p/ sin k, in which h and & are the angles between the ray and principal plane before and after refraction, respectively. 488 PHYSICS OF THE AIR Similarly, if h’ and k’=k are the angles at O’ corresponding toh and k at O, sin h’ = usin k’ = pw sin k. Hence, h=h' That is, the inclination of the ray to a principal plane is the same after leaving a prism as before entering it. Let ip be the angle between the normal, ON, and the projec- tion, OP, of the ray, CO, on the principal plane through O, and rp the angle betwen the normal extended, ON’, and the projection, OP’ of the refracted ray, OC’, onto the principal plane. Then (perhaps better seen by reversing OC’N’P’ toOC”N”P”), NP NP sin P= OP ~ OC cosh and z = N"” Pp” a N” Pp” 2 a eS gp? — Ge" se But NP = at B NY’ Pp" = “ N” PP” if OC = Oc", and es cosk . sn tp = cosh Yp. Hence a ray inclined to the principal plane of a prism of re- fractive index » is so bent that the projection of its path on this plane gives the index, p’ where ; cos k = pe a Sa? NS — einth) 2 186 le ee (u sin? fh) (1 sinh) The minimum deviation, therefore, D’,, measured in or pro- jected onto the principal plane, of such rays is given by the equation, Di) +A _ cosk. A ard 2 ~ " cos h a (5) and the maximum, D’m, by the equation, cos k cos [(180° — A) — D'nj =u — sin (A —a@) , (6) sh *° Tt may be interesting to note that this relation between the inclination of a ray to the principal plane of a prism and its deviation by that prism explains the curvature of spectrum lines as seen in an ordinary straight slit prism spectroscope. REFRACTION PHENOMENA 489 in whicha is the limiting value of the angle of refraction for the index »’, when ,_ , cos k- cos h pe The largest or limiting value of h at which light can still pass through the prism obviously is determined by the equation, D+A Se Des in which D is the minimum deviation as projected on the prin- cipal plane. In this case Disp A cok = A. : sin = =i n oo o =F : (7) Therefore, I = » 4 — sin? k) — w® — sinrh ety M cos? h = cos? h ‘Sis == 2 and cosh = 4122 ean = Ae =] 2 Hence, when A = 60°, as between alternate sides of a hexag- onal ice prism, or snowflake, the limiting value of h for »=1.31, is 60° 45’, and when 4 is go°, as between base and a side, 32° 12’. Internal Total Reflection and Its Effect on the Passage of Light Through Ice Crystals.—Since the limiting value of the “angle of incidence” is 90°, and the refractive index of ice 1.31, it follows that total reflection of an internal ray occurs at the angle a, given by the equation, sin 9c° = 1.31 sina = 1.31 sin 49° 46’. An internal ray, therefore, cannot leave an ice crystal if the angle it makes with the normal is greater than 49° 46’. Hence, as is clear from Fig. 163, a ray of light in the principal plane, and also most rays out of it, will pass through an ice crystal be- tween faces whose inclination is not greater than 49° 46’ at all angles of incidence (measured on the base side of the normal) from 0° to 90°. On the other hand, no light can pass through an ice crystal at any angle of incidence between planes whose inclination is greater than 2x 49° 46’. In proof of this latter 490 PHYSICS OF THE AIR statement, let 4B (Fig. 164) be a ray grazing the side of a crystal whose angle of refraction is 99° 32’ and entering at B. It will reach the opposite face at C, and either pass out in the direction CD or else suffer total reflection. But as CD lies along the face of the crystal, it is clear that any decrease of the angle of incidence at B from 90°, or increase of the inclination of the Fic. 163. Limiting angle of emission. Fic. 164. Limiting angle of transmission. crystal faces to each other, each of which increases the angle BCE, causes total reflection at C, and thereby prevents transmission. Refracting angles intermediate between the above extremes ob- viously transmit light incident through an angular range less than 90° and greater than 0°. REFRACTION PHENOMENA 491 The largest angle of incidence clearly is 90°, and the smallest i, as determined by the equation, sini = msinr = 1.31 sin (A — 49° 46’) If, then, 4 =60°, 1=13° 27’, giving a transmission range of 76° 33°; if d=90°, 1=57° 48’, range 32° 12’; and similarly for other possible values of A. General Illumination of the Sky Through Ice Crystals.—The deviation of a ray of light through refraction and m internal reflections obviously is given by the equation, D=iti + nz — SA, in which X A is the sum of the several angles passed by the ray in its course through the crystal. If these angles are all equal - the equation becomes D=i+i7 + ne —- (w+ 1) A. If, then, as frequently is the case, the ice crystal is a thick hexagonal disk floating horizontally, the position it oscillates about in falling, both angles passed by a once reflected ray will be go°, provided the entering and emergent branches lie in the same plane, and the deviation will be D=21, as readily seen in Fig. 165. Hence, such crystals illuminate the sky at all distances from the sun out to 115° 36’. The effect, however, is not sufficiently striking ordinarily to arrest attention. Parhelia of 22’.—Whenever the air through any depth or at any level contains innumerable hexagonal snow crystals with their sides vertical (the position about which relatively broad crystals oscillate) two colored bright spots, known as parhelia or sun dogs, appear at 22°, or more, from the sun, one to the right, the other to the left. Each bright spot is in the direction of maximum light or minimum refraction, and has the same altitude as the sun. When the refraction is in a principal plane, that is, as the sides of the crystal are vertical, when the sun is on the horizon, the angular distance, D,, of each spot, also on the horizon, is given by the equation, derived from (3), , in Dy + 60° . 60° Sl = sin, == 2, i" 2 492 PHYSICS OF THE AIR For yellow light (#=1.31), D)»=21° 50’; for red light (#=1.307), Dy=21° 34’; and for violet (#=1.3117), Dy =22° 22’. The order of the colors, therefore, counting from the sun, is red, yellow, etc., to violet, and the length or dispersion 48’ for a point source. For the sun, diameter 30’, the total length is 1° 18’, and width 30’. Since the above are minimum angles, it follows that slight changes in either the inclination or orientation of the crystals causes rays of each color to come also from somewhat greater Fic. 165. 5 oO e %Q- oO @ cA Illumination of the sky by flat snow crystals. distances from the sun. Hence, the only color thus produced that appears approximately pure is the darker portion of the red. Yellow and green are also moderately distinct, but blue, and especially violet, scarcely perceptible because of so much admix- ture of colors. When the angular elevation of the sun is h, the distance, D’. in azimuth, of each of these parhelia from the sun is given by the equation, derived from (5), D' + 6c° cos k i 60°. sin —————_ = —— sin — 2 * cos h 2 REFRACTION PHENOMENA 493 The angular distance, 4,, measured on the arc of a great circle, between the sun and each of these parhelia, may be found from the right spherical triangle formed by the three sides: zenith to sun (complement of /2) ; zenith to mid point between sun and a parhelion; “ mid point ’’ to sun, fe The angle thus formed igs aie ; at the zenith is >, and the angle at the “mid point” go°. Hence, a WN Dt sin — = cos fA sin — 2 2 For »=1.31 the following relations 187 exist between h, D’, and A,. h D’ Ao 0° = Dy=Ay = 21° 50’ u ° € ° ¥ 5, 22° 2! 21° 56" 10° 22°30’ 22°10 15° 23°20’ 22°32’ 20° 24°34’ 23° 4’ 25° 26°22’ 23° 50’ 28° 44’ 24° 40’ 35° ar” 56’ 26° BY 40° 36°20’ =. 27° 38’ 45° 42° 30’ 29° 42" 50° 51°30’ = 32° 26’ 55° 66° 2’ 36° 26’ 60% 98° 48" 44° 38" 60°45’ 120° 0’ 50° 4’ All the above values pertain, as explained, to minimum devi- ation. But as the orientation of the crystals is fortuitous, it fol- lows that all possible deviations from minimum to maximum will occur, and the parhelia, therefore, be drawn out into streaks the lengths of which depend upon their angular altitude. The maximum deviation for refraction in a principal plane (for sun on the horizon when the crystal edges are vertical) is given by the equation, derived from (4), cos (180° — 60° — Dm) = psin (60° — 49° 46’). The value of the maximum deviation in azimuth, Dm, cor- responding to the solar altitude, h, is given by equation (6), and the actual maximum, Am, by the equation, _ A . D'm sin — = cosh sin —- 2 2 *" Pernter-Exner, Meteorologische Optik, pp. 314, 315. 494 PHYSICS OF THE AIR The following table '88 gives interesting relations between the quantities indicated: h Dm An Am—Ao ce} , o , ° , $ ge fe ue o ° w ° o * i 44° 8" 43° a, 21° 16 5, AS 59, 43, 8! ° 8’ 20. 4c 1D, 43, tA 20 ; 25, 4 ° oi 43, to! 18° 22’ 30, 5°, ae 43, a 35 53° 1 43 co 40° 57, 9) 42° 58" 15° 22 a. ea a 43, ei 3 46" 50 68 48° 43° 10" 10° 4 eee gee 4 54 40°44 oe 60°45’ 120° 0’ 50° 4 0° oO From the computed values of An—A,, fully supported by observations, it appears that when the angular elevation of a parhelion of 22° is moderate to small, 20° or less, it may extend over an arc, parallel to the horizon, of more than 20°. The end next the sun, produced by minimum deviation, is colored, begin- ning with red, through a short range. Similarly, the distal end, due to maximum deviation, is also colored, terminating with violet, though always too faint, perhaps, to be distinctly seen. Through the rest of its length the blending of the colors is quite complete, giving white, of course, as the result. At greater altitudes the possible lengths of the parhelia of 22° become less and less, as shown by the table, though the color dis- tribution remains the same. Halo of 22°.—When the refracting edges of the ice crystals are vertical, as they tend to be in the case of relatively thin snow- flakes falling through still air, parhelia are produced, as just explained. But, in general, these edges lie in all directions, espe- cially at the windy cirrus level and when the crystals are of the short columnar type; and as refracted light reaches an observer in every plane through his eve and the sun (or moon) to which the refracting edges are approximately normal, it follows that the effect produced by fortuitously directed snow crystals must be more or less symmetrically distributed on all sides of the exciting luminary. There may. however, be a maximum brightness both % Pernter-Exner, Meteorologische Optik, p. 317. REFRACTION PHENOMENA 495 directly above and directly below the sun since ice needles tend to settle with their refracting edges horizontal. As before, when the refracting angle is 60° and “= 1.31, cor- responding to yellow light, D) = 21° 50’, and is independent of solar elevation. The inner portion of this, the most frequent and best known of all halos, is red, because light of that color is least refracted. Other colors follow, with increase of distance, in the regular spectral sequence, but with decrease of wave-length they so rapidly fade that even green is indistinct and blue seldom de- tected. This is owing to the variation in deviation caused by the tipping of the needles, as previously fully explained. The brightest portion of the ring clearly is at the angle of minimum refraction from the sun. With increase of distance, light produced in this manner gradually fades (not all the crystals are ever simultaneously in position to give minimum refraction) until it ceases to be perceptible at 15° to 20° beyond the inner portion, or, say, 40° from the sun. On the other hand, no such light reaches the observer from places within the ring of maxi- mum brightness, and, therefore, this portion of the sky is com- paratively dark, except, and for an entirely different reason, to be explained later,1®° near the sun itself. When the sun is within 10° of the horizon, the halo of 22°, and the parhelia of 22°, are practically superimposed. At greater altitudes they become distinctly separated, as per the accompany- ing table 79° for »=1.31, in which =solar elevation, A, = par- helic angular distance from the sun and D, = angular distance of halo from sun. h Ao—Do 0° 0° of 10° 0° 20’ 20° 1° 14’ 30° 2° 59’ 40° 5° 48’ 50° 10° 36’ 60° 22° 48’ 60°45’ 28° 14’ Arcs of Lowitz, or Vertical Arcs of the 22° Parhelia.—On rare occasions oblique extensions of the parhelia of 22°, concave towards the sun and with red inner borders, are seen, in addi- tion to their horizontal tails, above described. These are known * See chapter on diffraction. * Pernter-Exner, Meteorologische Optik, p. 32!. 496 PHYSICS OF THE AIR as the arcs of Lowitz, after the astronomer who described them 19! as seen in the famous Petersburg halo complex (Fig. 166) of July 18, 1794. Their general explanation is simple, though exact Fic. 166. Nowa dela dead Imp Je Leteopot. Tom.VIE Tab, VU. wa a Ke ¥ : f = , i ‘ é : bm i K ' i & f | if P Benth a i é : | ‘, : Petersburg halo of July 18, 1794. computations of their outlines and of the relative intensities of their parts for different altitudes of the sun are rather tedious. ™ Nova. Acta Acad. Pctropol., 8, 1704, p. 384. REFRACTION PHENOMENA 497 As already explained, parhelia and their horizontal extensions are produced by ice crystals whose principal axes are vertical, the former by those set to minimum refraction, and the latter by crystals turned more or less from this unique position. When, however, the principal axes oscillate about the ver- tical, as they obviously do in the case of snowflakes, the arcs of Lowitz, or obliquely vertical extensions of the parhelia of 22°, necessarily are produced, though rarely seen, because of the dif- fusion of their light in the midst of a general glare, as will be explained below. Consider, first, for Sisley, the doubly special case in Fic. 167. Formation of the arc of Lowitz, crystals vibrating in solar vertical. which the sun is on the horizon and the principal axes of the crystals oscillate in a vertical plane passing through the sun. Let C (Fig. 167) be the position of an ice crystal whose principal axis is in the direction CZ. Let an observer be at O and let the incident ray, SC, lying between Z and P make the angle h with the principal plane, CP. On emerging this ray, in its new direc- tion, S’O, has the same inclination as formerly to the axis. Hence, SC and S’C may be regarded as elements of a right cone of vertex C and axis CZ, and as the plane CZS is vertical, if S is on the horizon, as seen from O, the element CS (lowest element), being parallel to OS, owing to the great distance of S, will lie in 498 PHYSICS OF THE AIR a plane tangent to the cone and parallel to the plane of the horizon, while every other element, such as C'S’, will lie above it. S”’, there- fore, the apparent position of S due to refraction of the ray SC by the ice crystal at C is above this plane and, also, as seen from O at the same angular distance above the horizon. Similarly, when the axis of the crystal is tipped beyond the vertical in the opposite direction, S’ drops below the horizon. Further, let ZP and ZP’ be arcs of great circles intersecting SC and S’C at B and B’, respectively. Then the projection of the deviation SCS’, or SOS’, on the principal plane is given by the angle D between these arcs, and on bisecting D, thus dividing ZBB’ into two equal right spherical triangles, and putting BB’ =A, it is obvious that n= = sin os cos h (1) 2 2 and cot B = tan 2 sin h (2) Clearly, then, the locus of S” is given when the arc BB’ is known in terms of the angle B. On eliminating 4 from the above equations, it appears that cot? B = tan? 2 cos? a — sin? a - (3) Hence, that either A or B may be found when the other is given, it remains only to express tan P in terms of a function or functions of A. But from (7), (p. 4890), sin? as A = Soe k sin? A 2 cos? h 2 = {1 + (# — 1) sec? nf sin? < Also from (3), (p. 486), REFRACTION PHENOMENA 499 and from (1), (p. 498). sg dD sin? = sect h = = sin? = Hence, sin? D+A 2 sin? Do + A = 2A sin? D 2 = 2 x 2 snip th sin? = sin? — sin? = 2 or opel fe) _ D gD. xs Do . Do 2 aes. — ae 2 oe — sint 2 sin (2 + 4) sin sin’ > sin (244) sn®. Dividing by cos 2 cos A, sin (P44 dat ton 2 epg D SN 2 2 2 sin’? > tan > + sin? > tan A = — cos A ik _ cos (Do + A) Pt sali } (: cos A aS Putting cos (Do +4) _ te ° , eee cos = cos 73° 30 D 2 tan A sin? S 2 tan = 2 cosA — cosB “= (4) On using this value of tan 2 (3) reduces to 2 pd sin > yV 4 sint 2 cos? ° tan? A — (cosA — cos/3)? cot B = cosA — cosf ” From (5) B is readily computed for any assumed value of 4, as is also D from (4). Further, i can be found from (1) when Aand D are known, or from (2) when B and D are known. The following table, copied from Pernter-Exner,*? as are ™ Do, p. 327. 500 PHYSICS OF THE AIR most of the above equations, gives data for drawing the locus of S’ when the sun is on the horizon. Since the value of A in this table increases with », other things being equal, it follows that these arcs must be colored and that their inner borders must be red, as stated. h A B 0° 21° 50° go° of 5° 21° 55/ 89° 5’ 10° 22° 10’ 88° 1’ 15° 22° 38’ 86° 54’ o ° ft ° eee SS 30° 24° 49’ 82° 38° oO ° ¥ og t 35, 3, a 38 40° 27° 38° 78° 5 45° 29° 42" 74, 36° 5°, a se oe ee oe 3 o age a 5 # 0° 44° 38° 44° 4U 60°45 50° 4 33° 29 This table is graphically represented by Fig. 168, in which the circle is the 22” halo, HH the horizon, S the sun and S’S”’ the curve in question, dotted below the horizon where, of course, Fic. 168. Ss S' r XN (Q Sse eo a Arc of Lowitz, sun on horizon, crystals vibrating in solar vertical. REFRACTION PHENOMENA 501 like the under portion of the circle, it is invisible, except from a suitable elevation. Obviously, the optical effect is independent of the manner by which the inclination of the principal axis of the crystal to the incident ray is produced, and, therefore, crystals tilted in the ver- tical plane through the sun to an angle, E +h, to the plane of the horizon give the same result, if E is the solar elevation, as do crystals tilted to only the angle / in this plane when the sun is on the horizon.. The points of contact with the halo of 22°, being due to crystals whose principal axes are normal to the incident rays, lie, therefore, at equal altitudes on opposite sides of the halo and in a plane that passes through the sun. Consequently, the angular altitude of these points is less than that of the sun, except when the latter is on the horizon. If, as before, E is the elevation of the sun and E’ that of the points of contact in ques- tion, then, from the right spherical triangle formed by the radius Fic. 169. O Arcs of Lowitz, elevation of sun 40°, crystals vibrating in solar vertical. of the halo and the zenith distances of the sun and point of con- tact, respectively, cos (90° — E’) = cos (90° — E) cos 21° 50’. Fig. 169 represents, approximately, the outline of the bright band produced in this manner when the elevation of the sun is 40° ; making that of the points of contact 36° 38’. O is the posi- tion of the observer, S the centre of the halo of 22°, PP parhelia of 22°, TT the points of tangency to this circle of the arcs of Lowitz, PT PT. In order that the arc may reach the halo, the tilt of the crystal must at least equal the elevation of the sun, and 33 502 PHYSICS OF THE AIR no portion of the lower branch (part below point of tangency) is given unless the tilt is greater than this elevation. Hence, if the extent of the tilting of snow crystals is less, in the great majority of cases, than 30’, as it probably is, only the upper branch is likely to be produced when the sun is 30° or more above the horizon. Consider, now, the effect of the vibration of the principal axis in a vertical plane at right angles to the vertical plane through the sun. Let £ be the elevation of the sun and / the inclination of the principal axis to the vertical, then the angle between the incident ray and principal plane is given by the equation, sin h = sin (90° — 12) -sin E. Let EF =30°, and i=20°. Then the angular distance from the sun to a parhelion of 22° is 24° 49’, or say 3° from the halo Fic. 170. Arcs of Lowitz, crystals vibrating at random. of 22°. Also h=28° 1’, and the corresponding distance of image from halo is about 2° 40’, at approximately 20°, measured from centre of halo, above or below the parhelion, owing to direction of tip. Vibrations of the principal axis in intermediate planes give images, of course, in intermediate positions, so that the total REFRACTION PHENOMENA 503 effect, when the elevation of the sun is 30°, may be somewhat as represented in Fig. 170, in which tilting is supposed to be re- stricted to 30° and less from the vertical. In this Figure, PP are the parhelia of 22°, aa, bb, and cc the outlines of the images corresponding to minimum refraction ° when the principal axis is oscillated in a vertical plane through the sun, true tangent arcs; at 45°, roughly interpolated, to this sun plane; and at 90° to it, respectively. It will be noticed that this light, nearly always too faint to be distinguished from the general glare, would be more concen- trated, if the orientation of the ice crystals were fortuitous, which, presumably, often is the case, and consequently brighter below the parhelia than above them. Hence, because of limited tilting, as above explained, and because of the greater concen- tration of light in its lower branches, this halo, whenever seen at all, appears as short arcs including the parhelia and extending mainly below them. Tangent Arcs of the Halo of 22°.—-Obviously, when the sun is on the horizon, ice crystals whose principal axes lie or oscillate Tangent arcs of the halo of 22°. in horizontal planes must produce the same optical effects above and below (theoretically) the halo of 22° that are produced on its sides, as above explained, by crystals whose principal axes oscillate in the vertical plane through the sun. Each set of curves might properly be called tangent arcs of the halo of 22°, but as a matter of fact only those well-known and fairly common arcs that occur above and below the circular halo are so designated. Similarly, when the elevation of the sun is E, arcs identical 504 PHYSICS OF THE AIR with those just described and tangent to the halo at its highest and lowest points, as shown in Fig. 171, are formed by crystals whose principal axes oscillate in.planes normal to the solar vertical and inclined at the angle & to the plane of the horizon. But ice spicules or needles tend to float with their principal axes horizontal. Hence, it is necessary carefully to determine the optical effects of crystals in this particular position, as may be done by noting the transformations of the tangent arcs as the crystals are so turned as to carry their principal axes from the inclined to the horizontal plane. Let, then, the principal axis of an ice needle lie parallel to OP (Fig. 171) in which O is the position of the observer, HSH’ the inclined plane and S the sun at elevation E. Let / be the inclination of the principal axis to the incident radiation and let a or b be the position of the resulting image. Now, let the crystal, as suggested above, be so turned as to carry its axis from an In- clined to a horizontal position, and in such manner as to keep constant the angle between the principal axis and the direction of the incident ray. That is, change the direction of the axis from parallel to OP to parallel to OP’, with SP=SP’. Under these conditions the refracted ray will turn precisely as does the prin- cipal axis. Hence, if a’ and b’ are the new positions of a and b, the angle aSa’ = bSb' = PSP’ But from the right spherical triangle OSP’ cos OSP’ = sin PSP’ = tan E cot SP’ = tan E tanh, and aSa’’ = }Sb’ arc sin tan E tan h. Since the points of tangency of the “ tangent arcs’ under con- sideration are 90° from the corresponding points of the similar “arcs of Lowitz,” it follows that the angle B of Fig. 167 and table on page 500 equals TSa (Fig. 171). Hence, ae S = B+ arc sin tan E tanh The following table, adapted from Pernter-Exner, ‘‘Meteo- rologische Optik,” pp. 338-339, gives the necessary data for accurately constructing tangent arcs corresponding to different solar elevations: REFRACTION PHENOMENA 505 Values of Angle S. E 5° 10°55" 15° 20° 25°2' Bot- bot- h A Top | tom Top | tom Top |Bottom|| Top |Bottom|| Top | Bottom 0° | 21°50/}| 0° o’| 0° o//| 0° o’| 0° o/!| 0° of] 0° O/| 0° of 0° of 0° of 0° of 5 21 55 I 21 0 290 I50]/ 0 0 216] —o 26 245] —055 316] — 1 26 Io 22 10 252 I 06 356] 002 442] —0 44 5 40] —1 42 642] — 244 15 22 38 427 I 45 604] 0 08 713} —I or 8 42 | —2 30 1017} — 405 20 23 04 615 235 8 27 0 25 || I0 or | —I I1 12 02] —3 12 I412| — 5 22 25 23 51 8 OL 3 21 || Io 51 0 31 I2 52] —I 30 |] 15 27] —4 05 1816] — 654 30 24 49 |} Io 16 4 28 || 13 46 0 58 |] 16 16 | —1 32 |] 19 30 | —4 46 23 01 | — 817 35 26 03 || 12 53 5 51 || 17 08 I 36 |] 20 11 | —1 27 || 24 08 | —5 24 28 28| — 944 40 | 27 38 |) 1608] 7 42 || 21 14] 2 36/) 2455] —1 05 || 29 42 | —5 52 |] 3459] —11 19 45 | 29 42 || 20 25 | 10 23 || 26 31] 417 || 3057] —0 09 || 36 45 | —5 57 || 43 16] —12 28 50 32 26 || 26 16] 14 18 |] 33 34] 700]! 3855 I 39 || 46 10] —5 26 5407 | —13 33 55 | 36 26 || 35 13 | 20 51 || 44 02 | 12 02 || 50 32 5 32 || 59 21} —3 17 69 53] —13 49 60 44 38 || 54 02 | 36 36 || 64 50] 25 48 || 72 58 17 40 || 84 25 6 13 9919] — 841 60°45’ | 50 04 |] 65 30 | 47 32 || 76 40 | 36 22 || 85 06| 2756 || 97 04] 15 28 |] 113 02 0 0 E 29°15’ 35° 4o° 45° 50° h A Top |Bottom || Top |Bottom Top. |Bottom Top |Bottom || Top | Bottom 0° |21°50’|| 0° of 0° of 0° of 0° oO, 0° of 0° of 0° of 0° o/|| 0° of 0° of 5 |21 55 344/- 154 4 26|— 2 36 5 08 |— 318 5 56]— 406 6 54|/— 5 04 Io |22 10 739/}— 341 9 04]— 5 06]] 10 30|]— 6 32 ]] 12 09 |}— 8 11 || 14 07 |—10 09 15 (22 38 || 11 54|— 5 32 || 13 51 }— 7-43 |} 1606|)— 9 54]| 18 39 |—12 27 || 21 44 | —15 32 20 |2304]] 1611 |— 7 21 I9 II |—I0 21 22 12|—13 22 || 25 46 |—16 56 |] 20 08 | —21 18 25 |23 51 || 20 49|— 9 27 |] 24 45 |—13 23 |] 28 43 |—17 21 || 33 29 | —22 07 || 39 26|—28 04 30 |24 49 || 26 14 |—II 30 || 31 12 | —16 28 || 36 20 | —2I1 36 42 38 |—27 54]| 50 50 | —36 06 35 |26 03 || 32 27 |—13 43 || 38 43 |—19 59 || 45 21 | —26 37 |] 53 48 |—35 04 |] 65 55 |—47 Ir 40 |27 38 || 39 57 |—16 07 || 47 54 | —24 04 || 56 40 | —32 50 || 68 57 | —45 07 |/101 55 | —78 05 45 |29 42 || 49 27 |—18 39 59 50 |—29 02 72 26 |—41 38 ||/105 24 |—74 36 ae gar [waa S ae 50 |32 26 || 62 09 | —21 35 |] 76 50 | —36 16 |/110 17 | —69 43 |]... .. Eat ute i cases ee 55 |36 26 || 81 09 | —25 07 ||118 02 |—61 58 Beem thet | semes aoe Misuse See [iat cai'selflersaces hate! || aimee ote 60 144.38 Wit27 TS |-—- 3037 I|oax xe [ease ae |lgaw ee Josinee ve |fece vie Pewee ae fle sce ons 60°45"|50 04 1/146 3% |—33 29 Wea ox | see aa. [lene oe leas ws Iewe oe lrewe oy E 55° 60° 70° 80° h A Top Bottom Top Bottom Top | Bottom Top Bottom 0° 21°50’ 0° of 0° of 0° of 0° of 0° of 0° o’|| 0 ° of 0° of 5 21 55 8 06 — 616 9 38 — 748 I4 50 —13 00 30 40 —28 50 10 22 10 16 34 —I2 36 19 46 —15 48 30 58 —27 00 9Il 59 —88 o1 15 22 38 25 36 —I19 28 30 45 —24 33 50 31 —44 19 sie. fea? || Ei ees 20 23 04 35 45 26 57 41 31 —34 41 94 25 BES ||. caste | aieae ae 25 23 SI 47 26 —36 o1 59 34 —48 12 Ne eis | eather | | Bee » |) Soden? Be 30 24 49 || 62 54 | —48 07 OF 212? || 2K ae dee | akgate deal ee Bee | wesc kes 35 26 03 99 22 —80 38 Goh dea) | anaes wae Hl ae pak fe tataey BE, lI) , or z (a —r cos a) sin 6, , in which A is the wave-length. Also, since the displacement at P owing to the element at b is given by the expression sin 27 & r da dr. i in which ¢ is the time of travel from b to P and T the period, the total displacement, X, at P is given by the equation, ar a j : . -{ fo [(p-tet ) + t oe Joana 7 ? ° ° Hence, developing, and putting 20 a i cos 29 ( sin 6 cosa \r dadr =A oO oO Ly [som ( (F sino cosa) r da dr = B = A sin 27 7a) + B cos 27 Foe"). and t DIFFRACTION PHENOMENA 531 Therefore, d and B are components at right angles to each other of the resultant amplitude. Hence, the intensity, J, is given by the equation, = A? 4+ B?’, Putting mr sin 6 sin 0 _ * fo cos (28 r cos a) da rdr But "Sar 5 ip cos*nada = Be ge 52 sxegws 2n —1 ie Bee Oe spare 2n Oo Hence "4 | A= ands apts ama =] [2 dr % I F (a 2)? a 2 3) + B ai I Bt a’ I B® a8 = ae m8 ee [a zy F 3 (1-2): 4 (ts 2 oy + | and, putting 3 ma sin 6 2 ! = =m m I m4 I 2 2= 2, ae Im i ; A = was E 2 I F 3 (1-2)? 4 (1-2-3) “2+ ve + -| A similar development gives the other component in terms of a series of odd valued sines of a Hence, as the elements are symmetrically distributed on either side of the diagonal bd’, B=o, and I = A? On giving m various values, tables and curves of intensity may be constructed. The following table by Airy, copied from Mascart’s “ Traité d’optique,” v. I, p. 310, is restricted to that portion of the expression within the brackets. The following table of diffraction maxima and minima is also copied from Mascart, l.c., p. 312. 532 PHYSICS OF THE AIR m A I m A I 0.0 1.0000 1.0000 3.0 — 0.0922 0.0085 O.1 0.9950 0.9900 3.1 —0.0751 0.0056 0.2 0.9801 0.9606 3.2 —0.0568 0.0032 0.3 0.9557 0.9134 333 —0.0379 0.0014 0.4 0.9221 0.8503 3-4 — 0.0192 0.0004 0.5 0.8801 0.7746 3-5 —0.0013 0.0000 0.6 0.8305 0.6897 3.6 0.0151 0.0002 0.7 0.7742 0.5994 3-7 0.0296 0.0009 0.8 0.7124 0.5075 3.8 0.0419 0.0017 0.9 0.6461 0.4174 3.9 0.0516 0.0027 1.0 0.5767 0.3326 4.0 0.0587 0.0035 1.1 0.5054 0.2554 4.1 0.0629 0.0040 1.2 0.4335 0.1879 4.2 0.0645 0.0042 1.3 0.3622 0.1312 4-3 0.0634 0.0040 1.4 0.2927 0.0857 4-4 0.0600 0.0036 1.5 0.2261 0.0511 4.5 0.0545 0.0030 1.6 0.1633 0.0267 4.6 0.0473 0.0022 1:7 0.1054 O.O1II 4-7 0.0387 0.0015, 1.8 0.0530 0.0028 4.8 0.0291 0.0008 1.9 0.0067 0.0000 4.9 0.0190 0.0004 2.0 — 0.0330 0.0011 5.0 0.0087 0.0001 2.1 —0.0660 0.0044 5.1 — 0.0013 0.0000 2.2 — 0.0922 0.0085 5.2 —0.0107 0.0001 2.3 —O.1116 0.0125 5:3 —0.019I 0.0004 2.4 —0.1244 0.0155 5.4 —0.0263 0.0007 2.5 — 0.1310 0.0172 5.5 —0.0321 0.0010 2.6 —0.1320 0.0174 5.6 — 0.0364 0.0013 2.7 —0.1279 0.0164 5-7 —0.0390 0.0015 2.8 —0.1194 0.0143 5.8 —0.0400 0.0016 2.9 —0.1073 0.0115 5.9 — 0.0394 0.0016 3.0 — 0.0922 0.0085 6.0 — 0.0372 0.0014 Diffraction Maxima and Minima. m Maxima Pe Minima 7 Diff. I T Diff. I I 0.000 1.00000 0.610 0 0.819 0.506 2 0.819 0.01745 1.116 oO 0.527 0.503 3 1.346 0.00415 1.619 0 0.512 0.502 : 4 1.858 0.00165 2.121 oO 0.504 0.501 5 2.362 0.00078 2.622 oO 0.500 0.500 6 2.862 0.00043 2.122 oO 0.500 0.500 3.362 0.00027 3.622 oO 0.500 0.501 8 3.862 0.00018 4.123 oO 0.500 0.500 9 4.362 0.00012 5.623 o DIFFRACTION PHENOMENA 533 It will be noticed that the decrease of intensity from maximum to minimum, though large at first, quickly becomes very small. From the values of = , corresponding to diffraction minima, it is evident that z sin 6 = (nm + 0.22) bar Very nearly, in which 2 is the order of the minimum, counting from the centre. This important equation gives the angular distance from the light source at which the successive diffraction minima occur for any particular wave-length and size of drop or disk. It also gives the diameter of the drop when the wave-length, angular distance from the centre, and order of the minimum are known. Fur- thermore, it shows that the larger the wave-length and the smaller the droplet the larger the diffraction circle, or halo. The above discussion applies to a single circular disk on the wave front. An exact duplicate disk obviously would produce an exact duplicate diffraction pattern. If, then, two such disks occur close together, and if the distance between their centres, or other homologous points is b, and ¢ the angle between the line connecting these points and the line connecting the farthest to the point of observation, then the difference in phase between the two lights at the latter place is 27 ee and a secondary diffraction pattern, in addition to the two primary circular ones, is produced, directed at right angles to the line connecting the centres of the disks. Similarly, conspicuous diffraction patterns are produced by any regular geometric distribution of many disks. Let, however, the disks, or droplets, be numerous, irregularly distributed, and all of the same size (if of various sizes their effects cannot easily be summed up). Let each produce at a given point a disturbance whose amplitude is 4, but let the phases be a, ¢ en, and let R be the resultant amplitude. Then, R? = = (A cose)? + & (A sin ©)’, = A? [ cos e) + cose, + --- + cosen)? + (sin &; + siné: + - + sin ay R? = A? (n cos* + n sin’e + 2n cos © cos &’ + 2m sin € sin e’), = Am + 2A? n cos (€ — *'), 35 ° 534 PHYSICS OF THE AIR But as 2 is large and the disks irregularly scattered, it is clear that the phase difference, © — «’, between the innumerable pairs will have all manner of values with, on the whole, the positive and negative well balanced. Hence, as close as can be detected, R? = nA’, That is, the diffraction rings, corona, for instance, produced by a large number, 7, of irregularly distributed neighboring drop- lets are the same as those produced by any one of them, but « times as bright. When the incident light is complex, the diffraction pattern produced by the several wave-lengths necessarily overlap and produce correspondingly colored rings—red, if present, being the outermost, and blue the innermost. Size of Cloud Particles ——Since the diffraction pattern pro- duced by a great many irregularly distributed droplets of uni- form size is the same as that due to a single one, it is clear that the size of the cloud particles producing coronas may be deter- mined by the equation, A sin @ = (” 0.22) — (x + 0.22) —, in which, as already explained, @ is the angular distance from the centre of the corona to the mth minimum corresponding to light of the wave-length, A, and a, the radius to be determined. Measurements made in this manner have shown that the radii of corona-producing cloud droplets, though varying over a considerable range, commonly average about .007 mm. to .o1o mm. It may be interesting to note in this connection that a con- tracting or decreasing corona implies growing droplets and, per- haps, the approach of rain; and that an expanding corona implies. on the other hand, decreasing or evaporating droplets and, pre- sumably, the approach of fair weather. Fig. 186, copied from an instructive article by Simpson,?%* gives the angular and intensity distribution of the monochro- matic light A= .000571 mm. in a corona produced by droplets of .O1 mm. radius. Droplets versus Ice Needles as Producers of Coronas.—When "SQ Ir. Rov. Met. Soc., 38, p. 201, 1912. DIFFRACTION PHENOMENA 535 coronas are seen in clouds whose temperature is above 0° C., or in which halos do not form, it is certain that they are due to droplets. It is well known, however, that the most brilliant coronas—those of multiple rings and large diameter—usually are formed by very high clouds whose temperature often must be far below freezing. Naturally, then, it has been inferred that these coronas are produced by the diffractive action of ice needles. Simpson,’®® however, appears to have dis- proved the probability that they are formed in this manner. “On no occasion,” he says, referring to his stay in the Antarctic, “were a corona and halo seen at the same time on the same cloud.” Furthermore, he explains, as the axes of the needles are essentially horizontal, this being their stable position, only those Fic. 186. > 2 ” z uJ F.O1 Z ! CO UJ ~ Na Pee — 2 4° 6° 8° 10° ~—s 12 Distribution of intensity by droplets, radius = 0.01 mm., 4 = .571 w. at right angles to radii from the sun, or other luminary, could produce coronas of the kind observed, while the equally numer- ous crystals of every other orientation would produce such dif- ferent patterns that the total effect probably could be but little more than white light—certainly nothing approaching the pure brilliant colors often seen in these coronas. Presumably, therefore, the brilliant coronas of high clouds are due to very small undercooled water droplets of approxi- mately uniform size, and not, as has generally been supposed, to ice needles. Iridescent Clouds—Thin and perhaps slowly evaporating 9) o. 536 PHYSICS OF THE AIR cirro-stratus and cirro-cumulus clouds occasionally develop num- erous iridescent borders and patches of irregular shape, especially of red and green, at various distances from the sun up to 30° or more. A brilliantly colored iridescent cloud of considerable area is justly regarded as one of the most beautiful of sky phenomena, but one of which until recently there was no satisfactory ex- planation. Simpson,2°° however, has shown that the colored patches in question, presumably, are only fragments of coronas formed by exceedingly small droplets of very approximately Fic. 187. mm O10 9 008 O jae a S 1, 006 \ YS : % y Ke 5 004 Sy Se} f 26 Wo 002 SSan}y = . thea | a | °° 4° 8° io 6 6ie6@6—C BO a RADII OF 137 AND 2228 RED BANDS Relation between size of drop and size of corona. uniform size. The relation between the radius of droplet and angular distances from the centre to the first and second red bands is shown in Fig. 187, also copied from the paper cited, from which it appears that coronas of the requisite size may occur, and, therefore, that the assumption that iridescent clouds are only fragments of unusually large and exceptionally bril- liant coronas presumably is correct. Bishop’s Ring.—After the eruption of Krakatoa in 1883, of 0 on DIFFRACTION PHENOMENA 537 Mont Pelé in 1902, and of Katmai in Ig12, a faint reddish- brown corona was often seen, under favorable circumstances, around the sun. This is known as Bishop’s ring, after Mr. Bishop of Honolulu, who first described it. The width of this ring, as seen after the eruption of Kra- katoa, was about 10°, and the distance from the sun to its outer edge, that is, to the first minimum, 22° to 23°. Substituting this value of the angular radius of the first minimum in the equa- tion, explained above, ‘ 2 sinA#=(n + 0,22) ca and letting 4=.000571 mm., it appears that the diameter of the dust particles, assumed either spheres or circular disks of ap- proximately uniform size, that produced this peculiar corona is given by the equation, .00057Imm. 2a = 1.22 — 3 sin 22° 30’ = ,00182 mm. about. Glory or Brocken-Bow.—When favorably situated, one oc- casionally may see rings of colored light around the shadow of his own head as cast upon a neighboring fog bank or cloud. This phenomenon, to which several names have been given— glory, Brocken-bow, Brocken-spectre, mountain-spectre—is pro- duced by the diffraction by particles comparatively near the sur- face of light reflected from deeper portions of the fog or cloud. The reflected light obviously emerges in every direction, but the nearer one looks along the path of incidence the larger the ratio of illuminated to non-illuminated particles in his line of sight. Indeed, at any appreciable angle from this special direc- tion a considerable proportion of the droplets in one’s vision evi- dently must lie in the shadows of others nearer the surface. Hence, not only will the shadow of one’s head be surrounded by the brightest reflected light, like the “ heiligenschein’ one may see around the shadow of his head on a bedewed lawn, but it will also be the centre of the brightest and only perceptible glory or reflection halo, and that for the simple reason that the more intense the initial light the more brilliant its diffraction effects. CHAPTER VII. PHENOMENA DUE TO SCATTERING: COLOR OF THE SKY. THE color of the cloudless sky, though generally blue, may, according to circumstances, be anything within the range of the entire spectrum. At great altitudes the zenithal portions are distinctly violet, but at moderate elevations often a clear blue. With increase of the angular distance from the vertical, however, an admixture of white light soon becomes perceptible that often merges into a grayish horizon. Just after sunset and also before sunrise portions of the sky often are distinctly green, yellow, orange, or even dark red, according especially to location and to the humidity and dust content of the atmosphere. Hence, these colors and the general appearance of the sky have rightly been used immemorially as more or less trustworthy signs of the coming weather. Early Ideas—Many attempts have been made to account for the blue of the sky ?