For aËronautic uses the atmosphere may be regarded as a mixture of two substances, dry air and water. The first remains always in the gaseous state; the second shifts erratically through all possible states. Rain drops freeze or evaporate; sleet, snow, and hail evaporate or melt; the aqueous vapor condenses or congeals. Thus the world is wrapped in a dual sea, one part naturally serene, the other capricious, protean, and turbulent. Dry air, indeed, is a composite of many gases of vast concern in chemistry and biology; but in relation to aËronautics it is practically a single permanent gas. This placid element and its inconstant mate, so curiously mingled, constitute the medium whose flux and vicissitudes the aËrial sailor has duly to learn before he can navigate with skill or safety.[56]

But these aËrial oceans, the moist and dry, are of very different depth. They commingle only in the lower levels of the atmosphere, whose qualities vary accordingly, both physical and transportational. While the dry air may reach up to more than a hundred miles, substantial enough to singe a meteorite, the sea of aqueous vapor is bounded practically by the shallow region of the visible clouds. Beyond the feather-like cirri, which just overtop the loftiest mountain peaks, there is scant, if any, moisture. Never rain, nor cloud is there, nor tempest nor any great perturbation. Beyond the highest excursions of the cirri, at an elevation of some ten miles, stretches the deep ocean of eternal sunshine, of equable and nearly constant temperature. Into that zone of perpetual serenity no tumult of the nether atmosphere can penetrate; against the floor of the isothermal layer the cyclonic currents spread and dissipate. The upper air has, of course, a considerable drift, like a majestic river or stream of the sea, but never turmoil or tempest disturbs its stately march.

In some respects, therefore, that lofty ocean is an ideal one for swift transportation. But at present it is beyond the range of any navigable craft of human invention. Occasionally, indeed, a gauzy balloon from the hand of some inquisitive weather sage penetrates a little way into the exalted deep next the cosmic void, bearing its delicate recorders of heat and pressure; but it wanders alone in a silent and vast solitude outcubing all the habitable space allotted to bird, beast and fish; then at last sinks down to deliver the story of its strange voyage in that lifeless outer sphere. Volcanic and celestial dust may flourish there, tingeing the twilight with rosy flush, but no biologic forms from the teeming underworld may find refuge or sustenance. It is the unconquered domain of who knows what meteoric craft of the future, sweeping the globe from continent to continent, with now unimaginable celerity, grace and precision.

Incidentally and aside from its aËronautic interest, the composition of the atmosphere may be presented in fuller detail, showing the wide variations from level to level, and the manifold complexity of the fluid we daily breathe, not to mention the myriads of motes and germs inhabiting every inch of it. The gaseous components and their distribution are well exhibited in the following table,[57] which represents an average condition:

Percentage Distribution of Gases in the Atmosphere

Fixing attention first upon the gases other than water, it will be at once observed from the table that these gases show a very uniform mixture in the moist and turbulent region, while farther aloft the lighter of them tend to predominate in relative proportion. This uniformity of composition at the lower levels, which accords with experience, is due to the constant circulation and turmoil in that region. But for this constant agitation, the uniformity of mixture could not last. If the atmosphere were perpetually at rest throughout, or moving only in horizontal flow, each constituent gas would assume the same status and distribution as if the others were absent. Each, therefore, obeying Dalton’s law of diffusion, would form an atmosphere of itself, independent of the others, and unaffected in density by them. Such a condition is assumed for the higher levels. The percentage distribution in the higher levels is calculated from the known elasticity and density of the gases, assumed as resting in perpetual calm at a constant temperature of .55° C. beyond eleven kilometers, or above the highest ascent of man, and, furthermore, as having at the earth’s surface 1.2 per cent moisture and a temperature of 11° C.

But only in the quiescent outersphere can that dynamic gradation be established or perpetuated. Below this lofty region is the sea of water vapor, mingled intimately with the dry air, and churned with it, yet not sharing its uniformity of distribution. Why this rapid diminution of moisture with elevation, as shown in the table? Because throughout the moist region the temperature falls rapidly—about 6° C. per kilometer ascent above the earth—thus chilling and precipitating the vapor, whose pressural resistance to liquefaction diminishes with waning temperature. The explanation is obvious; but why does it not apply as well to the other elements of the atmosphere: why do not the other gases present liquefy with falling temperature as well as the water vapor, which is merely water in the gaseous state? The question cannot be answered very profoundly, but an essential condition of liquefaction of any gas can be stated in learned phraseology, after the preliminary exposition of certain general properties of matter.

We may first set forth those general physical properties, then apply them to answering the above question. Every known substance may exist in either of three states, the solid, liquid or gaseous. For every substance there is a critical temperature above which it can exist only as a gas, and cannot be liquefied by any pressure, but below which a suitable pressure will cause liquefaction. Below its critical temperature a gas is called a vapor, above it a permanent gas. Now in the free atmosphere some of the gases are never below their critical temperatures and, therefore, cannot be liquefied by any pressure, without special cooling; others are sometimes below their critical temperatures and are then capable of liquefaction by sufficient pressure, which however is not always found in free space, but can be supplied by a compression pump; one other gas, that is water vapor, is always below its critical temperature in the free atmosphere, and therefore may always be turned into water by sufficient pressure at its actual atmospheric temperature. Such sufficient pressure in the water vapor actually occurs from time to time in all parts of the atmosphere from the earth’s surface to the highest cirrus region, but more frequently in the nimbus levels, a mile or two above the earth. Thus at all parts of the lower atmosphere liquefaction of aqueous vapor is sometimes observed, either as mist or rain, snow or ice particles, and on the earth as dew or frost. In order to illustrate the above ideas by numerical citation, the accompanying table is given, showing the critical temperature and pressure of the chief gaseous constituents of the atmosphere.