°!—the other colors being comparatively ignored. Some have held that it is just the nature of the atmos- phere, or of particles in it, to reflect the blue of sunlight and to transmit the other colors. But as they did not explain how the atmosphere, or these particles, happened to have such nature the mystery actually remained as profound as ever. Another interest- ing hypothesis, suggested by Leonardo da Vinci, was to the effect that the blue is the resultant of a mixture of more or less white light, reflected by the atmosphere, with the black of space. But the futility of this idea is immediately obvious from the fact that gray alone could be produced by any such mixture. The first logical attempt to explain (as that term is now understood) why the sky is blue was made by Newton,?°? who supposed it to be due to the same sort of interference between the rays reflected from the front and rear surfaces of transparent objects (in this case minute water drops) that produce the colors of soap bubbles. In fact, he thought that the “ blue of the first order,” the blue nearest the black central spot of the “ Newton’s rings,” 1s of the same color as the blue of the sky, and that they were produced in the same way. This explanation, though er- ™ See summary and bibliography by Dorsey, Monthly Weather Review 28, p. 382, 1900. * Optics, hook ii. 538 PHENOMENA DUE TO SCATTERING 539 roneous, and based only on analogy, was accepted without modi- fication for nearly 175 years. At about the end of this period, however, Clausius *”* demonstrated analytically that a cloud of droplets of the small size assumed by Newton would cause the stars and other celestial objects to appear enormously magnified. He, therefore, modified Newton’s theory by assuming that the droplets are larger but vesicular with very thin walls. In this way the magnification trouble is avoided, but the theory is not improved. First, because water droplets are not hollow; and, second, because, as shown by Briicke,?°* the color of the sky differs radically from the blue of the “ first order.” Although the above appears to have been the first serious criticism of the Newtonian theory of sky colors, observational and experimental data sufficient to render it untenable had long been known. This consisted of (a) Arago’s?°® discovery in 1811 that sky light is partially polarized and that this polariza- tion is a maximum along a circle about 90° from the sun; and (b) Brewster’s 7° discovery, shortly thereafter, that polariza- tion by reflection is a maximum when the tangent of the angle of incidence is equal to the refractive index of the reflector divided by that of the adjacent medium. If, then, sky light is the result of simple reflection, the ang'e of polarization (angle of incidence corresponding to maximum polarization) of the reflecting medium must be 45°—since the arc of maximum polarization is 90° from the sun. But the angle of polarization of water in air is about 74°. Hence, the color of the sky cannot be due to reflection from water droplets, as Newton and many others assumed. Modern Theory.—The real origin of the blue of the sky, scat- tering of light by particles far too small to reflect specularly, appears to have been first indicated by Briicke’s °° experiments, which showed (a) that a transparent medium, rendered turbulent by sufficiently small particles, appears blue when illuminated with white light ; and (b) that objects may be seen through such medium clearly and distinctly. A few years later, Tyndall °°* made a large Crell’s Jr., 34, p. 122, 1847; p. 185, 1848; Pogg. Ann., 72, p. 204, 1847. ™ Pogg,. Ann., 88, p. 363, 1853. ** Ocuvres, 7, p. 394, and p. 430. * Phil. Trans., 33, p. 125, 1815. ed ™ Phil. Maq., 37, p. 384, 1869; 38, p. 156, 1869. 540 PHYSICS OF THE AIR number of experiments on the action of chemically formed “clouds ” on incident white light, and found that not only did they scatter blue light when their particles were very small, but also that this light was completely polarized at right angles to the incident beam. Here, then, was the experimental solution of the problem of the blue of the sky and its polarization. About two years later, Lord Rayleigh °° supplied the necessary theory, and thus, at last, one of the oldest and most difficult of the many problems of meteorological optics became completely solved. In a later paper Lord Rayleigh 21° showed that in the absence of dust of all kinds “the light scattered from the molecules [of air] would suffice to give us a blue sky, not so very greatly darker than that actually enjoyed.” And still later, King 211 concluded that “ The analysis of the present paper seems to support the view that at levels about Mount Wilson [1730 metres] molecular scattering is sufficient to account completely both for attenuation of solar radiation and for the intensity and quality of sky radiation.” However, whether the scattering be by fine dust or by individual molecules the theory is the same, and, as developed in Ray- leigh’s first paper, substantially as follows: Let a beam of light of wave-length A be incident, say, to be definite, from the zenith. There will be little or no scattering from that portion of the beam in free ether, as is obvious from the facts (a) that extremely distant stars are still visible, and (5) that interstellar spaces are nearly black. From the portion in the atmosphere, however, there is abundant lateral scattering bv the innumerable particles of dust and molecules of air, each of which is optically denser than the ether and so small in compari- son to A® that the applied force is practically constant through- out its volume. Each such particle merely increases the local inertia of the ether, and, thereby, since the rigidity is not affected, correspondingly reduces the amplitude of a passing light wave. If, then, a force should be applied to each particle, such as to counterbalance the increasing inertia, the light would pass on exactly as in empty space and, therefore, without scattering. On the other hand, precisely the same force, but reversed in di- rection, if acting alone on free ether would produce the same 7° Phil. Mag., 41, pp. 107, 274, 447, 1871; 12, p. 81, 1881. 7° Phil. Mag., 47, p. 375, 1809. ™ Phil. Trans., A.. 212, 375, 1913. PHENOMENA DUE TO SCATTERING 541 ettect that the disturbing part.cle produces. This force obvi- ously must have the same period and direction as the undisturbed luminous vibrations and be proportional to the difference in optical density between the particle and the ether. The only factors that conceivably can affect the ratio of the amplitude of scattered to incident light are: direction, or, rather, angle between directions of force and point of observation; ratio between the optical densities of the disturbing particle and the ether; volume of particle; distance from particle; wave- length; and velocity of light. Hence, in comparing the extents to which lights of different colors are scattered, the first two factors may be neglected, since they apply in equal measure to all. Furthermore, as the ratio in question, like all ratios, is a mere number and, therefore, dimensionless, the last factor must be omitted, since it and it alone involves time. There remain, then, only the volume of the particle, distance from it, and the wave- length to consider. But from the dynamics of the problem it appears that the ratio of the two amplitudes must vary directly as the volume of the particle and inversely as the distance from it. That is, n= SF, in which N is some number, L a unit of length, and f(A) that function of A that renders the equation dimensionless. Hence, f@=%, and, therefore, the ratio of the two intensities is proportional to \*. Obviously, then, light from a serene sky should belong essentially to the blue or short wave-length end of the spectrum. If, as commonly expressed, the displacement in the incident waye is A cos (AS *), in which A is the amplitude; v the ve- locity of light, A the wave-length; and ¢ the time since any con- venient instant when the displacement was 4, then the corre- sponding acceleration is 2 © Acos art =-A (F v) cos = wt, Hence, the force that would have to be applied to a sufficiently minute particle in order that the wave might pass over it un- disturbed is SD =p yA CZ) cos = ot, 542 PHYSICS OF THE AIK in which D’ and D are the optical densities of the particle and ether, respectively; and T the volume of the particle. And this, as explained, is also the expression for the force which, if oper- ating alone on the ether, would produce the same light effects that actually are induced by the particle in question. Now it has been shown by Stokes,?!2 and also by Lord Ray- leigh,?1* that the displacement X produced by the force F cos 2nru. f é —z is given by the expression, = F sine 4rvDr in which @ is the angle between the direction of the force and the radius vector, 7, that connects the centre of the force with the point at which the displacement is observed. Qn cos a (vt — r) 7 . + 20 t . On substituting for the force F cos = its value, one finds that x= a= 7 Pat sina cos = (vt — r) Hence, the intensity of the light scattered by a single par- ticle is D'—D\? wT? _, A? ( D ) prs sin-a@. and for a cloud ft (F5°) 7 sina ~ T° D 7a? 7 : eae 2 in which © a is the sum of the values of cs for all the par- ticles in the line of sight, or » (D' -— D\ * sin’a c\ Ee) ae oe) in which N is the total number of particles in the line of sight, and (yi, the mean of the several values of (¢Z ; The above equations are based on the assumption that the displacements in the incident wave are all in the same plane— that the incident light is plane polarized. If, however, they lie in parallel planes, passing through the axis of propagation, that is, if the incident light is unpolarized, we may resolve each dis- 22 Camb. Phil. Trans., 9, p. 1, 1849; Math. and Phys. Papers II, pp. 243- 328. ™3 Phil, Mag., 41, p. 107, 1871. PHENOMENA DUE TO SCATTERING 543 placement, always normal to the line of travel, into two com- ponents at right angles to each other and obtain their joint effect in any given direction. Let the line from the centre of the force to the point of observation make the angles a, 8, and 7 with these components and the direction of travel, respectively. Then, since sin’a + sin?8=1+cos*y (see Fig. 188), the intensity of the scattered light at the angle y from the direction of travel of a non-polarized beam is, A 7? - 2)" m (1 + =o n (4). According to this equation, a maximum amount of scattered Fic. 188. xX a I 8 y I \ ! Y | 3 b ! a aa ; a * ' gr Z L # ve! ee ed eee ee o, Z ce % & Intensity of scattered light in a given direction. light is along the path—forward and back—of the incident beam, and least at right angles to it. Also, the intensity is directly proportional to the square of the volume of the disturbing par- ticle, provided it is sufficiently small. The effect of the size of particle on scattering as it ap- proaches 4° is not well known. However, Lord Rayleigh ?14 has shown that the intensity of the light scattered by relatively large spherical particles varies as the inverse 8th power of the wave-length. Extinction Coefficient—The intensity or brightness of solar or other radiation is decreased with increase of air path by (a) scattering, (b) selective absorption, (c) diffraction, (d) reflec- ™ Phil. Mag.. 12, p. 81, 1881. 544 PHYSICS OF THE AIR tion, and (¢) refraction. When the sky is clear, however, only (a) is particularly effective in the visual region, but here it is quite effective, since each disturbing particle evidently scatters energy from incident radiation in proportion to the expression, m™ T2/D! — D\? - | te 8x3 T? (D’ — D\? =al?s) sin 7a27 r? sinada = is D ) : ° Let E be the energy delivered per unit cross-section of the incident beam in any interval of time, and let be the number of disturbing particles (all alike) per unit volume. Then the energy gain (negative) during the same time per unit cross-sec- tion, and penetration, dx, is given by the ara D' — D dE = — En dx a (eS It, then, Ey is the energy in the ea before any scattering took place, and E the energy remaining after penetrating the distance x into the turbulent medium in question, B=, € in which the extinction coefficient _ _ 8rn T? ve —D -o Sr Elasticity Density of ether =1, » for either =1), »=refractive index. Also, in the case of scattering by air molecules, or by any small particles in a medium whose refractive idex is I, nT (25) = vv in which D” = average optical density of the turbulent space. If wis the refractive index of the medium, air, say, But D= p? (from the equations, 7= = !, density ie nT (7E* = w—1 = (wu +1) (uh — 1) = 2 (hp — 1), nearly, since p» differs but little from unity. Hence, substituting, e= =o (4 — I, approximately. Clearly, then, the intensity of atmospheric and dust haze rapidly decreases with increase of wave-length, a fact that jus- tifies the use, on aeroplanes, for instance, of “haze cutters” (filters that transmit only the longer waves) for both visual and photographic work. A fog haze, however, cannot be much cut. PHENOMENA DUE TO SCATTERING 545 This is because the extinction it produces, being due, owing to the relatively large size of the fog droplets, chiefly to diffraction and reflection, is nearly equally effective for all colors. The scattering of light by the molecules of the atmosphere and the suspended fine dust particles decrease the intensity of both the direct insolation and the scattered radiation, but at the same time gives to all portions of the sky, other than that occu- pied by the sun, a luminosity that otherwise would not exist— without scattering there would be no sky light at all. The residual sunlight and the total sky light vary greatly with time of day, latitude, altitude, season, weather, and dustiness of the atmos- phere. Kimball,?1° for instance, finds “that photometric meas- urements made at Mount Weather, Va. [Lat. 39° 4’ N., Long. 77° 54’ W., altitude 526 m.], show that with a clear sky the total mid-day illumination on a horizontal surface varied from 10,000 foot-candles in June to 3600 foot-candles in January. It is less than the direct solar illumination on a normal surface from September to February, inclusive, but exceeds the latter from May to August, inclusive, for a period of from four to eight hours in the middle of the day. “ The illumination on a horizontal surface from a completely overcast sky may be half as great as the total illumination with a clear sky, and is frequently one-third as great. On the other hand, during severe thunderstorms at noon in midsummer, the illumination may be reduced to less than 1 per cent. of the il- lumination with a clear sky. “The ratio of sky-light illumination to total illumination on a horizontal surface at noon in midsummer varies from one-third to one-tenth. In midwinter it varies from one-half to one-fifth. “When the sky is clear, the twilight illumination on a horizon- tal surface falls to 1 foot-candle about half an hour after sunset, or when the sun is about 6° below the horizon.” Prevailing Color.—If I, is the initial intensity and J, the remaining intensity after penetrating the uniformly turbulent medium, the distance x, then, Rx L=Ihhe 7 where 327 aye ai (hu 1) This residual light, in turn, is scattered, and if J, is the in- R= ™ Monthly Weather Review, 42, p. 650, 1914. 546 PHYSICS OF THE AIR tensity of the light scattered by a single particle at the angle a from the direction of displacement k! Ie = I, 7A where pe (7 ai V/sinta, r D and kx k’ RA Hence, the ratio of intensity received to initial intensity, or I,/I,, is small both for very long and very short wave-lengths. Its maximum value occurs at Atm = kv, where 2 Be G\Cy ey Z) ~ AToJm \ 4 e or, if J) is uniform throughout the spectrum, Ian\4 = (27) ; In = Im (=) é A According to Abbot, Fowle, and Aldrich,?1® the mean energy intensities of J), in arbitrary units, are: = 0.390 0.42 0.43 045 047 0.50 055 0.60 0.70 I,= 3614 5251 5321 6027 6240 6062 5623 5042 3644 The luminous intensities would show greater contrasts, since the eye is more sensitive to the mid-region of the visible spectrum than to either end. From these values of J,, and the equation for the intensity of I,, it can be shown that the prevailing color of the clear sky, except when the sun is on or below the horizon, is neither violet nor red, but some intermediate color, generally blue, as we know by observation. Twilight Colors.—As the sun sinks to and below the horizon during clear weather, a number of color changes occur over large portions of the sky, especially the eastern and western. The phenomena that actually occur vary greatly, but the following may be regarded as typical, especially for arid and semi- arid regions: (a) A whitish, yellowish, or even bronze glow of 5° or 6° radius that concentrically encircles the sun as it approaches the horizon, and whose upper segment remains visible for perhaps 20 minutes after sundown. *° Annals Astrophys. Obsy., Smithsonian Institution, 3, p. 197, 1913. PHENOMENA DUE TO SCATTERING 547 The chief contributing factors to this glow appear to be (1) scattering, which is a maximum in the direction, forward and back, of the initial radiation, and (2) diffraction by the dust particles of the lower atmosphere. In both cases blue and violet are practically excluded, owing to the very long air paths. (b) A grayish blue circle that rises above the eastern horizon as the sun sinks below the western. This is merely the shadow of the earth. (c) A purplish arch that rests on the earth shadow and gradually merges into the blue of the sky at a distance of per- haps 10°, and also fades away as the arch rises. Obviously, any direct sunlight in the lower dusty atmosphere to the east must have penetrated long distances through the denser air, and thus have become prevailing red, while that reach- ing the higher atmosphere is still rich in blue and violet. Hence, the observer sees red light scattered from the first of these layers and blue to violet from the other, and thereby gets the effect of the superposition of the opposite ends of the visible spectrum, that is, purple. The effect is most pronounced when the luminous layers are seen more or less “end on.’’ Hence, the light is bright- est at the border of the earth shadow. The fact that the red component of the purple is from the lower atmosphere and the others from the higher is evident from the bluish crepuscular rays that often radiate, apparently, from the antisolar point— shadow streaks cast through the lower dust-laden air by western clouds or mountain peaks, often below the horizon. (d) A bright segment only a few degrees deep but many in extent that rests on the western horizon just after sundown. The lowest portion often is red and the upper yellowish. A product essentially of scattered light by the lower and dustier portions of the atmosphere, where the light before being scattered is al- ready reduced essentially to the colors seen. (e) A purple glow covering much of the western sky, reach- ing its maximum intensity when the sun is about 4° below the horizon and disappearing when it is about 6° below. The ex- planation of this purple glow in the western sky presumably is the same as that in the eastern sky as given above under (c). The crepuscular rays of this region, apparently radiating from the sun, often are greenish-blue. (f) A faint purple glow covering the entire sky when the sun is 6° or more below the horizon, and gradually disappearing 548 PHYSICS OF THE AIR in the west when the sun is 16° to 18° below the horizon. This appears to be due to secondary scattering of light from the il- luminated atmosphere far to the west. The foregoing descriptions, which, of course, apply equally to dawn, are by no means universally applicable. Indeed, the sky very commonly is greenish instead of purple, probably when the atmosphere is but moderately dust-laden. Furthermore, the explanations are only qualitative. A rigid analysis, even if the distribution of the atmosphere and its dust and moisture content were known—which they are not, nor are they constant—would be at least difficult and tedious. Duration of Astronomical Twilight. (Interval Between Times When the Upper Edge of the Sun is on and the True Position of Its Centre 18° Below the Horizon.) North latitude Date o° | 10°} 20° | 25° | 30° | 32° | 34°] 36° | 38° | 40° | 42° | 44° | 46° | 48°| 50° h.m.|h.m.}h.m,.|h.m.jh.m.|/h.m./h.m.|h.m./h.m./h.m.jh.m./h.m.}h.m.|h.m.|h.m. January I jl I4|t I5]t r8jx 2r]x 26/1 28/r 20/1 31] 34]1 37|1 4t|x 45/1 4olr 53|1 so Ir |r r4|r r4]z 18]/r 2rlr 25/1 27}1 20/1 31/1 33/1 36/1 30}1 43/1 37/1 S2lr 57 21 |£ 13]t 13}t 17/1 20/1 23/1 25/r 28/1 Zolr 32/1 34]x 38/1 4r|x 45|x 4olr 54 February Io|E 12/1 12j1 r5]x 18]r 22/1 24/r 26]r 28]1 30/1 33/1 36]1 39/1 43/1 47}r s2 IT {I LIjL L2)r I4jl I7]L 21/L 23/1 25/1 27/1 29]1 32/1 34\I 37/1 41/I 45/1 49 21 |f IO/T L1]t 13/r 16}x 2ol]r 22/1 24]1 26/1 28|r 31/1 33/1 36/1 golx 44lx 48 March I |r Lojr rrlx 13] 16}x 20] 2z]zr 23]x 25]r 28]1 30] 33]1 36/1 Zo|r 43]1 48 Ir |f OO/E IOjL 13]X 16]z xoOlx 2r}xr 23]r 25/1 28/1 30/1 33/1 36/1 30|1 43]r 48 21 |L OO}L LO}I 13]X I6]x 2o}x 22}r 24/1 26/14 29/1 31/r 34/1 37/1 4tlx 45|z 50 April Xo |r OO/r r1]r I4]q I7/x 21/x 23/r 25/1 27/1 30/1 33) 36]1 4golx qgalr golr 54 II |1 rolt IL] 15]x 18]x 22]r 24/1 27/1 30|1 33]1 36|1 30|r 43/1 48]1 54/2 00 21 |I Ir|t L2]t 16|r 20/1 24/r 27\1 29/2 32|/1 36/1 39/1 43|r 48]1 54]2 o1|/2 08 May I |t 12]r 13]r 18|r 22]r 27] Z0jr 33]1 36]1 3Z30]1 43]1 48]1 54/2 o1|/2 rol2 20 II |f 13] I4]I IO]T 24/1 Zolr 33]r 36]r 40/r 43]r 48]z 54l2 o1l|2 10/2 20]2 35 21 |1 13]t 15|1t 21/1 26|r 32/r 36/1 Z30]r 43}1x 48]1 54/2 o1]/2 rol2 20/2 35\2 58 June I [ft I4]x r6]x 23}r 28] 35/1 38]r 4z|t 46/1 52/1 sol2 o7]2 18]2 31l\2 sal.... II |r 15|q 17/1. 24/1 29/1 36/1 4o]r 44/1 4o|1 55]2 02/2 12/2 23/2 4o|3 rr. 2I |r 15] 1B]r 24/1 29/1 37/1 41]z 45/1 50/1 56/2 03]2 13/2 25/2 44]3 Io}. 3 2 2 July I ft IS]r m7]r 24/1 29/1 36/1 40/1 44]t 40|Ir 55]2 02/2 12/2 23]2 40 II |t rq4]t 16]r 23/1 28}r 35/1 38]1 q41|xt 46/1 s2}x sol2 o7]2 18/2 31 2I |E 13/2 I5|r 21|r 26] 32]r 36/1 39]1 43|r 48\1 54]2 o1j2 1ol2 21 Io}. 54]. -- 36|3 00 August I JE 13]/L L4]I IO} 24/1 30/1 33]1 36]/1 40] 44}x 48lr 54/2 o2|/2 r1oj2 20/2 35 II |£ 12/r 13]t 18] 22}r 27/1 30/r 33}1 36|r 39/1 43}1 48|1 54l2 o1l2 1oj2 20 21 |r II/r 12}q 16]x 20} 24/1 27\1 Z30]r 33]r 36/1 30]1 43]r 48\xr 542 ot|2 09 September I |r rolr r1j/t I4/I 18/r 22/1 24]1 27/1 30/1 33/1 36/1 39] 43|r 48]1 53]2 00 II |f OO/E II]L 1Z/T 7/1 2I/r 23)r 25/1 27/1 30]/r 33/1 36/1 30]1 44]1 4olr 54 21 |E OO|I IO/I 13]/~ 16]r 20/1 22]1 24]1 26]1 29/1 31/1 34|1 37/1 41/1 45|1 50 October I [I OO}t TOjI 13]1 16]r rO}x 21jr 23/1 25|r 28/1 3o]r 33]1 36/1 30/1 43/1 48 IX |Z O/T II/I 13/L LOL TO]X 21]xr 23/1 25/1 28/1 30/1 33}1 36|1 390|1 43\r 48 21 |X LO/L IIL 13]X 16]zr 20/1 22/1 24/1 26/1 28/1 31/1 33/1 36]1 golr 44\rt 48 November 1 |r I4r/r 12/r r4}1 17/1 21/r 23/1 25/1 27|1 29\r 32/I 34/1 38/1 41/1 46/1 49 IX |r L2|r 12]r r6jr 18]r 22/1 2q4/x 26/1 28/1 30/1 33/1 36/1 4olr 43/1 47\r 52 21 |L 13/1 13/1 17/1 20/1 24/1 26/1 28}1 30/1 32/1 35]/1 38\1 42/t 46/1 4olr ss December I |I I4}1 14/1 18/1 21/1 25/14 27/1 29/1 3r/r 33/1 36]1 4olr 44|I 47|1 52]1 57 TX JI I4/r 15}q 18/1 22/1 26/1 28/1 Zojr 32/1 34]r 37/1 41/1 45|1 4olr 53|1 so 21 |E IS|X 16/x IO]x 22/1 26/1 28] Zo]r 32/1 35]x 38]x gilt 45\1 4olr sali 59 PHENOMENA DUE TO SCATTERING 549 Duration of Civil Twilight. (Interval Between Times When the Upper Edge of the Sun is on and the True Position of Its Centre 6° Below the Horizon.) North latitude Date 10° | 20°| 25°] 30°| 32°| 34°) 36°| 38°] 40°! 42°| 44°| 46°} 48? | 50° January I 22 | 22 | 24 | 25 | 27 | 27 | 27 | 28 | 29 | 30 | 32 | 33 | 34 | 36 | 39 II 22 | 22 | 24 | 25 | 26 | 27 | 28 | 28 | 29 | 30 | 31 | 32 | 33 | 35 38 21 22 | 22 | 23 | 24 | 26 | 26 | 27 | 27 | 28 | 29 | 30 | 32 | 33 | 34 | 37 February 1 22 | 22 | 23 | 24 | 25 | 26 | 27 | 27 | 27 | 28 | 29 | 31 | 32 | 34] 35 Il 22 | 22 | 22 | 23 | 25 | 26 | 26 | 27 | 27 | 28 | 29 | 31 | 32 | 34 | 35 21 21 | 22 | 22 | 23 | 24 | 25 | 25 | 26 | 27 | 28 | 28 | 29 | 30] 32 | 33 March I 21 | 22 | 22 | 23 | 24 | 24 | 25 | 26 | 27 | 28 | 28 | 29 | 30] 31 | 33 II 21 | 21 | 22 | 23 | 24 | 24 | 25 | 26 | 26| 27 | 27 | 28 | 30] 31 | 33 21 21 | 21 | 22 | 23 | 24 | 24] 25 | 26 | 26 | 27 | 27 | 28 | 30 | 31 | 33 April I 21 | 21 | 22 | 23] 24 | 25 | 25 | 26 | 27 | 28 | 28 | 29 | 30] 32 | 33 Il 21 | 22 | 22 | 23 | 24 | 25 | 26 | 26 | 27 | 28 | 28 | 29 | 31 | 32 | 34 21 22 | 22 | 22 | 23 | 25 | 25 | 26| 27 | 28 | 28 | 29 | 30] 32 | 34 | 35 May I 22 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 28 | 29 | 30 | 32 | 33 | 35 | 36 II 22 | 22 | 23 | 24 | 26 | 27 | 28 | 29 | 29 | 30| 31 | 33 | 35 | 36] 39 21 22 | 22 | 24 | 25 | 27 | 28 | 28 | 29 | 30| 31 | 33 | 35} 36| 38} 41 June I 22 | 22 | 24 | 25 | 27 | 28 | 28 | 29 | 31 | 32 | 34 | 36] 37| 40] 43 II 22 | 23 | 24 | 26 | 28 | 28 | 29 | 30] 31 | 33 | 34| 36] 38 | 41 | 44 21 22 | 23 | 25 | 26| 28 | 29 | 29 | 30 | 31 | 33 | 34 | 36 | 38 | 42 | 44 July I 22 | 23 | 24 | 26 | 28 | 28 | 29 | 30| 31 | 33 | 34] 36] 38] 41] 44 II 22 | 22 | 24 | 25 | 27 | 28 | 28 | 29 | 31 | 32 | 34| 36 | 37] 40] 43 21 22 | 22 | 24 | 25 | 27 | 28 | 28 | 29 | 30| 31 | 33 | 35 | 36] 38] 41 August I 22 | 22 | 23 | 24 | 26 | 27 | 28| 29 | 29 | 30] 31 | 33 | 35 | 36] 39 Il 22 | 22 | 23 | 24 | 25 | 26| 27 | 28 | 28 | 29 | 30 | 32 | 33 | 35 | 36 21 22 | 22 | 22 | 23 | 25] 25 | 26| 27 | 28] 28 | 29 | 30| 32 | 34] 35 September 1 21 | 22 | 22 | 23 | 24] 25 | 26| 26] 27 | 28 | 28 | 29 | 31 | 32 | 34 II 21 | 21 | 22 | 23 | 24] 25 | 25] 26] 27 | 28} 28 | 29 | 30] 31 | 33 21 21 | 21 | 22 | 23] 24 | 24 | 25 | 26| 27 | 27 | 27 | 28 | 30] 31 | 33 October I 21 | 21 | 22 | 23 | 24] 24] 25 | 26| 26| 27 | 27 | 29 | 30] 31 | 32 II 21 | 22 | 22 | 23} 24 | 24] 25 | 26| 27 | 28 | 28] 29 | 30] 31 | 33 21 21 | 22 | 22 | 23 | 24] 25 | 25 | 26 | 27 | 28 | 28 | 29 | 30 | 32 | 33 November 1 22 | 22 | 22 | 23 | 25 | 25 | 26| 27 | 28 | 28 | 29 | 30 | 31 | 33 | 34 II 22 | 22 | 23 | 24 | 25 | 26] 27 | 28 | 28 | 29 | 30] 31 | 32 | 33 | 35 21 22 | 22 | 23 | 24| 26 | 26 | 27 | 28 | 28 | 29 | 30 | 32 | 33 | 34| 37 December 1 22 | 22] 24 | 25 | 26] 27 | 28| 28 | 29 | 30} 31 | 33 | 34] 35 | 38 II 22 | 22|24| 25] 27] 27 | 28| 28| 29 | 30| 32 | 33 | 34| 36] 39 21 22 | 23 | 24] 25 | 27 | 27 | 28 | 28 | 29 | 31 | 32 | 33 | 34 | 37 | 39 36 a0 POUYSiS OF THE ALR Relative Illumination Intensities. Source of illumination Intensity Hetie i eae Foot-candles Lenit lial, SUM essa: seca Wiciadsin eee: ced apaeiek ye eae 9,600.0 465,000.0 Twilight at sunset or sunrise....................-. 33-0 1,598.0 Twilight centre of sun 1° below horizon............. 30.0 1,453.0 Twilight centre of sun 2° below horizon............. 15.0 727.0 Twilight centre of sun 3° below horizon............. 7.4 358.0 Twilight centre of sun 4° below horizon............. 3.1 150.0 Twilight centre of sun 5° below horizon............. 1.1 53-0 Twilight centre of sun 6° below horizon............. 0.40 19.0 (End of civil) Twilight centre of sun 7° below horizon............. 0.10 5.0 Twilight centre of sun 8° below horizon............. 0.04 2.0 Twilight centre of sun 8°40’ below horizon.......... 0.02 1.0 Genithal Pull wnGOM ysis ch owes vote ae wae we aces aa 0.02 1.0 Twilight centre of sun 9° below horizon............. 0.015 0.75 Twilight centre of sun 10° below horizon............ 0.008 0.40 LATIN fg eset atie eatena gain AG aU ADS macdben awn aus 0.00008 0.004 Duration of Twilight—The duration of twilight, whether civil, that is, the time after sunset or before sunrise during which there is sufficient light for outdoor occupations, or astronomical, the time until or after complete darkness, varies with the amount of cloudiness and inclination of the ecliptic to the horizon. In the case of clear skies, civil twilight ends, or begins, when the true position of the sun (centre) is about 6° below the horizon, and astronomical twilight when it is about 18° below. The tables of twilight duration (pages 667 and 668) were computed by Kimball ?!* from the equation, — sina — sin @ sind cos @ cosd in which /: is the sun’s hour angle from the meridian, « the sun's altitude (negative below the horizon), 8 the solar declination, and ¢ the latitude. Twilight Illumination—The brightness of twilight changes slowly or rapidly, according as the sun is less or more, respec- tively, than about 4° below the horizon. The last table above, based on photometric measurements by Kimball and Thiessen,2'® gives the approximate value of a number of clear-sky, twilight and other natural illumination intensities on a fully exposed horizontal surface. ™ Monthly Weather Review, 44, p. 614, 1016. *® Monthly Weather Review, 44, p. 614, 1916. CHAPTER VIII. PHENOMENA DUE TO SCATTERING: SKY POLARIZATION THE polarization of sky light, discovered in 1811 by Arago,?® often is more or less modified by specular reflection from rela- tively large particles—cloud droplets, coarse dust, etc.—but in gerteral it results from the combination of primarily and second- arily scattered radiation. Condition of Primarily Scattered Light—As explained by Lord Rayleigh,®*° the light scattered from an incident beam by a gas molecule or other sufficiently small object is symmetrically distributed about the line of enforced motion of that particle as an axis, and completely polarized in the plane at right angles to this line. This follows directly from the fact that plane polar- ized light is merely light whose vibrations are all normal to the same plane—the plane of polarization. If, then, the incident beam is non-polarized, ordinary sunlight, for instance, the scat- tered light, therefore, will be completely polarized at right angles to the direction of incidence. and partially polarized in other directions. And, since the plane of polarization is fixed by the sun, observer, and point observed, it follows from Fig, 188 that the ratio polarized light _ sin? y total light 1 + cos? y where y=the angular distance of the point observed from the sun. That is, the polarization increases from zero in the direc- tion both of the sun and the antisolar point to a maximum (com- plete) midway between them, or normal to the incident rays. Condition of Secondarily Scattered Light——While. primary scattering of ordinary light by gas molecules and fine dust par- ticles accounts for a large part of the observed polarization and other phenomena of sky light, the non-polarized light that always exists in a greater or less amount at 90° from the sun; the luminosity—partially polarized—of shaded air masses; and the existence of neutral points (small regions whose light is not ™ Astronomie Populaire, 2, p. 99. *° Phil. Mag.. 41, p. 107, 1871. 551 a2 PHYSICS OF THE AIK polarized) are all due, as Soret 221 has shown, to secondary scat- tering. Tertiary and indefinitely higher scattering obviously also exist, but their effects are too small to justify consideration. To determine the nature and magnitude of secondary scat- tering, let O (Fig. 189) be the position of a particle shielded from direct insolation but otherwise exposed, and consider its effect on the total incoming sky light. Let the sun be on the horizon; let OX be parallel to the solar radiation, OZ vertical, and oy normal to the plane ZX; let m be any particle a unit distance from O; and let Om make the artgle ¢ with the vertical, and its projection on the plane XY the angle 9 with OX. Fic. 189. Z Y Intensity of secondarily scattered light. As the solar rays are non-polarized they may be treated as consisting of two parts of equal amplitude, J, say, polarized at right angles to each other. For convenience, let the displace- ments be parallel to OZ and OY, corresponding to polarization in the horizontal and vertical planes, respectively. On resolving the vertical amplitude into two components, one normal, the other parallel, to Om and the former (which alone is operative on the particle at O) in turn into components parallel to the X, ’, and Z axes, respectively. one finds that, l’y = — Ising cos? cosé l'y = — Ising cos¢d sing VRS 1 sin’ ** Archives de Sci. Phys. ct Nat., 20, p. 439, 1888. PHENOMENA DUE TO SCATTERING 553 Similarly, on resolving the horizontal amplitude into com- ponents normal and parallel to the plane OZm, and these in turn parallel to the three axes, one obtains, I" aby LZ ll 1 cos’ sin@ cos@ — 1 sin@ cosé@ = — / sind sin@ cosé 1 cos*@ sin’@ + 1 cos? 6 — lsin¢ cosé sin iol As a crude first approximation let the distribution of the atmosphere about O be equal in all upward directions and assume all parts to be equally illuminated. Further, let a per unit area be the number of particles that, if distributed over the hemi- spherical shell, would produce at O the same optical effect that actually obtains. Then, the total intensity components at O (found by squaring the amplitudes and integrating over the hemisphere) ar# given by the equations, t pe Ivy =2u ef : (sin’@ cos’s cos’@ + sin‘ sin’6 cos’@) sind dé dé 0 ° Iy = 2al? of ° sing do dé a pg Iz =20P 7 (sint4d + sin’ cos’? sin’6) sind db dé ° 10 Tr Ny {sl Tv [ (sin’¢ cos °¢ sin’@ + cost sint@ + 2 cos*@ sin’6 cos”8 + cos‘@) oO Or, Tx =27al? X 2/15 Ty =2rTalk? X 3/5 Iz =e27al? X 3/5 The intensity components of secondary diffusion at the centre of a sphere of uniformly distributed particles would be just twice the above, which, as stated, applies to the centre of a hemisphere. Since there is an appreciable amplitude along all three of the rectangular axes, it follows that secondary scattering sends 554 PHYSICS OF THE AIR more or less non-polarized light in all directions, and, therefore, prevents sky light from being completely polarized even at right angles to the direction of insolation—the direction of complete polarization by primary scattering. The above assumption that the light-scattering particles ‘are distributed equally along any upward radius from O obviously is not in close agreement with the actual distribution of the at- mosphere and its dust content as visible from any given point in it. Let this distribution be a(n +1) —an cos ¢ particles per unit area of the hemisphere instead of a, as previously assumed. Then, Ix = 2raP [2715 (n+ 1) — 1/16 | Iy = 27a? [3s (n + 1) — 17/748 n| Iz = 27a? [s/s (n+ 1) — 5/24 n |. If n= 12, that is, if the horizon is 13 times brighter than the zenith—a common condition, Ix =27al X 0.983 Iy =27al? X 3.55 Ig =2ral’ X 5.3 This distribution of intensities still gives non-polarized light in all directions. It also gives a preponderant amount of polar- ization, J:, in the horizontal plane, which neutralizes at certain places the polarization in the vertical plane due to primary scattering. The combination, then, of primarily and secondarily scat- tered light must produce a variety of polarization and other phe- nomena which necessarily vary with the altitude of the sun, dust content of the atmosphere, and state of the weather. Many ob- servational studies have been made of sky polarization and the facts found to agree with the above theoretical considerations. The principal facts are: (1) Part of the light from nearly all points in a clear sky is plane polarized, whatever the season, location, altitude of the sun, or other conditions. (2) The polarized portion of sky light, in turn, is divisible into two parts: (a) the positive, due to the first or primary scat- tering, in which the plane of polarization (plane normal to the PHENOMENA DUE TO SCATTERING 555 vibrations) is given by the source (sun), point of observation, and eye of the observer; and (b) the negative, due to secondary scattering, in which the plane of polarization is normal to that of the primary, and, therefore, because of the ring-like distribution of the atmosphere about any point on the earth’s surface, essen- tially horizontal. (3) Generally speaking, the percentage of polarized light along any great circle connecting the sun and the antisolar point increases from zero near either to a maximum midway between them, which, in turn, increases with the altitude of the point in question. (4) The point of absolute maximum polarization is in the solar vertical and ordinarily about go°, as stated, from the sun. (5) In general, the percentage of polarization decreases with the amount of light reflected through the sky, whether from the surface or from relatively large particles in suspension. It there- fore decreases with (a) percentage of snow covering; (b) per- centage of cloudiness; (c) dustiness, or anything that itself leads to an increase of dustiness, such as high winds, especially over arid regions, but everywhere during dry weather, strong vertical convection—hence, generally less during summer than winter— volcanic explosions of the Krakatoa type, etc. (6) The percentage of polarization generally increases with the wave-length of the light examined. (7) Even shaded masses of air, if exposed to sky radiation, emit perceptible amounts of polarized light. (8) Three small regions of unpolarized light, Babinet’s, Brewster’s and Arago’s neutral points, occur on the solar ver- tical; the first some 15° to 20” above the sun, the second about the same distance below it, and the third 20°, roughly, above the antisolar point. (9) As the sun rises above or sinks below the horizon the antisolar distance of Arago’s point increases from about 20° to, roughly, 23°; while the solar distance of Babinet’s point decreases from a maximum of, approximately, 20° to, perhaps, 18°, for a solar depression of 5° or 6°, and to 0°, as does also Brewster's point, as the zenith is approached. (10) When the upper atmosphere is greatly turbid, as it has often been after violent volcanic explosions, other neutral points, in addition to those above mentioned, are occasionally observed. PART IV. FACTORS OF CLIMATIC CONTROL. CuHapTeErR I. GENERAL SUMMARY. INTRODUCTION. THE following is a discussion of the principal factors, and the effects of their possible changes, that determine what the climate —the various averages and extremes of weather—of any given place shall be; a discussion of the physics of climate and not of its geographic distribution. Many people, relying on their memories alone, insist that our climates are now very different from what they used to be. Their fathers made similar statements about the climates of still earlier times, as did also their fathers’ fathers, as their several writings show, and so on through the ages; and the bulk of this testimony is to the effect that our climates are getting worse—evidence, per- haps, that flesh has always been heir to ills. The records, how- ever, of the past 100 years show that while there have been several slight and short-period (2 to 3 or 4 years) climatic changes during that time, that will be explained later, there have been no long-period ones. There is, though, much evidence that appre- ciable climatic changes of many years’ duration have occurred within historic times. This evidence, which many do not accept as conclusive, is found in the growth rings of old trees; the known changes in the areas and depths of several inland seas; the records in regard to the breaking up of ice in rivers and the opening of navigation ; and in a variety of other more or less significant facts. But whatever the truth in regard to historic climates may be, nothing is more certain than that during the geologic past there have been many and important climatic changes of great dura- tion. Innumerable fossil remains both in the Arctic and Antarctic regions tell of long ages when genial or, at least, temperate cli- mates extended well among the higher latitudes, while deep scor- 556 GENERAL SUMMARY 557 ings and ancient moraines, hundreds and even thousands of miles from the nearest existing glacier, tell quite as positively of other ages when vast ice sheets spread far into the zones we now call temperate; and this in spite of the fact (there is no good evi- dence to the contrary) that from the beginning of geologic rec- ords the surface temperatures have been distributed in the same general sense as at present—highest in equatorial regions and lowest about the poles. It must be remembered, of course, that the previous existence of comparatively mild climates in limited high latitude regions does not prove that the average temperature of the world as a whole was then much if any higher than it is now, but only that at those places the growing seasons were long enough to permit the then indigenous vegetation to mature its seeds (a much more rapid process in high latitudes owing to the greater length of the summer days than in low). and that the temperature of the lit- toral waters at the same places was such as to foster the local marine life. Both conditions conceivably might have been met by a free and therefore abundant oceanic circulation; or, perhaps, locally by protection from cold currents and drifting ice. Simi- larly, local glaciation doubtless often was produced by local causes. But, on the other hand, such extensive glaciation as sev- eral times obtained must have required a world-wide lowering of temperature. Indeed, no escape seems possible from the con- clusion that the world has experienced many a profound climatic change of both types, local and universal. When this series of climatic changes began there is no sure means of knowing, for the records, especially those of glacial origin, grow gradually fainter and more scanty with increase of geologic age, so scanty indeed as to force the belief that the effects of many of the earlier changes may long since have been completely obliterated. But, however this may be, it is well-nigh certain that from the time of the earliest known of these changes down to the very present the series has been irregularly continu- ous, and the end, one might reasonably assume, is not yet. Change after change of climate in an almost endless succession, and even additional ice ages, may still be experienced, though when they 58 PHYSICS OF THE AIR or shall begin (except in the case of the small and fleeting changes to be noted below), how intense they may be, or how long they shall last, no one can form the slightest idea. Clearly, then, a matter so fundamental as this, namely, the profound modification of those agencies that not only fashion the face of the earth, but also control its flora and govern its fauna, challenges and deserves every contribution that science can give to its complete or even partial elucidation. Hence it is that during the past fifty years, or more, numerous attempts. some of them invoking purely terrestrial and others extra-terrestrial or cosmical conditions, have been made to find a probable and at the same time an adequate physical basis for, or cause of, the known climatic changes of the distant past, and especially for those disas- trous changes that brought about the extensive glaciations that prevailed during the so-called ice ages. But nearly all the older suggestions and working hypotheses as to the cause of the ice ages have been definitely and finally abandoned, either because of inconsistency with known physical laws, or abandoned because they were found inadequate to meet the conditions imposed upon them by the results of the very investigations which, in many cases, they themselves had helped to inspire. FACTS OF CLIMATIC CHANGES. Among the more important facts with respect to climatic changes that appear to have been established and which presum- ably, therefore, must be met by any theory that would account for such changes, or explain specifically the origin of ice ages, are the following: ’ (a) The number of larger climatic changes were at least sev- eral, the smaller many. (b) The greater changes and doubtless many of the smaller also were simultaneous over the entire earth (there is accumulat- ing evidence in favor of this conclusion), and in the same sense; that is, the world became colder everywhere at the same time (climatically speaking) or warmer everywhere. (c) They were of unequal intensity. GENERAL SUMMARY 559 (d) They were of irregular occurrence and of unequal duration. (e) They, at least one or more, progressed with secondary variations of intensity, or with advances and retreats of the ice front. (f) There often were centres of maximum intensity—cer- tainly of ice accumulation and, doubtless, of other effects. (g) There were numerous local changes, suggestive of local causes. (1) They have occurred from early, probably from the earli- est, geological ages down to the present, and presumably will continue irregularly to recur for many ages yet to come. EXISTING FACTORS OF CLIMATIC CONTROL. Before attempting to find the probable cause or causes of cli- matic changes it will be convenient first to consider the present factors of climatic control, since the variations of some of these undoubtedly have produced such changes, even, presumably, some if not all of those great changes that brought on maxima and minima of glaciation. It is possible, of course, that neither singly nor collectively were the factors in question largely productive of the known changes in geologic climates, but as climate to-day is subject to a complex control, all terms of which are more or less variable, it is certain that the climates of that portion of the geologic past (the only portion that will here be considered) dur- ing which the earth had an atmosphere and a hydrosphere, were also subject to a similar complex control consisting certainly of all the factors that now are effective, and probably of no others. Hence, while it is conceivable that some one dominant cause such as marked and age-long changes in the solar constant, the passage of the solar system through a vast nebula, and the like, may have produced all the great changes of geologic climates, it seems far safer to assume that climate was then controlled essentially as climate is now controlled, and, therefore, that the climatic changes of the past, whatever their nature, intensity, or duration, were due to changes in those factors of climatic control which are now operative and known to be appreciably variable. The following list includes the principal factors of climatic control as they exist to-day: 560 PHYSICS OF THE AIR Chief Factors of Climatic Control. Name Character 1. Latirupe. 2. BRIGHTNESS OF Moon AND PLANETS. 3. SOLAR ‘‘CONSTANT” AT A Frxep DIstANCE. 4. Socar DISTANCE. 5. OBLIQUITY oF EcLIP- TIC. 6. PERIHELION PHASE. Invariable to within negligible amounts. Widely variable, but of no climatic significance, since they jointly produce a temperature varia- tion of only o.o001° €., roughly. Slightly variable. There are small irregular varia- tions of, roughly, a seven to ten day period and probably also a small variation coincident with the eleven year sun spot period. Other changes are not known, but may exist. Slightly variable, with a geologically negligible annual period due to eccentricity of the earth’s orbit; and also, for the same reason, both a 100,000 year, roughly (now about 80,000 year), secular period; and a much longer pseudo period. The larger of these eccentricity changes undoubtedly are of climatic impor- tance, but, as presently explained in the dis- cussion of Croll’s theory, there is strong evidence against the assumption that they were the chief or even an important factor in the production of glaciation. There also are slight monthly changes in the solar distance due to perturbations by the moon; and other slight changes owing to perturbations by the planets. In any case, however, the climatic effect due to perturbations is negligible—a maximum temperature change (computed) of, roughly, o.o1° C. Slightly variable. According to Sir John Herschel this variation never exceeds 1° 20’ on either side of the mean; and according to Newcomb, while the limit of variation is still unknown, the amount does not exceed 2° or 3° in a mil- lion years. In either case recent geologic cli- mates, including that of the last ice age, could not have been much influenced by this factor. Variable through a period of, roughly, 21,000 years. By virtue of this variation the winter of the southern hemisphere, say, may at one time occur, as it now does, at aphelion, and there- fore be long and cold; and again at perihelion, when it must be relatively short and mild. However, while this is a climatic factor which varies with the eccentricity of the earth’s GENERAL SUMMARY 561 Chief Factors of Climatic Control.—Continued. Name Character orbit, the period is too short to permit of its being considered as of great influence in the production of either the glacial or interglacial climates. 7. Extent AND Compo-| Probably somewhat variable through geological SITION OF THE AT- periods, otherwise relatively fixed. MOSPHERE. 8. VULCANISM. Irregularly variable. 9. Sun Spots. Greatly variable, with an 11-year period and probably other periods also, both longer and shorter. 10. Lanp ELevaTION. Greatly variable through geological periods, other- wise relatively fixed. 11. LAND) AND WaArTER| Greatly variable through geological periods, other- DistRIBuTION. wise relatively fixed. 12, ATMOSPHERIC Circu-| Largely dependent upon the distribution of land LATION, and water, upon land elevation and upon oceanic circulation, and, therefore, in many regions radically variable through geological periods. 13. OCEAN CIRCULATION. Greatly variable through geological periods, other- wise relatively fixed. 14. SURFACE CovERING. Greatly variable, in many places, from season to season; and also irregularly so from age to age. Since these are the factors that now control climate, it seems probable, as already stated, that even those profound: climatic changes with which the geologist is concerned were also caused by variations in one or more of these same factors. Indeed, certain of these factors—vulcanism, land elevation, and oceanic circula- tion—are known to have varied greatly during the several geologic periods, while the extent and composition of the atmosphere are suspected also to have changed. It will be well, therefore, to con- sider what effects such variations probably could have—in some cases surely have had—on our climates. This will constitute the first step in the problem of geologic climates. The next step must be taken by the geologist himself, for he must say whether the climatic changes possible through the supposed causes would be sufficient to account for the observed results, and especially whether the known climatic changes and the known variations in 562 PHYSICS OF THE AIR the factors here considered occurred at such times and places as to permit of the assumption that they were actually related in the sense of cause and effect. These several factors will be considered in the same order as above listed. 1. Since the wandering of the pole is limited to only a few metres, it is obvious that the resulting changes in the latitude produce no appreciable climatic effects. 2. The brightness of the moon, and also that of each of the several planets, is known in terms of that of the sun. On the assumption that the heat they supply is in proportion to their light it appears that at most their variations in phase and dis- tance can alter the temperature of the surface of the earth by no more than o.coo1® C., an amount that obviously is wholly negligible. CHAPTER II. PRINCIPAL ICE-AGE THEORIES. FACTORS 3, 4, 5, 6, 7. Ir would be easy to catalogue perhaps a score of more or less rational hypotheses in regard to the origin of the ice ages, the subject under which the greater climatic changes generally are discussed, and doubtless even a larger number that are quite too absurd ever to have received serious consideration, and to point out in each case the known and the suspected elements of weal- ness. But this would only be a repetition of what, in part at least, has often been done before and, therefore, could serve no good purpose. As already stated, only a few of these hypotheses still survive, nor do all of even these few really merit the following they have. Indeed, the only ones which still claim a large number of ad- herents are, respectively : 3. (a) The Solar Variation Theory—tThis is based on the assumption that the solar radiation (the only solar influence that by any known process can affect terrestrial temperatures and terrestrial climates) has waxed and waned, either cyclically or irregularly, through considerable ranges and over long inter- vals of time. This theory is seductively attractive—it looks so simple, so sufficient, and so safe from attack. There are, however, two criticisms of it that should be mentioned: (1) A change of the solar constant obviously alters all surface temperatures by a roughly constant percentage. Hence a decrease of the heat from the sun would, in general, cause a decrease of the interzonal tem- perature gradients; and this in turn a less vigorous atmospheric circulation, and a less copious rain or snowfall—exactly the re- verse of the condition, namely, abundant precipitation, most favorable to extensive glaciation. (2) If the solar variation theory is true it follows, as will be shown later, that great solar changes and extensive mountain building must usually, if not always, have been coepochal—a seemingly complete reductio ad absurdum. 563 564 PHYSICS OF “DH Uk 4, 5, 6. (b) Croll’s Eccentricity Theory.2—To make this theory clear, it is necessary to recall two important facts in regard to the earth’s movement about the sun: (1) That the orbital posi- tion of the earth at any season, that of midsummer, say, progres- sively changes at such rate as to describe a complete circuit in about 21,000 years. This necessarily produces a cyclic change of the same period in the length, temperature and contrast of the sea- sons, and also in the contrast between the climates of the two hemispheres, northern and southern. Thus, when aphelion is attained near midsummer of either hemisphere as it now is for the northern, that part of the earth enjoys comparatively long, temperate summers, and short, mild winters; while the opposite hemisphere, the southern at present, is exposed to short hot sum- mers, and long, cold winters. Hence, on such occasions, the cli- matic contrast between the two hemispheres is at a maximum, pro- vided, of course, that their ratios of land to water areas and other factors are the same. After about 10,500 years another maxi- mum contrast occurs, but with the climates of the two hemispheres interchanged, and so on indefinitely. (2) That the eccentricity of the earth’s orbit, never greater than 0.07, and at rare intervals dropping to nearly or even quite zero, undergoes irregular but always slow and long cyclic changes. In addition to a change usually, though not always, relatively small whose average period is roughly 100,000 years (now about 80,000), the eccentricity has also a far more irregular and generally much larger change whose average period, if a thing so irregular may be said to have a period, is three or four times as great. That is, as a rule, the eccentricity of the earth’s orbit is continuously large, within the limit 0.07, or continuously small, for a period of 200,000 years, more or less; but in each case unequally so, because of the shorter period and more regular changes. The first of these phenomena, the continuous change of the perihelion phase, varies, as explained, the relative lengths and intensities of the summers and winters of the northern and south- ern hemispheres; while the second, or the change of eccentricity of the earth’s orbit, varies the magnitudes of these contrasts. Now Croll’s theory of the ice ages assumes that when the earth’s orbit is very eccentric, or when the earth’s maximum solar distance differs largely from its minimum solar distance, ice will ? Phil. Mag.. 28. p. 121, 1864. and elsewhere. PRINCIPAL ICE-AGE THEORIES 565 accumulate to a great extent over that half of the globe which has its winter during aphelion. For some time this theory was very generally accepted, and it seems still to have many adherents, despite the destructive criticisms of Newcomb ® and Culverwell.4 The chief objections to Croll’s theory are: 1. That the assumption that midwinter and midsummer tem- peratures are directly proportional to the sun’s heat at these times is not at all in accord with observed facts. 2. That each ice-age (within a glacial epoch, when eccen- tricity is large) would be limited to a fraction of the secular perihelion period, 21,000 years, which, according to most geolo- gists, is too short a time. 3. That the successive ice ages would have occurred alter- nately in the northern and southern hemispheres instead of, as is generally believed to have been the case, in both hemispheres simultaneously. 4, That during the past 3,000,000 years there would have been fully 100 extensive glacial advances and retreats in each hemisphere (eccentricity having been rather large through much the greater portion of this time), a deduction unsupported by confirmatory geological evidence. 5. That the last extensive ice sheet in either hemisphere must have retracted roughly to its present limits some 80,000 years ago (eccentricity having become small about that time and remained small ever since) instead of less than gooo as Gerald de Geer ® has well-nigh conclusively demonstrated. As W. B. Wright ® puts it: “An almost fatal objection to Croll’s famous theory is the date it assigns to the end of the last Ice Age, which it places at some 80,000 years back. If, as De Geer seems to have clearly established, the ice-margin retreated north past Stockholm only about go00o years ago, this practically ex- cludes any possibility of a connection between glaciation and changes in the eccentricity of the earth’s orbit.” That changes in the maximum and minimum distances of the earth from the sun have affected our climates and that they will ® Amer. Jr. Sci., 11, p. 263, 1876; Phil. Mag., 17, p. 142, 1884. * Phil. Mag., 38, p. 541, 1894. * Geolog. Congress, Stockholm, 1910. °The Quaternary Ice Age, p. 451, Macmillan and Co., 1914. 37 566 PHYSICS OF THE AIR continue to affect them seem too obvious to admit of doubt, but that such changes ever were, or ever will be, of sufficient magni- tude to be the sole, or even the chief, cause of an ice-age appears to be flatly contradicted both by rigid deductions from the laws of physics and meteorology and by close observations of geo- logical. records. 2; 7. (c) The Carbon Dioxide Theory—This theory, advo- cated by Tyndall,’ Arrhenius,’ Chamberlin ® and others, is based on the selective absorption of carbon dioxide for radiation of different wave lengths, and on its assumed variation in amount. It is true that carbon dioxide is more absorptive of terrestrial than of solar radiations, and that it therefore produces a green- house or blanketing effect, and it is also probably true that its amount in the atmosphere has varied through appreciable ranges, as a result of volcanic and other additions on the one hand, and of oceanic absorption and chemical combination on the other. But it is not possible to say exactly how great an effect a given change in the amount of carbon dioxide in the atmosphere would have on the temperature of the earth. However, by bringing a number of known facts to bear on the subject it seems feasible to determine its approximate value. Thus the experiments of Schaefer 1° show that, at atmospheric pressure, a column of car- bon dioxide 50 centimetres long is ample for maximum absorp- tion, since one of this length absorbs quite as completely as does a column 200 centimetres long at the same density. Also the experiments of Angstr6m,"™ and those of E. v. Bahr,}” show that the absorption of radiation by carbon dioxide or other gas in- creases with increase of pressure, and, what is of great import- ance, that both qualitatively and quantitatively this increase of absorption is exactly the same whether the given higher pressure be obtained by compression of the pure gas to a column of shorter length, or, leaving the column unchanged, by the simple addition of an inert gas. According to these experiments, if a given column or quan- tity of carbon dioxide at a pressure of 50 mm. absorbs 20 per Phil. Mag., 22. p. 277, 1861. ® Phil. Mag., 41, p. 237, 1806. ° Ir. Geol., 7, Pp. 545, 1899. ” Ann. der Phys., vol. xvi, p. 93, 1905. " Arkiv for Matematik, Astron. och Fysik, vol. iv, No. 30, 1908. ™ Ann. der Phys., vol. xxix, p. 780, 1900. PRINCIPAL ICE-AGE THEORIES 567 cent. of the incident selective radiation, then, at 100 mm. it will absorb 25 per cent., at 200 mm. 30 per cent., at 400 mm. 35 per cent., and at 800 mm. about 38.5 per cent. Now, the amount of carbon dioxide in the atmosphere is equivalent to a column of the pure gas, at ordinary room tem- pefature and atmospheric pressure, of roughly 250 centimetres in length. Hence, as a little calculation proves, using the coefficients of absorption at different pressures given by the experiments of Angstrom and E. v. Bahr, just described, the carbon dioxide now in the atmosphere must, under its present vertical distribution, absorb radiation very approximately as would a column 475 centimetres long of the pure gas at the barometric pressure of 400 millimetres. But Schaefer’s experiments above referred to show that such a column would be just as effective an absorber as a cylinder two or three times this length, and, on the other hand, no more effective than a column one-half or one-fourth as long; in each case the absorption would be complete in the selective regions of the gas in question. Hence, finally, doubling or halving the amount of carbon dioxide now in the atmosphere, since this would make but little difference in the pressure, would not appreciably affect the total amount of radiation actually absorbed by it, whether of terrestrial or of solar origin, though it would affect the vertical distribution or location of the absorption. Again, as explained by Abbot and Fowle,'* the water vapor always present in the atmosphere, because of its high coefficients of absorption in substantially the same regions where carbon dioxide is effective, leaves but little radiation for the latter to take up. Hence, for this reason, as well as for the one given above, either doubling or halving the present amount of carbon dioxide could alter but little the total amount of radiation actually absorbed by the atmosphere, and, therefore, seemingly, could not appreciably change the average temperature of the earth, or be at all effective in the production of marked climatic changes. Nevertheless, in spite of the above objections, there appears to be at least one way (variation in absorption at levels above the water vapor) by which a change, especially if a decrease, in the ® Annals of the Astrophysical Observatory, Smithsonian Institution, vol. li, p. 172, 1908, 568 PHYSICS OF THE AIR amount of carbon dioxide in the atmosphere might affect tem- peratures at the surface of the earth. Hence, the above arguments do not perhaps fully warrant the idea that no such change was ever an appreciable factor in the production of an ice age. Further consideration of this particular point will be taken up later, after the discussion of certain other questions essential to a clear understanding of the subject. These three theories, then, of the origin of the ice ages, namely: The solar variation theory, the eccentricity theory, and the carbon dioxide theory, are the only ones that at present appear to have many adherents, and even these few seem more likely to lose than to gain in number and ardency of defenders. The first is strong only as, and to the extent that, other theories are disproved or shown to be improbable; the second has failed utterly under searching criticism; while the third has been sadly impaired. Cuapter III. 8. VULCANISM : THEORY. GASEOUS CONTRIBUTION TO THE ATMOSPHERE. ALTHOUGH a variety of gases, vapors and fumes are given off by active volcanoes, probably only one of them, carbon dioxide, is of sufficient volume and of such nature as to produce any effect on climate. Indeed, besides carbon dioxide, the only at- mospheric constituents that are especially effective in modifying the average temperature of the earth are water vapor and, prob- ably, ozone. The former of these, or water vapor, except as locally modified by temperature and topography, including loca- tion and extent of land and sea, presumably has varied but little in amount since the formation of the earliest oceans, while a prac- tically continuous series of animal fossils from beyond the earli- est paleozoic age to the present is abundant proof of an equally continuous supply of free oxygen. Hence, in an effort roughly to determine what climatic changes might have been caused by variations in the atmosphere, whether produced by vulcanism or otherwise, it would appear that only the amount of carbon dioxide need be considered. But this has been discussed above, to some extent, and will be taken up again in its proper order. Suffice it to anticipate here the general conclusion that while variations in the amounts of carbon dioxide in the atmosphere may have somewhat modified our climates, it probably never was the controlling or even an im- portant factor in the production of any one of the great climatic changes of the past, nor can be of any great climatic change the future possibly may bring. “4 CHANGE IN SURFACE COVERING. The effect of volcanic ejecta, whether in the nature of ash, or lava flow, is to convert the region so covered into a temporary desert, even where rain may be abundant, and, therefore, to sub- ject it to an increased range of temperature extremes, and at the same time, if in a previously vegetated region, slightly to increase its average temperature, owing to decrease of evaporation. How- 569 570 PHYSICS OF THE AIR ever, it seems highly probable that the areas so deprived of vege- tation were never at any one time sufficiently large to produce marked effects upon the climate of the world as a whole, nor indeed anywhere except over themselves and within their own immediate neighborhoods. Hence, in considering universal cli- matic changes, it seems safe to neglect this special effect of volcanic activity. DUST IN THE UPPER ATMOSPHERE. It was suggested a number of years ago by the cousins P. and F. Sarasin !4 that the low temperature essential to the glaciation of ice ages was caused by the absorption of solar radiation by high volcanic dust-clouds. But the idea that dust of this nature, when scattered through the atmosphere, may lower the tempera- ture of the surface of the earth was already old, having been advanced at a much earlier date, in fact, long before even the existence of ice ages had been suspected, much less attempts made to find their cause. Thus, in May, 1784, Benjamin Franklin (and he may not have been the first) wrote as follows: During several of the summer months of the year 1783, when the effects of the sun’s rays to heat the earth in these northern regions should have been the greatest, there existed a constant fog over all Europe, and great part of Nerth America. This fog was of a permanent nature: it was dry, and the rays of the sun seemed to have little effect toward dissipating it, as they easily do a moist fog arising from the water. They were indeed rendered so faint in passing through it that, when collected in the focus of a burning-glass, they would scarce kindle brown paper. Of course, their summer effect in heating the earth was exceedingly diminished. Hence the surface was early frozen. Hence the first snows remained on it unmelted, and received con- tinual additions. Hence perhaps the winter of 1783-4 was more severe than any that hap- pened for many years. . The cause of this universal fog is not yet ascertained. Whether it was adventitious to this earth, and merely a smoke proceeding from the con- sumption by fire of some of those great burning balls or globes which we hap- pen to meet with in our course round the sun, and which are sometimes seen to kindle and be destroyed in passing our atmosphere, and whose smoke might be attracted and retained by our earth; or whether it was the vast quantity of smoke, long continuing to issue during the summer from Hecla, in Iceland, and that other volcano which arose out of the sea near that island, which “ Verhandlungen der Naturforschenden Gesellschaft in Basel, vol. xiii, p. 603, 1901. VULCANISM: THEORY 571 smoke might be spread by various winds over the northern part of the world, is yet uncertain. It seems, however, worthy the inquiry, whether other hard winters, re- corded in history, were preceded by similar permanent and widely-extended summer fogs. Because, if found to be so, men might from such fogs con- jecture the probability of a succeeding hard winter, and of the damage to be expected by the breaking up of frozen rivers in the spring; and take such measures as are possible and practicable to secure themselves and effects from the mischiefs that attend the last.’® The idea, then, that volcanic dust may be an important factor in the production of climatic changes is not new, though by what physical process it could produce this result apparently has not formerly been explained, nor has the idea previously been spe- cifically supported by a long series of direct observations. This is not to be taken as a criticism of the above-mentioned pioneer paper by the Sarasin cousins, for indeed the arguments, now easy, necessary to show that it must be a factor, were at that time impossible, because the observations upon which these arguments largely are based had not then been made. In fact, the absorption of radiation by volcanic dust, by which they supposed the earth’s temperature to be lowered, can now be shown to be, of itself alone, not only insufficient, but even productive, in all probability, of the opposite effect—of a warming instead of a cooling of the earth’s surface. To make this point clear: Consider a thin shell of dust about the earth and let J be the average intensity of the normal com- ponent of solar radiation on it, and Je the intensity of the radia- tion reaching the earth. Further, let a be the average coefficient of absorption of the dust shell for solar radiation, a coefficient independent, presumably, of intensity, and b its coefficient of absorption for terrestrial radiation, also independent of intensity. Obviously, in the case of equilibrium, all the energy absorbed by the dust is radiated away; half of it, very approximately, to the earth and half of it to space. Hence, starting with J as the in- tensity of the solar radiation normally incident per unit area and unit time, upon the dust layer, we have, ° h=t}1+ko-at (A.) *See Sparks's “ Life of Benjamin Franklin,” vol. vi, 455-457 (cited in Proceedings of the Amer. Phil. Soc., vol. xlv, p. 127, 1906.) 572 PHYSICS OF THE AIR beaferde (Eyton (Hf Now 0 is positive, and, therefore, k is also positive. Hence in which I I + —a = according as fs ( ) < , ing < The conclusion, therefore, is: The total amount of radiation reaching the carth is increased, unchanged, or decreased owing to absorption by the surrounding dust layer according as the dust’s coefficient of absorption of terrestrial radiation is greater than, equal to, or less than its coefficient of absorption of solar radiation. Actually nearly all, both of the incoming and oi the outgoing radiation, is oblique, but as equal portions of each pass through equal thickness of the shell it follows that the conclusion reached for normal radiation applies also for the oblique radiation. While this general conclusion is self-evident, and, therefore, might have been stated without the use of symbols, nevertheless equation (.1), to be used later on, will be found convenient in attempts to obtain quantitative values. Now, in the case of many, if not all, rocky materials, such as make up the particles of volcanic dust, the coefficient of absorp- tion is much greater for terrestrial radiation than for solar radia- tion,?® or, in terms of the above symbols, in the case of volcanic dust, b is greater than a. Hence, so far as mere absorption of radiation is concerned, the only action mentioned by the cousins Sarasin, a veil of volcanic dust, in all probability, would slightly increase and not, as they supposed, decrease the average tem- perature of the earth. But, then, absorption is not the only effect of a dust veil on radiation; reflection and scattering both are important and must be fully considered. These actions, however, reflection and scattering, depend fundamentally upon the ratio of the linear dimensions of the particles concerned to the wave length of the incident radiation, and, therefore, before undertaking to discuss them in this con- nection, it will be essential to determine the approximate size of the individual grains of floating volcanic dust, and also the *Coblentz, Publications of Carnegie Institution of Washington, Nos. 65 and 97. VULCANISM: THEORY Bys average wave lengths in the regions of the respective maximum intensities of solar and terrestrial radiation. It will be desirable, also to consider whether or not, and, if so, how, dust of any kind can remain long suspended in the atmosphere. And this point, involving the structure of the atmosphere, will be examined first, since, obviously, the longer the dust can float the more important, climatically, it may have been in the past and in the future may again become. Physical Structure of the Atmosphere.—The atmosphere is divisible into the stratosphere and the troposphere; or the iso- thermal region and the convective region; or, in other words, that region, in middle latitudes at and beyond about 11 kilometres above sea level, where, because of freedom from vertical convec- tion, ordinary clouds never form, and that other, or turbulent, stormy region below this level, which is frequently swept by clouds and washed by snow and rain. The physical reason for or cause of the existence of the isothermal region is well known (see Chapter III, Part I) and is such that it is certain that ever since the earth was warmed by solar radiation, as at present, rather than by internal heat, the temperature of its atmosphere beyond a certain level, whatever its composition, must have varied but little, as it now varies but little, with change of altitude, and therefore that this region must then have been free, as it now is free, from clouds and condensation. Obviously, then, this peculiar physical structure of the atmosphere is of great importance in determining the duration of dust suspension for, clearly, any volcanic or other dust, that by whatever process is gotten into and distributed through the isothermal region where there are no clouds or other condensation to wash it out, must drift about until gravity, overcoming the viscosity of the atmosphere, by slow degrees shall have pulled it down to the region of clouds and storms, where it becomes moisture laden and quickly brought to the earth. How long such process must take depends, of course, upon a number of things, among which the size of the particles is vitally important. Size of Volcanic Dust Particles.—For two or three years after the eruption of Krakatoa, in 1883, also after the eruption of Mont Pelé and Santa Maria, in 1902, and again after the erup- tion of Katmai, in 1912, a sort of reddish-brown corona was 574 PHYSICS OF THE AIR often, under favorable conditions, observed around the sun. It was from Io to 12 degrees wide, and had, to the outer edge, an angular radius of from 22 to 23 degrees. This phenomenon, known as Bishop’s ring, clearly was a result of diffraction of sun- light by the particles of volcanic dust in the upper atmosphere, and therefore it furnished a satisfactory means for determining the approximate size of the particles themselves. The subject has been rather fully discussed by Pernter,’7 who finds the diameter of the particles, assuming them spherical, to be approximately 185 x 10% cm., or 1.85 microns. The equation used has the form, page 531. m 2 =z sind r= in which ¢ is the radius of the dust particle, A the wave length of the diffracted light (here taken as 571x107 cm., or 0.571 micron), 6 the angular radius of the ring, and m a numerical term which for the outer edge of the ring, and successive minima of brightness, has the approximate values, see page 532. ; (n + 0.22) in which n= 1, 2, 3, ..., respectively. Now, since the width and angular dimensions of Bishop’s ring, as seen at different times and different places, have varied but little, the above value, 1.85 microns, may provisionally be assumed to be the average diameter of those particles of volcanic dust that remain long suspended in the atmosphere. Time of Fall—The steady or terminal velocity of a minute sphere falling in a fluid, assuming no slip between fluid and sphere is given by Stokes’s *§ equation. Sepp l Se Pe) in which V is the velocity of the fall, g the acceleration of gravity, r the radius of the sphere, o the density of the sphere, p the density of the fluid, and » its viscosity. However, there always is slip, so that the actual velocity of fall is, according to Cunningham,?® r= Fe (S2)(04 8) " Met, Zeit., 6, p. 401, 1880. * Math. and Phys. Papers, vol. iii, p. 59. * Proc. Roy. Soc., 83 A, p. 357, 1910. VULCANISM: THEORY 575 in which / is the free path of the gas molecules, 4 a constant, and the other symbols as above explained. _ Obviously, J, other things being equal, is inversely propor- tional to the gas density, or pressure, if temperature is constant, and directly proportional to the absolute temperature if the pres- sure is constant. Hence, ee pot | CP B wah?) ee) © in which B is a constant for any given temperature, p the gas pressure, or, if preferred, barometric height. Now, a series of valuable experiments by McKeehan 2° has shown that for 21” C., and when p is the pressure in terms of millimetres of mercury, B = .0075 + 3. The value of », for dry air, is also closely known from the work of a number of experimenters, all of whom obtained sub- stantially the same results. From a careful review of the whole subject, Millikan 21 finds that at 23° C., =F Es, u = 1824x10 + ( more recently 18226 x 10 and that, for the temperature, ¢, Centigrade, a= see 10’, approximately, where 7 = 273.11 +t. It is easy, therefore, to compute, by the aid of equation (1), the velocity of fall of volcanic dust, assuming gravity to be the only driving force. There is, of course, radiation pressure, both toward and from the earth, as well as slight convective and other disturbances, but presumably gravitation exerts the con- trolling influence. The following table of approximate velocities and times of fall for volcanic dust was computed by substituting in equation (1) the given numerical values, namely : ” Phys. Rev., 33, p. 153, IQTI. “Ann. der Phys., 41, p. 759, 1913. 576 PHYSICS OF THE AIR g = 981 sec. Yr == .000092 cm. « — 2.3, approximate density of Krakatoa dust. p = 0, being negligible relative to g. # —1416 X 10°, appropriate to -55° C., roughly the temperature of the isothermal region in middle latitudes. B—.0056, appropriate to -55° C. p = millimetres barometric pressure. According to this table, it appears that spherical grains of sand of the size assumed, 1.85 microns in diameter, would require about one year to fall from only that elevation already reached by sounding balloons, 35.08 kilometres,?* down to the under sur- face of the isothermal region, at the height of 11 kilometres. Velocity and Time of Fall Height in Barometric | Centimetres | Seconds kilometres pressure | per second per centimetre nee Save = =e a | Sn eeeeseel —— caer: 40 ! 1.84 | 1.0215 0.979 30 . 8.63 | 0.2414 4.143 20 ; 40.99 | 0.0745 . 13.427 15 89.66 0.0503 i 19.874 rit 168.00 | 0.0408 24.492 oO 760.00 0.0258t 38.760f * Isothermal level of middle latitudes. + Temperature 21° C. As a matter of fact, volcanic dust, at least much of it, con- sists of thin-shelled bubbles or fine fragments of bubbles, and, therefore, must settle much slower than solid spheres, the kind above assumed. Indeed, the finest dust from Krakatoa, which reached a great altitude, probably not less than 40 nor more than 80 kilometres, was from two and a half to three years in reach- ing the earth, or, presumably, as above explained, the upper cloud levels. At any rate, volcanic dust is so fine, and the upper atmosphere above 11 kilometres so free from moisture and vertical convec- tion, that once such dust is thrown into this region, as it obviously was by the explosions of Skaptar Jokull and Asamayama in 1783, Babuyan in 1831, Krakatoa in 1883, Santa Maria and: Pelé in 1902, Katmai in 1912, and many others, it must require, as a rule, because of its slow descent, from one to three years to get ” L'Astronomiec, 27, p. 329, 1013. VULCANISM: THEORY B97 back to the earth. And this clearly has always been the case since the earth first assumed substantially its present condition, or had a cool crust and a gaseous envelope. Obviously, then, it is only necessary to determine the present action of such dust on incoming solar and outgoing terrestrial radiation in order to reach a logical deduction as to what its effect on climate must have been in the past if, through extensive volcanic activity, it ever more or less continuously filled the upper atmosphere for a long or even considerable term of years, as may have happened several times during the geologic ages. And the same conclusion in regard to the possible effect of dust on the climates of the past clearly applies with equal force to the climates of the future. Action of Dust on Solar Radiation.—Since solar radiation at the point of maximum intensity has a wave-length less than 5x 10° cm.,?8 or half a micron, and since fully three-fourths of the total solar energy belongs to spectral regions whose wave- lengths are less than 10 cm., or one micron, it follows that the cubes of solar wave-lengths must, on the whole, be regarded as small in comparison with the volume of a volcanic dust particle, the diameter of which, as above explained, is nearly 2 microns. Hence, in discussing the action of volcanic dust on incoming solar radiation, we can, with more or less justification, assume the particles to be opaque through reflection or otherwise, and, therefore, use Rayleigh’s ?* arguments as applied to a similar case. Let r be the radius of the particle, m the number of particles per cubic centimetre, and a the projected joint area of these par- ticles. Then, for random and sparsely scattered particles, a = nt? Hence, on dividing a plane parallel to the wave-front into Fresnel zones, it is seen that for each centimetre traversed the amplitude of the radiation is reduced in the ratio of 1 to 1 — mmr’. Therefore, if A is the initial amplitude, and dz the amplitude after passing through + centimetres of the uniformly dusty region, assuming nmr? to be only a small fraction of a square centimetre, —yr rv 2 =A(i—nzp)t = Ae PT T* * Abbot and Fowle, Annals Astrophys. Obsy., Smithsonian Inst., vol. ii, Pp. 104, 1908. * Phil. Mag., 47. P. 375, 1899. 578 PHYSICS OF THE AIR Further, if J is the initial and Jz the final intensity, then in jg Oe Hence, in the case of volcanic dust, where, as already ex- plained, r = 92 x 10° centimetre, 2, Ax = Ae Pe* (92)? 1 and Te = Ie7 207% (92)? 10 * Presumably, the particles of dust are not absolutely opaque and, therefore, /< probably is a little larger than the value here given, though even so this value is at least a first approximation. Action of Dust on Terrestrial Radiation.—Terrestrial radia- tion, at the point of maximum intensity, has a wave-length of roughly, 12 x 10+ centimetres, and, therefore, the wave-lengths of nearly all outgoing radiation are large in comparison with the diameters of those volcanic dust particles that remain long sus- pended in the atmosphere. Hence, while such particles abun- dantly reflect solar radiation, as is obvious from the whiteness of the sky when filled by them, they can only scatter radiation from the earth, according to the laws first formulated by Rayleigh,?® whose papers must be consulted by those who would fully under- stand the equations which here will be assumed and not derived. Let & be the intensity of terrestrial radiation as it enters the dusty shell, or as it enters the isothermal region, and Ey its in- tensity after it has penetrated this region, supposed uniformly dusty, a distance y centimetres; then, remembering that the dust particles are supposed to be spherical, according to Rayleigh, Ey = Ee hY where h = 247°n Ce aT a (K’ +2Ky a in which 2 is the number of particles per cubic centimetre, K the dielectric constant of the medium, K’ the dielectric constant of the material of the particles, T the volume of a single particle, and A the wave-length of the radiation concerned. * Loc. cit. VULCANISM: THEORY 579 But K=1, and, since the dust seems generally to be a kind of glass, it may not be far wrong to assume that K’=7. Hence, with these values, goss h = 1175n =>, nearly. A Relative Action of Dust on Solar and Terrestrial Radiation.— To determine whether such a dust layer as the one under discus- sion will increase or decrease earth temperatures it is necessary to compare its action on short wave-length solar radiation with its action on long wave-length radiation from the earth. In the case of solar radiation, as explained, Ges Te 207% (92)? 107 Clearly, then, the intensity of the solar radiation is reduced in the ratio of I to e, or Ix. IT =1:e 12 : 88) ax si when += ye. centimetres = = kilometres, approximately. 10 2a (63 a On the other hand, in the case of terrestrial radiation, where 2 le 3, Ey = Ee UIT" Gas the intensity is reduced in the ratio of 1: ¢, or Ey:E=1:%e, when 7A 4 OS ag? centimetres, in which T= 4 x (92)3 10778 and A” = 12x10 %, the region of maximum intensity. Hence, y= we kilometres, approximately. Therefore, finally, yi x = 30:1, roughly, 580 PHYSICS OF THE AIR or the shell of volcanic dust, the particles all being the size given, is some thirty-fold more effective in shutting solar radiation out than it is in keeping terrestrial radiation in. In other words, the veil of dust produces an inverse greenhouse effect, and hence, if the dust veil were indefinitely maintained, the ultimate equilibrium temperature of the earth would be lower than it is when no such veil exists. The ratio 30 to 1 in favor of terrestrial radiation in its ability to penetrate the dusty atmosphere may at first seem quite too large, but it should be remembered that the dust particles in ques- tion are to terrestrial radiation in general as air molecules are to solar radiation, in the sense that in both cases but little more than mere scattering takes place. Now it is obvious that the dust particles are many fold more effective in intercepting solar radiation, which they appear to do chiefly by reflection, than is an equal mass of air molecules which simply scatter it; and hence it may well be that the above theoretically determined ratio, 30 to 1, is no larger than the ratio that actually exists, or, at any rate, that it is of the correct order. It must be distinctly understood that certain of the assump- tions upon which the foregoing is based—uniformity of size, complete opacity andsphericity of the dust particles, for instance— are only approximately correct, but they are the best that at pres- ent can be made, and doubtless give at least the order of magni- tude of the effects, which, indeed, for the present purpose, is quite sufficient. It may be well, in this connection, to call attention to the fact that the excessively fine dust particles, or particles whose diam- eters are half, or less, the wave-length of solar radiation (region of maximum intensity), and which, therefore, remain longest in suspension, shut out solar radiation many fold more effectively than they hold back terrestrial radiation. This is because both radiations, solar and terrestrial, are simply scattered by such small particles, and scattered in proportion to the inverse fourth power of the wave-length. Indeed, since the ratio of solar wave-length to terrestrial wave-length (region of maximum intensity in both cases) is, roughly, 1 to 25, and the ratio of their fourth powers as I to 39x 10%, about, it follows that the interception of out- going radiation by the very finest and therefore most persistent VULCANISM: THEORY 581 dust is wholly negligible in comparison with its interception of incoming solar radiation. Number of Dust Particles—The intensity of the solar radia- tion, J», after it has passed through + centimetres of the dust layer of the atmosphere, is given, as previously explained by the equation, Tx = Ie 27% (92)? X 10"? But, according to numerous observations made during the summer and fall of 1912, when the solar radiation had passed entirely through the dust layer at such an angle that it met, roughly, twice as many dust particles as it would have met had it come in normally, or from the zenith, it was reduced by about 20 per cent. That is to say, under these conditions In = 0.8 J. Hence 10 = Be2"*™ (92)? io Let 2+ = 2N. the total number of particles passed in a cylinder of one square centimetre cross section. Then 12 10 = get (92)? 10 | Hence the number of particles in a vertical cylinder of one square centimetre cross section is given, roughly, by the equation N = 34 X 104, Temperature Correction Due to Dust Radiation—With the number and size of the dust particles known it is easy to determine at least an upper limit to the effect of the direct radiation of the particles themselves on the temperature of the earth. The temperature of the dust particles, obviously, is very nearly that of the upper atmosphere in which they float, that is, approxi- mately —55° C., or 218° C. absolute. Also, as previously ex- plained, the quantity of radiation from the atmosphere below the isothermal region is substantially that which would be given off by a full radiator at 256° C. absolute. Now assume the dust particles to be concentrated side by side on a common plane, and, further, assume them to be full radiators —conditions that would raise their effect to the theoretical upper limit. Let E be the intensity or quantity per square centimetre 38 582 PHYSICS OF THE AIR of the outgoing planetary radiation, and D the intensity of the incoming dust radiation. Then E:D = (256)! : a(218)4, in which a is the projected area of all the particles in a vertical cylinder of one square centimetre cross section. But a = 347 104(92)"10 7? =9 X10 %, Hence E=211D. Now, when the radiation D is absorbed by the lower atmos- phere, it follows that its temperature will be so increased that, when equilibrium is reached, the intensity of its new radiation will be to that of its old as 212 is to 211. Hence AT the ef- fective temperature increase of the lower atmosphere, is given by the equation (256 + AT)! _ 212 (256)4 271" from which AT = 0°.3C. But, as stated above, the dust particles, presumably, are not full radiators, and, therefore, probably one-fifth of a degree C. is as great an increase in temperature as may reasonably be expected from this source. But this icrease, 0.2° C., is small in compari- son with the decrease, 6° C. to 7° C., caused by the interception of solar radiation, already explained. Hence it appears reasonably certain that the sum total of all the temperature effects produced by volcanic dust in the upper atmosphere, equal in amount to that put there by the explosion of Katmai, must be, if long continued, a lowering of the surface temperature by several degrees C. Total Quantity of Dust—Let nx =2N, the total number of particles passed in a cylinder of one square centimetre cross sec- tion. Then, as explained above, ‘mit 10 = getN= (92)? X 10 Hence N = 34 X 108 roughly = number of particles in a vertical cylinder of one square centimetre cross section. VULCANISM: THEORY 583 If A is the entire area of the earth in square centimetres, then the total number of dust particles, assuming the dustiness every- where as just found, is NA = 1734 X 10%, But the radius of each particle is 92 x 10° cm., and its volume, assuming it spherical, 33 x 107% cubic centimetre. Hence the total volume of the dust, assuming the particles spherical, is equal, roughly, to a cube 179 metres, or about 587 feet, on the side, an amount that certainly is not prohibitively large. As just stated, the total quantity of dust sufficient,as explained, to cut down the intensity of the direct solar radiation by 20 per cent., and therefore, if indefinitely continued, capable, presumably, of producing an ice age, is astonishingly small—only the 174th part of a cubic kilometre, or the 727th part of a cubic mile, even assuming that the particles are spherical. Since, however, in large measure, the particles are more or less flat, it follows that the actual total mass of the dust necessary and sufficient to reduce the intensity of direct solar radiation by 20 per cent. probably is not more than the 1500th part of a cubic mile, or the 350th part of a cubic kilometre. Hence, even this small amount of solid material distributed once a year, or even once in two years, through the upper atmos- phere, would be more than sufficient to maintain continuously, or nearly so, the low temperature requisite to the production of an ice age; nor would it make any great difference where the vol- canoes productive of the dust might be situated, provided only that it was driven high into the isothermal region or stratosphere, since, from whatever point of introduction, the winds of the upper atmosphere would soon spread it more or less evenly over the entire earth. A little calculation shows, too, that this quantity of dust yearly, during a period of 100,000 years, would produce a layer over the earth only about half a millimetre, or one-fiftieth of an inch, thick, and therefore one could hardly expect to find any marked accumu- lation of it, even if it had filled the atmosphere for much longer periods. Whether periods of explosive volcanic activity—and in this case, since the locality of the volcano is a matter of small im- portance, the whole earth must be considered—occurred at such 584 PHYSICS OF THE AIR times as to synchronize with the ice ages and with other epochs of great climatic change is, of course, a problem for the geologist to solve. However, this much appears well-nigh certain: Since the beginning of reliable records, say 160 years ago, the average temperature of the earth has been perceptibly lower, possibly as much as 0.5° C., than it would have been if during all this time there had been no volcanic explosions violent enough to put dust into the isothermal region of the atmosphere. Similarly, on the other hand, if, during this period, violent volcanic explosions had been three or four times more numerous than they actually were, the average temperatures probably would have been 1° C. to 2° C. lower, or low enough, if long continued, to depress the snow line roughly 300 metres, and thus to begin a moderate ice age. Effect of Dust on the Interzonal Gradient.—lf I is the initial intensity of radiation of a given wave-length and al its intensity after passing a unit distance through a homogeneous absorbing or scattering medium, then its remaining intensity, after traveling 1 units distance through this medium, will be J a" But u, in the case of solar radiation passing through the atmosphere, is pro- portional to the secant of the zenith distance of the stun; and from this in turn it is evident that, in general, variations of dust in the upper atmosphere must change the temperatures of the high lati- tude regions more than these within the Tropics. Hence, an increase of such dust would steepen the interzonal temperature gradients, strengthen the winds, and make heavier the rain and snowfall, a condition favorable to extensive glaciation. Of course, the increased circulation would, in turn, more or less reduce the new temperature difference, but, nevertheless, a portion, at least, of the increase clearly would remain, and with it the correspond- ing increases of wind and rain. CHAPTER IV. VULCANISM : OBSERVATIONAL. Ir will be interesting and profitable now to consider the sup- plementary portion of the theory of the relation of vulcanism to climate. That is, to consider the observational evidence, pyrheli- ometric or other kind, bearing on the effect of volcanic dust on solar radiation, and thus obtain some idea of those absolute values essential to even a rough determination of the climatic consequence of volcanic dust in the high atmosphere. Pyrheliometric Records.—Direct measurement of solar radiation by means of the pyrheliometer, an instrument that measures the total heat of sunshine, shows marked fluctuations from year to year in the intensity of this radiation as received at the surface of the earth. This subject has been carefully studied by Dr. H. H. Kimball,?° of the United States Weather Bureau, who prepared the accompanying table, graphically represented by Fig. 190. Since the yearly values are given in terms of the average value for the entire period, it is obvious that percentages of this average do not represent the full effect of the disturbing causes, of which volcanic dust certainly is the chief. The following table of intensities was computed from observa- tional data obtained at the following stations: Montpellier, France, monthly means (noon values).. 1883-1900 Pavlovsk, Russia, monthly maxima............--.+5- 1892-1913 Lausanne, Switzerland, monthly means (noon values) . . 1896-1904 Warsaw, Russia, monthly maxima ..........--.+++-5 IQOI-I913 Washington, D. C., and Mount Weather, Va., monthly means for air MASS 2.0.........00: cece reece 1905-1913 Sim'a, India, monthly means (noon values)........ 1906-1913 Paris, France, monthly maxima .......--..-+eesee ees 1907-1913 The marked decrease in the pyrheliometric readings for 1884, 1885, and 1886 doubtless were largely, if not almost wholly, due to the eruption of Krakatoa in the summer of 1883 ; the decreased values of 1888 to 1892, inclusive, occurred during a period of exceptional volcanic activity, but were probably due essentially to the violent eruptions of Bandaisan (1888), Bogoslof (1800), and “OAT, IV. R., 46, p. 355, 1918. 585 586 PHYSICS OF "IEE AIK Awoe, on Great Sangir (1892); the low values of 1903 to the eruptions of Santa Maria (1902), Pelé (1902) and Colima (1903); and the low values of 1912-1913, to the explosion, June 6, 1912, of Katmai. The slight depression in the curve cor- Year Number of stations Radiation 1883 I 103 1884 I 92 1885 I 89 1886 I 96 1887 I 105 1888 I IOI 1889 I 100 1890 I 96 1891 I 95 1892 2 99 1893 2 104 1894 2 102 1895 2 103 1896 3 103 1897 3 103 1898 3 104 : 1899 3 103 1900 3 IOI IQOI 3 102 1902 3 99 1903 3 88 1904 3 06 1905 3 100 1906 3 102 1907 5 98 1908 5 99 1909 5 102 1910 5 102 IQII 5 103 IQI2 5 92 1913 5 93 responding to the year 1907, during which no violent eruptions were reported (this does not exclude the possibility of such occurrence in remote and unfrequented regions), according to Dr. Kimball, probably was caused by local haze at Washington, D. C., where his observations were made, and elsewhere, and this supposition is partially supported by the fact that his values for VULCANISM: OBSERVATIONAL 587 the year were not uniformly low, and by the further fact, inferred from a publication by Gorczynski,?" that during that year the solar radiation was but little below normal at Warsaw, Russia. There is, then, abundant pyrheliometric evidence that volcanic dust in the upper atmosphere actually does produce that decrease in direct solar radiation that theory indicates it should, and, as the theory is well founded and the observations were carefully taken, this mutual confirmation may be regarded as conclusive both of the existence of volcanic dust in the upper atmosphere (isothermal region) and of its efficiency in intercepting direct radiation from the sun. ; Fic. 190. 456789 F123456789 8123456789 212 Annual average, pyrheliometric values. It should be remembered, however, in this connection, that the intensity of the solar radiation at the surface of the earth depends not only upon the dustiness of the earth’s atmosphere, but also upon the dustiness, and, of course, the temperature, of the solar atmosphere. Obviously, dust in the sun’s envelope must more or less shut in solar radiation just as, and in the same manner that, dust in the earth’s envelope shuts it out. Hence it follows that when this dust is greatest, other things being equal, the output of solar energy will be least, and when the dust is least, other things being equal, the output of energy will be greatest. Not only may the intensity of the emitted radiation vary because of changes in the trans- parency of the solar atmosphere, but also because of any variations *C. R., 157, p. 84, 1913. 588 PHYSICS OF THE AIR in the temperature of the effective solar surface, which, it would seem, might well be hottest when most agitated, or at the times of spot maxima, and coolest when most quiescent, or at the times of spot minima. Now, the dustiness of the solar atmosphere, manifesting itself as a corona, certainly does vary through a considerable range from a maximum when the sun-spots are most numerous to a minimum when they are fewest, and, therefore, partly because of changes in the transparency of the solar envelope, and partly because of changes in the solar surface temperatures, if, as in all probability they do, such temperature changes take place, we should expect the solar constant also to vary from one value at the time of spot maximum to another at the time of spot mini- mum, and to vary as determined by the controlling factor, dust or temperature. If the above reasoning is correct, it follows that pyrhelio- metric readings are functions of, among other things, both the so- lar atmosphere and our own terrestrial atmosphere; and as the former is altered chiefly by sun-spots or at least varies with their production and existence, and the latter by volcanic explosions, a means is at hand for comparing the relative importance of the two radiation screens. Fig. 191 shows one such comparison. The upper curve gives smoothed annual average pyrheliometric readings (not solar con- stants, though closely proportional to them) and the lower curve sun-spot numbers. It will be noticed that in their most pronounced features the two curves have but little in common, and that the great drops in the pyrheliometric values occur simultaneously with violent volcanic explosions, as already explained, and not at the times of sun-spot changes. Hence tt appears that the dust in our own atmosphere, and not the condition of the sun, is a very important, if not the controlling, factor in determining the magni- tudes and times of occurrence of great and abrupt changes of insolation intensity at the surface of the earth. Temperatures at the Surface of the Earth—lf a veil of dust actually should intercept as much as one-fifth of the direct solar radiation, as Fig. 190 indicates that at times it does, it would seem that in those years the temperature of the atmosphere at the sur- face of the earth should be somewhat below the normal. Of course, the great supply of heat in the ocean would produce a lag VULCANISM: OBSERVATIONAL 589 in this effect, particularly over the oceans themselves, and, besides, there must be both an increase of sky light by scattering and some interception of earth radiation by the dust which, since it is at great altitudes, receives the full, or nearly the full, planetary radiation of the earth. This increase of sky radiation, together with the return terrestrial radiation, obviously compensates in some measure for the loss of direct insolation. However, meas- urements made by Abbot ?8 at Bassour, Algeria, during the sum- mer of 1912, show that at this time and place the direct radia- Fic. 191. N %@ 8 g 3 —~3 456789012345678991 2345678398123 104 98 92 8&6 Relation of pyrheliometric values to sun-spot numbers and volcanic eruptions. tion and the sky radiation, which obviously included both the scattered solar radiation and some return terrestrial radiation, were together less by about 10 per cent. than their normal com- bined values; and there is no reason to think that in this respect Bassour was at all different from other places, certainly a large portion of the northern hemisphere, at least. covered by the veil of dust. Clearly, then, if this decrease in the radiation received were universal and should continue indefinitely, the ultimate radiation of the earth would also decrease to the same extent, or 10 per cent. Now. since the earth. or rather the water vapor of ® Sinithsonian Miscellaneous Collections, vol. 1x, No. 29, 1913. 590 PHYSICS OF THE AIR the atmosphere, radiates substantially as a black body and, there- fore, proportionally to the fourth power of its absolute tempera- ture, it follows that a 10 per cent. change in its radiation would indicate about a 2.5 per cent. change in its temperature. But the effective temperature of the earth as a full radiator, which it closely approaches, is about 256° A.?® Hence a change of Io per cent. in the radiation emitted would imply 6.4° C. change in tem- perature, an amount which, if long enough continued, would be more than sufficient to produce glaciation equal probably to the most extensive of any known ice age. As above implied, not much lowering of the temperature could be expected to take place immediately ; however, some early cool- ing over land areas might well be anticipated. To test this point the temperature records of a number of high altitude (together with two or three very dry) inland stations have been examined. High altitudes were chosen because it was thought that the tem- perature effects of dust in the upper atmosphere probably are most clearly marked above the very and irregularly dusty layers of the lower atmosphere; and the condition that the stations should also be inland was imposed because these are freer, pre- sumably, than many coast stations, from fortuitous season changes. Thus, stations in the eastern portion of the United States were rejected because of the great differences in the winters, for example, of this section depending upon the prevailing direction of the wind,?° a condition wholly independent, so far as known, of variations in the intensity of direct radiation. The number of stations was still further limited by the avail- able recent data. Hence the records finally selected, and kindly put in shape by the Climatological Division of the United States Weather Bureau, Mr. P. C. Day in charge, were obtained at the following places: * Abbot and Fowle, Annals Astrophys. Obsy., Smithsonian Institution, vol. ii, p. 175, 1908. *® Humphreys, Monthly IVeather Review, vol. xlii, p. 672, 1914. VULCANISM: OBSERVATIONAL 591 TABLE II. Stations Whose Data Were Used. AMERICA. Name. Latitude. Longitude. Elevation in feet. Baker wal eds d atcacaageetona eens sas 44° 46’N. | 117° 50’ W. 466 Bismarck iio. cian iacen an’ ere eectee ath 46° 47’ N. | 100° 38’ W. os Cheyenne. caine dues cous asia han eee hey 41° 08’ N. | 104° 48’ W. 6,088 Denver: . yao saggercn cae ss sate er oa: 39° 45’ N. |-105° 00’ W. 5,291 Dodge! City se vxigviea cand cet cmen nals 37° 45’ N. | 100° 00’ W. 2,509 OIPPAaSOiii acid ce scaca ia avayied dak shad, peatvnawe 31° 47'N. | 106° 30’ W. 3,762 FRCLE HA sue cases cei aesied eihnined beela gaan 46° 34’N. | 112° 04/ W. 4,110 Huron........ nis Saas toca hee eon Ny 44° 21'N. | 98° 14’ W. 1,306 NGith: Platte’ ince 35 ce nkinag gaiees aun: 41° 08’ N. | 100° 45’ W. 2,821 Red Bluth. isc aay disc astew aes okie wen ees 40° 10'N, | 122° 15’W. 332 Sacramentos i va; aeecc eed oh eyes eae 38° 35’N. | 121° 30’ W. 69 Salt Lake: City sce os ehsecied east Gua Ae 3 40° 46’ N. | 111° 54’ W. 4,360 San Antonio....................00005 29° 27'N 98° 28’ W. 701 Santa Pe. ascaves a tenes hae adtaewa ba tee 35° 41’ N. | 105° 57’ W. 7,013 SPOkane. 4 isi vi cians crake cen eee eee 47° 40’ N. | 117° 25’ W. 1,929 WiAnneMmulCa esc cne.e soa spears ae hate ee 40° 58’N. | 117° 43’ W. 4,344 VRAIN Ae sh room ktid aanasiah or nor areaiaa anes Wa ieee 32° 45’N. | 114° 36’ W. 141 EUROPE Mont Ventoux...........-......-000. 4° 10'N 5° 16’ E 6,234 Obir..... ude Soe Geivan oS < ci eva dua fee aah 40° 30’ N 14° 29’ E 6,716 Prendt Mats 2. cag h dain aa os Rie hea bLON A 42° 56’ N. 0° 8’E. 9,380 Puy de DOME. wi... astra tee ene 45° 46’ N. 2°57’'E. 4,813 SAMNLIS 5 5 eee wie kd saad ccc techie aase Rite as ree 47° 15'N. 9° 20’ E. 8,202 Schneekoppe............-.-0.e eee 50° 44'N. 15° 44’ E. 5,359 Sonnblick> + gu. sis wewsnsan eee Ode se meme 47° 3'N. 12°57’ E. 10,190 INDIA. Simlascvccpeccs ton oe ten cee oot, | au GON. | yer ae*E. | ayage In Table III the first column gives the year in question. The second column gives the average departure in degrees F., for the seventeen American stations, of the annual average maximum, as determined from the monthly average maxima, from the normal annual maximum, or average of a great many annual average maxima. The third column gives smoothed values, determined from the actual values in the second column as follows: sat + = + a in which S is the smoothed value, b the actual value pertaining to the particular year for which S is being computed, a and c the actual values for the next previous and the next succeeding years, respectively. The fourth and fifth columns give, respectively, the actual and the smoothed average departures of the annual average minima, while the sixth and seventh columns give the corre- sponding average departures of the annual average means. 592 PHYSICS OF THE AIR TaBLe III. Average Temperature Departures from Temperature Normals. AMERICA. Maxima. Minima. | Means. Year. Actual. | Smoothed.| Actual. | Smoothed.| Actual. | Smoothed B88). ook mics bea =1.3 +0.03 —1.8 —0.68 = 1.7 —0.50 TSS Io. orien ekeeeid +0.2 —0.30 +0.6 —0.20 +0.1 —0.48 18822036. oR yee —0.3 —0.50 —0.2 —0.20 —0.4 —0.50 EOS 3.hec acc Gas oyu « —1.6 |’ —1.33 —1.0 —0.70 —1.3 1.15 | oto ne a ee —1.8 —1.20 —0.6 —0.28 —1.6 — 1.05 WS85 oo ovis ncn vaca +o0.4 —9.18 +11 +0.43 +0.3 —0.30 US8G6.3. 3 ncdasuea ce +0.3 +9.35 +o.1 +0.10 —O,2 —0.03 DOS Rice opens wines +0.4 + 9.38 —0.9 —0.45 0.0 +0.07 LBS csteats: geioaiacits 5 +0.4 +0.53 -O.1 —0.13 +0.5 +0.53 TS 80 viscsz yc memes +0.9 +0.63 +0.6 +0.23 +11 +0.85 WS QO viii c cin ace ghate sted +0.3 +0.15 0.2 —0.05 +0.7 +0.58 VOQUian sender Os ex —0.9 —0.58 —0.4 —0.38 —0.2 +0.05 L8Q 25: 23s yews Bed —0.8 —0.85 —oO.1 —0.33 —O.1 —0.20 TSQ3jco0s pag ee ays —0.9 —0.73 —0.7 —0.38 —0.4 —0.08 FSQ4 stems aaa iss —0.3 —0.55 +0.4 —0.18 +0.6 +0.13 1895...... ice SOP —0.35 —0.8 —0.08 —0.3 +0.25 1896...... eee $0.3 —0.18 +0.9 +0.28 +1.0 +0.45 TSO Zin atd cee s...| 0.6 —0.30 +0.1 +0.13 +O +0.28 WSOQS8e sees eres-ive cain aif). FOL, —0.65 —0.6 —0.45 —o0.1 —0.13 TSO 0m nah aceon —0.8 —0.13 —0.7 —0.10 —0.4 +0.25 TOO awa ake ae ¢ +14 +0.78 +1.6 +0.90 +1.9 +1.23 DOOM ne ee owe poy +1.1 +0.83 +1.1 +1.08 +165 +1.35 PSs ee Ss aes be ~O,3 —0.13 +0.5 +0.38 +0.5 +0.53 FOO Mi a keh t sana: aE —0.43 —0.6 —0.05 =O.) +0.18 TOO Aw 55-2 coy 2aieads +0.6 —0.15 +0.5 +0.05 +1.0 +0.38 TOR oct ica ben ean —0.8 6.40 —0.2 +0.08 —O.1 “++0.33 MOOG. « ceendowdaia —0.2 — 0.30 +0.2 +0.08 +0.5 +O.33 TQO7 sa, css 0% emarets 0.0 +0.10 +0.1 +0.10 +0.4 +0.50 1908s. 5 ie some eeaiars +0.6 +0.15 0.0 —0.08 +0.7 +0.43 LQG so cose sect eet ais —0.6 +0.38 —0.4 —0.05 —oO.1 +0.55 TOTO a naan eee +2.1 +0.80 +0.6 +0.08 +1.7 +0.75 BOG Ts. o.a's vee 64 ee 0.4 +0.03 —0.5 —0.35 = 0.3 +0.05 IQ12y chases see es Sis —0.70 —1.0 —0.63 —0.9 —0.53 Fig. 192 shows the graphical equivalents of the smoothed por- tions of Table IIL. It will be noticed that the three curves of Fig. 192, marked maximum, minimum, and mean, respectively, are, in general, quite similar to each other. Hence, because of this mutual check and general agreement, it seems reasonably certain that any one set of temperature data, the means, for instance, furnishes a fairly safe guide to the actual temperature and climatic fluctuations from year to year or period to period. Table IV gives the weighted actual average departures and the smoothed departures in degrees F. of the annual mean tem- peratures of the selected seventeen American, seven European, and one Indian stations listed in Table I. VULCANISM: OBSERVATIONAL 593 TABLE IV. Weighted Departures of Mean Temperatures from. Normal Temperatures. WORLD. Date Actual, |Smoothed. Date Actual. |Smoothed. S72 isn sees eee —0.78 —0.30 80 3isca vee eos — 0.34 —0.06 AS73y cist wane cies — 0.65 —0.47 1894............ +0.34 +0.03 TSA eer ha mead eles +0.20 —0.34 TSQG india kGenas —0.21 +0.10 1S 75 che ical ee as —1.12 —0.61 1896............ +0.49 +0.28 1876 irane aavdars wastes —0.40 —0.60 TSO Pints qeenirsa +0.34 +0.45 IS7 Fg veweae a as —0.48 — 0.32 TSO 8: weston cere cdicnainis +0.61 +0.46 T8786 3 oo4 ee oad says +0.07 0.00 T8997 shave ee woe +0.27 +0.59 TS7OAvess awe eaead +0.33 +0.04 || 1900............ +1.19 +0.76 TS 8O ik sectors alereees —0.50 —0.13 TOOLS genes Hess +0.40 +0.55 TEST: ndadue Heoaga 2 +0.14 —0.02 || 1902............ +0.20 | +0.13 PSS 2c scr doen hh akals +0.14 —0.16 LOOP eet nag — 0.30 +0.10 TS 8O se Saas ne cine — 1.04 —0.68 1904 vss be ane sy +0.81 +0.20 TS8A insite ite dates —0.79 —0.61 TOOS a ckecuen ae —0.51 +0.01 TOSS tig stay ool x +0.17 —0.09 |} 1906............ +0.23 +0.05 1886.2: cas ees ane +0.11 +0.03 1907 ote ain sna aia +0.23 +0.30 TSB 7 yond Sisce ye te —0.29 —0.05 1908%3 2322 Sasa ek +0.51 +0.21 DSSS oonicuicn ore bes +0.26 +0.24 VQ: :ieeeesas —0.43 +0.11 W880 ia 8 ooo ews +0.74 +0.57 TQ1O2 cca een ys +0.69 +0.30 T8905..2407caey +0.54 +0.40 TOT 25 c 2asees +0.23 +0.09 TOOT iver makoneds x —0.21 +0.06 TQIQ: yeh atvisdes —0.80 —0.40 T8092 .secad ean Pa +0.10 —0.09 FIG. 192. +6° +3° MAXIMUM -.3° +.3° MINIMUM 3% 91234567898123456788 oa a - - n - 012345678928123 5 0 — Smoothed averages of the annual average temperature departures of 17 American stations. 594 PHYSICS OF THE AIR The average departures were calculated in accordance with the more or less correctly coefficiented equation, _444+2E +1 ; 7 in which D is the weighted departure, 4 the smoothed average American, E the smoothed average European, and J the smoothed Indian, departure of the mean annual temperature from the normal annual temperature. Table IV, extended, as well as the scanty early data, mainly from the given stations, will permit, back to 1872, is graphically represented by the continuous, light curve at the bottom of Fig. 181. In 1880 and again in rgor the curve probably does not very closely represent world-wide temperature departures, being, pre- sumably, at both places quite too low, owing, in each case, to an abnormally cold single month in America. The dotted curve from 1907 to I9II gives the average tem- perature departures for the American stations only, and pre- sumably represents world temperature departures much more closely than does the continuous light line for the same time. This is because of two or three exceptionally cold summer months in Europe. The dotted curve from 1872 to 1900 gives the smoothed averages of the annual temperature departures from the normal temperatures of the following stations as computed from the actual departures given by Nordmann#'; Sierra Leone, Recife (or Pernambuco), Port au Prince, Trinité, Jamaica, Habana, Manila, Hong Kong, Zikawei, Batavia, Bombay, Island of Rodri- guez, Island of Mauritius. All these, or practically all, are low-level stations, and most of them either tropical or semi-tropical, and, therefore, should show in general, from altitude influence alone, a smaller, and from latitude influence alone, a greater, abnormality than do the stations whose temperature departures are given by the continuous fine- line curve. Hence, all things considered, the average tempera- ture departures as calculated from the two sets of stations agree remarkably well, so that one can say with, presumably, a fair de- gree of confidence, that the heavy curve, T, approximately repre- sents the average of the departures of the mean annual tempera- tures from the normal annual temperatures of equatorial and D ™ Revue Générale des Sciences, August, 1903, pp. 803-808. Annual Report, Smithsonian Institution, 1903, pp. 130-149. VULCANISM: OBSERVATIONAL 595 high altitude regions of the earth, or that 7’, with the above re- strictions, is the curve of world temperatures. Much additional statistical evidence bearing on this point and supporting the conclusion just given, has been published by Mieike.** This consists of the average annual temperatures from 1870 to 1910 of 487 widely distributed stations, with, however, numerous and extensive breaks—in fact, the records of only a few stations cover the entire period. By grouping these stations ac- cording to zones, tropical, subtropical, warm temperate, cold tem- perate and frigid, and then averaging and smoothing the zonal annual temperature departures, giving all equal weight, values were found which run substantially parallel to those already found but of less (about half) amplitude, quite as anticipated from the fact that stations above the dust, fogs and many clouds of the lower atmosphere must be more sensitive to variations in the trans- parency of the outer atmosphere and to solar changes than are those (the great majority) located at, or not more than a few hundred metres above, sea level. Either curve might, therefore, be used in a discussion of the causes and periods of temperature changes, but in what follows the curve of larger amplitudes or the curve of high altitude stations will be used because: (a) data for it but not for the other are available through the period of the Katmai veil of dust, (0) it is freer from surface disturbances and therefore more representative of solar and high atmospheric con- ditions, (c) high altitude temperatures are more effective than those of sea level in modifying glacial conditions. Relation of World Temperatures to Pyrheliometric Values.— Curve P, also of Fig. 193, gives the smoothed course of the annual average pyrheliometric readings, as computed from the actual values given in Fig. 190. The insolation intensity data, covering the whole of the depression that had its minimum in 1885, were obtained at a single place, Montpellier, France, by a single ob- server, L. J. Eon,?? who confined himself to noon observations with a Crova actinometer. It may be, therefore, that merely local and temporary disturbances produced a local insolation curve that was not quite parallel to the curve for the entire world. At any rate, the drop in the solar radiation values obviously was due to dust put into the atmosphere by the explosion of Krakatoa in August, 1883, and it would seem that the effects of this dust both ® Aus dem Archiv der Deutschen Seewarte. 36, Nov. 3, 1913. ® Bulletin météorologique du Département de l’Hérault, 1900. 596 PHYSICS OF THE AIR on the surface temperatures and on pyrheliometric values must have been greater during the latter part of 1883 and in 1884 than they were in 1885, when much of the dust certainly had already settled out of the atmosphere, and this supposition is well sup- ported by the pyrheliometric and temperature drops that imme- diately followed the volcanic explosions of 1903 and 1912, and their partial recovery within a single year. Nevertheless, the pyrheliometric values must be accepted as obtained. Indeed, this exceptional lag is not quite unprecedented, since the coldest year following the similar, though more violent, explosion of Asama- yama, just one hundred years earlier, was not the year of the explosion, 1783, nor the following year, but 1785. It is probable that in the earlier, as certainly in the later, of these unusual cases the dust was thrown to such great altitudes that the finer portions were nearly, or quite, two years in reach- ing the lower level of the isothermal region. Clearly, too, much of this dust, while perfectly dry, probably was so fine as merely to scatter even solar radiation, and yet on reaching the more humid portions of the atmosphere the particles may have gathered suf- ficient moisture to assume reflecting size, and, therefore, seri- ously to interfere with insolation. This is merely suggested, but in no wise insisted upon, as a possible explanation of the unusual pyrheliometric lag after the explosion of Krakatoa. It is obvious, from a mere glance, that the pyrheliometric and the temperature curves, or curves P and T, have much in common. This is especially marked by the large and practically simultaneous drops in the two curves in 1912, following the eruption of Katmai. But while a relation between these curves thus appears certain, the agreement is so far from perfect as to force the conclusion that pyrheliometric values constitute only one factor in the determination of average world temperatures. Sun-spots and Temperature.—It has been known for a long time that the curve of sun-spot numbers, curve S, Fig. 193, and the curve of earth temperatures, curve T, follow or parallel each other in a general way, in the sense that the fewer the spots the higher the temperature, with, however, puzzling discrepancies here and there. Both these facts, the general agreement between the phe- nomena in question and also their specific discrepancies, are well shown by the curves S and T of Fig. 193, and, while the discrep- ancies are marked, it is obvious that, on the whole, the agreement is quite too close to leave any doubt of the reality of some sort VULCANISM: OBSERVATIONAL 597 of connection between sun-spots and atmospheric temperatures, Just how or by what process this relation conceivably may exist will be discussed below. Combined Effect of Insolation Intensity and Sun-spot Influ- ence on Atmospheric Temperatures.—Since it is obvious that the insolation intensity and the number of sun-spots each exerts an influence on the temperature of the earth, it is clear that some sort of a combination of the two curves P and S should more closely parallel the temperature curve, T, than does either alone. It is Fic. 193. Q ° ° x oD a ° ° © 34567892 12345678 9212345678 9912345678981 23 a 102 96 E 90 0 30 60 75 +60 +15 O -15 -45 -60 Smoothed pyrheliometric, sun-spot, and temperature curves. probable that the sun-spot effect is not directly proportional to the actual number of spots, but, however this may be, the direct combination of the curves P and S gives the resultant P + S, which, as a glance at the figures shows, actually parallels the curve of temperatures, 7, with remarkable fidelity. Exactly this same combination, from 1880 to 1909, has been made by Abbot and Fowle,?4 whose lead in this important particular is here being followed, and the resultant curve found to run closely parallel to the curve of “ smoothed annual mean departures” of the maxi- mum temperatures of fifteen stations in the United States. * Sinithsonian Miscellaneous Collections, vol. 1x, No. 29, 1913. 39 598 PHYSICS OF THE AIR Probably the most striking point of agreement, one that must strongly be insisted upon, as shown by Fig. 193, between the com- bination curve and the temperature, occurs in 1912, when, 1n spite of the fact that the sun-spots were at a minimum, indicating that, according to rule, the temperature should be high, the temperature curve dropped greatly and abruptly; obviously, because of the simultaneous and corresponding decrease in the intensity of solar radiation produced by the extensive veil of Katmai’s dust, pre- cisely as happened at spot minima after the explosion of Asama in 1783. Both cases, since they occurred during spot minima, show distinctly the great influence volcanic dust has on terres- trial temperatures. Temperature Variations Since 1750 as Influenced by Sun-spots and Volcanic Eruptions.—Sun-spot numbers ** month by month are fairly well known since July, 1749, and so, too, are the annual temperature variations °° from about the same time, and, there- fore, the data at hand for comparing these two phenomena over a continuous period of a little more than 164 years, or from at least the beginning of the year 1750 to the present date. Fig. 194* makes this comparison easy. The bottom curves give the smoothed annual temperature departures, as computed from Koppen’s actual annual departures, using all stations, while the top curve follows Wolfer’s annual average sun-spot numbers. Of course, the earlier observations, both of sun-spots and of tem- peratures, were few in number and more or less unsatisfactory in comparison with those obtained during the past thirty, or even forty, years. Nevertheless, it is clear from Fig. 194 that at least since 1750, the date of our earliest records, and presumably, there- fore, since an indefinitely distant time in the past, the two phe- nomena, atmospheric temperature and sun-spot numbers, have in general varied together, with, however, marked discrepancies from time to time. These we shall now consider, and shall show that they occurred, in every important case, immediately after violent volcanic eruptions. Volcanic Disturbances of Atmospheric Temperature Since 1750.—It must be distinctly remembered that the earlier tempera- ture records, because of their limited number, if for no other reason, give only the general trend of world temperatures. Again, ® Wolfer, Astronomische Mitteilungen, 93, 1902, and later numbers. * Képpen, Zeit. Oesterreich. Gesell. fiir Meteorologie, vol. viii, pp. 241 and 257, 1873. * Fig. 194 folded plate attached to inside of back cover. VULCANISM: OBSERVATIONAL 599 the record back to 1750 of even violent volcanic eruptions is necessarily incomplete; and, besides, not all great eruptions de- crease the surface temperature—only those that drive a iot of dust into the isothermal region, or very high atmosphere, and even then decrease it perceptibly in only those regions, usually extensive and at times world-wide, over which the dust spreads. Pronounced and long-continued sky phenomena, therefore, of the type that followed the eruption of Krakatoa, furnish the best evidence of volcanic vioience in the sense here used. Finally, there can be no particular test save where the temperature is low in comparison with that which the number of sun-spots would indicate. Obviously, then, no matter how close the actual rela- tion between the phenomena may be, the errors and the incom- pleteness of the recorded data would prevent the discovery of more than a general relation. Of course, it will naturally occur to one to ask about special cases, such as the cold.years of 1783—4—5, and, in particular, 1816, the famous “year without a summer,” “ poverty year,” or “eighteen hundred and froze-to-death.”” The first of these, 1783-5, followed, as already explained, the great explosion of Asama in 1783, while the second, the ‘“‘ year without a summer,” that was cold the world over, followed the eruption of Tomboro, which killed 56,000 people 7 and blew up so much dust that “ for three days there was darkness at a distance of 300 miles.”?$ There is a detail in the temperature curve for the years 1886-7 that needs special attention. The temporary depression where, seemingly, the temperature should be steadily rising, obviously was due to the great eruption of Tarawera (June 10, 1886), in New Zealand. This volcano is a little more than 38° south of the equator, and, therefore, furnishes a good example of an erup- tion on one side of the equator affecting the temperature far to the other side. Doubtless, however, when the dust gets but a little way into the isothermal region the effect is greatest on the vol- cano’s side of the equator. But if the temperature was decreased by Tarawera, why, one might ask, was not the pyrheliometric curve similarly affected? It was, for several months after the eruption, as the individual monthly values show,®® but the annual means, plotted in the figure, 37 Schneider, “ Die Vulcanischen Erscheinungen der Erde,” p. I, rgrt. * Rept. Krakatoa Committee Royal Society, 1888, p. 303. ® Bulletin Météorologique du Département de l’Hérault, p. 136, 1900. 600 PHYSICS OF THE ATR have the effect of making the pyrheliometric disturbance from Tarawera appear only as a retardation in the recovery from the effects of Krakatoa. Neglecting the smaller irregularities which may or may not have been of world-wide occurrence, and remembering that, other things being equal, temperature maxima are to be expected at the times of spot minima and temperature minima at the times of spot maxima, the marked discrepancies and their probable ex- planations may be tabulated as follows: Temperature and Sun-spot Discrepancies. Date. Nature of Probable cause. discrepancy. 175508 cr dig ba es Cold Kotlugia, Iceland, 1755, Oct. 17. 1766-7......-005-. Cold Hecla, Iceland, 1766. Apr. 15 to Sept. 7. Mayon, Luzon, 1766. 1977S —O2 G35 Warm Maximum number (annual) of sun-spots ever recorded and unusually short spot period. Can it be that the solar constant actually was notably greater than usual at this time? 1784-5-6........- Cold Asama, Japan, 1783, most frightful eruption on record. ’ Skaptar Jokull, Iceland, 1783, June 8 and 18 Vesuvius, Italy, 1785. TOO nana newires Cold Fuego (?), Guatemala. (Uncertain.) T8O0ws5 power wnens Cold St. George (?), Azores, 1808. (Uncertain.) Etna (?), Sicily, 1809. (Uncertain.) 1812-13-I4-15-16 Cold Soufriére, St. Vincent, 1812, Apr. 30. Mayon, Luzon, 1814. Tomboro, Sumbawa, 1815, Apr. 7 to 12, very great, EOSIRS oy, aawat as Cold Graham’s Island, 1831, July 10 to early in Aug. Babujan Islands, 1831. Pichincha, Ecuador, 1831. 1836-7-8......... Cold Coseguina Nicaragua, 1835, Jan. 20. Awatska, Kamchatka, 1837. 1856-7. Cold Cotopaxi (?), and others, 1855-6. (Uncertain.) TOPO HF. coi dah idsens Cold Vesuvius, Italy, 1872, Apr. 23 to May 3. Merapi, Java, 1872, April. 1875-6.... ..... Cold Vatna Jokull, Iceland, 1875, March 29 and during April. 1884-5-6......... Cold Krakatoa, Straits of Sunda, 1883, Aug. 27, greatest since 1783. Saint Augustin, Alaska, 1883, Oct. 6. Tarawera, New Zealand, 1886, June Io. 1890-I-2......... Cold Bogoslof, Aleutian Islands, 1890, Feb. Awoe, Great Sangir, 1892, June 7. 1902-3-4.. Cold Pelé, Martinique, 1902, May 8. Santa Maria, Guatemala, 1902, Oct. 24. Colima, Mexico, 1903, Feb. and Mar. IQI2T3.sncscnees Cold -| Katmai, Alaska, 1912, June 6. t VULCANISM: OBSERVATIONAL 601 For the sake of completeness as well as for such little value and interest it may have the following list is added of still earlier great volcanic eruptions and the kinds of seasons that history #° reports to have followed. Taken by themselves these ancient or preinstrumental records help but little to connect effect with cause. Nevertheless, it is at least pleasing to know that they report pre- cisely those general weather or seasonal conditions which from later and reliable instrumental observations we infer must have happened, provided only that the explosions were sufficiently great. Date of eruption, Volcano, Type of season, etc. TOs PUIG: Bbincre drivers Vesuvius. (De- | About 80, severe drought for several struction of years in middle Asia. (Accords with Pompeii.) low temperature but signifies very little.) 1631, Dec. 16..... Vesuvius. (Most | 1632, Apr. 27, destructive snow in violent since 79. Transylvania (Siebenburgen); May 1636, May 18 to winter Aug. TOOT isecins-ansitaagin Drsvittg 1694, Nov. 20 till 1695, April...... 1707, May 20 to Aug. 1707, May 25 and July 25 1721, May 11 till autumn Height of ash cloud, measured by Braccini, 48 kilometres.) Gunong Api..... Vesuvius......... Japanese nk Santorini .casens< Kotlugia......... 17, frost in Saxony; hot dry summer in Italy; Oct. 4, very cold in France, 37 soldiers frozen between Montpellier and Baziers. 1633, severe winter; May 22, snow and severe cold in Transylvania. 1637, long, severe winter. 1681, severe drought and cold spring (Evelyn's Diary). 1694, hard, snowy winter in both Italy and Spain; May 17, all vineyards of Troyes destroyed by frost. 1695, long, severe and dry winter; cool summer. 1708, very mild winter; cold summer; Dec. 10 to 20, very heavy snow in France. 1709, from Jan. 6, for'a month and a half extraordinary severe cold in nearly all Europe; Adriatic Sea and Thames frozen; snow 10 feet deep in Spain and Portugal; 50 days frost in England from Dec. 25, 1708 till March 12, 1709; mild winter in Con- stantinople, but very severe in east- ern North America; May 17, snow in Oedenburg; May 17 and 18, frost in Alsace; cool, rainy summer. 1722, cool, wet year. * Hennig, Abhand, des K. Preuss. Meteor. Inst., Bd. II, No. 4, 1904. 602 PHYSICS OF THE AIR Confining attention to the first of the above lists, since the value of the second in this connection is doubtful, it will be seen that excepting some ill-defined cases, all of the seeming irregu- larities in the temperature curve, and all of the known volcanic eruptions, are satisfactorily accounted for. It may be concluded, therefore, that the variations in the average temperature of the atmosphere of the kind and magni- tude shown by actual records depend jointly upon volcanic eruptions, through the action of dust on radiation, as already ex- plained, and upon sun-spot numbers, through, presumably, some intermediate action they have upon the atmosphere—possibly of the nature explained in the next chapter. Magnitude and Importance of Actual Temperature Changes. —The actual temperature range from sun-spot maximum to sun- spot minimum varies, roughly, from 0.5° C. to 1° C., or possibly more, while the effect of volcanic dust appears to be fully as great—on rare occasions even much greater. In some ways, and in respect to many things, a range of average temperatures of even 1° C. is well-nigh negligible, and, therefore, however im- portant the results may seem to the scientist, the ultra-utilitarian would be justified in asking, ‘* What of it?” Much of it, in a distinctly practical as well as in a purely scientific sense, as is true of every fact of nature. For instance, during the summer, or growing season, a change of 0.5° C. pro- duces a latitude shift of the isotherms by fully 80 miles. Hence, if there is but little or no volcanic dust to interfere, during sun- spot minima cereals and other crops may be successfully grown 50 to 150 miles farther north (or south in the southern hemi- sphere) than at the times of sun-spot maxima. This alone is of great practical importance, especially to those who live near the thermal limits of crop production. In addition to changing the area over which crop production is possible, a change of average temperature also affects, in some cases greatly, the time of plant development. Thus Walter *? has shown that a change of only 0.7” C. may alter, and in Mauritius has been observed actually to alter by as much as an entire year, the time required for the maturing of sugar cane. Hence the temperature changes that normally accompany sun-spot varia- +“ On the Influence of Forests on Rainfall and the Probable Effect of “Déboisement’ on Agriculture in Mauritius” (1908). VULCANISM: OBSERVATIONAL 603 tions, though small in absolute magnitude, are of great im- portance, and, by availing ourselves of the reasonable fore- knowledge we have of these changes, may easily be made of still greater importance. In forecasting these small but important climatic changes it must be distinctly remembered that to the fairly periodic, and therefore predictable, sun-spot influence must be added the irregu- lar and unpredictable volcanic effects. But even here the case is not bad for the forecaster, because the volcanic dust always pro- duces, qualitatively, the same effect—a cooling—and because both the amount of this cooling and its duration (generally only one or two years, as already explained) may approximately be estimated from the nature of the volcanic explosion itself. CHAPTER V. OTHER FACTORS OF CLIMATIC CONTROL. (9, 10, II, 12, 13, 14.) 9. SUN-SPOTS. As already stated, the average temperature of the earth as a whole varies inversely with the trequency of sun-spots. How Sun-spots \lay Change Earth 1 emperaturecs.—It the solar constant should remain the same from spot maximum to spot minimum it clearly would not be easy to see at a glance why the surface temperature of the earth should vary as it does with spot numbers; and the situation is still more difficult if, as ob- servations appear to indicate, the lowest temperatures occur when the solar constant is greatest and the highest temperatures occur when this constant is least. There is, however, a possible ex- planation of the paradox, and, while it may not contain the whole truth, it nevertheless is sufficient to show a fpriori that in all prob- ability our temperatures do change from spot maxima to spot minima without a corresponding change in the solar constant, and also to show that a decrease in our surface temperatures may accompany even a slight increase in the solar constant. The explanation in question has already been given else- where,*? and the original paper must be consulted by those who wish to weigh all the details of the argument. Briefly, however, the argument is as follows: 1. At the times of spot maxima the solar corona is much more extensive than it is at the times of spot minima—a well- known observation. 2. This corona consists, in part at least, of reflecting par- ticles, as many eclipse observations have shown, and so may be regarded as dust in the solar atmosphere. 3. The brightness of the sun, as every solar observer knows, drops off from centre to limb. 4. This drop, as reported by various observers, is greater the shorter the wave-length, and due, almost certainly, to diffuse scattering. From the observational facts it follows that during spot *” Humphreys, Astrophys. Jr., 32. p. 97, 1910. 604 OTHER FACTORS OF CLIMATIC CONTROL 605 minima, other things being equal, the solar spectrum must neces- sarily be richer in violet and ultra-violet radiation than it is dur- ing spot maxima. But, as experiment has shown,** ultra-violet radiation of shorter wave-length than A 1850 is strongly absorbed by oxygen with the result that some of the oxygen is converted into ozone. Hence, since the atmosphere of the isothermal region is cold and dry (conditions favorable to the stability of ozone) and since of the gases of the upper atmosphere only oxygen is appreciably absorptive of radiations between A 1250 and d 1900 ** the strato- sphere was believed to contain more or less ozone, a belief now fully confirmed by several observers,!® and long ago virtually confirmed by Angstrém.*® In so far, then, as this ozone is pro- duced by the action of ultra-violet solar radiation, it is also logical to expect it to be greater in quantity when the short wave-length radiation, to which it is due, is most intense, or, presumably, therefore, at the times of spot minima. Now, according to the experiments of Ladenburg and Lehmann,‘7 while ozone is some- what absorptive of solar radiation it is several-fold more absorp- - tive, in fact, highly absorptive, of terrestrial radiation. Hence, in this case, as in the case of the absorption of radiation by dust, already considered, equation A, page 571, is applicable. In this equation let a be the coefficient of absorption of the ozone in the isothermal region for solar radiation, and b its co- efficient of absorption for earth radiation. To be definite, let a=0.02 and b=0.10 at the time of spot maximum, and for a spot minimum let a=0.03 and b=0.15, quantities that would require really very little ozone. Then, since the earth radiates prac- tically as a full radiator, or black body, at the absolute tempera- ture 256° C.,if T max. and T min. are the equilibrium tempera- tures at the time of spotmaximum and spot minimum, respectively, 5 T max. \4 21 = 521, T max. = 258°.65 256 500 “Lyman, Astrophys. Jr., 27, p. 87, 1908. “Lyman (l.c.). * Fabry and Buisson. C. R.. 156, p. 782. 1913: Journal de Physique, 3, p. 196, 1913; Fowler and Strutt, Proc. Rov. Soc. A., 93, Pp. 377, 1917; Fowle, Smithsonian Miscellaneous Collections V.. 68. No. 8. 1917. * Arkiv for Matematik, Astronomi och Fysik. 1, p. 395, 1904. * Annalen der Physik, 21, p. 305, 1906. 606 PHYSICS OF THE AIR and oe) 2129 : ° = i=:T . = 260°.0 ach min 5 2000’ That is, under these conditions, and if the solar constant should remain exactly the same, the temperature at the time of spot minimum would be 1°.4 C. warmer than at the time of spot maximum. Hence, even a slight increase in the solar con- stant at the time of spot maximum might still leave the tempera- ture a trifle cooler than at the time of spot minimum. Obviously, too, a greater extent of cirrus and cirrus haze during spot maxima than during spot minima (a condition some observers have thought to exist; and due, perhaps, if it does exist, to auroral effects) would also tend to produce the concur- rent temperature difference. Of course, it is not asserted that either the ozone, or the cirrus haze, actually does vary in the manner assumed—observations are inadequate to decide either question; but as such changes are in complete accord with laboratory experiments, it seems that the possibility of their occurrence in nature, and their effects, should be mentioned. INFLUENCE OF CARBON DIOXIDE ON TEMPERATURES. It was stated in the early part of this discussion, under the carbon dioxide theory of ice ages, that the question of the possible effect a change in the amount of carbon dioxide in the atmosphere might have on temperatures would be taken up later. The way to this is now open through the above discussion of ozone. Like ozone, carbon dioxide also is more absorptive of terrestrial radiation than of solar energy. Hence, increasing the carbon dioxide in the atmosphere, and thereby increasing its amount in the isothermal region where it can be treated as a shell external to the radiating earth, obviously must have the same general effect on the temperature of the earth as increasing the ozone of this region would have. That is, other things being equal, a greater or less temperature increase would follow the introduc- tion into the atmosphere of a larger amount of carbon dioxide. Because of the constant mixing caused by vertical convection, it is probable that the percentage of carbon dioxide is very nearly as great at the under surface of the isothermal region as it is at the surface of the earth. If so, then the carbon dioxide of the OTHER FACTORS OF CLIMATIC CONTROL 607 isothermal region is equivalent, roughly, to a layer 40 centimetres thick at normal atmospheric pressure. In high latitudes, where the isothermal level is low, the equivalent layer probably is thicker than this, and in equatorial regions probably thinner. Now, according to the experiments of Schaefer,** a layer of carbon dioxide 40 centimetres thick is sufficient to produce very nearly full absorption, and, therefore, no increase in the amount of carbon dioxide in the atmosphere could very much increase its temperature. An approximate idea of the possible temperature change of the lower atmosphere as a result of the presence of carbon dioxide in the isothermal region can be obtained from known data. Thus, Abbot and Fowle #® have computed that carbon dioxide may ab- sorb 14 per cent. of the radiation from a black body at the tem- perature of 282.2° C. absolute. But as this is not many degrees, 25 or so, above the effective temperature of the earth as a radi- ator, it follows that 14 per cent. is, roughly, the upper limit to which terrestrial radiation can be absorbed by carbon dioxide in the isothermal region, while its absorption of solar radiation is very nearly negligible. Assuming that the present amount of carbon dioxide in the isothermal region absorbs 1 per cent. of the solar radiation and 10 per cent. of the outgoing earth radiation (values that seem to be, roughly, of the correct order), and using equation 4, page 571, it will be seen, if the experiments here referred to and the assump- tions are substantially correct, that doubling or even multiplying by several-fold the present amount of carbon dioxide, which would leave the absorption of solar radiation practically un- changed, and increase the absorption of terrestrial radiation at most to only r4 per cent., could increase the intensity of the radia- tion received at the surface of the earth about half of 1 per cent., and, therefore, the average temperature by no more than about 1.3° C. Similarly, reducing the carbon dioxide by one-half could decrease the temperature by no more than approximately the same amount, 1.3° C. It is not certain to what extent the percentage of carbon dioxide in the atmosphere has actually varied during the geologic past, but, if the above reasoning is correct, it seems that surface ® dun. der Physik, 16, p. 93, 1905. : ” Annals Astrophys. Obsy.. Smithsonian Inst., vol. 11, p. 172, 1908. 608 PHYSice OP “TRE Ak temperatures could never have been much increased above their present values through the action of this particular agent alone. Furthermore, the fact, so far as known, that within the tropics, at least, plant growth was quite as vigorous during the ice ages as it is now, shows that for a very long time, even in the geological sense, carbon dioxide has been abundant in the atmosphere— probably never much less abundant than at present. Hence, it seems likely that a decrease in temperature of a fraction of one degree is all that can reasonably be accounted for in this way. Finally, if the above reasoning is correct, it seems that changes in the amount of carbon dioxide in the atmosphere might have been a factor in the production of certain climatic changes of the past, but that it could not, of itself, have produced the ice ages. 10. LAND ELEVATION. Since many changes in land elevation are known to have taken place during the different geologic ages it is necessary, in con- sidering the climates of the past, to inquire what climatic effects such variations in level would of themselves produce. Changes in area will be considered later. The substantial answer to this question obviously is found in the present effects of elevation on climate. That is to say, the effects of elevation must then have been distant, local, and uni- versal, just as they now are. The distant effects obviously often extended, as they now extend, many hundreds of miles to the leeward of favorably situated high mountain ranges and con- sisted, as they now consist, essentially in a decrease of precipita- tion, owing to the extraction of moisture from the atmosphere by forced convection and the consequent tendency towards, or even culmination in, desert conditions beyond. The second or local effects clearly were both an increase in the local precipita- tion, especially on the windward side, and an average decrease in the temperature, approximately the same as at present, of about 1° C. for each 180 metres, 200 metres, and 250 metres difference in elevation on mountains, hills and plateaus, respectively.®° In one important case, namely, when the surface is extensive and snow-covered (probably to some extent also when bare), this relation of temperature decrease between mountain, hill and plateau does not hold, as is obvious from the following considera- Hann, “Lehrbuch der Meteorologie,” 2nd ed., p. rot. OTHER FACTORS OF CLIMATIC CONTROL 609 tion. During long, clear winter nights, such as obtain in high latitudes, the surface becomes greatly chilled through compara- tively free radiation to the still colder air far above and even to empty space beyond. Hence, the surface air also is chilled and its density made correspondingly greater. It, therefore, flows away to lower levels and at the same time its temperature is increased through increase of pressure, or at least prevented from falling so low as it otherwise would. When the slope is steep, as it usually is om the sides of hills and mountains, this flow clearly must be more or less rapid, especially along narrow valleys or ravines, and, therefore, an approach established, within this por- tion of the air current, to the adiabatic temperature gradient of about 1° C. per each 100 metres’ change in elevation. On the other hand, when the slope is very gentle, as it is over the interior of Greenland and over much of the explored portion of the Ant- arctic Continent, air drainage necessarily is sluggish and unable to keep pace with the surface cooling. Hence, in such cases the change of temperature with change in elevation (counting from sea level) can be, and usually is, far greater than adiabatic, or 1° C., about, per 100 metres. Hence, such regions, when there are no higher surrounding mountains, can and often do establish: (1) a circulation of the upper air from the ocean to the higher portions of the plateau; (2) a well-defined surface temperature inversion, or, for the first few hundred metres, an increase of temperature with increase of elevation; (3) a slow settling of this air onto the cold surface below; (4) the precipitation, with- out cloud, of fine snow crystals—‘ frost snow ”’; (5) drainage of this chilled and relatively dense air to lower levels; (6) drifting of the snow with the winds and the consequent extension, so far as temperature and other conditions will permit, of the ice- covered or glaciated area. All these conditions obtain to-day over the two great glaciers that still remain, that of Greenland and that of Antarctica, and, presumably, therefore. must also have obtained to a greater or less extent over all great glacial fields wherever and whenever found. .Mere changes in level, therefore, might cause, and doubt- less often have caused, somewhat corresponding fluctuations in the climates of both local and leeward regions, and especially in the extent and depth of local glaciations; but this obvious fact does not in the least justify the assumption that either the universal O10 PHYSICS OF TH Ak low temperatures and extensive glaciations of ice ages or the world-wide genial temperatures of the intervening periods had, on the whole, any such origin. It may be worth while in this connection to call attention to the fact that the thickness or depth of a glacial sheet cannot con- tinue indefinitely to increase with increase of elevation, but, on the contrary, for each given locality must have a level of maxi- mum development, above which it somewhat rapidly decreases. An important if not the chief contributing factor to this result is the relation of saturation to temperature, illustrated by Fig. 195, which shows by its shaded areas the relative amounts of precipitation for each 5-degree decrease in the temperature of saturated air, assuming the volume to remain constant. Now. as the wind blows up and over a mountain range its temperature decreases somewhat regularly with increase of elevation, and, therefore, at whatever temperature precipitation begins it must, as Tig, 195 shows, continue to decrease in amount as the cloud reaches higher and higher elevations—the effect of the accom- panying volume increase on vapor capacity being much less than the effect of the temperature decrease. If the precipitation always began at the same level, it is obvi- ous that this would be the level not only of initial but also of maximum precipitation. But as the level of initial precipitation actually varies through a considerable range, it follows that the level of maximum catch lies somewhere within this range, prob- ably, too, well within its lower half. Obviously, then, the level of maximum snowfall is not at, nor even close to, the tops of very high mountains, but far down near the lower snow limit. In addition to this, the generally increasing steepness of the higher reaches causes more frequent avalanches and a greater speed of flow. In short, the higher mountain levels not only catch less snow than do the somewhat lower, but also more rap- idly shed what they do catch. A full discussion of this subject would, of course, require an account of the rate of melting, evaporation, drift, glacial flow, and probably other phenomena; but the above, presumably, is sufficient to make it clear why maximum glaciation is not at the greatest elevations, but, on the contrary, at distinctly lower levels. The universal climatic effect of land elevation, mentioned above, a greater or !ess lowering of the average temperature over, OTHER FACTORS OF CLIMATIC CONTROL 611 perhaps, the entire earth, is a logical consequence of the other two. As is well known, water vapor is by far the world’s great- est conservator of heat. Hence, anything that diminishes the average amount of this substance in the atmosphere obviously must somewhat lower surface temperatures. Now precipitation through which the average humidity is Fic. 195. -25°0.557 -20° 44 0.892 15° A1.395 GRAMS OF WATER VAPOR PER SATURATED CUBIC METER. ~10" TEMPERATURE CENT. O 15" 207 25) 30" lowered is induced chiefly by vertical convection, a condition which mountain ranges vigorously and extensively produce, (a) by mechanical deflection of the winds, (b) by updrafts induced on their sides during summer insolation, and (c) by the air drainage down their valleys of clear nights. The first two types of convection are very efficient in removing moisture from the 612 PHYSICS OF THE AIR atmosphere, while the third spreads the cold of the exposed higher levels—exposed in the sense that they are above much of the protecting vapor blanket, and, therefore, subjected to more rapid cooling. Clearly, then, assuming the same total extent of land area, the average temperature of the world is lower when there are a number of high mountain ranges than when there are but few or none—lower because the exposed heights themselves are cold, because they drain their cold air over adjacent regions, and because they dry the atmosphere and thus prevent other portions of the earth from, having as efficient protection from heat loss as they otherwise would. This lowering of the average temperature necessarily de- creases the rate of evaporation and the saturation quantity, and, thereby, presumably, further accentuates the cooling. Hence, high mountain ranges, especially when along the coasts of ex- tensive continents, lead to low temperatures, local and windward glaciation, and reduced leeward precipitation. On the other hand, the absence of mountain ranges permits of a relatively humid atmosphere and comparatively high average temperatures. Conceivably, therefore, the great world-wide climatic changes of the past originated in corresponding changes of level, gradual or cataclysmic. Nevertheless, it seems most improbable (appa- rently it has not yet been definitely proved one way or the other) that all the several glaciated continents rose and sank together— that there neither is, nor ever was, a simultaneous swing, up and down, of all, or nearly all, continental areas on the one hand and ocean beds on the other ; at least not to any such extent as this hypothesis would demand. To be sure, there is much and in- creasing evidence *! that in geologically very recent times there has been an increase of sea level relative to that of the land of, roughly, 50 metres in many tropical and subtropical regions where, so far as known, glaciers have never existed. But the simplest interpretation of this appears to be, not that so extensive and such different ocean beds have everywhere sunk to sub- stantially the same extent and at about the same time, but rather that the phenomenon is only the inevitable result of the melting of the extensive glacial sheets of the Quaternary ice age. “Vaughan, Bull. Amer. Geographic Soc., vol. xlvi, p. 426, 1914; Daly, Amer. Jr. Sci., 41, 153, 1916. OTHER FACTORS OF CLIMATIC CONTROL 613 It will be assumed, therefore, that all effects, of whatever kind, changes in land elevation may have had on climate, local and leeward, were essentially as above explained, and hence that such changes, however important as contributory factors, con- stituted neither the sufficient initiating nor the whole sustaining cause either of the glacial or of the interglacial climates if, as is generally believed, these were simultaneously world-wide. 11, CHANGES IN LAND AREA. In addition to changes in land elevation, and largely because of such changes, there have also been many variations in land extent and, consequently, in the ratio, both local and world-wide, of water surface to land surface. The importance of this phe- nomenon may be inferred from the fact that, according to Schu- chert,°? North America alone has been submerged at least 17 times over areas that range from 154,000 to 4,000,000 square miles, or fully half its present extent. Hence, in a discussion of how the climates of the past have varied, and why, it is necessary to take this additional factor into consideration. An exact or quantitative evaluation of this factor is impossible, but its quali- tative effect, and even a rough approximation to its numerical value, may be inferred from the present climates, along the same latitudes, of continents and of islands, and also from the climatic contrast between the northern and the southern hemispheres, as shown in Fig. 197, by the mean annual isotherms. That is, any appreciable increase in the ratio of land to ocean surface pre- sumably accentuated the seasonal contrasts, or made the sum- mers warmer and the winters colder than they otherwise would have been. It must also have accentuated the latitude contrast or made warm regions warmer and cold ones still colder, as is also illustrated by Fig. 197. In short, any increase of land area must, in general, have rendered the local climate more continental and less marine, and all this for the obvious reason that while the solid portions of the earth, rock, sand, and soil, have no power of avoiding great temperature ranges through either evaporation, convection, or flow to other latitudes, all three methods belong abundantly to the ocean. From this, in turn, since the range of animal species is partly restricted and delimited by the extremes of temperature. and the ® Bull Geol. Soc. America, vol. xx, p. 601, 1910. 40 614 PHYSICS OF THE AIR range of vegetable species limited both by these extremes and by the length of the growing season, it follows that an age of great land extent must, through its fossils, give evidence of an exces- sive zonal climatic contrast, or appear in middle and higher lati- tudes to have been one of harsh climates, while an age of small land extent, even though the world as a whole had the same average temperature as before, must similarly record a much less zonal contrast and a spread of genial climates to far higher latitudes. In the above attention has been confined strictly to land sur- faces, their elevation and their areas, but continental mountain ranges and plateaus are not the only portions of the earth subject to changes in elevation and extent. Ocean beds and submarine ridges must also vary in both particulars, and, in turn, profoundly modify both local temperatures and zonal contrasts. Some of these ridges doubtless have alternately risen quite to the surface, perhaps at times much higher, and again sunk to considerable depths, and in each case inevitably have produced greater or less climatic changes through the resulting alterations in the oceanic and atmospheric circulations, and, perhaps, in other ways. 12. 133.5 ATMOSPHERIC AND OCEANIC CIRCULATION. As everyone knows, practically the entire amount of heat that maintains the surface temperature of the earth is the result of the absorption of solar energy, chiefly by the lower atmosphere and by the various superficial coverings of the surface—vegeta- tion, soil, rock, and water. On the average, the daily supply of this heat per unit area is much greater within the Tropics than it is at higher latitudes, a condition that maintains two distinct, though largely interdependent, systems of perpetual circulation, the at- mospheric and the oceanic, that tend to equalize the temperatures of the earth—that keep the tropical regions from becoming un- bearably hot and the frigid zones from being unendurably cold. Clearly, then, any modification of either of these circulations would produce a corresponding change of climates, and the cause of this modification might properly be regarded as the cause of the given climatic changes themselves. But preliminary to a con- sideration of the probable climatic effects of any such modifica- tion it will be necessary, first, briefly to examine both circulations as they now enist. OTHER FACTORS OF CLIMATIC CONTROL 615 Present Atmospheric and Oceanic Circulations—Despite in- numerable disturbances, great and small, the fundamental cir- culation of the atmosphere is from equatorial toward polar regions and return, over a surface that moves from west to east with a linear velocity that gradually decreases with increase of latitude. As a result of these conditions the prevailing winds of latitudes higher than 32°, roughly, N. and S., blow from the west towards the east, or, to be exact, have a west-to-east component, while the winds between these latitudes, in the neighborhood, therefore, of the equator and the tropics, commonly blow, in the same general sense as above, from the east towards the west. Now, the rotation of the earth has forced it to take the shape of an oblate spheroid—has bulged it at the equator and flattened it at the poles—and this distortion from the perfect sphere is such that an object on the surface is in equilibrium, so far as moving north or south is concerned, only when it has the same angular velocity about the axis of the earth that the earth itself has, or, in short, when it has no motion over the surface east or west. Obviously, then, an object moving from west to east, or with an angular velocity exceeding that of the earth, would be in equilibrium on a bulge greater than that which actually exists, and hence all winds with an eastward component, and, therefore, as stated, the prevailing winds outside latitudes 32° N. and S., must tend to climb up towards the equator. On the other hand, an object moving from east to west, or with an angular velocity less than that of the earth, as do the prevailing winds between lati- tudes 32° N. and S., must tend to slide down towards the adjacent or nearest pole. These opposite drifts of the winds, therefore, the drift of the winds of high latitudes toward the equator and the drift of the tropical winds toward the adjacent pole, obviously have produced the two belts of relatively high barometric pres- sure that roughly parallel the equator, the one at about latitude 32° N.; the other at approximately latitude 32° S. Each belt of high pressure is greatly disturbed where it crosses a continental area, owing chiefly to temperature inequalities, but it also happens that even on the oceans the belts are of unequal intensity, and, what is of especial importance, have relatively fixed absolute pressure maxima or anticyclonic centres. These permanent or nearly permanent centres of high pres- sure, or centres of action as they have been called. are five in PHYSICS OF THE AIR 616 (‘uvyong> “SIBQOST yenuur ues SOL 06 SL 09 Sb Of St O St OE S¥ 09 SL OG SOl Cel GEl OSI S9l O8l SOL OSL 09 Sv o¢ Gt Sl oe Sv 09 SL OSI SECLOZL SOL 06 GZ 09 Sv Of SL O Slt O€ GH 09 GFL OG SOI OZt GEL OSL SOl OGL SOL OSI og} St of Sl SL oe Sb 09 SL ‘961 “OIA OTHER PACTORS OF CLIMATIC CONTROL 617 number, as a reference to Fig. 196 will show; two in the northern hemisphere, one off the coast of southern California, the other “near the Azores; and three in the southern hemisphere, one off the coast of Chile, another just west of South Africa, and a third between South Africa and Australia. Further, as is shown by Fig. 197, there 1s, in the region of each of these permanent anti- cyclonic centres, a marked equatorial deflection of the annual average isotherms, showing clearly that while each high pressure belt as a whole is caused by the mechanical squeeze of the opposite air drifts, above explained, the additional pressure that produces each maximumi is a result of the local relatively low temperature, which causes a corresponding contraction and, therefore, in- creased density of the local atmosphere. And, finally, these par- ticular low air temperatures in turn are caused by cold ocean cur- rents, as is obvious from Fig. 198, and again from Fig. 199, which show the interrelations here considered between barometric pressure, air isotherms, and ocean currents. That both the mere existence of these anticyclonic centres and their several geographic locations are of great importance to the climates of neighboring regions, through their directing influence on the prevailing winds, is obvious from Figs. 200 and 201, that give the directions and indicate the average force and steadiness of ocean winds at different seasons. But all this influence on the winds, however vital to many a local climate, can properly be said to be only one of the important climatic effects of the existing ocean currents. In addition to the several permanent anticyclonic centres there are, also (see Figs. 200 and 201), one permanent cyclonic centre, the Icelandic “ low,” and one semi-permanent or winter cyclonic centre, the Aleutian “ low,” both of which are strongly influenced by ocean currents, the first by the Gulf Stream and the second by the Japan Current. The Icelandic ‘low’ results from the tem- perature contrast between the air over the relatively warm water and that over the glacial fields of Greenland and Iceland, in con- sequence of which there is established a circulation in the sense of an overflow from the warm region and counter under- flows from both the adjacent cold regions. This thermally in- duced circulation in conjunction with the rotation of the earth produces cyclonic conditions, and as the temperature contrasts are permanent (the Icelandic and the Greenland glaciers remain PHYSICS OF THE AIR 618 (ueyong) “suIsay}OSE jenuuc uva WwW OSL SeLozi SOl O6 SL 09 GH Of Sl Oa Gt o€ Sb O09 SL 06 GOL OZ SEL OSGi GOI OGL SOL OSI Ost Sel O@t SOL O06 SL 09 SH OF St O St Of FH 09 GL OG GOL OZl Get OSI G9 OBL SOL OSL *L61 ‘O1g 619 OTHER FACTORS OF CLIMATIC CONTROL ‘ULIEM ‘SAUT] pa}Op !pjoo ‘saury [[nyJ !s}ussns uvI00 OSL S$¢1 O21 SOL OG F242 09 Sv OF Gt O St OF Sr O09 SL OG GOL O@l GEL OSI GS9L OBL Sol OSI 09 S+ “da ock 09g GL OSI Sl ozt SOL O6 SL 09 Sw O€ StL O St OF SH O9 SL OG GOL O@L FEl OSI Sol OB! Sot ost "g61 “Oy PHYSICS OF THE AIR 620 “SIVQOSI PUL SUIIIYJOSI [PNUUL UBS UO SyUatIng UvaD0 JO uolpIsodiadng OGL SEL OZL GOL O6 GL 09 S¥ Of Gl O Gl OF Se 09 GL OG GOL OZI GEL OG! S91 OBl S9l OSI Qg 09 SR a PNT SSS EE Ee Sv oe oe SL St Of o€ Se 09 09 SL OL OSI sel OZl SOL O06 SZ 09 Se O€ SL O St O€ Sv 09 GL O06 GOL Oet Sel OSt SOL OBL SOL ost “661 “OlY OTHER FACTORS OF CLIMATIC CONTROL 6a1 2 ¢ z é ° ° “ : ow zur 3 ° =Crw eI Fut So Zazy Fee 3 at z¥ ge a ive = ° wre OPT >5h x gene he Ce ° ange : Z Luitg? Uh, ° a ¥ bp B= 63y eli + is eo dee i) i Zico i eo a iS “yhau ty : a a Ni Ret; SS AS i iM 2 ° = x ft +O a ANSSRS AES ee ola NWOARES ° ANY S ASN A a ERS : sl} ol SA ES Q | 2 5° t+ i 1 tnd IN N s a 4 ay TET INNS 5 , Ss Lak t Pept yy SS o 3 Si o | eae PISS © o & eae HIN 3 5 EG 4 PRG Sie 2 y 0 Zs ge S a ele < wit Oo ° 36 2 2 = o os o } a | 3 <6 a — | ° h f = ¢ ie es VES q ESAS E o| i: uc ° 6 © REN o | 4 = J NENA 8] Ar Ey 2 “CRS ‘ Sean ° gf Su 2 - i ig a) — “= Sy ° + < ° ° al Nl ne ° ° ° 2S ° ° o t 622 ‘1G. 201. PHYSICS OF THE AIR 120 140 | | 100 40 20 20 40 60 80 wil a ie 120 100 80 60 160 140 120 140 160 180 0 10 | ARROWS FLY WITH THE WIND LENGTH DENOTES HEASURE OF i ~Y WOASS eS Let NSS SS Ke Ss P= Sh IS ~ We it Ne GAN) LES, BASH eiy LZ WSS SS x WS NS STEADINESS THE DARKER THE ARROW_THE GREATER THE Ms a8 LEAL REA FORCE. yar shit ae | i) Ny aS i SoS i ale ee aaa, Iw \ $ ANY | Shy tas SUTTER NY 7 aatiatt I Re Vy = —| =f SS — b. SS A eee 7a =, ~. ae = =~ Ke 140 100 120 60 80 20 0 20 40 40 100 80 60 180 160 140 120 TOO 120 140 160 (Képpen.) Normal wind direction and velocity, July and August. OTHER FACTORS OF CLIMATIC CONTROL 623 throughout the year and indefinitely), the cyclonic conditions themselves of this region are also permanent. The Aleutian “low,” on the contrary, that is flanked by the Alaskan peninsula and the peninsulas of northeastern Siberia, has a circulation similar to that of the Icelandic “low,” and for sim- ilar reasons, only while the adjacent land areas are covered with ice and snow and, therefore, are relatively cold. In the spring, when the snow melts away, the cyclonic conditions also disap- pear, there then being nothing to sustain them. But the formation and geographic location of the above cyclonic and anticyclonic conditions—direction and force of winds, nature and frequency of storms, and the like—do not exhaust the more important climatic effects of existing ocean currents, as a glance at the annual average isotherms and ocean currents of the North Atlantic (Fig. 199) will show. In fact, the January isotherm of Chicago, Buffalo, and Boston (very approxi- mately on the latitude of Rome), though not particularly cold, passes, under the influence of the Gulf Stream, through Iceland and on well beyond the Arctic Circle to the north of Norway and Sweden; while, under the same influence, frost is practically unknown and semitropical vegetation flourishes on the Scilly Isles in the latitude of northern Newfoundland. Similarly, it is said that because of the Japan Current frost rarely, if ever, occurs on one or two of the Aleutian islands. Obviously, then, as the above several examples show, the ocean currents, driven by the winds, deflected by the rotation of the earth and by continental and island barriers, and otherwise modified by various minor causes, are both directly and indirectly of the greatest importance to the climates of many parts of the world; directly through the immense thermal interchange they establish between the torrid and the frigid zones, and indirectly through the centres of action, the permanent and semi-permanent “hiehs ” and “ lows,” they create and maintain. Possible Changes in the Oceanic Circulation and the Obvious Climatic Results —Clearly, if the immense system of hot-water heating by which the temperature of the whole surface of the earth tends to become equalized should be greatly modified, say by the opening of a valve here or the closing of another there, correspondingly reat climatic modifications surely would have to follow. And there are several, perhaps many, such valves that 624 PHYSICS OF ‘THE AIR have been opened or closed, irregularly, and from time to time, since the beginning of geological records. One such valve now partially open, perhaps at one time closed and at another still wider open than at present, lies between South America and the Antarctic continent. Another, now but a little way open, is Bering Strait, which doubtless has greatly changed from one to another geologic age. Still another, now wholly closed, but at one time probably wide open, is the Central American region between the Caribbean Sea and the Pacific Ocean. This par- ticular valve, if now widely opened, would, on the one hand, obliterate the Gulf Stream proper and probably diminish the Antilles current, and, on the other, greatly increase the Japan Current; and, of course, in each case induce widespread and marked climatic changes. Yet another valve, now rather wide open, that merits special mention, a valve that may have suffered many changes and have undergone its latest opening only in recent times, geologically speaking, is found in that ridge which by way of Iceland and the Faroe Islands connects Greenland with north Scotland. With this Greenland-Scotland valve closed and even with all the other valves, channels of flow and deflecting obstructions, substantially as they now are, it 1s well-nigh certain that the Icelandic “low” would shift to some point between Greenland and Newfoundland; that Labrador and the Hudson Bay region would receive a greatly increased precipitation; that the Nor- wegian Sea would become largely, if not wholly, ice-covered; and, finally, that Norway and Sweden, since they have the same latitude as Greenland, would be swept by winds of practically Arctic temperature and, therefore, eventually would become, like Greenland itself, almost wholly ice-capped. Indeed, any decided change in either the average intensity or average position of the Icelandic ‘‘ low,” if continued for even a few weeks, seems to produce a marked influence on the weather of west and north Europe. In general, whenever the average position of this “low” during a winter month is considerably to the west of its normal place, as occasionally happens, the average temperature of north Europe is likely to be several degrees below normal.** That is, the above conclusion that a permanent or age-long shift of the Icelandic ‘low’ far to the west of its present position would *’ Hann, “Handbuch der Meteorologie,” 3rd ed., pp. 632-3, 637, 630. OTHER FACTORS OF CLIMATIC CONTROL 625 lead to, or, at least, permit, the reglaciation of portions of north Europe appears to be abundantly supported by direct observation. Nor would these be all the profound climatic changes that prob- ably, indeed well-nigh certainly, would follow the closing of the Greenland-Scotland valve, but they are sufficient, if granted, to indicate how vitally important the direction and magnitude of the ocean currents are to our climates and to local glaciation. Doubtless many other valves have contributed their part in the control of the earth’s great water circulation and the regu- lation of its climatic details, but it would be tedious to take all of them up individually, and for the present purpose unnecessary, since it is desired here only to make clear the fact that oceanic circulation is a vital factor in the production and control of many a local climate. . 14, SURFACE COVERING. The contrast between land and water in respect to their cli- matic effects obviously is largely due to the inequality of their surfaces both as radiators and as absorbers. The values of these properties are approximately known for the ocean, but not for the continents. In fact, there are no fixed values for land areas; nor can there be, since their surfaces undergo many and great changes. Bare soil, luxuriant vegetation, and snow, for instance, are among the surface coverings that have very unequal powers of radiation and absorption; and, therefore, the changes from one to the other over any extensive area necessarily is a matter of climatic importance. To illustrate an extreme, but seemingly possible, climatic effect due to change of surface, assume: (1) That continental areas are unusually extensive; (2) that mountains are abundant and high; (3) that during a period of a few years volcanic explosions are frequent (one a year, say) and of such nature as to put large quantities of dust in the upper atmosphere, as did the Krakatoa and other explosions of historic times. The low temperatures due to the volcanic dust would lead to an abnormal extent of continental snow covering, and this, in turn, by its power of reflection, would render the insolation correspondingly less effective—would virtually decrease the solar constant, for all the reflected radiation that passes directly to ' 626 PHYSICS OF THE AIK space had as well never have reached the earth at all, so far as producing any heating is concerned. In this way an ice cover- ing of the land areas, far more extensive than previously existed, might be initiated by the volcanic, explosions, and then perpetu- ated over long periods, if not even added to, by the highly re- flecting snow cover. CHRONOLOGICAL RELATION OF GEOLOGICAL EVENTS. It is rarely possible to state in terms of years even approxi- mately when any prehistoric geological event occurred or, simi- larly, to measure its duration, but it is possible in large measure accurately to decipher the order of their occurrence and to learn their chronological relations to each other. Our present knowledge of geological chronology has been summarized by several geologists—Schuchert in his “ Climates of Geologic Time,” °+ for instance—all of whom, though differing in details, have much in common. In the course of his summary Schuchert °° says: The data at hand show that the earth since the beginning of geologic history has periodically undergone more or less widespread glaciation, and that the cold climates have been of short geologic duration. So far as known, there were seven periods of decided temperature changes, and of these at least four were glacial climates. The greatest intensity of these reduced tem- peratures varied between the hemispheres, for in earliest Proterozoic and Pleistocene time it lay in the northern, while in late Proterozoic and Permic time it was more equatorial than boreal. The three other probable periods of cooled climates are as yet too little known to make out their centres of greatest intensity. Of the four more or less well-determined glacial periods, at least three (the earliest Proterozoic, Permic, and Pleistocene) occurred during or di- rectly after times of intensive mountain-making, while the fourth (late Pro- terozoic) apparently also followed a period of elevation. The Table Moun- tain tillites of South Africa, if correctly correlated, fall in with the time of the making of the great Caledonian Mountains in the northern hemisphere. On the other hand, the very marked and world-wide mountain-making period, with decided volcanic activity, during late Mesozoic and earliest Eocene times, was not accompanied by a glacial climate, but only a cooled one. The cooled period of the Liassic also followed a mountain-making period, that of late Triassic time. We may therefore state that cooled and cold climates, as a rule, occur during or immediately follow periods of marked mountain- making—a conclusion also arrived at independently by Ramsay.” "Carnegie Institution of Washington, Publication No. 192, p. 285, 1914. 57 ¢., p. 286. ® Oversigt af Finska Vet.-Soc. Forhandl., vol. lii, pp. 1-48, roro. OTHER FACTORS OF CLIMATIC CONTROL 627 From the above, with which most geologists are in accord, it appears that neither cold climates nor even cool climates ever occurred except when mountains were either building or at least geologically young, and, also, so far as may be judged from the Strand line of North America, when the ratio of land area to ocean was relatively large. This coincidence appears to have occurred too frequently to admit of the idea that it was mere chance or due to anything less than some sort of a casual rela- tion—surely not that the cold climates produced the mountains, nor necessarily that mountain building was wholly responsible for glaciation, but rather that crustal uplift and the other geological phenomena, whatever they were, that went with it so combined as to produce at one time a small and at another a great climatic change. If, also, as supported by geological evidence, vulcanism (only violently explosive volcanoes are of especial climatological importance), was, in general, most active during the epochs of mountain building, but unequally so for different mountain sys- tems, then it follows that at each of these particular times there obtained to a greater or less degree precisely those formations and conditions—high mountains, extensive land area, restricted oceanic circulation and much volcanic dust—which are known to be effective to-day in reducing temperature, and which, presum- ably, are entirely sufficient, when properly codperating, to pro- duce not only a cool climate, such as, relatively speaking, now prevails, but even climates that are severely glacial. Which of these several causes was most effective in producing the low tem- peratures of any given age in the past (they must have been unequally active at different epochs) it may be impossible to de- termine, but the brief duration of distinctly glacial ages in com- parison to the much longer periods when mild climates prevailed seems strongly to favor the assumption that vigorous vulcanism was often at least an important contributing factor. But whatever else geologic chronology, as it is now under- stood, may teach in regard to the climatic changes of the past, the practical coincidence of cold ages with mountain building epochs appears at once and irretrievably to negative the entire group of cosmical ice-age theories—those that assume all great climatic changes to depend upon the sun, a condition in space, or anything else wholly outside the earth. Such theories, any solar theory, for instance, must also assume that those external changes, solar 628 PHYSICS OF THE AIR changes, say, which caused a marked lowering of terrestrial tem- peratures, occurred only at or about the times of mountain build- ing. That is, they must assume that either (a) the solar changes caused the mountain building, or (b) that mountain building caused the solar changes, or, finally (c) that both had some un- known but simultaneously acting common cause. But each of these assumptions is wholly untenable—it has no support what- ever in the logic of cause and effect—and, therefore, it seems that any theory that implicitly or otherwise is definitely hung on the horns of this dilemma, as is every cosmical ice-age theory, nebular, or what not, must itself be abandoned. This is not intended in the least to deny or even to question the existence of small solar changes of comparatively short dura- tion, but only to emphasize the fact that forces within the earth itself suffice to modify its own climate, and that there is much and accumulating evidence that these and these alone have actually caused great changes time and again in the geologic past; done so by building mountains, and by tearing them down; by emerging continents, and by submerging them; by restricting ocean currents, and by making wide their paths; by filling the atmosphere with volcanic dust, and by clearing it of foreign substances; and by every possible combination of these and other such phenomena. CONCLUSION. It appears from various considerations that, with a constant or nearly constant output of solar energy, the earth itself pos- sesses the inherent ability to profoundly modify its own climates, whether only local or world-wide. Thus, a mere change in land elevation, whether of plateau or of mountain range, a thing that appears often to have happened, must alter both the local and the leeward climates, and, by reducing the general humidity, some- what lower the average temperature. Besides, a change in land: elevation of any considerable extent is pretty certain to be accom- panied by a somewhat corresponding variation in continental area, and such modification of shore lines and ocean beds that greater or less changes must follow in the directions, tempera- tures, and magnitudes of ocean currents, in the location and in- tensity of permanent “highs” and permanent “lows,” in the direction, force and temperature of local winds, in the amount OTHER FACTORS OF CLIMATIC CONTROL 629 and kind of local precipitation, and in a host of other meteoro- logical phenomena. Again, as the laws of radiation indicate must be true, and as observations, at least back to 1750, the date of the earliest reli- able records, show, the temperature of the lower atmosphere de- pends in part upon the amount of dust in the upper air, in the sense that when this amount is great the average temperature at the surface of the earth is below normal, and when the dust is absent this temperature is comparatively high. Hence, as there appear to have been several periods of great volcanic activity in the past with intervening periods of volcanic quiescence, it is inferred that volcanic dust in the upper atmosphere was at least one important factor in some, if not all, of the great and uni- versal climatic changes that have left their records in abandoned beaches and forsaken moraines. How these various causes of climatic changes were related to each other during the geologic past is not yet entirely clear. This the geologist, most interested and most competent to judge, must determine. May it be that extensive upheavals and great volcanic activity often were synchronous? If so, the climatic effects of each obviously were added to those of the other, and hence it may be that the greatest of our past climatic changes were caused by the roughly synchronous variations in continental level and volcanic activity ; universal cold periods coming with increase in vulcanism, increase in elevation and the obstruction of inter- zonal oceanic circulation; universal mild periods when volcanic dust seldom veiled the skies, when thé continents had sunk or been eroded to low levels and when there was great freedom of oceanic circulation from equatorial to polar regions; mild uni- versal climatic oscillations with temporary changes in vul- canism; and mere local climatic changes with variations in such local climatic controls as near-by elevations and neighboring ocean currents. Finally, as the past is the pledge of the future, it is but reasonable to suppose that the world is yet to know many another climatic change, in an irregular but well-nigh endless series, often local and usually slight, though always important, but occa- sionally, it may be, as in the ages gone—whether towards the auspiciously genial or into the fatefully disastrous—universal, profound and momentous. 41 APPENDISC IT, GRADIENT WIND VELOCITY TABLES. To be used only in the absence of local disturbances—thun- derstorms, line squalls, and the like—or strong lorisontal tem- perature gradients, and when the isobars, as drawn, are free from any considerable reduction or other errors. Also to be used with discretion in the case of east winds in the middle latitudes, since at an altitude of 1 kilometre or more their actual velocitics are likely to be less than the computed, as explained on page 133. To find from the following tables the probable wind velocity at 1 to 2 kilometres elevation over any given place, one notes, a, the current system of winds, cyclonic or anticyclonic, at that place (this determines which table to use) ; 0, the latitude of the place in question (this determines the latitude division of the table in which the desired value is to be found) ; c, the pressure gradient shown on the concurrent weather map in terms of the differ- ence of the barometer reading in millimetres per too kilometres at right angles to the nearest isobar (this, through the closest tabu- lated gradient, locates the gradient division of the value sought) ; and, finally, d, the radius of curvature, in kilometres, ot this isobar (a sufficiently close practical value of r) at the place in question, on line with which the desired velocity is given in metres per sec- ond, kilometres per hour, and miles per hour. The wind at the given levels is roughly parallel to the corresponding surface 1so- bar, and so directed that on following it one will have the lower pressure to his left. In using these tables in conjunction with weather maps whose barometric interval is 0.1 inch, the interval used in the United States, it is only necessary in taking step c to note the number of miles between the 0.1 inch isobars and then select from the second expressions in the first columns the nearest to an equal gradient. The actual gradient, radius of curvature, density, and latitude usually will all differ somewhat from the tabulated values, but as the latter, except the density, which may be computed approxi- 630 GRADIENT WIND VELOCITY TABLES 631 mately, are given for small intervals it would be easy to add, with their proper signs, interpolated corrections. In practice, how- ever, this will hardly be necessary, partly because of the great number of intervals directly supplied by the tables themselves, and partly because actual velocities and computed gradient veloci- ties are likely to differ too much to justify minute corrections. They differ because the atmosphere never attains to a fixed or steady state of motion; because the actual density is likely to dif- fer from that assumed; and because the gradient at the level for which computation is made is not, as a rule, exactly the same as that given on the maps. In regions of great elevation, 1 kilometre or more, the isobaric lines, if drawn, as they commonly are, in accordance with values obtained by reduction of the barometer to sea level, may be seri- ously in error during both unusually warm and exceptionally cold weather. Obviously, therefore, it is not safe, at such times and places, to use the reduced distribution of isobars for the calcula- tion of gradient winds—nor, indeed, for any other purpose. The first line in each section of the anticyclonic table gives the maximum velocity for the given density and pressure gradient and the corresponding radius of curvature of the path. It will be noticed that this limiting radius grows smaller as the gra- dient is decreased, in accordance with the fact that steep gradients and strong winds can not occur near the centre of an anti- cyclonic region. 632 PHYSICS OF THE AIR TaBLeE I. Gradient Wind Velocity for Cyclonic Movement. (Computed for p=.oo11, a density that obtains at an elevation of about 1 kilo- metre above sea level.) AB (mm.) TOO Ei =barometric gradient, or difference of barometric reading in milli- 7 , : AB (tenths tn.) metres per 100 kilometres at right angles to isobars Sear ; 158 71. r=radius of curvature of isobars in kilometres. v™ =velocity in metres per second. vn =velocity in kilometres per hour. r yt = velocity in miles per hour. r Latitude 25°. AB(mm.) |. | ym yen ym | AB (mm.) pat yen yt 100 km. : | s hr | hr 100 km. ; 5 hr hr | | | | 0.2mm. _| 100 | 2.73) 9.83, 6.11 0.6mm. _ I0C = 5.99 21.56 13.40 100 km, | 200 | 3-13 | 11.27} 7.00|\ ;o0 km. | 200: 7.38 26.57, 16.51 0.1 in. 300 3.33 | 11.99) 7.45 0.1 in. | 300 , ee ' 29-45 18.30 zone 6, 400 1.3.45 | 12:42) 7.72 pee » 400 8.71 | 31.36) 19.49 wage | 500 | 3.53 | 12.71 | 7.90 263 mt. | §00 | 9-10 32.76, 20.36 ' 600 | 3.58 | 12.89] 8.01 ' 600} 9.40 | 33.84 21.03 ' 700 . 3.63 | 13.07| 8.12 | 700 | 9.64} 34.70! 21.56 | 800 3.66 | 13.18) 8.19 , 800 9.83 | 35.39) 21.99 / g0O 3.69 | 13.28! 8.25 | 900 | 9.99 | 35.96! 22.34 , 1000 | 3.71 | 13.36 8.30) | 1000 | 10.13 | 36.47 | 22.66 | 1200 | 3.74 | 13.46, 8.36 | | 1200 | 10.35 37.26 | 23.15 1500 | 3.78 | 13.61 | 8.46), | 15co | 10.58 | 38.09 | 23.67 2000 3.81 13.72] 8.53) | 2000 | 10.84 39.02 | 24.25 ' 3000 3.85 | 13.86] 8.61 i | 3000 | II.12 40.03 | 24.87 © 3.93 14.15) 8.79 : | © {11.79 | 42.44, 26.37 » ! : ! | | 0.4mm. _| 100 , 4.53 | 16.31 10.13 || 0.8 mm. — | 100 7.24 | 26.06: 16.19 too km. ‘| 200, 5.45 | 19.62 12.19 || joo km. ' 200 | 9.06 | 32.62 | 20.27 o.1in. | 300; 5:95 Be 13.31 0.1 in. | 300 | 10.15 | 36.54 ae Ceo 4. 400 .27 | 22.57 | 14.02 a et _ 400 10.90 | 39.24) 24.3 3951 | soo 6.49 | 23.36 | 14.52 ; T97 Mt. | S00 | 11.46 | 41.26! 25.64 | 600 6.66 | 23.98 | 14.90 | 600 | 11.90 42.84 | 26.62 700. 6.79 | 24.44 15.19) 700 12.25 | 44.10: 27.40 800 6.90 | 24.84 | 15.43 i 800 12.54 45.14, 28.05 ; 900 ' 6.98 | 25.13 15.62 I 900 . 12.78 | 46.01 28.59 1000 , 7.05 | 25.38 15.77 | ‘1000 (12.99 46.76 29.05 : 1200 13.32.47.95 29.79 16.30 1500 | 13.69 49.28. 30.62 | 2000 7.42 26.71 16.60 2000 I4.1I 50.80; 31.57 : 16.89 3000 14.58 52.49 32.62 ; @ 7.86 | 28.301 17.58 © 15.72 56.59 35.16 GRADIENT WIND VELOCITY—CYCLONIC 633 Latitude 25° (Continued.) AB (mm.) | m km mi || AB (mm.) m km | ,,mi 1ookm. |” We ee | Aap 100 km. " Pe | ie oe 1.0mm. _| 100} 8.35] 30.06) 18. cel atom, 100 | 14.59 | 52.52] 32.63 100km, | 200 | 10.58] 38.09 67'| t00 ae 200 | 19.21 | 69.16] 42.97 0.1 in. 300 | 11.94] 42.98 71|| O.1 in. 300 | 22.28] 80.21) 49.84 158 mi. 400 | 12.90| 46.44 a 86, 6a. wd. 400 | 24.60} 88.56) 55.03 ; 500 | 13.63 | 49.07 30.49) 500 | 26.44) 95.18] 59.14 600 | 14.20! 51.12] 31. 76. 600 | 27.97 |100.69} 62.57 700 | 14.67 | 52.81] 32.81/| 700 | 29.27 |105.37| 65.47 800 | 15.06 | 54.22 33-69), 800 | 30.40 |109.44] 68.00 goo | 15.39 | 55-40] 34.42) g00 | 31.38 |112.97) 70.20 1000 | 15.67 | 56.41) 35.05/| 1000 | 32.26 |116.14| 72.17 1200 | 16.13 | 58.07 36.05) 12CO | 33.74 |121.46, 75.47 1500 | 16.65 | 59.94] 37.25 1500 | 35.50 |127.80| 79.41 2000 | 17.24} 62.06 38.56), 2000 | 37.64 |135.50) 84.20 3000 | 17.92 | 64.51} 40. 08 3000 | 40.34 |145.22} 90.24 co) 19.65 | 70.74] 43.96): © | 49,13 |176.87! 109.90 | 1.5mm. _| 100 | 10.75} 38.70 see ae - 100 | 16.23] 58.43) 36.31 100 km. 200 | 13.87] 49.93) 31-03) ton km. 200 | 21.49 | 77.36) 48.07 0.1 in. 300 | 15.87 | 57-13) 35-5°!] o1in 300 | 25.04] 90.14) 56.01 105 mi 400 | 17.32 | 62.35) 38.74!, 53 mi. 400 | 27.74 99.86) 62.19 500 | 18.44 | 66.38] 41.23): 3 me. 500 | 29.92 |107.71| 66.93 600 | 19.35 | 69.66) 43.28) 600 | 31.73 [114.23] 70.98 700 | 20.11 | 72.40! 44.99]| 700 | 33.28 |119.81| 74.45 800 | 20.75 | 74.70} 46.42) 800 | 34.64 |124.70) 77.49 g00 | 21.30] 76.68 47.65|| g00 | 35.83 |128.99| 80.15 1000 | 21.78 | 78.41] 48.72 1000 | 36.89 |132.80) 82.52 1200 | 22.59 | 81.32} 50.53). 1200 | 38.71 |139.36| 86.59 1500 | 23.50; 84.60 52.57) 1500 | 40.88 |147.17) 91.45 2000 | 24.58! 88.49) 54.99 2000 | 43.56 |156.82) 97.44 3000 | 25.87| 93.13 57-87) 3000 | 47.01 |169.24/105.16 © | 29.48 106.13) 65.95), © | 58.96 |212.26 131.90 2.0mm, _| 100 | 12.79| 46.04| 28. 61!| 4.0mm. _| 100 | 19.15| 68.94! 42.84 100km, | 200 | 16.70) 60.12) 37. 361 100 km. | 200 | 25.57] 92.05) 57.20 0.1 in. 300 | 19.26| 69.34! 43.09: 0.1 Gn. 300 | 29.99 |107.96) 67.08 he nee 400 | 21.16 | 76.18] 47.34); 7 400 | 33.39 |120.20) 74.69 £9. 4 500 | 22.65 | 81.54' 50.67, 39 5C0 | 36.17 |130.21| 80.91 600 | 23.88} 85.97) 53.42! 600 | 38.51 1138.64) 86.15 700 | 24.92 | 89.71) 55-74) 700 | 40.53 |145.91| 90.67 800 | 25.80 | 92.88) 57.71). 800 | 42.31 |152.32| 94.65 goo | 26.58) 95.69] 59. 46" g00 | 43.89 |158.00; 98.18 1000 | 27.26| 98.14 60.98 1000 | 45.31 |163.12/101.36 1200 | 28.40 |102.24| 63.53! 1200 | 47.77 |171.97| 106.86 1500 | 29.74 |107.06, 66. 52, 1500 | 50.75 |182.70)113.52 2000 | 31.34 112.82! 70. 10. 2000 | 54.51 |196.24/121.94 3000 | 33.31 |119.92| 74. 52) 3000 | 59.48 }214.13|133.05 co | 39.31 141.52 87. oe o | 78.61 |283.00}175.85 634 PHYSICS OF THE AIR Latitude 30°. AB (mm.) - y” pen mi AB (mm.) r ym yen mi 100 km. s hr hr 100km. s hr hr | 0.2mm. | 100 2.48 8.93 5.55: 0.8 mm. 100 | 6.86) 24.70) 15.35 1ookm, | 200 | 2-79 10.04 6.24 100 km. 200 8.43 | 30.35, 18.86 Ort. , 3001 398) To. 55 6.50, ori. ee a eA ae eae a 400 3.01 10. Was See | 9.92 35.71 22. 789 mi. So 3.07! 110s] 6.8y, 197 | $00 10.35 37.26 23.15 600 3-10 I1.16 6.93 » 600 10.68 | 38.45, 23.89 70O (3.13 11.27! 70! 700 | 10.94 39.38 24.47 800 : 3.15 | 11.34 7.05 ' 800 | 11.16; 40. 18, 24.97 900 3.17, 11.41 7.09 | , 900 11.33 | 40.79, 25.35 1000 3.19) 11.48, 7.13: 1000 11.48) 41.33, 25.68 1200 3.21! 11.56 7. 13 ' 1200 | 11.72 | 42.19 26.22 "1500 | 3.23) 11.63) 7.23) | 1500 © 11.98 | 43.13] 26.80 2000 ; 3.25} I1.70) 7.27 ; 2000 12.26, 44.14 27.43 3000 3.28. 11.81 7.34) » 3000 12.57) 45.25 28.11 = 3-32 11.95. 7.43) 5-13.29! 47.84 29.73 O.4qmm. _ 100, 4.22, 15.19 9.44! 1,0 mm. ' 100 7-95 28.62 17.78 1ookm, 200. 4.96 17.86 11.10 joo km, | 200: 9.90 35.64. 22.15 0.1 in. 300 5.34; 19.22 11.94: O71 in. | 300 11.04 39.74 24.69 Sea 400° §.58. 20.09 12.48; — >. | 400 11.82 42.55 26.44 395 S00 5.74, 20.66 12.84 158 mt. | S00 + 12.40 44.04! 27.74 600 5.86 21.10 13.11 600 12.84 | 46.22, 28.72 7OO 5.95 | 21.42) 13.31 7OO 13.20, 47.52 29.53 800 6.02) 21.67, 13.47 800 13.49 48.56 30.17 goo 6.08 21.89 13.6C,, 900 | 13.74 49.46 30.73 1000 , 6.13, 22.07, 13.71 1000 13.95. 50.22 31.21 1200 | 6.21 22.36 13.89 1200 14.28 51.41, 31.95 1500 6.28, 22.61, 14.05 | 1500 14.65. 52.74 32.77 2000 6.37; 22.93. 14.25' 2000 | 15.06 54.22 33.69 3000 6.56 23.62! 14.68. 3000 | 15.51 55.84 34.70 © 6.64 23.90) 14.85), o 16.61 59.80 37.16 0.6mm. _ 100 §.63) 20.27 12.60) 1.5 mm. | 100 , 10.32 37.15 23.08 100 km. 200. 6.80) 24.48. 15.21) 100 km. 200 13.12 47.23, 29.35 0.1 in. 300 per apr 16. $4 O.L in. ca | 35-46, 33-22 Sat 400 7.85) 28.26 17.5 ee ae 4 16.07 57.85 35. a 500 | 8.15 | 29.34! 18.23) Og mt _ §00 | 17.00 | tie ak a6 | 8.37 | 30.13, 18.72) ' 600 | 17.73 63.83 39.66 700. «68.54 30.74 19.10) . 700 | 18.33 65.99: 41.00 800 | 8.68) 31.25 19.42! | 800 | 18.84 67.82: 42.14 | goo | 8.79 | 31.64) 19.66. | 900 | 19.27 69.37: 43.10 1000 ; 8.89) 32.00 19.88 , | 1000 19.63: 70.67 43.91 1200 | 9.04 32.54 20. 22) 1200 20.24 72.86 45.27 1500 9.20! 33.12' 20.58), ' 1500 ! 30, 92° 75.31 46.80 2000 | 9.37 | 33-73, 20. 96. 2000 21.69, 78.08, 48.52 3000 , 9.55 | 34. 38) 21.36. _ 3000 Lae: 58 81.29 50.51 @ | 997 35.89) 22.30 m "24.92 Bo71 55.74 GRADIENT WIND VELOCITY—CYCLONIC = 635 Latitude 30° (Continued). AB (mm.) | | m km smi | AB (mm.) m km mi 100km. | t | Y Ve 3 hr | 100 km. | m | We : ae ie i | | 2.0 mm. x 100 | 12.34 | 44.42| 27.60 || 3.0mm, _ 100 | 15.77 56.77 | 35-27 100 km. | 200 | 15.90) 57-24) 35-57 || 100 km. 200 | 20.64 74.30} 46.17 O.1 in. 300 | 18.16] 65.38) 40.62 0.1 in. 300 | 23.85 85.86, 53-35 79 mi. | 400 | 19.79) 71.24) 44.27 53 ae 400 | 26.24 94.46, 58.70 500 | 21.06; 75.82] 47.11 : 500 | 28.13 |101.27; 62.93 | 600 | 22.08 | 79.49] 49.39 600 | 29.85 |107.46| 66.77 | 700 | 22.93 | 82.55] 51.29 700 | 31.00 |I111.60! 69.34 | 800 | 23.64 | 85.10} 52.88 800 | 32.14 ]115.70| 71.89 ' 900 | 24.26| 87.34) 54.27 900 | 33.12 |119.23) 74.09 | 1000 | 24.79 | 89.24] 55.45 1000 | 33.99 |122.36) 76.03 | 1200 | 25.68 | 92.45] 57-45 1200 | 35.46 |127.66| 79.32 | 1500 | 26.71 | 96.16] 59.75 1500. | 37.19 |133.88| 83.19 | 2000 | 27.89 |100.40| 62.39 2000 | 39.27 |141.37| 87.84 3000 | 29.30 | 105.48] 65.54 3000 | 41.84 |150.62} 93.59 | © | 33.22 |119.59| 74.31 @ | 49.84 ]179.42 111.49 ey \ 2.5mm, _| 100 | 14.14) 50.90] 31.63 || 4.0 mm. _ 100 | 18.67 | 67.21| 41.76 1ookm, | 200 | 18.38] 66.17) 41.12 | roo km. 200 | 24.68] 88.85) 55.21 O.Lin, | 300 | 21.13} 76.97) 47.27 0.1 in. 300 | 28.73 |103.43 | 64.27 63 mi- 400 23.15 | 83.34) 51.78 39 mi. 400 | 31.88 |114.77 |) 71.32 » §00 | 24.74 | 89.06] 55.34 ve 500 | 34.26 |123.34| 76.64 600 | 26.05 | 93.78] 58.27. 600 | 36.31 |130.72| 81.23 | 700 | 27.12) 97.63| 60.66 700 | 38.06 /137.02 | 85.14 800 28.05 | 100.98] 62.75 800 | 39.59 |142.52| 88.56 ' goo | 28.85 | 103.86] 64.54 goo | 40.93 |147.35| 91.56 | 1000 | 29.55 | 106.38) 66.10 1000 | 42.12 |I51.63 | 94.22 1200 | 30.74 |110.44| 68.63 1200 | 44.16 |158.98| 98.79 | 1500 | 32.11 |115.60) 71.83 1500 | 46.48 |167.33 | 103.98 | 2000 | 33.73 |121.43] 75-45 2000 | 49.59 |178.52 | 110.93 | 3000 | 35.70 |128.52| 79.86 3000 | 53.41 |192.28 |119.48 © | 41.53 |149.51, 92.90 © | 66.45 |239.22/148.64 Latitude 35°. 0.2mm. _ 100! 2,28 | 8.21' 5.10 |! 0.4mm. 100 | 3.94 | 14.18 | 8.81 100 km. 200 2.52 | 9.07 5.64 I! 100 km ' 200} 4.55 | 16.38) 10.18 0.1 in. 300 | 2.62 | 9.43 | 5.86), o1in ' 300 | 4.85 | 17.46) 10.85 Ronit 400 , 2.68 9.65 | 6.00 i Wie ' 400 ; 5.04 | 18.14 11.27 789 mi. | 300 2.72 | 9.791 6.08!) 395 | 500 5.16 | 18.58 11.55 600 | 2.75 9.90. 6.15 | 600 | 5.24 18.86 | 11.72 700 | 2.77 9.97 | 6.20 | 700 | 5.31 | 19.12 11.88 800 | 2.78 | 10.01 | 6.22 | 800 | 5.36 | 19.30) 11.99 goo | 2.79 | 10.04 6.24. . goo | 5.41 | 19.48 12.10 | L000 | 2.80 | 10.08 6.26 | , 1000 | 5.44 19.58 12.17 1200 | 2.82 |10.15 | 6.31. | 1200 | 5.49 19-76 | 12.28 | 1500 | 2.83 | 10.19} 6.33 | | 1500 | 5.55 19.98 | 12.42 | 2000 | 2.85 | 10.26: 6.38 ' 2000 | 5.61 | 20.20; 12.55 | 3000 | 2.86 | 10.30 | 6.40 | | 3000 , 5.67 | 20.41 | 12.68 © | 2.90 | 10.44 6.49 _ @ =| 5.79 | 20.84} 12.95 PHYSICS OF THE AIR Latitude 35° (Continued). AB (mm.) km mi | é ym yen yout 100 km e Me tee Nhe | 100 km. 5 hr hr +75| 22.21 0.6 mm 100 | 5.32 | 19.15 | 11.90 || 1.5 mm. _ a ade ae abe 00 km. 200 | 6.31 | 22.72] 14.12 |! 109 km. Me levee ge aelaos Dini Be eee 2p. in. re 15.00 54.00) 33.55 , 400 | 7.16 | 25.78 | 16.02 16 Fe. aes oe 26.771 nae aGyane 500 | 7.39 | 26.60 | 16.53 5 = Al teen see, 600 | 7.55 | 27.18 | 16.89 600 ae ae 700 | 7.68 | 27.65 | 17.18 ‘od on eas 800 | 7.78 | 28.01 | 17.40 00 ia a 900 | 7.87 | 28.33 | 17.60 goo a BL er tie he 1000 | 7.94 | 28.58 | 17.76 1000 a eat eo 1200 | 8.04 | 28.94 | 17.98 1200 ie aaa 1500 | 8.16 | 29.38 | 18.26 1500 : : an 8 gee Ban Geese ee 3000 20.11 | 72.40 44.99 -4I | 30.2 : \ ee 8.69 oe 19.48 co | 21.72 os 48.58 pion ae paaons i : | 95! 26.6 0.8 mm. 100 | 6.51 | 23.44 | 14.57 || 2.0 mm. _ se ieie are ae te | 200 | 288 28-37 | 278) | 200 th, 00 17.19 orgs. 38.45 OC eth 300 | 8.62 | 31.03] 19.28 || oy in. 3 Ou ee bare Oelits 400 | 9.11 | 32.80 | 20.38 Sal 400 ol ee 197 mt. | soo | 9.45 | 34.02 | 21.14 500 oa co 600 | 9.71 34.96 | 21.72 00 aS cS he 700 | 9.91 | 35.68 | 22.17 hae ae ee in 800 | 10.07 | 36.25 | 22.52 00 a 4 send ve g00 | 10.20 | 36.72 | 22.82 900 cane en ou 1000 | 10.31 | 37.12 | 23.07 1000 : 7 ao oe 1200 | 10.49 | 37.76 | 23.46 1200 ce peed oe 1500 | 10.68 | 38.45 | 23.89 1500 cia an a oe ef ae So 6 248 7060 3032 94-33, 58.61 11.10 : : oS 11.58 tebe 25.90 o | 28.96 Hace 64.78 1.0 mnt. 100 | 7.59 | 27.32 | 16.98 || 2.5 mm. = te ee oi eed Set =| agg 9-31 | 33-52 | 20.83 || 100 km. 2 ee a oe pe 300 | 10.27 | 36.97 | 22.97 0.1 in. ee ste ae ee Qed: 400 | 10.92 | 39.31 | 24.43 6a. nel. ae ee ees 158 mz. 500 | 11.38 | 40.97 25.46 5 eo ees 600 | 11.74 | 42.26 | 26.26 00 437 ce ae 700 | 12.02 | 43.27 | 26.89 700 2 ae ee 800 | 12.24 | 44.06 | 27.38 ao eee Ae Bae goo | 12.43 44.75 | 27.81 9 : a se po 1000 | 12.59 | 45.32 | 28.16 1000 73 pee ae 1200 | 12.84 | 46.22 | 28.72 ae 25 ee pe 1500 | 13.11 | 47.20 | 29.33 150 9-34 ae oe mado. tes i. ae 000 hae 115.56 71.81 000 | 13. 9.4, . : cs rae es 32.39 © | 36.20 |130.32) 80.98 GRADIENT WIND VELOCITY—CYCLONIC 637 Latitude 35° (Continued). AB (mm.) m | vkm | ymi || AB (mm) | ym | em | ad 100 km, ‘ Vs Vir Vir 100 km. , Ve | Viv Vir t | Omm. _| 100 | 15.34] 55.22) 34.31 |) 4.0 mm. _ 100 | 18.22 65.59] 40.76 100 km. 200 19.86) 71.50} 44.43 || 100 km. 200 | 23.87 | 85.93] 53-39 0.1 in. 300 | 22.77 81.97] 50.93 0.1 in. 300 | 27.59} 99.32) 61.71 53 mi. 400 | 24.91} 89.68] 55.73 39 mi. 400 | 30.37 |109.33| 67.93 500 | 26.57 95.65] 59.43 500 | 32.57 |117.25) 72.86 600 | 27.91 |100.48) 62.44 600 | 34.38 |123.77| 76.91 700 | 29.04 |/104.54! 64.96 700 | 35.91 |129.28) 80.33 800 | 30.00 {108.00} 67.11 800 | 37.22 1133.99} 83.26 g00 | 30.82 |110.95| 68.94 900 | 38.37 |138.13} 85.83 1000 | 31.55 |113.58] 70.58 1000 | 39.38 141.77} 88.09 1200 | 32.76 |117.94| 73.28 1200 | 41.10 |147.96| 91.94 1500 | 34.15 |122.94| 76.39 1500 | 43.11 |155.20| 96.44 2000 | 35.79 |128.84| 80.06 2000 | 45.54 |163.94| 101.87 3000 | 37.76 |135.94| 84.47 3000 | 48.54 |174.74) 108.58 © | 43.44 |156.38| 97.17 @ | 57.92 |208.51/129.56 Latitude 40°. 0.2mm, _| 100 | 2.11) 7.60} 4.72)|0.6 mm. _ 100 | 5.04| 18.14] 11.27 100 km. | 200 | 2.30| 8.28) 5.14|! too km. 200 | 5.90| 21.24] 13.20 0.1 in. 300 | 2.38) 8.57! 5.33 O.1 in. 300 | 6.33 | 22.79) 14.16 Bo HA 4co | 2.43) 8.75| 5.44 S64 FHL. 400 | 6.60 | 23.76! 14.76 769m. | Sco. 2.46| 8.86] 5.51 Somes 500 | 6.78 | 24.41 | 15.17 G00 | 2.48| 8.93] 5.55 600 | 6.91 | 24.88 | 15.46 | 700 | 2.49} 8.96! 5.57 70O ; 7.01 | 25.24] 15.68 800 | 2.50} 9.00] 5.59 800 | 7.08 | 25.49} 15.84 goo 2.51} 9.04] 5.62 goo 7.15 | 25.74] 15.99 1000 | 2.52| 9.07] 5.63 1000 | 7.20| 25.92! 16.11 1200 | 2.53| 9.11} 5.66 1200 | 7.28 | 26.21 | 16.29 1500 | 2.54} 9.14] 5.68 1500 | 7.37 | 26.53} 16.49 2000 ; 2.55} 9.18} 5.70 2000 | 7.46! 26.86] 16.69 | 3000 | 2.56) 9.22| 5.73 3000 | 7.55«\ 27.18 | 16.89 0 2.58| 9.29! 5.77 © 7-75 | 27.90 | 17.34 | 0.4mm | 100 3.71 | 13.36] 8.30)/0.8 mm. _ 100 | 6.23 | 22.43; 13.94 100 km. =| 200 | 4.22}15.19| 9.44|| 100 km. 200 | 7.41 | 26.68} 16.58 0.1 in | 300 | 4.46 | 16.06} 9.98]| o7 in. 300 | 8.04} 28.94| 17.98 mi, | 40° 4.61 | 16.60 | 10.31 197 mi. 400 | 8.44! 30.38 | 18.88 395 m1. 500 | 4.70 16.92 | 10.51 500 | 8.72 | 31.39 | 19.50 600 | 4.77 | 17.17 | 10.67 600 | 8.92 | 32.11} 19.95 a 4.82 | 17.35 | 10.75 700 | 9.08 | 32.69 | 20.31 | 800! 4.85 | 17.46| 10.85 800 | 9.21 | 33.16) 20.60 | goo | 4.89 | 17.60| 10.94 900 | 9.31 | 33.52 | 20.83 | 1000 | 4.91 | 17.68 | 10.99 1000 | 9.40 | 33.84 | 21.03 | 1200 ; 4.95 17.82 | 11.07 1200 | 9.53 | 34.31 | 21.32 | 1500 4.99] 17.96| 11.16 1500 | 9.67 | 34.81 | 21.63 | 2000 , 5.03} 18.11] 11.25 2000 | 9.82] 35.35 | 21.97 | 3000 ' 5.08 / 18.29 11.36 3000 | 10.09 | 36.32 | 22.57 | o | §.17| 18.61) 11.56 © | 10.34 | 37.22) 23.13 638 PHYSICS OF THE AIR Latitude 40° (Continued). | . 4 : AB (mm.) m km mi AB (mm.) m km mi 100 km, f Vis vg | Vy | 100 km, f VS ' r Vie 1.0mm, _' 100; 7.28) 26.21 | 16.29) 2.5mm. _ 100 | 13.34 48.02, 29.84 1ookm, . 200 8.80 31.68/19.69 yoo km. 200 | 16.96 61.06: 37.94 0.1 in. 300 9.63 34.67 21.54 0.1 in. 300 | 19.20! 69.12! 42.95 158 mi, 400 10.17 36.61 | 22.75 Ea ai 400 | 20.79 74.84 46.50 . 500 10.55 37.98 | 23.60 SME 500 | 21.99 79.16, 49.19 600 10.83 38.99 | 24.23 600 | 22.95 82.62) 51.34 700 11.06 39.82 | 24.74 700 | 23.73 85.43 53.08 800 | 11.24 40.46 | 25.14 800 | 24.38 87.77 54.54 ' 900 11.39, 41.00 | 25.48 | 900 | 24.94 89.78 55.79 1000 II.51 41.44|)2575 | 1000 | 25.42 91.51 56.86 ' 1200 11.71 42.16 | 26.20 1200 | 26.20° 94.32 58.66 1500 | II.91 | 42.88 | 26.64 1500 | 27.09 97.52 60.60 , 2000 | 12.14 | 43-70 | 27.15 | 2000 | 28.09 101.12 62.83 3000 - 12.38 , 45.57 | 28.32 | 3000 | 29.26 105.34 65.45 @ 12.92 | 46.51 : 28.90 | co | 32.30 |116.28 72.25 1 | t | ' | I 1.5mm. _ 100 9.60 34.56! 21.47'' 3.0 mm, _ 100 | 14.95 | 53-82 33.44 100 km. _- 200.-—s«11.87° 42.73' 26.55 yoo km. 200 | 19.17 | 69.01| 42.88 o.1in, 300 | 13.19 47.48] 29.50), 0.1 in, 300 | 21.83 78.59; 48.83 TOs anh, 400 14.09 §0.72| 31.52. 53 mi 400 | 23.74 85.46) 53-10 ‘ 500 14.74 53.06} 32.97) : 500 | 25.21 | 90.76) 56.40 600 ' 15.25! 54.90} 34.11: 600 | 26.39! 95.00 59.03 700 15.65| 56.34; 35.01 700 27.36| 98.50 61.21 800 15.98 57.53) 35-75 800 | 28.18 |101.45 63.04 g00 16.25 §8.50) 36.35 900 | 28.88 |103.97' 64.60 | 1000 16.48, 59.33] 36.87: 1000 | 29.49 |106.16; 65.96 1200 , 16.86 60.70) 37.72 1200 | 30.50 |109.80, 68.23 '1§00 17.26. 62.14) 38.61 1500 | 31.65 |113.94. 70.80 ' 2000 17.71 63.76} 39.62 2000 | 32.97 |118.69' 73.75 | 3000 ' 18.21 , 65.56) 40.74 3000 | 34.50 |124.20, 77.17 © | 19.38 69.77| 43-35 © | 38.77 |139.57 86.72 | | | 2.0mm. _' 100 | 11.57 | 41.65) 25.88 4.0mm. _ 100 | 17.82] 64.15} 39.86 100 km, | 200 | 14.55; 52.38) 32.55 100 km. 200 | 23.14 | 83.30 51.76 oti, ; 900) 16.35 58.86) 36.57 0.1 in. 300 | 26.58} 95.69 59.46 en 400 | 17.60! 63.36 39-37 || 39 mi. ie 400 | 29.11 |104.80 65.12 FOTN: 500 | 18.52 | 66.67] 41.43 | . 500 | 31.08 |I111.89) 69.53 600 Lee | 69.34) 43.09 ‘ 600 | 32.69 |117.68, 73.12 700 19.84 71.42| 44.38 700 | 34.04 |122.54 76.14 800 20.33) 73-19] 45.48 |! 800 | 35.18 |126.65) 78.70 | 900 | 20.74.) 74.66] 46.39 || 900 | 36.18 |130.25] 80.93 1000 | 21.10 75.96] 47.20 | 1000 | 37.05 |133.38 82.88 1200 j 21.67 78.01| 48.47 | 1200 | 38.50 |138.60) 86.12 | 1500 22.41 | 80.32] 49.91 || 1500 | 40.20 |144.72} 89.93 | 2000 | 23.02 | 82.87] 51.49 i 2000 | 42.19 |151.88) 94.37 | 3000 | 23.83 85.79) 53.31 3000 | 44.60 |160.56} 99.86 © 25.84 93.02 S7to © | 51.69 |186.08!115.62 GRADIENT WIND VELOCITY—CYCLONIC = 639 Latitude 45°. AB (mm.) ym | ykm-\> mi || AB (mm.) m km mi r0ookm. | my Vs | Mig , Vis 100 km. # Ve Ve ay | | 0.2 mm =| 100 | 1.97) 7.09 seat 0.8mm. _ 100 | 5.96, 21.46 12.87 100 km | 200 | 2.13 | 7.67 477, 100 km. 200! 7.01 25.24 15.68 O.L in | 300 vad Lee 4-90 | 0.1 in, 300 Zo alae 16.89 400 | 2.23) 8.03 | 4.99} 7777 400 | 7.89! 28.40: 17.42 ane 500 | 2.25 8.10 | 5.03 | 197 ™ 500 | 8.12 29.23) 18.16 600 | 2.27| 8.17 | 5.08 600 | 8.29 | 29.84] 18.54 700 | 2.28/ 8.21 | 5.10 700 | 8.42 30.31) 18.83 800 | 2.29) 8.24 | 5.12 800 | 8.52] 30.67} 19.06 900 | 2.29) 8.24 | 5.12! 900 | 8.60} 30.96] 19.24 1000 | 2.30} 8.28 | 5.14! 1000 | 8.67 | 31.21] 19.39 1200 | 2.31| 8.32 | 5.17" 1200 | 8.78] 31.61} 19.64 1500 | 2.32} 8.35 | 5.19 | 1500 | 8.89} 32.00] 19.84 2000 | 2.33| 8.39 5.21 | 2000 | 9.01 | 32.44| 20.16 3000 | 2.33} 8.39 | 5.21., 3000 | 9.14 32.90) 20.44 oo 2.35 8.46 5.26 || co 9.40 | 33.84) 21.03 | l! | : I \ 0.4 mm 100 | 3.52 | 12.67! 7.87 || 1.0mm. _ 100 | 7.40 | 26.64] 16.55 100 km. 200 | 3.94) 14.18) 8.81) joo km. 200 ; 8.36|30.10| 18.70 O.. in, | 300 er: 14.90] 9.26 | o.4 in. 300 | 9.08 | 32.69 20.31 er 400 | 4.20) 15.34 9-53) Tog yay 400 | 9.54 | 34.34 | 21.34 395 mt 500 | 4.33, 15.59, 9.69), 158 mt. 500 | 9.86 | 35.50) 22.06 600 | 4.39 15.80! 9.82 600 | 10.10 | 36.36} 22.59 ' 700) 4.43} 15.95 9.91 | 700 | 10.28 | 37.01 | 23.00 800 | 4.46 | 16.06] 9.98 ° 800 | 10.43 | 37.55| 23-33 g00 | 4.49; 16.16, 10.04 g00 | 10.55 | 37.98 | 23.60 1000 | 4.50 | 16.20] 10.07 1000 | 10.65 | 38.34 | 23.82 1200 , 4.53 16.31] 10.13 1200 | 10.80 | 38.88 24.16 | 1500 | 4.56 16.42) 10.20 1500 | 10.97 | 39.49 | 24.54 2000 | 4.60 16.56) 10.29 2000 I1.15| 40.14 | 24.94 | 3000 | 4.63 | 16.57| 10.36 3000 | 11.33 | 40.79 | 25.35 “ @ | 4.70) 16.92) 10.51 co 11.75 | 42.30 26.28 | 0.6 mm |; 100) 4.81 17.32) 10.76 1.5mm. _ 100 | 9.28 | 33.41 20.72 “100 km. 200, 5.55 | 19.98) 12.42) 1090 km. 200 | 11.36 | 40.90| 25.41 0.1 in. 300 nee | 21.31! 13.24) 0.7 in. 300 | 12.54 a oS eres oo .13; 22.07] 13.71} — 7 400 | 13.32 | 47.95 29.79 263 mt ee Bot | 2208 14.05), 105 ™t- 500 | 13.88 | 49.97 31.05 600 | 6.39 | 23.00) 14.29 | 600 | 14.31 | 51.52 | 32.01 700 | 6.47 | 23.29 14.47) 700 | 14.65 | 52.74 32.77 800 | 6.53] 23.51) 14.61) 800 | 14.92 | 53.71 | 33-37 goo | 6.58] 23.69 14.72 g00 | 15.15 | 54.54| 33.89 : 1000 | 6.62] 23.83) 14.81. 1000 | 15.34 | 55.22| 34.31 1200 | 6.69} 24.08 14.96 1200 | 15.64 | 56.30) 34.98 1500 | 6.75| 24.30 15.10) 1500 | 15.97 | 57-49 35.72 2000 | 6.82] 24.55] 15.25 2000 | 16.33 | 58.79 | 36.53 ' 3000 | 6.90; 24.84) 15.43 | 3000 | 16.72 | 60.19 37.40 2 7-05} 25.38 15.77) | © | 17.62 63.43 39-41 ! 640 PHYSICS OF THE AIK Latitude 45° (Continued). AB (mm.) 1‘ om km | .,mi ABi(mm.) | m km mi 100 km Besides Va | Me ‘ Loo km. ag ; Vir Vie I! 2.0mm, _| 100 | 11.24 | 40.46: 25.14 3.0mm. _ 100 ; 14.59 | 52.52) 32.63 100 km. 200 | 14.00 | 50.40 31.32. jookm. | 200 ; 18.55) 66.78 41.50 O.1 in. 300 | 15.61 | 56.20'34.92'' gy in: 300 21.00/ 75.60) 46.98 79 ie 400 | 16.72 | 60.19 | 37-40 . 53 mi. 400 22.72 81.79) 50.82 500 17.53 | 63.11 , 39.21 ‘ 500 | 24.04 86.54) 53.77 600 | 18.16 | 65.38 | 40.62 | | 600 25.08 90.29) 56.10 700 | 18.67 67.21 41.76° ! 700 | 25.93 | 93-35) 58.00 800 | 19.08 | 68.69 | 42.68 | | 800 | 26.64; 95.90) 59.59 900 | 19.43 | 69.95 43.47 g00 27.24 98.06 60.93 1000 | 19.72 | 70.99 | 44.11 ; 1000 | 27.77 | 99.97, 62.12 . 1200 20.20 | 72.72 45.23 | 1200 , 28.62 103.03) 64.02 1500 | 20.72 | 74.59 | 46.35 ' 1500 | 29.58 |106.49| 66.17 2000 | 21.30 76.68 : 46.78 2000 30.68 110.45, 68.63 3000 | 21.94 | 78.98 | 49.08 | 3000 | 31.94 /114.98| 71.45 © | 23.49 84.56 52.54 / (35:24 126.86) 78.83 | i i I j 2.5mm | 100 12.99 | 46.76, 29.05" 4.0mm, _ ! 100 | 17.45 | 62.82} 39.03 100 km. 200 | 16.37 | 58.93! 36.62| T00 km. 200 | 22.48 | 80.93) 50.29 O.1 in. 300 | 18.41 66.28 41.18! O.L in. 300 | 25.68; 92.45) 57-45 63 mi. 400 19.83 71.37! 44.355 39 mi. 400 | 27.99 ,;100.76; 62.61 : 500 , 20.90, 75.24 46.75 ; 500 29.78 107.21) 66.62 600 21.74 78.26! 48.63: 600 | 31.23 112.43) 69.86 700 | 22.41 80.68 50.13 700 ' 32.42 116.71 72.52 800 | 22.97 | 82.69 51.38 800 33.44 120.38) 74.80 900 23-44 | 84.38 52.43 | 900 34.31 123.52: 76.75 1000 23.85 85.86 53.35 1000 | 35.06 126.22 78.43 | 1200 | 24.51 | 88.24 54.83 1200 | 36.32 |130.75| 81.25 , 1500 25.25; 90.90 56.48 1500 | 37.77 135-97 84.49 | 2000 | 26.07 | 93.85! 58.32 2000 | 39.45 \142.02| 88.25 | 3000 27.01 97.24 60.42 3000 41.43 149.15 92.68 | @ | 29.37 105.73 65-70 © | 46.99 '169.16' 105.11 Latitude 50°. 0.2mm, _| 100, 1.86 6.70 4.16 y 0.4mm. _ 100 | 3-34 |12.02| 7.47 100 km. 200 | 1.99 7.16 | 4.45 i 100 km. 200 | 3.72 | 13.39 8.32 O.1 in. he oe ce a | O.L in. 300 ate 14.00 oe Steal 400 | 2. 4 4.631; Joe 400 | 3.98 | 14.33 -90 FBO Tks 500 2.09 | 7.52 | 4.67, 395 mt. 500 | 4.04 14.54) 9.04 600 | 2.10 | 7.56| 4.70!! 600 | 4.09 | 14.72| 9.15 700 2.11 | 7.60 | 4.72 | 70O | 4.12 14.83} 9.22 800 | 2.12 | 7.63! 4.74° 800 | 4.15 | 14.94] 9.28 900 | 2.13 | 7.67| 4.77) 900 | 4.17 15.01} 9.33 1000 2.13 | 7.67, 4.77 1000 | 4.18 | 15.05; 9.35 1200 © 2.14 | 7.70: 4.79 | 1200 | 4.21 | 15.16) 9.42 1500 2.14 7.70! 4.79 1500 | 4.23 | 15.23, 9.46 2000 | 2.15 7.74) 4.81) 2000 | 4.26 | 15.34| 9.53 3000 2.15 7-74. 4.81 3000 | 4.28 115.41! 9.59 o ' 2.17 7.81 | 4.85 ; © 4.34 | 15.62 9.71 GRADIENT WIND VELOCITY—CYCLONIC 641 Latitude 50° (Continued). AB (mm.) | pm Rm mi AB (mm.) m km | mi 100 km. | v Ee he Ve j 100 km. . Ke Vie Vie 0.6 mm | 100 | 4.61 | 16.60 | 10.31 || 1.5 mm, _ 100 | 9.01 | 32.44 | 20.16 100 km 200 | 5.27 | 18.97/| 11.79 || too km 200 | 10.92 | 39.31 | 24.43 0.1 in. 300 | 5.58 | 20.09 | 12.48 0.1 in 300 | 11.98 | 43.13 | 26:80 263 mi 400 | 5.76 | 20.74 | 12.89 105 mi 400 | 12.67 | 45.61 | 28.34 500 | 5.89 | 21.20 | 13.17 500 | 13.16 | 47.38 | 29.44 | 600 | 5.97 | 21.49 | 13.35 600 | 13.53 | 48.71 | 30.27 » 700 |} 6.04 | 21.74 | 13.51 700 | 13.82 | 49.75 | 30.91 800 | 6.09 | 21.92 | 13.62 800 | 14.06 | 50.62 | 31.45 900 | 6.13 | 22.07 | 13.71 900 | 14.25 | 51.30 | 31.88 1000 | 6.17 | 22.21 | 13.80 1000 | 14.41 | 51.88 | 32.24 1200 | 6.22 | 22.39 | 13.91 1200 | 14.66 | 52.78 | 32.80 | 1500 | 6.27 | 22.57 | 14.02 1500 | 14.93 | 53-75 | 33.40 | 2000 | 6.33 | 22.79 | 14.16 2000 | 15.23 | 54.83 | 34.07 | 3000 | 6.38 | 22.97 | 14.27 3000 | 15.54 | 55.94 | 34.76 © 6.51 | 23.44 | 14.57 o | 16.26 | 58.54 | 36.38 | | ; 0.8mm. _| 100] §.73 | 20.63 | 12.82 || 2.0mm. _ 100 | 10.95 | 39.42 | 24.49 100km. | 200 | 6.68 | 24.05 14.94) 100 km. 200 | 13.51 | 48.64 | 30.22 0.1 in. | 300 | 7-15 | 25.74 | 15.99 0.1 in. 300 | 14.99 | 53.96 | 33.53 197 mi 400 | 7.44 | 26.78 | 16.64 a9 oni 400 | 15.98 | 57.53 | 35.75 | 500 | 7.63 | 27.47 | 17.07 500 | 16.70 | 60.12 | 37.36 600 | 7.77 | 27-97 | 17.38 600 | 17.25 | 62.10 | 38.59 700 | 7.88 | 28.37 | 17.63 700 | 17.69 | 63.68 | 39.57 800 | 7.97 | 28.69 | 17.83 800 | 18.04 | 64.94 | 40.35 g00 | 8.03 | 28.91 | 17.96 g00 | 18.34 | 66.02 | 41.02 1000 | 8.09 | 29.12 | 18.09 1000 | 18.59 | 66.92 | 41.58 _ 1200 | 8.18 | 29.45 | 18.30 1200 | 18.99 | 68.36 | 42.48 1500 | 8.27 | 29.77 | 18.50 ' 1500 | 19.43 | 69.95 | 43.47 ' 2000 | 8.36 | 30.10 | 18.70 2000 | 19.91 | 71.68 | 44.54 3000 | 8.46 | 30.46 | 18.93 | 3000 | 20.44 | 73.58 | 45.72 © 8.67 | 31.21 | 19.39 ; © | 21.69 | 78.08 | 48.52 1.0mm. _ 100} 6.76| 24.34) 15.12 || 2.5 mm. _ 100 | 12.69 | 45.68 | 28.38 100 km. | 200 | 7.99 | 28.76 | 17.87 || 100 km. 200 | 15.86 | 57.10 | 35.48 O.1in. ‘ 300/ 8.63 | 31.07 | 19.31 0.1 in. 300 | 17.73 | 63.83 | 39.66 SicBinid: | 400 | 9.02 | 32.47 | 20.18 hone 400 | 19.02 | 68.47 | 42.55 15° mt — S00 | 9.29 | 33-44 | 20.78 3 Mt: 500 | 19.97 | 71.89 | 44.67 , 600 | 9.50 | 34.20 | 21.25 600 | 20.71 | 74.56 | 46.33 | 700 | 9.65 | 34.74 | 21.59 700 | 21.30) 76.68 | 47.65 | 800 | 9.77 | 35.17 | 21.85 || 800 | 21.79 | 78.44 | 48.74 ; 900 } 9.87 | 35.53 | 22.08 900 | 22.21 | 79.96 | 49.68 1000 | 9.96 | 35.86 | 22.28 1000 | 22.55 | 81.18 | 50.44 1200 | 10.09 | 36.32 | 22.57 1200 | 23.12 | 83.23 | 51.72 1500 | 10.22 | 36.79 | 22.86 1500 | 23.74 | 85.46 | 53.10 2000 | 10.36 | 37.30 | 23.18 , 2000 | 24.47 88.09 | 54.74 3000 | 10.52 | 37.87 | 23.53 ' 3000 | 25.21 | 90.76 | 56.40 | © | 10.84} 39.02 | 24.25 © | 27.11 | 97.60 | 60.65 | I 642 PHYSICS OF THE AIR AB (mm.) 1 om km mi AB (mm.) m km mi 100 km. eS Me ee | ' hr | 100 km. . us Viv Vie | 3.0mm, _, 100 | 14.28] 51.41 31.95 || 4.0 mm. _ 100 | 17.12} 61.63} 38.29 100km, 200 | 18.01 | 64.84 40.29] joo km. —-- 200: | 21.90, 78.84) 48.99 O.1 in, | 300 | 20.27 | 72.97 45.34 O.L in. 300 j 24-89 89.60| 55.67 ees 400 | 21.85 | 78.66) 48.88 |, 7 o 400 | 27.03] 97.31] 60.47 53 mt. | 500 | 23.03 | 82.91] 51.52 39. mt. 500 | 28.66 | 103.18 64.11 | 600 | 23.96; 86.26) 53.60 600 | 29.97 |107.89) 67.04 | 700 | 24.72 | 88.99] 55.30 | 700 | 31.04 |111.74} 69.43 | 800 | 25.34 | 91.22] 56.68 800 | 31.95 |115.02| 71.47 | 900 | 25.87| 93.13] 57.87 900 | 32.72 |117.79| 73-19 | 1000 26.33 | 94.79) 58.90 1000 | 33.39 |120.20, 74.69 ' 1200 | 27.07 | 97.45] 60.55 || 1200 | 34.50 |124.20) 77.17 1500 | 27.89 | 100.40| 62.39 |) 1500 | 35.75 |128.70| 79.97 2000 | 28.81 |103.72| 64.45 | 2000 | 37.19 |133.88) 83.19 | 3000 29.86 | 107.50] 66.80 | | 3000 | 38.87 | 139.93] 86.95 » © | 32.53 | 117.11| 72.77 |: | wo | 43.37 |156.13| 97.01 Latitude 55°. 0.2 mm. _| 100 | 1.77) 6.37; 3.96 || 0.6mm. _ 100 | 4.44!15.98] 9.93 100 km. | 200| 1.88! 6.77] 4.21 |lroo km. 200 | 5.03 | 18.11 | 11.25 0.1 in. 300 | 1.93/ 6.95) 4.32]| o.1 in, 300 | 5.30 | 19.08 | 11.86 Bo ans 400 | 1.95) 7.02} 4.36 aan 400 | 5.46 | 19.66 | 12.22 189 500 | 1.96) 7.06] 4.39 SMEs 500 §.57 | 20.05 | 12.46 , 600) 1.97) 7.09| 4.41 600 | 5.64 | 20.30 | 12.61 ! 700 | 1.98! 7.13} 4.43 700 | 5.70) 20.52 | 12.75 , 800] 1.99, 7.16! 4.45 800 | 5.74) 20.66 | 12.84 - goo} 1.99, 7.16) 4.45 900 | 5.77 | 20.77 | 12.91 | 1000 | 1.99) 7.16/ 4.45! 1000 | 5.80 | 20.88 | 12.97 | 1200 | 2.00] 7.20 4.47 | 1200 | 5.85 | 21.06 | 13.09 1500 | 2.00| 7.20) 4.47 1500 | 5.89 | 21.20] 13.17 2000 | 2.01) 7.24! 4.50 2000 | 5.94 | 21.38 | 13.29 3000 | 2.02) 7.27, 4.52 3000 | 5.99 | 21.56 | 13.40 © 2.03! 7.31 | 4.54 7 © 6.08 | 21.89 | 13.60 0.4mm, _| 100} 3.20] 11.52| 7.16 | 0.8 mm. _ 100 5.54. 19.94 | 12.39 100 km. 200 | 3.53] 12-71| 7-90 || 100 km. 200 | 6.40 23.04 | 14.32 oO. in. 300 ao 13.25 oe 0.1 in. 300 | 6.82 | 24.55 ae ee 400 | 3.76| 13.54 eAT I Sees 400 | 7.07 | 25.45 | 15.81 395. | soo | 3.81 | 13.72] 8.53 || 197 Mt 500 | 7.24) 3B08 en 600 | 3.85] 13.86, 8.61 600 | 7.36 26.50 | 16.47 700 | 3.88| 13.97! 8.68 700 | 7.45 | 26.82 | 16.67 800 | 3.90| 14.04| 8.72 800 | 7.52 | 27.07 | 16.82 goo | 3.91] 14.08! 8.75 900 | 7.58 | 27.29 | 16.96 1000 | 3.93} 14.15| 8.79 1000 | 7.63 | 27.47 | 17.07 1200 | 3.95| 14.22} 8.84 1200 | 7.70 | 27.72 | 17.22 1500 | 3.97] 14.29] 8.88 1500 | 7.77 | 27.97 | 17.38 2000 | 3.99 | 14.36] 8.92 2000 | 7.85 | 38.26) 17.56 3000 | 4.01] 14.44| 8.97 3000 | 7.94 28.58 | 17.76 oo 4.06 | 14.62| 9.08 © 8.11 29.20 18.14 GRADIENT WIND VELOCITY—CYCLONIC 643 Latitude 55° (Continued). AB(mm.) | m km | . mi AB(mm.) | im km, mi 100 km Le Ms Var hr roo km. is Fy Vw hr | 1.0mm. _ 100 6.55 23.58 14.65 2.5mm, _| 100 12.43 44.75) 27.81 Lou kM. 200 7.08 | 27.051 17.18)! yoo km. | 200 | 15.41 55-43 34-47 0.1 in. 300 8.24 | 29.66 , 18.43 O.1 in. 300 17-15 61.74 38.36 158 mi. | 400 | ee | 30.92 | 19.21 63 ik 400 | oe ee 40.76 : “| 500 8.83 31.79 19.75 ; 500 19.19 | 69.08 42.92 600 | 9.01 | 32.44 | 20.16 600 . 19.85, 71.46) 44.40 700 9.14 | 32.90 | 20.44 700 20.38% 73.37 45-59 | 800 | 9-25 | 33.30 | 20.69 . 800 20.82 74.95 46.57 “geen! Bap Geer aay Tee stay eae aes 1000 | 9.40 | 33.84 , 21. : ‘ | 1200. 9.51 | 34.24 | 21.28 1200 | 21.98 79.13 49.17 1500 ; 9.63 | 34.67 | 21.54 1500 22.52, 81.07 50.37 | 2000 9.74 | 35.06 | 21.79 | 2000 | 23.12, 83.25 51.72 3000 | 9.87 35.53 | 22.08 i 3000 ; 23.77) 85.57 53-17 © 10.14 | 36.50 | 22.68 | @ | 25.35) 91.26 56.71 = ; 1.5mm. 100 | 8.77 | 31.57 | 19.62 | 3.0mm, _ 100 , 14.00! 50.40 31.32 1ookm, (200 _-: 10.55 37.98 23,60 | 100 km 200 - or 63.14 ae 0.1 in. 300 | IE.51 41-44 25-75), o.1 in, 300 | 19.05 | 70.74: 43.9 105 mi. 400 | 12.13 | 43.07 | 27.14 | 53 mi 400 | 21.00! 75.60 46.98 ‘ 500 12.56, 45.22 28.83 | 500 | 22.18 | 79.85 49.62 600 | 12.89 | 46.40 | 28.83 600 25.08 a 51.52 Boo 13.38 | 48.06 | 29.86 | boo | 24.26 | 87.34, 3427 900 | 13.51 | 48.64 | 30.22 | § 900 | 24.73 89.03 55.32 1000 | 13.65 | 49.14 | 30.53 | | 1000 | 25-13 90.47 56.22 1200 | 13.87 | 49.93 31.03. ' 1200 | 25.79 | 92.84 57.69 1500 | 14.10 | 50.76 | 31.56 | 1500 | 26.50 95-40 59.28 § 2000 | 14.35 | 51.66 | 32.10 | ' 2000 | 27.30! 98.28) 61.07 » 3000 | 14.62 | 52.63 | 32.70 3000 oe 101.52] 63.08 o + 15.21 | 54.76 | 34.03 o | 30.42 |109.51/ 68.05 | { : | 2.0 seit | 100 | 10.70 | 38.52 | 23.94 ! 4.0 mm. _! 100 16.84 | 60.62) 37.67 100 km. | 200 | 13-10 47.16] 29.30 | 100 km 200 | 21.40| 77.04 47.87 OL. 300 | 14.45 | 52.02 | 32.32 | 0.1 in | 300 | 24.21 | 87.16; 54.16 mo mn, | $00 |2585/ 5526/9498) pam. 400 [2020) 93:96 Sat > 500 | 16.00 | 57.60 | 35.79 | ; ; I. 600 | 16.48 | 59.33 36.87 | ' 600 | 28.91 |104.08) 64.67 700 | 16.88 | 60.77 | 37-76, 700 | 29.88 |107.57| 66.84 800 | 17.19 | 61.88 | 38.45 | 800 | 30.70 110.52) 68.67 900 | 17.45 | 62.82 | 39.03 || . 900 | 31.39 |113.00! 70.22 1000 | 17.67 | 63.61 | 39.53 1 ‘ 1000 | 31.99 115.16) 71.56 1200 | 18.02 | 64.87 | 40.31 || | 1200 | 32.95 118.62) 73.70 1500 | 18.39 | 66.20 | 41.14 | | I§00 | 34.08 | 122.69] 76.24 2000 | 18.80 | 67.68 | 42.05 | 2000 | 35.34 |127.22) 79.05 3000 | 19.25 | 69.30 | 43.06 3000 | 36.79 |132.44| 82.29 co | 20.28 | 73.01 | 45.37 © | 40.56 ee 90.73 | | | PHYSICS OF THE AIR Latitude 60°. AB (mm.) m | km smi DB (mm) | ykm | mi 100 km i MS ie | Var 4 100 km. . Ree Vr | | 0.2mm. _| 100 1.69 6.08, 3.78 0.8mm. _ 100 5.38 19.37: 12.04 1ookm. | 200 1.79 6.44 4.00 jookm. — 200 06,17! 22.21 13.80 Orin, | 300 1-83 6.59) 4.10 ovr in. 300 , 6.54 23.54’ 14.63 789 aa | 400! 1.85 6.66 4.14 Toe: 1 4997 6.77; 24 37) 15-14 : 500 1.86 6.70 4.16 of | 500, 6.92 24.91 15.48 | 600 1.87 6.73, 4.18 | 600 | 7.02| 25.27! 15.70 | 700 «1.88 6.77) 4.21 ' 700 | 7.10 25.56 15.88 | 800 1.88 6.77. 4.21 ' 800 | 7.17) 25.81! 16.04 ' goo 1.89 6.80 4.23 / g0O0 7.22 25.99 16.15 / 1000 «1.89' 6.80 4.23 ' 1000 | 7.26: 26.14' 16.24 / 1200 1.90; 6.84 4.25 1200 7.32): 26.35 16.37 1500! 1.90) 6.84 4.25 '1§00 7.38. 26.57 16.51 2000 1.90! 6.84 4.25 2000 7.45 26.82 16.67 ' 3000 1.91) 6.88 4.28 | 3000 7.53: 27.11 16.85 | o ior, 6.88 4.28 | | « 7.60 27.36 17.00 | 1 0.4mm, _| 100° 3.08 I1.09 6.89 | L.omm, _ 100 6.37 22.93 14.25 100 bm. 200 3.38 12.17 7.56|) 100 hm. 200 7.42 26.71 16.60 O.1 in, On | ee | 12.64, 7.85) o.1 in. 300 | cs 28.55 aes Se 400 , 3.5 : ; San oe 400 8.25 29.70) 18. 395 S00 | 3.63, ESE a 500 8.46 30.46 ie 600 3.66 600 8.61 31.00 | 19.26 700 3.68 Foo =68.73. 31.43 19.53 800 3.70 800 8.82 31.75 | 19.73 goo | 3.72 i 900 8.90 | 32.04 19.91 1000 3.73 1000 8.96 32.26 20.05 1200 | 3.74) 1 1200 } 9.05 | 32.58 | 20.24 1500 3.76 | 1500 , 9.15 | 32.94 | 20.47 2000 | 3.78 | 2000. 9.25 | 33.30 | 20.69 3000 | 3.80 | 3000 | 9.37 | 33-73 20.96 © | 3.80 | © | 9.50 | 34.20 | 21.25 | —- | 0.6mm, _| 100°) 4.29 | Lgmm. _ , 100. 8.57 30.85 | 19.17 100 km 200 4.83 ‘| 00 km. | 200 | 10.24 | 36.86 | 22.90 Oi 300 ! oe 0.1 in. | 300 | aes 40.03 | 24.87 400 .22 aS ak | 400 , II. 42.05 | 26.1 263 mt. | Soo! 5.31 105 M1. + S00 | 12.08 | 43.49 ae 600 | 5.37 ‘ 600 | 12.37 | 44.53 | 27.67 700 | 5.42 | 700 | 12.59 | 45.32 | 28.16 800 | 5.46 | 800 (12.77 | 45.97 | 28.56 900 |; 5.49 900 | 12.02 | 46.51 | 28.90 1000 | 5.51 | 1000 | 13.05 | 46.98 | 29.19 1200 | 5.55 1200 | 13.23 | 47.63 | 29.60 1500, 5.59 | 1500 13.44 | 48.38 | 30.06 2000 | 5.63 2000 | 13.65 | 49.14 | 30.53 3000 | 5.67 3000 | 13.88 | 49.97 | 31.05 o 5-70 | @ (14.25 51.30 31.88 GRADIENT WIND VELOCITY—CYCLONIC 645 Latitude 60° (Continued). | 1 AB (mm.) ym m | ykm) mi | QB (mm.) m | km mi 100 km. E s | Vie ! Me 100 km. e My are Vw | ‘ i 2.0mm. _| 100 | 10.48 | 37.73 | 23.44 || 3.0mm, _ 100 | 14.77 53.17, 33-04 100 km. 200 | 12.75 | 45.90 | 28.52 || :o9 km. 200 | 17.14} 61.70, 38.34 0.1 in. 300 | 14.01 | 50.44 | 31.34|! o.r in. 300 | 19.12) 68.83] 42.77 Gane 400 | 14.83 | 53-39 | 33-17 || ; 400 | 20.48 | 73.73) 45.81 79m. | S00 | 15.42 | 55.51 | 34.49 || 53 500 | 21.47 | 77.29) 48.03 600 | 15.86 | 57.10 | 35.48 | 600 | 22.24 80.06) 49.75 700 | 16.21 | 58.36 | 36.26 700 | 22.86 | 82.30] 51.14 800 | 16.49 | 59.36 | 36.88 | 800 | 23.36] 84.10! 52.26 900 | 16.72 | 60.19 | 37.40 |, 900 | 23.79} 85.64! 53.22 1000 | 16.92 | 60.91 | 37.85 |) 1000 | 24.15 | 86.94) 54.02 1200 | 17.22 | 61.99 | 38.52 |; 1200 | 24.73} 89.03) 55.32 | 1500 | 17.56 | 63.22 | 39.28 |) 1500 | 25.38} 91.37| 56.77 ; 2000 | 17.92 | 64.51 | 40.08 | 2000 | 26.08 ; 93.89) 58.34 3000 | 18.30 | 65.88 | 40.94 | 3000 | 26.87 | 96.73] 60.10 | @ | 18.99 | 68.36 | 42.48 co | 28.49 |102.56! 63.73 | 2.5mm. _| 100 | 12.20; 43.92) 27.29) 4.0mm. _ 100 | 16.59 | 59.72) 37-11 100 km. 200 | 15.03 | 54.11) 33-62 |' 190 km. 200 | 20.96 | 75.46] 46.89 0.1 in. 300 | 16.66) 59.98 37.27 | 0.1 tn, 300 | 23.63 | 85.07) 52.86 63 mi. 400 | 17.75 63.90 39.71 || 39 mi. 400 | 25.00} 91.80] 57.04 . 500 | 18.54 | 66.74) 41.47 |, : 500 | 26.90 | 96.84] 60.17 600 | 19.14 | 68.90) 42.81 |. 700 | 19.62 | 70.63! 43.89 800 | 20.01 | 72.04) 44.76 || 900 | 20.34 | 73.22] 45.50 900 | 30.29 |109.04]| 67.76 1000 | 20.61 | 74.20) 46.10 |! 1000 | 30.84 |I11.02| 68.98 600 | 28.01 100.84] 62.66 | | | 1200 | 21.05) 75.78) 47.09 | 1200 | 31.73 |114.23) 70.98 | | 700 | 28.91 | 104.08} 64.67 800 | 29.66 | 106.78} 66.35 1500 | 21.53) 77.51) 48.16 |) 1500 | 32.72 |117.79| 73.19 2000 | 22.05 79.38) 49.32 2000 | 33.83 |121.79| 75.68 3000 | 22.63 | 81.47| 50.62 3000 | 35.11 |126.40| 78.54 © | 23.74 | 85.46| 53.10 © | 37-98 |136.73/ 84.96 42 646 PHYSICS OF THE AIR TABLE II. Gradient Wind Velocity for Anticyclonis Movement. Latitude 25°. AB (mm.) m km mi || AB (mm.) m km mi 100 km. ‘ Ne Mie Vin 100 km. zu er Var | Vir 0.2mm, _|255.1| 7.86 | 28.30 | 17.59 || 0.8mm. _ 1020.4) 31.44 113.18) 70.33 100 km. 300 | 5.67 | 20.41 | 12.68 || 100 km. 1200 | 22.67| 81.61) 50.71 0.1m. | goo | 4.91) 17.68|10.99|| 0-17”. — 1500 | 20.09 | 72.32, 44.94 789 mt. 500 | 4.63 | 16.67 | 10.36 197 mi. 2000 | 18.50; 66.60) 41.38 600 | 4.47 | 16.09 | 10.00 3000 | 17.35 | 62.46, 38.81 ee 4.38 | 15.77 ee | o | 15.72| 56.59' 35.16 00 | 4.31] 15.52] 9.64 | i g00 | 4.26) 15.34] 9.53 | 1000 | 4-22/ 15.19} 9.44 | 1200 | 4-17 | 15.01 u | 1500 | 4.11 ee a 1.0mm. _ 1275.5 39.30 141.48, 87.91 2000 | 4.07/14.65| 9.10 || 1° km. 1500 | 28.34 |102.02] 63.39 3000 | 4.02| 14.47) 8.99 OE tie 2000 | 24.54| 88.34) 54.89 s 3.93 | 14.15) 8.79 158 m1. | 3000 | 22.36| 80.50; 50.02 | © | 19.65] 70.74, 43.96 aca | | | 0.4 mm, | 2 : robe 7/2422 1842 $85913526) umm, 13.896 226 131.89 0.1 in. 7 , eo. 53 100 kim. | 2000 | 48.80 |175.68) 109.16 700 | 10.34! 37.22 | 23.13 : 395 mi. 800 | 9.82 | 35.35 | 21.97 OTM, | 3000 ee 132.52! 82.34 goo. | 9.48 | 34.09 | er.2t 105 mt. 1 29.48 | 106.13] 65.95 1000 | 9.25 | 33.30 | 20.69 |' 1200 | 8.94 | 32.18 | 20.00 || 1500 | 8.68 | 31.25 | 19.42 | 2000 | 8.44 | 30.38 | 18.88 2.0 mm. _ | 2551 | 78.62 283.03) 175.87 3000 ee se = I sei ve | 3000 | 56.68 '204.05|126.79 2 7: 26.30 | 17.5 ao 2 | © | 39.31 |141.52| 87.94 79 m1. a ot ee ele I etl | 0.6mm | 0.0 mm. _| 765.3 | 23-58 | 84.89 52-75 | 100 km. 800 | 19.52 | 70.27 | 43.66 Od ns goo | 17.01 | 61.24 | 38.05 263 mt- | 1000 | 15.89 | 57.20 | 35.54. 1200 | 14.72 | 52.99 | 32.93 1500 | 13.87 | 49.93 | 31.03 2000 | 13.21 | 47.56 | 29.55 3000 | 12.66 | 45.58 | 28.32 } co TT.79 42.44 26.37 | | GRADIENT WIND VELOCITY—ANTI-CYCLONIC 647 Latitude 30°. . || 4 AB (mm.) m jem mi AB (mm.) .m km mi 100 km. " Vs “hr Var | 100 km. Le Vee || ee 0.2 mm. _|182.25| 6.64 | 23.90 14.85 || 0.8mm. _ | 729 | 26.58} 95-69] 59.46 100 km. 200 | 5.12 | 18.43} 11.45 || 100 km. 800 | 20.48! 73.73) 45.81 O.1 in. 300 | 4.08 | 14.69] 9.13 O.1 in. goo | 18.51 | 66.64) 41.41 789 mi. | 400] 3.82) 13.75] 8.54 197 mi. | 1000 | 17.48 | 62.93) 39.10 500 | 3.70| 13.32| 8.28 1200 | 16.34 | 58.82] 36.55 600 | 3.62] 13.03] 8.10 1500 | 15.48 | 55.73] 34.63 700 | 3.57) 12.85) 7.98 2000 | 14.79! 53.24] 33.08 800 | 3.54.| 12.74] 7-92 3000 | 14.21 | 51.16] 31.79 goo | 3.51 12.64] 7.85 cs 13.29] 47.84| 29.73 1000 | 3.49|12.56| 7.80 1200 | 3.46) 12.46) 7.74 1500 | 3.43 12.35] 7.67 2000 | 3.40 | 12.24 7.61 L.O mm. _ |911.25) 33-22 119.59] 74.31 3000 | 3-38) 12.17] 7-56 || 00 km. 1000 | 25.60| 92.16) 57.26 2 3-32 | 11-95] 7-43 O.1 in. 1200 | 22.29 | 80.24] 49.86 158 mt. 1500 | 20.43 | 73-55) 45-70 2000 | 19.12 | 68.83) 42.77 000 | 18.11] 65.20] 40.51 0.4mm, _ | 364.5 | 13.28 | 47.81 | 29.71 a 16.61 rs ae 100 km. 400 | 10.24 | 36.86 | 22.90 0.1 in, 500 | 8.74: 31.46 | 19.55 395 mi. 600 ee toe elie ei ce ae ee 1.5mm. _ |1367.9| 48.84 |179.42| 111.49 goo | 7.50 | 27.00 | 16.78 || 10° km. “1500 | 38.40 |138.24| 85.90 1000 | 7.40) 26.64 | 16.55 O.1 aM. |) 2000 | 31.89 |114.80) 71.33 1200 | 7.24 | 26.06 | 16.19 105 mi. 3000 | 28.68 }103.25| 64.16 1500 | 7.11 | 25.60] 15.91 © | 24.92 | 89.71) 55.74 2000 | 6.98 ; 25.13 | 15.62 3000 | 6.86 | 24.70] 15.35 oo 6.64 | 23.90 | 14.85 2.0mm. _ |1822.5| 66.44 |239.18|148.62 100 km. 2000 | 51.20 |184.32]114.53 O.L in. 3000 | 40.85 |147.06} 95.76 0.6 mnt. _|546.75) 19.94 | 71.78 | 44.60 79 mi. o | 33.22 |119.59| 74.31 100 km. 600 | 15.36 | 55.30 | 34.36 0.1 tn. 700 | 13.58 | 48.89 | 30.38 263 mi. 800 | 12.76 | 45.94 | 28.55 goo | 12.26 eae a 2.5mm. _ |2278.1) 83.06 |299.02|185.80 1000 | IT.9T | 42.88 | 20.64 | Toq km. | 3000 | 55.72 |200.59|124.64 1200 | 11.49 | 41.36 | 25.70 0.1 in © | 41.53 |149.51| 92.90 1500 | 11.09 | 39.92 | 24.81 oe 2000 | 10.76 | 38.74 | 24.07 63 mt. 3000 | 10.47 | 37.69 | 23.42 © 9.97 | 35.89 | 22.30 3.0mm. _ |2733-8) 99.68 | 358.85) 222.98 100 km. 3000 | 76.79 |276.44|171.77 | oO.r in © | 49.84/179.42/111.49 53 me PHYSICS OF THE AIR Latitude 35°. gegen rs LRA EL a a tanyshe ‘on, i foe Sees larson Ty SSS Ss se: i AB (mm.) m Am | mi AB (mm.) { m km mi 100 km if ie y hr | hr; 100 km t | Vs MOE Vr oc el re. 0.2 mm. _|138.5| 5.80 | 20.8 | 12.88 | 0.8 mm. _ | 1500 | 12.92 | 46.51 | 28.90 = OLS | eee ; = 9 100 km 200 | 3.73 | 13-43) 8.35 || 100 km 2000 | 12.52 cae 28.01 0.1 in 300 | 3.34| 12.02, 7.47'| 0.1 im 3000 oe ae 27.22 789 mi 400 | 3.20) 11.52) 7.16) 197 mi @ | 11.50 | 41.09 | 25.90 500 | 3.13] 11.27 7.00! 600 | 3.09] 11.12; 6.91 i 700 | 3.06] 11.02 ° 6.85 i Lomm. _ | 692.5| 28.96/104.26| 64.78 B08 ee oe eg || 100 km 700 | 26.24) 94.46, 58.70 eae ae eo ae O.1 in 800 | 21.19) 76.28 47.40 0 o 8 16: 66 : 158 mt. goo 19.57) 70.45) 43.78 one 2 pet 10; ie 6 Z 1000 | 18.63! 67.07° 41.68 5 ‘97 | pO) 0.04 | 1200 | 17.55} 63.18) 39.26 2000.) 2995 ee ee 1500 | 16.71) 60.16, 37.38 ses a Ric oe | 2000 | 16.01] 57.64] 35.82 eo ©3000 | 15.43) 55.55) 34-52 0.4 mm, _| 277.0 | 11.58 | 41-69 | 25.90 | © | 14.48) 52.13] 32.39 100 km, 30) 9.07 | 32.65 | 20.30 O.1 on. 400 | 7.46 | 26.86) 16.61) 1.5 mm. = 1038.7! 43-44 156.38) 97-15 395 m1. a nee oye pe | 100 km. 1200 , 31.79/I14.44) 71.11 se os ay 5 arcs | 0.1 im. 1500 ' 27.95/100.62! 62.52 ; ‘S 3-47 | 14.58 | 105 mi. 2000 . 25.66] 92.38! 57.40 00 | 6.41 | 23.08 | 14.34 || 600: || .21.02| 86 900 | 6.32 22.75 | 14.14 |' a + a ee 1000 | 6.26 | 22.54 | 14.01 || y BETA) TRIG) 488° 1200 | 6.17 | 22.21 | 13.80 || 1500 | 6.09 | 21.92 | 13.62 2 2000 | 6.01 21.64) 13.45 | 2.0 mm. _ 1385.0] §7.92|208.51) 129.56 3000 | 5.93 | 21.35 | 13.27 |) 10° km. 1500 | 45.36/163.30 101.47 oo 5-79 | 20.84] 12.95; O-F 2000 ; 37.26/134.14) 83.33 { 79 mi. 3000 + 33.41|120.28) 74.70 0.6 mm. _| 415.5 | 17.38 | 62.57 | 38-88 wo | 28.96)104.26) 64.78 100 km. 500 | 12.31 44.32 | 27.54 | 7 ae ae as sae od 2.5mm. _ 1731.2, 72.40, 260.64) 161.95 2 a + . . ee, gs eee | ea mn miaieee, ate 800 | 10.26 | 36.94 | 22.95 || 10° km. 2000 | 52.98/190.73]118.51 g00 | 10.02 | 36.07 | 22.41 On: 3000 | 43.87/157-93! 98.13 1000 | 9.85 | 35.46 | 22.03 63mi. | © 36.20]130.32| 80.98 1200 | 9.61 | 34.60 | 21.50 i 1500 | 9.39 | 33.80 | 21.00 2000 | 9.19 | 33.08 | 20.56 || 3.0mm. _ (2077.5, 86.88|)312.77\194.35 3000 | 9.01 | 32.44| 20.16 || too km. | 3000 | 55.89/201.201125.02 © | 8.69 | 31.28/19.48|| ori. 0 | 43.44|1536.38| 97-17 0.8 mm. _| 554.0 | 23.16 | 83.38 | 51.81 53 Mt. 100 km. 600 | 18.14 | 65.30 40.58 0.1 in. 700 | 15.91 | 57-28 | 35-59 || 4.0mm. _ |2770.0|115.84|417.02|259.12 197 mt. ae nae oo ae 100 km. 3000 | 90.72)326.59 202.93 1000 | 13.89 | 50.00 | 31.07 O.tin. | © | §7.92/208.51|129.56 1200 | 13.36 | 48.10 | 29.89 39 Mts GRADIENT WIND VELOCITY—ANTI-CYCLONIC 649 Latitude 40°. nm em mi AB (mm.) m km mi 100 km, ke Ke Vp Vie 100 km. ” ve Vie Vie 0.2 mm. _|110.25| 5.16 | 18.58 | 11.55 || 0.8 mm. _ | 1200 | 11.52] 41.47| 25.77 100 km. 200 | 3.10/ 11.16] 6.93 |! 100 km. 1500 | I1.24) 40.46] 25.14 O.Lin. | 300] 2.88) 10.37! 6.44 0.1 in. 2000 | 10.98] 39.53} 24.50 789 mi. 400 | 2.79/| 10.04] 6.24 197 mi. 3000 | 10.75] 58.70) 24.05 500 | 2.74| 9.86] 6.13 © 10.34] 37.22} 23.13 600 | 2.72] 9.79] 6.08 700 | 2.70} 9.72] 6.04]| 1.0 mm. _ 551.25 25.84) 93.02| 57.80 800 | 2.68) 9.65) 6.00 || too km. 600 | 20.12} 72.43} 45.01 900 | 2.67] 9.61] 5.97 1.0 in. 700 | 17.69] 63.68] 39.57 1000 | 2.66) 9.58] 5.95 158 mi. 800 | 16.59] 59.72} 37-11 1200 | 2.65) 9.54] 5.93 900 | 15.93] 57-35) 35-64 1500 | 2.63 9.47) 5.88 1000 | 15.48] 55-73] 34.63 2000 | 2.62) 9.43] 5.86 1200 | 14.89] 53.60] 33.31 3000 | 2.61} 9.40] 5.84 1500 | 14.39] 51.80) 32.19 ~ 2.58) 9.29| 5.77 2000 | 13.96] 50.26] 31.23 3000 | 13.58) 48.89) 30.38 0.4 mm, _ | 220.5 | 10.34 | 37-22 | 23.13 oo 12.92] 46.51) 28.90 100 km. 300 | 6.83 | 24.59 | 15.28 0.1 in. 400 | 6.19 | 22.28 | 13.84 L5 mm. _ | 826.9} 38.76/139.54| 86.71 395 m1. a pe ark rae 100 km. g00 |; 30.18)108.65) 67.51 700 | 5.66 | 20.38 | 12.66 OBIT: 1000 | 27.38) 98.57) 61.25 800 | 5.59 | 20.12] 12.50 105 mi. 1200 | 24.89 Be 55-68 900 |} 5.53] 19.91 | 12.37 1500 | 23.22) 83.59) 51.94 1000 | 5.49 | 19.76 | 12.28 2000 | 21.95! 79.02! 49.10 1200 | 5.43 | 19.55 | 12.15 3000 | 75-38 46.84 1500 | 5.37 | 19.33 | 12.01 = 9-38) 99-77, 43.35 2000 | 5.32| 19.15 | 11.90 3000 | 5.27 | 18.97] 11.79 || 2.0mm. _ | 1102.5) 51-68 186.05/115.61 oo 5.17 | 18.61 | 11.56 || 100 km. 1200 | 40.23/144.83 89.99 0.1 in. 1500 | 34.13|122.87 76.35 0.6 mm. _|330.75| 15.50 | 55.80 | 34.67 79 mi. 2000 | 30.96/111.46 69.26 100 km. 400 | 10.95 | 39.42 | 24.50 3000 | 29.77|107.17 66.59 O.1 in. 500 | 9.80 | 35.28 | 21.92 co | 25.84) 93.02 57.80 263 mi. | 600} 9.29 | 33.44 | 20.78 700 | 8.98 | 32.33 | 20.09 || 2.5 mm. _ | 1378.1) 64.60/232.56'144.50 800 | 8.78 | 31.61 | 19.64 || too km. | 1500 | 50.29/181.04|112.50 900 | 8.64 | 31.10 | 19.32 0.1 in. 2000 | 41.48]149.33) 92.79 1000 | 8.53} 30.71 | 19.08 oe 3000 | 37.23 134.03. 83.28 1200 | 8.38] 30.17 | 18.79 3 mt. co | 32.30/116.28 72.25 1500 | 8.23 | 29.63 18.41 ! 8 } 2000 .10 | 29.16 | 18.12 | 3000 | 7.98 | 28.73 | 17.85 || 3.0mm. _ 1653.75} 77-54|279-14 173.45 @ 7-75 | 27-90 | 17.34 |} 100 km. 2000 | 54.76/197.14,122.50 O.1 in, 3000 | 46.43|167.15|103.86 0.8 mm. _| 441.0 | 20.68 | 74.45 | 46.26 53 mi. o | 38.77 139.57 86.72 100 km. 500 | 15.39 | 55-40 | 34.42 ones ae rormi, | Yoo |1288| 430) sey | $2MM = | 2205.0105-s8fa72.17 31.25 197 m1. a 12.38 a 27.69 100 km. 3000 | 68.25/245.70|152.67 900 | 12.06 | 43.42 | 26.98 0.1 in. © | §1.69)186.08| 115.62 1000 | 11.83 | 42.59 | 26.46 39 mt. 650 PHYSICS OF THE alk Latitude 45°. AB (mm.) m km mi’ AB (mm.) m km ms 100 km. ® Ye Vag ae 100 km. a Vs Var Vie ] 0.2 mm. _|91.33| 4-70 | 16.92 | 10.51 |! 0.8 mm. _ | 365.33 18.80 | 67.68) 42.05 100 km. 100 | 3.62 | 13.03 8.10 100 km. 400 | 14.48] 52.13) 32.39 O.1 in. 200 | 2.70| 9.72 6.04 | 0.1 in. 500 | 12.36! 44.50] 27.65 789 mi. 300 | 2.56| 9.22| 5.73 197 mi. 600 | 11.55| 41.58} 25.84 400 | 2.50] 9.00| 5.59 700 | II.II | 40.00} 24.85 500 | 2.47} 8.89] 5.52 800 | 10.82} 38.95; 24.20 600 | 2.45] 8.82] 5.48) g00 | 10.61 | 38.20! 23.74 700 | 2.43} 8.75| 5.44: 1000 | 10.46; 37.66; 23.40 800 | 2.42, 8.71} 5.41; 1200 | 10.25! 36.90, 22.93 900 |} 2.41} 8.68) 5.39 1500 | 10.05} 36.18) 22.48 1000 | 2.41} 8.68] 5.39, 2000 | 9.87] 35.53) 22.08 1200 | 2.40| 8.64] 5.37 | 3000 | 9.70] 34.92) 21.70 1500 | 2.39] 8.60] 5.34 o 9.40 | 33.84) 21.03 2000 | 2.38; 8.57] 5.33 ° = 3000 | 2.36] 8.50 5-28 | Lomm. _ | 456.66 | 23.50 | 84.60) 52.57 © 2.35 8.46; 5.26'| 100 km. 500 | 18.10] 65.16) 40.49 | O.T in, 600 | 15.76; 56.74) 35.26 0.4 mm. _ 182.66) 9.40 | 33:84 | 21-03 || T58 mi. | 700 |14.77| 53-17] 33-04 100km. | 200, 7.24 | 26.06] 16.19 | 800 | 14.19; 51.08 31.74 0.1 in. 300 | 5.78 20.81 | 12.93 | g00 | 13.80) 49.68] 30.87 395 mi. 400 , 5.41 | 19.48! 12.10 | 1000 | 13.52 48.67] 30.24 500 | 5.23 | 18.83 | 11.70) 1200 | 13.14 47.30| 29.39 600 | 5.12; 18.43 | 11.45, 1500 12.81 | 46.12) 28.66 / 700 | 5.05: 18.18 11.30. 2000 | 12.50] 45.00) 27.96 | 800 | §.00| 18.00 | 11.18 | 3000 | 12.23} 44.03) 27.36 | 900 | 4.97/ 17.89) 11.12, oo 11.75 | 42.30) 26.28 1000 | 4.94 17.78] 11.05 : [, 3 1200 | 4.89 17.60] 10.94) E-5 mm. _ | 685.0 | 35.24 !126.86) 78.83 1500 | 4.85) 17.46! 10.85 | 100 km. 700 | 30.54 109.94; 68.31 2000 | 4.81/17.32|10.76 O.1 in. 800 | 25.50! 91.80) 57.04 3000 | 4.77 | 17.17 | 10.67 | 105 mi. g00 | 23.64 85.10) 52.88 © 4.70 | 16.92 | 10.51 | 1000 | 22.55 81.18) 50.44 | 1200 | 21.28) 76.61! 47.60 0.6mm. _ 274.0] 14.10 | 50.76 | 31.54 1500 | 20.28; 73.01) 45.37 100 km. 300 | 10.86 | 39.10! 24.30 2000 | 19.45 70.02} 43.51 0.1 in. 400 | 9.02 | 32.47 | 20.18 3000 | 18.76) 67.54) 41.97 263 mi. 500 | 8.43 | 30.35 | 18.86 © | 17.62! 63.43) 39.41 600 | 8.11 | 29.20 18.14 GS 700 | 7.92 | 28.51 | 17.72 || 2-0 mm. _ | 913-33 | 46.98 | 169.13| 105.09 800 | 7.78 | 28.01 | 17.40 || 100 km. 1000 | 36.20 |130.32| 80.98 900 | 7.69 | 27.68 | 17.20 O.1 in. 1200 | 31.52 /113.47} 70.51 1000 | 7.61 | 27.40} 17.03 79 mi. 1500 | 28.89 |104.00] 64.62 1200 | 7.50 | 27.00 | 16.78 2000 | 27.04 97-34] 60.48 1500 | 7.40 | 26.64 | 16.55 3000 25.61 | 92.20) 57.29 2000 | 7.31 | 26.32 | 16.35 © 23.49 | 84.56) 52.54 3000 | 7.21 | 25.96! 16.13 a ; | ——= a 7.05 25.38) 15.77 || 2:5 mm. _ |1141.66 58.74 |211.46/131.39 i 100 km. 1200 47.93 |172.55|107.22 oa 7 | OE an. 1500 39.40 |141.84) 88.14 63 mi. 2000 | 35.46 |127.66) 79.32 3000 32.86 |118.30) 73.51 ° canis 105.73] 65.70 GRADIENT WIND VELOCITY—ANTI-CYCLONIC 651 Latitude 45° (Continued). A fmm.) | m km mt AB (mm.) m km mi 100 km, e ie vie Vhr 100 k ‘ i Vor Vir 3.0 mm. _|1370.C) 70.48 |253-73|157-66|, 4.0 mm. _ | 1826.66] 93.98 |338.33]210.23 100 km 1500 | 54.30 |195.45|121.46]| 100 km. 2000 | 72.40 |260.64|165.53 0.11 2000 | 45.10 |162.36)/100.89]| 0.1 in. 3000 | 57.77 |207.97|129.23 53 mi__-| 3000 see ae aes 39. mi. o | 46.99 | 169.16] 105.11 wafer, WEA NORE Oe Latitude 50° 0.2 mum. _ 77-66 | 4.34 | 15.62 | 9.71 0.6 mm. 1500 | 6.78] 24.41] 15.17 100 km. 100 | 2.94) 10.58) 6.57 ; 100 km. 2000 | 6.71 | 24.16; 15.01 O.1 in. 200 | 2.43! 8.75) 5.44 0.1 in. 3000 | 6.64] 23.90] 14.85 789 mi 300 | 2.33/ 8.39) 5.21) 263 mi. © 6.51 | 23.44) 14-57 AGO?) B20) 1 B24) a2) | eee | 500 | 2.26) 8.14 5.06); 0.8mm. _ |310.66) 17.34 | 62.42) 38.79 | 600 | 2.24] 8.06] 5.01 | 100 km. 400 | 11.78) 42.41} 26.35 | 700 | 2.23, 8.03) 4.99), ‘o.rin. 500 | 10.74 38.66 24.04 ' 800 | 2.23' 8.03] 4.99 | 197 mi 600 | 10.24 36.86 22.90 - goo | 2.22) 7.99] 4.96 ; 700 | 9.94 35.78 22.23 1000 | 2.21 7.96} 4.95 | 800 ; 9.74| 35.06) 21.79 1200 | 2.21| 7.96) 4.95) g00 | 9.59} 34.52] 21.45 1500 |} 2.20; 7.92| 4.92 1000 | 9.48: 34.13] 21.21 2000 | 2.19] 7.88] 4.90: 1200 | 9.31, 33.52] 20.83 3000 | 2.19) 7.88) 4.90 | 1500 } 9.18 | 33.05) 20.54 oo 2.17| 7.81) 4.85 2000 |} 9.04) 32.54| 20.22 ee a iy 3000 | 8.91) 32.08] 19.93 0.4. mm. _ ‘155.331 8.68) 31-25) 19.42)| | | «8:67, 31.27) 19-39 100 km. 200 | 5.89 | 21.20/ 13.17) 1 9 mm 388.33| 21.68 78.05) 48.50 OFF | ae | oe te Od || 100 km. — | 400 | 18.51 | 66.64] 41.41 395 1. : : : ; 0.1 in 500 14.721 52.99 32.93 500 | 4.74 | 17.06 | 10.60 : 600 | 13.60 | 48.96) 30.42 600 | 4.66 | 16.78 | 10.43 158 m1. fe Gebel oa at 700 | 4.61 | 16.60 | 10.31 |; 700 | 13. 46.04) 29. 800 | 12.63} 45.47) 28.25 800 | 4.57 | 16.45 | 10.22 |) ae A ae 6 900 | 4.54 | 16.34 | 10.15 sees ieee baa ae 1000 | 4.52 | 16.27 | 10.11 seat 0 poet ee 1200 | 4.49 | 16.16 | 10.04 200 2 42:04 eee 1500 | 4.46} 16.06} 9.98 1500 ELBS (A Ts4 re 2000 | 4.42/|15.91| 9.89 | es ee van ee 3000 | 4.40| 15.84) 9.84 3 at 4 oe a ae o | 4.34] 15.62] 9.71 || ee ee eee 2 as 1.5mm. _ | 582.5 | 32.52 |117.07| 72.75 0.6 mm. 233.0 | 13.02 | 46.87 | 29.12 |; 100 km. 600 | 27.76 99-94 ae =) 30 8.83 | 31.79 | 19.75 O.1 in. 700 | 23.07) 83.05) 51.60 aan’ 400 | 7.90 | 28.44 | 17.67 105 mi. 800 | 21.38 | 76.97] 47.83 one 500 | 7.52 | 27.07 | 16.82 goo | 20.41 | 73.48) 45.66 203 mi. 600 | 7.30 | 26.28 | 16.33 1000 | 19.76) 71.14) 44.20 700 | 7.16 | 25.78 | 16.02 1200 | 18.94 68.18) 42.36 800 | 7.06 | 25.42 | 15.80 1500 | 18.25 | 65.70] 40.82 goo | 6.99 | 25.16 | 15.63 2000 | 17.66] 63.58) 39.51 1000 | 6.94 | 24.98 | 15-52 | 3000 17.14] 61.70) 38.34 1200 | 6.86 24.70 15.35 | o | 16.26) §8.54) 36.38 652 PHYSICS OF THE, AIR Latitude 50° (Continued). AB (mm.) m km mi AB (mm.) m km mi 100 km. e Me Vie Vir 100 km, e US Vin Vir | 2.0mm. _ |776.66) 43.38 |156.17| 97-04)! 3.0 mm. _ |1165.0 65.06 |234.22/145.54 100 km. 800 | 37.02 |133.27| 82.81], 100 km. 1200 | 55.53 |199.91|124.22 0.1 in. 900 | 31.65 |113.94, 70.80 O.1 im. 1500 | 44.17 |159.01| 98.80 79 mi. 1000 | 29.45 |106.02| 65.88 53 mi 2000 | 39.52 |142.27| 88.40 1200 | 27.21 | 97.96) 60.87 3000 | 36.51 |131.44! 81.67 1500 | 25.60] 92.16] 57.27 Cy 32.53 |117.11| 72.77 2000 | 24.34} 87.62) 54.44 3000 | 23.31 | 83.92! 52.15]; 4.0 mm. _ |1553.33] 86.74 312.26 194.03 co | 21.69} 78.08) 48.52) too km. 2000 | 58.90 |212.04/131.75 O.1 in. 3000 | 51.19 |184.28) 114.51 2.5mm, _ 970.8 | 54.22 |195.19/ 121.29 Bea oe) 43.37 |156.13) 97.01 39 m1. 100 km. 1000 | 46.27 | 166.57) 103.50 0.1 in, | 1200 | 37.72 |135.79| 84.38 63 mi. 1500 | 34.05 |122.58) 76.17 2000 | 31.57 |113.65| 70.62 | 3000 | 29.75 |107.10) 66.55 co |27.11 | 97.60, 60.65 | Latitude 55°. 0.2 mm. _ | 67-9 | 4.06| 14.62] 9.08 | 0.6 mm. _ | 203.7 | 12.16 | 43.78 | 27.20 100 km. 100 | 2.59] 9.32] 5-79 || 100 km. 300 | 7.77 | 27.97 | 17.38 0.1 in. 200 | 2.24| 8.06) 5.01 O.1 in. 400 | 7.16 | 25.78 | 16.02 SOA ane: 300 | 2.16] 7.78] 4.83 sit 500 | 6.88 | 24.77 | 15.39 789 Wt: 400 | 2.12! 7.63] 4.74 i 600 | 6.71 | 24.16 | 15.01 500 | 2.10] 7.56| .4.70 700 | 6.61 | 23.80 | 14.79 600 | 2.09; 7.52| 4.67 800 | 6.53 | 23.51 | 14.61 700 | 2.08! 7.49| 4.65 900 | 6.48 | 23.33 | 14.50 800 | 2.07/ 7.45] 4.63 1000 | 6.43 | 23.15 | 14.38 goo ; 2.07] 7.45| 4.63 1200 | 6.37 | 22.93 | 14.25 1000 | 2.06; 7.42] 4.61 1500 | 6.31 | 22.72 | 14.12 1200 | 2.06; 7.42] 4.61 2000 | 6.25 | 22.50 | 13.98 1500 | 2.05] 7.38} 4.59 3000 | 6.19 | 22.28 | 13.84 2000 |} 2.05| 7.38] 4.59 © 6.08 | 21.89 | 13.60 3000 | 2.04) 7.34] 4.56 é co 2.03 | 7-31| 4.54 || 0.8mm, _ | 271.6 | 16.22 | 58.39 | 36.28 100 km. 300 | 12.41 | 44.68 | 27.76 0.4mm. _ | 135.8| 8.12 | 29.23 | 18.16 0.1 in. 400 | 10.36 | 37.30 | 23.18 100 km. 200 | 5.18 | 18.65 | 11.59 197 mi. 500 | 9.68 | 34.85 | 21.65 oO. in. 300 | 4.66 | 16.78 | 10.43 600 | 9.33 | 33.59 | 20.87 395 mi. 400 | 4.48 | 16.13 | 10.02 700 | 9.10 | 32.76 | 20.36 500 | 4.40/ 15.84] 9.84 800 | 8.95 | 32.22 | 20.02 600 | 4.32] 15.55] 9.66 900 | 8.84 | 31.82 | 19.77 700 | 4.27|15.37| 9.55 1000 | 8.75] 31.50 | 19.57 800 | 4.25| 15.30] 9.51 1200 | 8.63 | 31.07 | 19.31 g00 | 4.22} 15.19} 9.44 1500 | 8.52 | 30.67 | 19.06 1000 | 4.20) 15.12] 9.40 2000 | 8.41 | 30.28 | 18.82 1200 | 4.18} 15.05} 9.35 3000 | 8.30 | 29.88 | 18.57 1500 | 4.15} 14.94] 9.28 oo 8.11 | 29.20 | 18.14 2000 | 4.13 | 14.87] 9.24 3000 | 4.10); 14.76] 9.17 oo 4.06 | 14.62] 9.08 GRADIENT WIND VELOCITY—ANTLCYCLONIC 653 Latitude 55° (Continued). AB (mm.) m km | 1,mi AB (mm.) km mi 100 km, te ue Var Vn 100 km. Ve Vir ae 1.0 mm. _ | 339.5 | 20.28 | 73.01 45.37 || 2.0 mm, 1200 | 24.45 | 88.02) 54.69 100 km, 400 | 14.60 | 52.56] 32.60 || 100 km. 1500 | 23.31 | 83.92) 52.15 O.1 in. 500 | 12.95 | 46.62| 28.97 0.1 in. 2000 ae eoee oes Pes ane 00 | 12.23 | 44.00, 27.34 Se 3000 | 21.58} 77.69| 48.27 il 700 | 11.81 | 42.52| 26.42 ie Hk © | 20.28) 73.01} 45.37 800 | 11.53 | 41.51] 25.79 goo | 11.34 | 40.82) 25.36 || 2.5 mm. 848.7 | 50.70 | 182.52] 113.41 1000 | II.19} 40.28) 25.03}; 100 km. 900 | 40.94 |147.38] 91.58 » 1200 | 10.98 | 39.53] 24.56 O.1 in. 1000 | 36.50 |131.40| 81.65 1500 | 10.79} 38.84] 24.13 63 mi. 1200 | 32.90 |118.44; 73.60 2000 | 10.61 | 38.20) 23.74 : 1500 | 30.56 |110.02| 68.36 3000 | 10.44! 37.58] 23.35 2000 | 28.83 |103.79| 64.49 o | 10.14 | 36.50] 22.68 3000 | 27 45 | 98.82) 61.40 wo | 25.35] 91.26) 56.71 1.5 mm. _ | 509.2 | 30.42 |109.51) 68.05 | — 100 km. 600 | 21.90] 78.84] 48.99 || 3:0 mm. 1018.5] 60.84 |219.02/136.09 0.1 in. 700 | 19.99 | 71.96] 44.71 || 100 km. 1200 | 43.80 | 157.68} 97.98 105 ah. 800 | 18.98 | 68.33] 42.46 O.1 in. 1500 | 38.84 |139.82; 86.88 , goo | 18.34 | 66.02) 41.02 53 mi. 2000 | 35.78 |128.81 80.04 1000 | 17.89 | 64.40] 40.02 3000 | 33.56 |120.82) 75.07 1200 | 17.30 | 62.28) 38.70 @ | 30.42 |109.51|} 68.05 1500 | 16.78 | 60.41! 37.54 2000 | 16.33 | 58.79) 36.53 || 4.0 mm. 1358.0] 81.12 |292.03| 181.45 3000 | 15.92 | 57.31) 35-61 100 km. 1500 | 62.04 |223.34/138.78 o | 15.21) 54.76) 34.03 0.1 in. 2000 | 51.78 |186.41| 115.83 39 mi. 3000 | 46.62 |167.83|104.28 2.0 mm, _ | 679.0 | 40.56 | 146.02) 90.73 © | 40.56|146.02| 90.73 100 km. 700 | 34.57 | 124.45) 77-33 0.1 in. 800 | 29.20 |105.12| 65.32 79 mi. g00 | 27.12 | 97.63] 60.66 1000 | 25.89 | 93.20] 57-91 Latitude 60°. | 0.2mm. 60.75| 3-82|13.75| 8.55 || 0.4mm. _ | 121.5] 7.60 | 27.36 | 17.00 100 km. — 100! 2.36] 8.50] 5.28]; 100 km. 200 | 4.72 | 16.99 | 10.56 0.1 in. 200 | 2.09] 7.52| 4.67 0.1 in. 300 4-33 eee 9.69 SOnuany oo | 2.03} 7.31) 4.54 Se aii: 400 | 4.18] 15. 9.35 a ne 2.00| 7.20| 4.47 395 1. 500 | 4.10] 14.76); 9.17 500 |} 1.98} 7.13| 4.43 600 | 4.05] 14.58] 9.06 600 | 1.97| 7.09 4.41 700 | 4.02|14.47| 8.99 700 | 1.96!) 7.06 4.39 800 | 3.99] 14.36! 8.92 800 | 1.96} 7.06] 4.39 goo | 3.98] 14.33} 8.90 goo | 1.95] 7-02} 4.36 1000 | 3.96] 14.26] 8.86 1000 | 1.gs| 7.02] 4.36 1200 | 3.94/ 14.18) 8.81 1200 | 1.94| 6.98! 4.34 1500 | 3.92| 14.11 8.77 1500 | 1.94| 6.98} 4.34 2000 | 3.90; 14.04 8.72 2000 | 1.93} 6.95] 4.32 3000 | 3.87} 13.93| 8.66 3000 | 1.93] 6.95] 4.32 CJ 3.80 | 13.68 | 8.50 © 1.91} 6.88} 4.28 1 654 PHYSICS OF THE AIR Latitude 60° (Continued). AB (mm.) m km mi AB (mm.) m km mi 100 km. ie Vir Vy 100 km. a ie Vr Vir a | 0.6 min. _ |182.25| 11.40 | 41.04 | 25.50 || 1.5 mm. _ | 455.6 | 28.50 |102.60) 63.75 100 km. 200 | 8.87 | 31.93 | 19.84 || 100 km. 500 | 22.17 | 79.81} 49.59 O.1 in. 300 | 7.08 | 25.49 | 15.84 0.1 in. 600 | 19.30] 69.48) 43.17 263 mi. 400 | 6.62 | 23.83 | 14.81 105 mi. 700 | 18.09 | 65.12] 40.46 500 | 6.40 | 23.04 | 14.32 800 | 17.37 | 62.53] 38.85 600 | 6.27 | 22.57 | 14.02 goo | 16.90 | 60.84] 37.80 700 | 6.19 | 22.28 | 13.84 1000 | 16.56} 59.62| 37.05 800 | 6.13 | 22.07 | 13.71 1200 | 16.10} 57.96] 36.02 900 | 6.08 | 21.89 | 13.60 1500 | 15.69 | 56.48) 35.09 1000 | 6.05 | 21.78 | 13.53 2000 | 15.31 | 55.12} 34.25 1200 | 5.99 | 21.56 | 13.40 3000 | 14.98 | 53.93) 33-51 1500 | 5.94 | 21.38 | 13.29 co 14.25 | 51.30] 31.88 2000 | 5.89 | 21.20 | 13.17 3000 | 5.84 | 21.02 13.06 || 2.0mm. _ | 607.5 | 37-98 |136.73| 84.96 2 5-70 | 20.52 | 12.85 || too km. 700 | 28.14 |101.30| 62.94 8 0.1 in. 800 | 25.74 | 92.66) 57.58 0.8 MIN. _ | 243-0 | 15.20 | 54.72, 34-00) 2g ni. goo | 24.44 | 87.98) 54.67 100 kn. 300 | 10.69 | 38.48) 23.91 |) 1000 | 23.59 | 84.92) 52.77 O.L tn, 400 | 9.43) 33.95) 21.10], 1200 | 22.53) 81.11) 50.40 197 mi. 500 | 8.94! 32.18) 20.00]) 1500 | 21.66 | 77.98) 48.45 600 | 8.66] 31.18} 19.37], 2000 | 20.92! 75.31} 46.80 700 | 8.49) 30.56) 18.99 3000 | 20.26 | 72.94) 45.32 800 | 8.37) 30.13] 18.72 wo | 18.99 68.36) 42.48 goo | 8.28) 29.81] 18.52 1000 | 8.21} 29.56] 18.37 | 2.5mm. _ | 759.4 | 47.48 |170.93! 106.21 1200 8.11 | 29.20] 18.14 '| too km. 800 , 39.14 140.90] 87. 1500 | 8.01 | 28.84) 17.92] o.1 in, 900 ae ue 76.88 2000 , 7.92) 28.51) 17.72 63 mi. 1000 | 32.18 115.85, 71.99 3000 | 7.84) 28.22) 17.54 1200 | 29.86 107.50] 66.80 o 7-60 | 27.36] 17.00 1500 | 28.17 |101.41| 63.01 lata 2000 | 26.83 96.59] 60.02 1.0 mm. _ |303.75 19.00] 68.40) 42.50, 3000 | 25.72) 92.59| 57.53 100 km. 400 | 12.87 | 46.33] 28.79! © | 23.74) 85.46] 53.10 O.1 in, 500 | 11.79 | 42.44] 26.37 158 mi. — | co 40.57| 25.21|| 3.0mm. _ |911.25) 56.98 |205.13|127.46 10.95 | 39.42) 24-49 | 100 km. 1000 -34 159.62 .18 ae na ce ee 0.1 in. | 1200 38.01 120.00 ae : ; : mt. 1500 | 35.38 |127. Be 1000 | 10.46 | 37.66) 23.40 53 2000 | 33.12 £5 5 a 1200 | 10.29 | 37.04] 23.02 3000 } 31.37 |112.93| 70.17 1500 | 10.13 | 36.47| 22.66 © | 28.49 |102.56) 63.73 2000 | 9.99 | 35.96) 22.34 gee ae 35-46 22.03]! 4.0 mm. _ [1215.0] 75.96 |273.46|169.92 9-50 | 34.20) 21.25]| Tog km, 1500 | 53.44 |192.38|/119.54 O.1 in, 2000 | 47.18 |169.85/105.54 39 mi. 3000 | 43.32 |155.95| 96.90 | © | 37.98 |136.73| 84.96 APPENDIX II CONSTANTS AND EQUIVALENTS The following numerical values are taken, chiefly, from the Smithsonian Meteorological Tables, fourth edition, 1918: Standard Values Gravity acceleration ........... 980.665 centimetres per second. Gram weight .................. 980.665 dynes. Atmospheric pressure .......... 1013250.144+ dynes per square centi- metre; that is, the pressure of a mer- cury column at standard gravity and o° C. 760 millimetres high. Bar (meteorological) .......... 1,000,000 dynes per square centimetre. Temperature Scales The temperatures of melting ice, and of boiling water (steam just over boiling water), each at standard atmospheric pressure, are indicated as follows: Freezing: 32°F.; o° R.; 0° C.; 273°.13A.. Boiling: 212° F.; 80° R.; 100° C.; 373°.13 + A.. Hence CC. F° — 32° R° 5 9 4 and, on the perfect gas scale, or after correction, A&c= C° + 273.13 +. ? Linear Equivalents I metre = 39.3700 inches* =3.280833+ feet. 1 foot = 0.3048006 metre. 1 kilometre = 0.621370 mile. 1 mile = 1.609347 kilometre. * U.S. statutory equivalent. Velocity Equivalents I metre per second = 2.236932 miles per hour = 196.85 feet per minute. I mile per hour -=0.4470409 metres per second. Weight Equivalents I avoirdupois pound = 453.5924277. grams 1 kilogram = 2.204622 avoirdupois pounds. I gram = 15.432356 grains. I grain = 0.06479892 gram 655 656 PHYSICS OF THE AIR Densities (Grams Per Cubic Centimetre) Mereuryiat:0° Ce saiccasgaeces eevee e neues 13.5951 Air, dry, free from carbon dioxide, and at standard atmospheric pressure ........ 0.0012928 Air, dry, containing 3 parts carbon dioxide per 10,000 (normal amount) and at standard atmospheric pressure ........ 0 0012930. Weight of standard dry air ............000 1.2930 kilograms per cubic | metre; 565.039 grains, or 1.29152 ounces, per cubic foot. INDEX Abbe, Cleveland, 228, 235, 254 Abbot, C. G., 44, 75, 76, 81, 84, 86, 87, 200, 546, 567, 577; 589, 590, 597, 607 Absorbing gases and surface tem- perature, 89 Absorption of radiation, laws of, 82 Adiabatic processes, 29 temperature decrease, 31 effect of water vapor on, 31 Adjustment of winds, automatic, 145 Aerial cascades, 218 Air breakers, 224 bumps in, 214 cataracts, 218 decrease of temperature of, with elevation, 37 density of, 656 equivalent molecular weight of, 95 foyntains, 215 holes in, 214 sinks, 217 temperature changes with eleva- tion of rising mass of, 34 torrents, 224 Airy, Sir G. B., 465, 470, 473, 531 Aldrich, L. B., 200, 546 Alexander, W. H., 329 Alto-cumulus, 283 -stratus, 283 Anderson, O. P., 297 Anemometer, Robinson cup, 6, 7 pressure, 6 Angot, A., 234 Angstr6ém, K., 85, 566, 567, 605 Anthelion, 519 oblique arcs of, 520 Anticyclone, 197 mechanical, 197 migratory, 197 paths of, 198 radiational (permanent), 198 semipermanent, 210 thermal, 200 transitory, 200 velocity of travel of, 198 wind velocity in, 198 Anticyclonic winds, greater than cyclonic, 141 Antitrade winds, 171 Antitrades, height of, 172 Apjohn, J., 14, 247 Arago, D. F. J., 539, 551 Arc, circumhorizontal, 514 Arc, circumzenithal, 511 Kern’s, 513 Archibald, E. D., 150 Arching of cloud bands, 427 Arcs, lateral tangent, halo of 46° 514, 515 oblique anthelic, 520 tangent, halo of 22°, 503 of Lowitz, 495 Areas, conservation of, 126 Aristotle, 439 : Arrhenius, S. A., 566 Aschkinass, E., 87 Assmann, J., 16 Atmosphere, composition of, 60 and latitude, 61 and elevation, 69 homogeneous, 62 normal state of, 161 weight of, and elevation, 64 Atmospheric circulation, a gravita tional phenomenon, 93 density, and elevation, 72, 73 irregularities, nature of, 443 optics, classification of phenom ena of, 426 pressure, 4 and elevation, 72 measurement of, 4 standard, 655 August, E. F., 14 Aurora, 422 cause of, 424 color of, 422 height of, 424 periodicity of, 422 types of, 422 variation of, with latitude, 422 Auroral streamers, apparent diver gence of, 428 Auto-convection, 102 Aviation, winds adverse to, 214 Avogadro’s Law, 62 Bahr, E. v., 566, 567 Balloons, sounding, 26, 27 Banner cloud, 300 Barnard, E. E., 290, 354 Barograph, 5 Barometer, aneroid, 5 height of, and temperature, 55 mercurial, 4 657 658 Barometric hypsometry, 61 ripples, 228 Barraclough, S. H., 391, 304 Bauer, L. A., 410, 413, 418 Bavendick, F. J., 523 Beal, J., 232 Beccaria, G., 408 Bell, H., 143 Bennett, W. J., 232 Bentley, W. A., 302, 374, 483, 512 Berson, A., 152 Bezold, W. v., 32, 317 Billow cloud, 296 Bishop, S., 537 Bishop’s Ring, 536 Blowing caverns, 117 Bolometer, 20 Bora, 118 Bouguer equation, 82 Bourdon tube, 2 Bowie, E. H., 180, 181, 198 Boyle’s Law, 61 Braak, C., 323 Bravais, M. A., 512 Breeze, forest, 108 lake, 108 t land, 110 mountain, 110 sea, 108 valley, 106 Brewster, D., 539 Brocken bow, 537 Brocken-specter, 537 Briicke, E., 539 Brunkow, W. H., 523 Buisson, H., 85, 605 Bumps, 214 Bumstead, H. A., 417 Burton, E. F., 408 Calvert, E. B., 353 Capus, G., 391 Carbon dioxide, absorption by, 88 and temperature, 606 Carrier, W., 14 Caverns, blowing, 117 Centrifugal force of winds, 136 Ceraunograph, 390 Chamberlin, T. C., 566 Chapman, §S., 240 Characteristic constant, 28 Charles’ Law, 62 Chinook, 209 Chree, C., 6 Circulation, a gravitational nomenon, 93 in the stratosphere, 165 effect of, on temperature, 614 Circumhorizontal arc, 514 phe- INDEX Circumzenithal arc, 511 Cirro-cumulus, 283 -stratus, 280 Cirrus, 277 Clausius, R. J. E., 539 Clayden effect, 379 Clayton, H. H., 75, 159 Climatic changes, facts of, 558 control, existing factors of, 559 Cloud bands, apparent arching of, 427 currents, 218 heights, 306 from temperature point, 256 squall, 359 thickness of, 309 and fog, distinction between, 272 Cloudiness, how expressed, 16 levels of maximum, 307 regions of minimum, 308 Clouds, classification of, 277 determination of velocity of, 24 direction of travel of, 24 kinds of, 16 measurement of elevation of, 24 relation of, to sun spots, 92 velocities of, 310 Coblentz, W. W., 572 Condensation, 250 by contact cooling, 250 by dynamic cooling, 254 by mixing, 252 forms of, 263 nuclei of, 271 Conservation of areas, 126 Constancy of mass flow, 158 Continental fallwinds, 120 Convection, auto-, 102 chief facts of, 99 cumulus, 105 one-way, 99 pseudoadiabatic, 260 vertical, 94 ways of thermally inducing, 99 Convectional instability, 321 Cooke, H. L., 408 Coronas, 528 Coulomb, C. A., 412 Covert, R. N., 4o1 Crepuscular rays, 428 Crest cloud, 299 Croll, J., 560, 564 Crosses, 523 Culverwell, E. P., 565 Cumulo-nimbus, 291 Cumulus, 289 convection, 105 and dew INDEX Cumulus, turbulence within, 316 Cunningham, E., 574 Cyclones, classification of, 186 extra-tropical, 178 mechanical, 188 migratory, 189 permanent, 188 traveling, characteristics of, 193 tropical, 173 Cyclonic winds less than anticyclo- nic, 141 Dalibard, T. F., 407 Dalton, J., 249 Daly, R. A., 612 Day, P. C., 327, 590 De Blois, L. A., 380, 382, 397 Deflecting force, total, 137 of earth’s rotation, 133 Deflection, due to curvature of path, 136 to rotation of earth, 132 angle, 183 Deviation, minimum, 457 total, 457 Dew, 264 point, definition of, 11 determination of, 12 Dewey, F. P., 245 Diffraction, size of particles by, 534 theory of, 530 Dines, W. H., 194, 196 Diurnal variation of electrical con- ductivity of air, 414 of potential gradiant, 410 of pressure, 220, 233 of wind direction, 161 of wind velocity, 160 Divergence of auroral streamers, 428 Dodd, W., 392 Doldrums, 170 Dorsey, N. E., 538 Drift, interzonal, 124 Drizzle, 264 Droplets, vapor pressure of, 12 Drops, free, 263 Dryness of air, reason for, 268 Dust particles, size of volcanic, 573 volcanic, action of, on solar radia- tion, 577 action of, on terrestrial radiation, number of particles of, 581 relative action of, on solar and terrestrial radiation, 579 time of fall of, 574 total quantity of, 582. whirls, 101 659 Dust, when and where most frequent, 105 Earth’s charge, origin and main- tenance of, 419 Egnell’s Law, 158 . Electric currents in the air, 416 Electrical condition of the air, 420 annual variation of, 414 diurnal variation of, 414 relation of, to elevation, 414 weather, 414 Elevation and pressure gradient, 153 and wind velocity, 149 Ellerman, F., 275, 278, 279, 281, 282, 284, 288, 379 Elster, J., 417 Emden, R., 44 Eon, L. J., 595 - Equatorial winds, 161 Equilibrium, neutral, 31 stable, 31 unstable, 31 Equivalent molecular weight of air, 95 i Espy, J. P., 160 Evaporation, 241 effect of area of surface on, 248 of dryness on, 247 of pressure on, 248 of salinity on, 247 of temperature on, 248 empirical equations of, 248 from circular areas, 243 elliptical areas, 244 tubes, 242 into wind, 244, 248 measurement of, 18 Everett, J. D., 440 Everett, W. H., 376 Exner, F. M., 34, 426, 466, 470, 473, 493, 494, 495, 499, 504, 506 Extinction coefficient, 543 Extra-tropical cyclone, 178 chief paths of, 179 convection in, 185 direction of travel of center of, 178 of winds in, 182 frequency of, 181 insolational, 187 of tropical origin, 196 relation of velocity to precipi- tation, 185 semipermanent, 186 size of, 178 thermal, 186 velocity of travel of, 180 wind velocity in, 184 660 Fabris, C, 150 Fabry, C., 85, 605 Fall of raindrops, limiting velocity of, 315 Fallwinds, continental, 120 Norwegian, 119 False cirrus, 303 Fassig, O. L., 264 Fata Morgana, 455 Ferguson, A., 246 Ferguson, G. H., 525 Ferguson, O. J., 378 Ferrel, W., 14, 126, 210 Finley, J. P., 210 Fitzgerald, D., 249 Foehn, 209 Fog, advection, 274 falling, more rain, 117 radiation, 272 rising, rain over, II7 and cloud, distinction between, 272 Forel, F. A., 455 Fowle, F. E., 44, 75, 76, 81, 84. 86, 87, 546,-567, 577, 590, 597, 605, 607 Fowler, A., 86, 605 Fox, P., 386 Fracto-cumulus, 291 -nimbus, 287 Franklin, B., 407, 570 Fraunhofer lines, 81 Fresnel, A. J., 528 Frost, 264 Funnel cloud, 306 Gases, absorbing. and surface tem- perature, 89 Geer, G. de, 565 Geitel, H., 408 Geological events. order of, 626 Glacier winds, 117 Glaze, 264 Glory, 537 Gold, E., 44, 140, 196 Gorczynski, L., 587 Gradient velocity, 138 nomogram, 143 relation of, to curvature of path, 143. to latitude, 142 to pressure gradient, 142 Gradient wind, 138 tables of, 632 Grains to grams, 655 Graupel, 264 Gravity acceleration, 655 normal, 63 standard, 65 wind, IIo chronological INDEX Gray, S., 407 Greatest winds, latitude of, 160 season of, 159 and least winds, hours of, 160 Green flash, 445 Grossmann, L. A., 14 Guldberg, C. M., 254 Gulik, D. v., 325 Gusts, 123, 221 Hail, 264, 365 Halo, Bouguer’s, 510 Halo of 22°, 494 of 46°, 509 of 90°, 510 of 136°, 510 of Hevelius, 510 of unusual radii, 517 Halos, secondary, 517 singular, 517 Hamrick, A. M., 299, 300 Hann, J. v., 37, 60, 61, 234, 252, 254, 608, 624 Hastings, C.S., 451, 452, 454, 525 Hawksbee, F., 407 Haze, dust, 21 optical, 21, 444 Hazen, H. A., 15 Heat, detection of gain or loss of, 1 sources of, 74 Heiligenschein, 537 Hellmann, J. G., 325 Helmholtz, H. v., 228, 296 Hennig, R., 601 Henry, A. J., 204, 205 Hermite, G., 43 Herschel, Sir John, 560 Hertz, H., 32. 254 Hildebrandsson, H., 104 Holes in the air, 214 : Homogeneous atmosphere, 62 oe of greatest and least winds, 160 Humidity, absolute, 9 determination of absolute, 12 of relative, 12 instrumentation, II relative, II spectific, 11 Humphreys, L. W., 286, 292 ys W. J., 44, 235. 328, 590, 04 Huyghens, C., 528 Hygrometer, hair, 16 oe eee equation, approximate, 7 complete, 65 Hypsometry, barometric, 61 _ effect of errors in data on, 66 INDEX Ice-age, carbon dioxide theory of, 566 Croll’s eccentricity theory of, 564 solar variation theory of, 563 Illumination of sky by ice crystals, 491 Infralateral tangent arcs to halo of 46°, 515 Insolation, 74 equality of, in each hemisphere, 77 relation of, to hour angle, 79 to latitude, 79 to solar declination, 79 relative, at different latitudes on certain days, 80 days, 80 total, 79 and solar altitude, 78 Interzonal drift, 124 Inversion level, 116 temperature, 116 Ionic density, 415 velocity, 415 Iridescent clouds, 535 Isothermal region, 43 height of, 50 relation of temperature of, to lati- tude, 58 Ivory, J., 14 Jans, C. de, 376 Jeffreys, H., 244, 246 Juday, C., 481 Katabatic wind, 111 Kelvin, Lord (see Thomson, Sir William) Kern’s arc. 513 Kimball, H. H., 545, 550, 585, 586 King, L. V., 540 Kite, meteorological, 25 Kolhérster, W., 408, 410 Koppen, W., 508 Krogness, O., 424 Ladenburg, E., 88. 605 Lamb, H., 162. 238, 240 Land area, effect on temperature, 613 breeze, I10 Langevin, P., 408, 416 Langevin ions, 415 Lapse rate, 35 Larmor, J. S. B., 402 Larmor, Sir Joseph, 402 Larsen, A., 368, 360, 371, 372 Lateral tangent arcs to halo of 46°, 514 Latham, W., 449 661 Latitude and composition of atmos- phere, 61 temperature of isothermal region. 58 of greatest winds, 160 Lawrence, O. H., 289 Leduc, S. A., 375 Lehmann, E., 88, 605 Le Monnier, L. G., 408 Lenard, P., 314, 315 Lenticular cloud, 299 Leonardo da Vinci, 538 Lightning, 367 ball, 376 beaded, 378 dark, 379 quantity of electricity in, 397 return, 379 rocket, 376 sheet, 377 streak, 368 chemical effects of, 390 crushing effects of, 391 danger from, 399 duration of, 380 explosive effects of, 301 genesis of initial discharge, 373 length of streak of, 380 protection from, 401 special dangers of, 406 spectrum of, 386 temperature of, 385 visibility of, 386 with snowstorm, 316 and soil fertility, 391 discharge, direct not alternating, 82 from where to where, 381 rods, attachment of, 405 bends in, 405 connection to neighboring con- ductors, 406 ground connection, 405 joints in, 405 material of, 403 system of, 404 terminals of, 404 Line squall, 349 Linss, W., 408, 412 Livingston, G. J., 247 Liznar, I., 268 Lodge, O., 404 Looming. 448 Lorenz, H.. 2 Lowitz, I. T., 406 Lyman, T., 605 McKeehan, L. W., 575 McLennon, J. C., 408 662 Maloja wind, 209 Mammato-cumulus, 303 Marvin, C. F., 15 Mascart, M. E., 451, 470, 477, 531 Mass flow, constancy of, 158 Maude, Sir F. S., 454 Mawson, Sir Douglas, 121 Maximum pressure gradient, level of, 157 seasonable pressure change, level of, 158 Maxwell, C., 14, 247, 477 Mercury, density of, 656 Meteorological information, sources of, 21 Metres per second to miles per hour, 655 to feet, 655 Mielke, J., 595 se per hour to metres per second, 55 Millikan, R. A., 575 Mirage, inferior, 453 lateral, 454 superior, 450 Mist, 264 Mistral, 119 ! Mohn, H., 254 Monsoons, 167 depth of, 169 secondary, 108 Moody, H. W., 29 Mountain breeze, 110 convection, 117 Neuhoff, O., 32. 254, 260, 261, 262 Newcomb, S., 560, 565 Newton, Sir Isaac, 538, 539 Nimbus, 287 Noah’s Ark, 428 Nomogram, gradient velocity, 143 Nordmann, C., 504 Normal gravity, 63 Northrup, E. F., 395, 398 Norwegian fallwinds, 119 Ocagne, M. d’, 143 Oceanic circulation and climate, 623 Optical phenomena of the air, 21 classification of, 426 Ozone, atmospheric, 85 absorption by, 88 Parhelia of 22°, 491 of 46°, 508 of 90°, 522 of 120°, 521 Parhelic circle. 518 Parry, Sir William E., 525 INDEX Penetrating radiation, 418 Peppler, A., 185, 198 Pernter, J. M., 426, 466, 470, 473, 477, 493-495, 499, 504, 506, 574 Peters, O. S., 401 Pictet, R., 104 Pillars, 523 Pitot tube, 6 Pockels, F. C., 397 Polar bands, 428 Polarization, sky, facts of, 554 theory of, 551 Pollock, J. A., 391, 394 Potential, electrical of raindrops, 374 gradient, 409 annual variation of, 409 diurnal variation of, 410 relation of, to meteorological ele- ments, 410 to elevation, 411 to location, 409 Pounds to grams, 655 Precipitation, intensity of, 268 measurement of, 18 summer and winter, 269 Pressure, atmospheric, aud eleva- tion, 72 vapor, ‘and elevation, 72 changes, diurnal, 229, 233 level of maximum seasonal, 158 regional, 227 seasonal, 226 semi-diurnal, 234 storm, 227 tidal, 240 gradient, maximum, level of, 157 and elevation, 153 Pring, J. N., 88 Pringsheim, E., 47 Pseudoadiabatic processes, 32 Psychrometer, aspiration, 16 sling, 16 theory of, 15 Psychrometric equation, ta Puffs, 123 Pyrheliometer, 20 Pyrheliometric recoreds, 585 values and world temperatures, 595 Radiation, absorption of monochro- matic, 82 absorption of, polychromatic, 83 laws of, absorption of, 82 measurement of, 20. 84 Radioactive content of the air, 417 Rain, electrification of, 312, 313 formation of, 264 INDEX Rain, relation of, to fog, 117 Rainbow, 456 distribution of colors in, 475 formation of, 462 horizontal, 481 intensity and distance from mini- mum ray in, 470 and size of drops, 477 and wave-length, 477 popular questions about, 478 primary, 456 principal, 456 reflected, 480 reflection, 480 region of minimum brightness, 463 secondary, 456 supernumerary, 457 origin of, 463 tertiary, 456 wave front, equation of, 465 why none without internal reflec- tion, 482 Raindrops, formation of, 264 velocity of fall of, 267 Rain-gush, 364 Ramsay, W., 626 Rayleigh, Lord, 232, 265, 266. 435, 528, 540, 542, 543, 551, 577, 578 Reflection, internal in ice crystals, 489 : Refraction, astronomical,. 431 effect of inclination on, 487 minimum deviation in, 483 prismatic, deviation in, 483 terrestrial, 446 Regnault, H. V., 14 Respighi, L., 430 Richardson, L. F., 124 Rime, 264 Rising and setting of heavenly bodies, 444 Rood, O. N., 397 Rubens, H., 87 Rudge, W. A. D., 316 Rutherford, Sir E., 373. 408, 418 Sandstrém, J. W., 119 Sarasin, F., 570 Sarasin, P., 570 Saturation deficit, 11 pressure, II quantity, I1 Scarf cloud, 300 Schaefer, C., 87, 566, 567, 607 Schneider, K., 599 Schuchert, C., 613, 626 Scintillation, planetary, 443 sun and moon, 443 stellar, 439 663 Scintillation, terrestrial, 444 Scoresby, W., 453 Scud, 287 Sea breeze, 108 circulation in, 109 depth of, 108 Season of greatest winds, 159 Seasonable pressure changes, 226 Seasons, temperature of and solar distance, 77 Shadow bands, 444 Shaw, A. N., 12 Shaw, Sir Napier, 113, 138, 141, 150, 170, 191 Shimmering, 444 Simpson, G. C., 280, 311, 313, 315- 316, 373, 408, 419, 534-530 Sinking, 449 Sky, apparent shape of, 429 prevailing color of, 545 colors, cause of, 539 early ideas of, 538 Sleet, 264 Snow, 264 electrification of, 314 Solar constant, changes in, 75 eleven-year period of, 76 evaluation of, 84 and solar distance, 77 corona and earth temperatures, 92 distance and seasonable tempera- tures, 77 energy, absorption of, 80 spectrum curve of, 86 transmission of, 80 Sone, T., 118 Soret, C., 552 Sounds, transmission of, mountains, 210 Stair-step clouds, 427 Standard gravity, 65 Stars, apparent distance between, 430 Steadworthy, A., 368, 387 Steam cloud, 117 Stefan, J., 14, 19, 242, 243, 247 Steffens, O., 326 : Stellar declinations, inequality of, in opposite hemispheres, 439 Stelling, E. R., 249 Stevenson, T., 150 Still-weight, 98 Stokes, G. G., 267, 473, 528, 542, 574 Stooping, 449 Stormer, C., 423-425 Strato-cumulus, 287 Stratosphere, 43 across 664 Stratosphere, equality of temperature changes in, 192 circulation in, 165 Stratus, 291 Strutt, R. J., 86, 605 Sun and moon, apparent size of, 430 Sunshine, measurement of, 19 Sun-spots and temperature, 596, 604 Supralateral tangent arcs of halo of 46°, 515 Surface covering, effect on tempera- ture, 625 Siiring, R., 154 Suzuki, S., 118 Swann, W. F. G., 410, 413, 418, 419 Tangent arcs, frequency of, 507 of halo of 22°, 503 of 46°, 514, 515 Taylor, G. I., 124, 245 Teisserenc de Bort, L., 43, 104 Temperature, comparison of, I condition of equality of, 1 decrease with altitude, adiabatic, 31, 34. with altitude, cause of, 41 definition of, 1 effect on, of changes in land area, 613 inversions of, 39, 116 potential, 34 registration of, 2 relation of, to circulation, 614 to land elevation, 608 to solar corona, 92 to sun spots, 92 to surface covering, 625 surface, decrease of, with eleva- tion, 37 and absorbing gases, 89 variations of, since 1750, 508 volcanic disturbances of, 598 and height of barometer, 55 changes of upper and lower air, inequality in, 50 gradients, storm, 51 summer, 53 vertical, 38 winter, 52 scales, interconversion of, 655 Thermal belts, ae Thermograph, 2, Thermometers, > wet-bulb, 14 Thermometer shelters, 2, 3 Thiessen, A. H., 550 Thomas, N., 246 Thomson, Sir William, 12, 408 INDEX Thunder, 387 distance heard. 389 rumbling of, 388 Thunderstorm, 311 anticlyclonic, 350 border, 350 course of events in, 352 cyclic period, 324, 329 cyclonic, 348 geographic distribution of, 329 heat, 347 hours of maximum, 322, 323 humidity associated with, 364 meteorological elements ‘of, 352 origin of cold air of, 355 periodic recurrence of, 322 pressures in, 361 schematic illustration of, 360 season of maximum frequency, 323, 324 ; temperatures associated with, 363 tornadic, 349 velocity of travel of, 365 winds of, 122, 350 electricity, origin of, 311 weather, 331 Thunderstorms and annual precipi- tation, 327 Thuras, A. L., 205 Toepler, M., 377 Tornado, 210 cause of, 212 cloud, 306 why most frequent States, 213 Towering, 449 Trade winds, 170 depth of, 172 Traveling cyclone, of, 193 Tropical cyclone, 173 direction of travel, 174 of winds in, 174 distinction from cyclone, 173 maintenance of, origin of, 175 places of occurrence, 173 shape of, 174 size of, 174 velocity of travel, 175 of winds in, 174 Troposphere, 57 Turbidity, 21 Turbulence in the atmosphere, 124, 22aT Twilight. colors. 546 duration of, 550 illumination, 550 in United characteristics extra-tropical 175 INDEX Twyford, L. C., 304 Tyndall, J., 539, 566. Valley breeze, 106 when present, 108 Van Orstrand, C. E., 245 Vapor pressure of droplets, 12 and elevation, 72 Vaughan, T. W., 612 Vegard, L., 424, 425 Velocity, effect of, on weight, 97 Vena contracta in whirlwinds, 104 Venturi tube, 7 Vertical convection, 94 Vince, S., 450 Violle, M. J., 376 Virtual height, air, 67 and gas, 68 Volcanic dust (see Dust, volcanic) Vulcanism, dust in upper atmos- phere due to, 570 effect on surface covering, 569 gases produced by, 569 and temperature, 5098 and ice ages, 584 Wagner, A., 196, 253, 265 Walcott, C. D., 301 Wall, 407 Walter, A., 602 Walter, B., 367-372 Water spouts, 213 vapor, absorption by, 88 Weed, A. J., 273, 285, 293 Wegener, A., 21, 296 Wegener, W. H., 305 Weight, condition of, no velocity change in, 98 effect of. velocity on, 97 factors determining, 95 of air, 656 Weightman, R. H., 180, 181, 198 Weilenmann, A., 249 Wells, P. V., 265 Wet-bulb thermometer, 14 Whipple, F. J. W., 136 Whirls, dust, 101 Whirlwinds, 101 Wien, W., 206 Williwaws, 119 Wilson, C. T. R., 399, 408, 417 Winds, adverse to aviation, 214 antitrade, 171 automatic adjustment of, 145 canyon, III centrifugal deflecting force of, 136 classification of, 100 direction of defined, 8 determination of direction of, 9 » direction of, effect of earth’s rota- tion on, 132 diurnal shift of, 161 rate of change of, 135 eddies, 208 equatorial, 161 glacier, 117 gradient, 138 gravity, I10 katabatic, £11 Maloja, 2090 measurement of velocity of, 6 relation of, to elevation, 147 thunderstorm, 122 trade, 170 Wind billows, 221 eddies, 222 gusts, 221 layers, 219 vane, 9, 10 velocity and elevation, 149 and latitude. 124 Wirtinger, W., 465 Wolfer, H. A., 508 Wood, R. W., 380, 388 Woolard, E. W., 524 Wright, W. B., 563 I ul | N ° | NV uw PRESSURE GRADIENT | Ww ° 49 ANTICYCLONE MILLIMETERS BAROMETER PER 100 KILOMETERS Fic, 41. 35 40 150 t § f D 30 ’ i ag f N i oO 4 / 25 ft 200 c fi 24 / E 23 / 22 / Sa . 280 Ss 2 13 14 CY CLONE 15 16 in 17 ‘ Xe \. 300 9 N \ 20 \ \ 2 \ “250 23 24 % CG 25 \ 200 35 40 Gradient velocity nomogram. LOMETERS OF CURVATU RADII 20° is 10° — ss o— 228 Fic. 104. 4 830 1 I 750 1 2 3 4 56 7g 9 1760 1 2 3 4 5 6 7 8 OL 2 3 4 5 6 7 g_9 1780 1 23 4 5 6 7 8 aft? 24 5 6 7 8 9 18001 2 3 4 3 S74 ait 23 4 5 6 7 8 9 80l 2 3 4 5 6 7 8 OF 28 5 7 8 9 18401 2 8 48 651 8 feo i 8 4 5 6 ae == St SSS Se eae + Sp +— + Se + > i T 7 1 CI st +—t [ oT + | | Vig eile 4 7 = | lig Pee [seve see eres He etree E eae cr PI a hes a ee elec de ase: Joie she sf sl the hs aS na ah ak = +1 : ; | —-4-—+--4-—4 —}- - ——--+_++ —+— + —t-— -—{-4 shes 2 etl ese ee aot + = 5 T 4 i | | | | | | | eat is es Gn (anes Gn GO os on on i = — 4 4 | o++++ +++ — t-—+—+ +444 47+ — a ae ate shtat - 44 ++ 15 —— ote te I = + T = 30 Tre 7 = PT ra = a [ AP Pe | | 4 a an 4 p= a. T 45) ++ : t444- +\H--+ + t 4 Bi i 60) ——|- | > of ra r — t amp a l rl “mi +— 7 H+ ——4—- — | ++ +- — +—A—- t+ + 4 + + s 1 +-- —*\ {- — t— J +— +—— r oO + 90 —+—— —— 4 +44 + [ 1 1] 105, —j—L ——}—- —+—+ +4-+— t- +- 4 Ey, Pee | a el ped tee | | 4 | al Ee ae ya : | 185 opt - | ~ + a t— L ope aah +—-++— tot T sea. alk 150+ 7 [ i [ ae 1H t-— a+ t-—+— feo a + + + T + 4 a + 4+ T [ ta t +185 ap —- | —+——+ Co + —+— +1 + pt — t 1 | 4 + +— + —+ + + + +— +120 + + + + t + - t +—J —t 1 ++ } T rT | Teen +4 +-1.05 T i | [ TI abe E | i 0.90 en +++ t eI 0.75 fod jj jt = ++ ie | 4 i + Em + 4 4 60 + | = [ | a | : 8 +— +t + I 4 + =. . 4 +—+— - | 1 << 1 :30|—+ | 7 | | le | | | | || +-0.15 oT 2 ’ | Ee 0.16 + + t : -+ 4 t = 30 1 [ t = t + x | + t - +—}__| — = inl 04s t + rot rc pa 7 [ > | | De Et FAH Eo | | 0.90 t i 4{__} __} + 4 j—J,05 1 + i +--+ + 3 +4 + + —-f + ak a T —120 1 T T | 1 ‘a | = ++ qt [ T = T T 2 T i —t- 4 + [ {- - —18 af + ro 1 TT T | r ] TTT ] 1 Too | + —150) + + + + + T T 1 T at Tort 1 | 4 i | + +—- +—t+ aa + + + +——+ = —165) T : + + + + [ . "i | ab [ ve + + + + 180 t aa ia I | i ome T AT ‘ & 1 1 Cal to Kea ES ee ee ho ZY, aa 2 RD KOTLUGIA HecLA MAYON ASAMA SKAPTAR VEsuUVUS FUEGO St. GEORGE ETNA SouFRIERE MAYoN TOMBORO BABUYAN COSEGUINA JoKu ? 2 ? ——_- AND OTHERS Relations of pyrheliometric values and mean temperature departures to sun-spot numbers and violent volcanic eruptions. “IG. 10d. See eee ee eee un 12 3 4 65 6 7 8 910? 3 2 pis 8 4 5 6 7 8 9 Wt 34 5 6 7 8 9188501 2 8 4 5 6 7 8 918601 28 4 5 6 7 8 9 18701 8 5 6 7 8 9 1880-1 345 67 8 9901 2 8 4 5 6 7 8 OT Pen I Pete a 4 TT | | 102 i i + } + + ] —| + + + I 4 j_ 4 4 =| 4—- u I L zl | | qe) ee a |_| 96 a ; fsiaet cet zoed a | coh | 3 | | | 2] 1 98 | : 4 1: 4+ ae 1 eee PyrtediohetRib Wauues +P ~ | 1 + + +———+ | ] i ——+ I — = at 411+ i a 1 TI =T + — 4 + + }-—}- | r — pes oooh 2S cea HANA : 4 ! HE tat faecal =a 4 r 1) poe { [" UntsPot_| NUMBERS ct i Peete ica oI : { | | | Peak, | | +44 | | 1—| al + | 1 + + T ++ —_ +t + + + = 1 —+— + — + —> +— a a ieee a Co a ley hepa bal Pi+/S a [ + + ttt) + + iz = T + St, + +— —+ + + — i } | f | zis} 4 | fot st { hd } i + + 4 jt dr 4—4 | i [ +—t { 4 T i +——+ —— + +——+ ++} — + H+ : H FE Perr Lt t —+ —— 4 44 {1 __} + 1 br : =e t + + [| ay | i Sees TEMPERATURE! De PARTURES - (MEANS) pa dl + $+—}-—_F T + ee — +— — + —+}——+ i dh + + + fo ol [ + + | + = + { [ + 4 4 | ans Ba = T 7 a A Ft r ane | [] GE | | | | L = : ~ te 4 1 | t - | 1 Ba | iE | | t | 4 SS < E Ls [is hese pe) : AAS Rat 6 oh t of SPS Rags ink AO ssl GQ heh YAN COSEGUINA Vesuvius MERAPI VATNAJOKULL KRAKATOA TaRAWwERA BocostoFr AWoeE Pete’ SANTA COLiMA 4ERS BANDAISAN Maria partures to sun-spot numbers and violent volcanic eruptions. PROPERTY OF DEPT, GF Sc iE620L06Y