Critical Temperature and Corresponding Pressure of Liquefaction for the Chief Constituent Gases of the Atmosphere.

A glance at this table shows that for the pressures and temperatures prevailing in our atmosphere most of the constituents are permanent gases. The conspicuous exception is water which, when in the gaseous state, always exists as a vapor, and never as a permanent gas, since it never even approaches the critical temperature. Fortunately for all life on earth the aqueous vapor condenses at very ordinary temperatures and pressures, else there would be no rainfall for irrigation and drinking. Fortunately also the other gases do not so precipitate, else the world might be flooded with liquid nitrogen and oxygen, entailing who knows what disastrous consequences.

After this digression on the composition of the atmosphere, we may henceforth regard the aËrial ocean as a mixture of two substances, dry air and water; the first, a permanent gas; the second, a variable element, existing at times in either the solid, liquid, or vaporous state. For the sake of convenience we may first study the dry atmosphere, then the moist. The dynamic properties of the dry atmosphere may in large measure be deduced by an application of two well-established laws of physics. These will be taken in order.

By careful investigation it has been proved that throughout a considerable range of pressure and temperature the permanent gases very approximately obey the following law; the volume of a permanent gas varies directly as its absolute temperature and inversely as its pressure. In other words the product of its pressure and volume equals the absolute temperature multiplied by a numerical constant. This may be expressed algebraically by the following formula:

PV = RT (1)

in which P is the pressure and V the volume of a given portion of gas at the absolute temperature T, and R is a numerical constant for the gas in question.

The value of R in the foregoing equation has been determined experimentally for the component gases of the atmosphere, and for dry air as a whole. For dry air, which, under such conditions as surround the aËronaut, may be treated as a single uniform gas, the equation applied to one kilogram gives R = PoVo/To = 29.27, where Po, Vo, To, are respectively the pressure, volume and temperature, in the metric system, of the one kilogram of air under standard conditions; i. e., Po = 10,330 kilograms per square meter, being the normal atmospheric pressure; Vo = 1/1.293 cubic meter, being the volume of one kilogram of dry air at normal pressure and freezing temperature; To = 273° C., being the absolute temperature of freezing. In passing, be it said that the absolute temperature is that measured from the absolute zero, which on the Centigrade scale is 273° below freezing, on the Fahrenheit, 460.6° below freezing.

The second law referred to follows directly from the principle of the permanence of mass. It is a general observation in physics that a given portion of matter is of constant mass, however its pressure, volume, temperature and other conditions may vary. In particular, the mass of a given portion of matter always equals the product of its mean density and volume, since density is defined as the amount of mass in the unit volume. Expressing this physical law, or relation algebraically, gives ?V = mass = ?o, Vo, in which ?, V, are the general symbols for the density and volume of the given portion of matter under any condition, while ?o, Vo, are the specific values of ? and V observed for some one state and circumstance of the substance in question. In particular, if the mass of air be unity, we may write:

?V = 1 (2)

This relation, together with that expressed in equation (1), will enable us to deduce many of the properties of dry air and of a dry atmosphere.

First let us observe from equation (1) the effect, in turn, of keeping constant one of the quantities P, V, T, while the other two vary. The equation shows that if the temperature of a gas is kept constant the volume is inversely proportional to the temperature. This is called the law of Boyle and Mariotte from its two independent discoverers, of whom Boyle seems to have been the first. As an example of Boyle’s law, if any empty glass, or diving bell, be inverted over water, then submerged deeper and deeper, the air within it will shrink with increase of pressure, its volume becoming one half when the pressure is doubled, one third when the pressure is trebled, etc. In particular, if the pressure changes by one unit, the corresponding change of volume is 1/P part of that volume. For example, if a captive balloon is anchored in air at constant temperature, while the barometric pressure changes from 30.0 inches to 30.1 inches, the volume of the balloon will contract 1/300 part of itself.

Again equation (1) shows that if the pressure of a gas is kept constant, the volume is proportional to the absolute temperature. This is the law of Charles and Gay Lussac, so called from its discoverers, of whom Charles is thought to have been the first. As an example of this law, if a captive thin rubber balloon is heated, or cooled, its volume will vary directly as its absolute temperature. In particular, if the temperature is changed one degree, the volume changes 1/T part of itself. For example, if the temperature of a balloon in air of constant barometric pressure is heated from 300° C. to 301° C., its volume will expand 1/300 part of itself. Historically, be it said, this law of Charles and the law of Boyle were discovered separately, then combined, giving equation (1).

Still a third, though not independent relation may be read from equation (1), thus: when the volume of a gas is kept constant, the pressure is proportional to the absolute temperature. In particular, if the temperature is changed one degree, the pressure varies accordingly by 1/T part of itself. For example, if an air tank or gas tank, in a room at 500° F., changes one degree in temperature, its pressure will change 1/500 part.

With minute detail these three conclusions from the general equation (1) have been set forth and illustrated, because of their practical importance. Other valuable results may be obtained by similar reasoning. Thus equation (2) may be read; the volume of a unit mass of any substance is the reciprocal of its density. Hence, if in the three foregoing conclusions, the reciprocal of the density is everywhere written for the volume, three new relations will be obtained which are of frequent practical use. Two of them may be expressed in the following important law; the density of a gas varies directly as its pressure and inversely as its temperature. Useful applications of this law in aËronautics suggest themselves at once.

By means of the various foregoing equations, the value of either one of the four quantities P, V, T, ?, representing respectively the pressure, volume, absolute temperature, and the density, may be obtained in terms of any two of the others. If then any two of the quantities is observed, the others can be at once computed. If, for example, the pressure and temperature of dry air be observed at any point, its density can be computed from the formulÆ, also its volume per kilogram weight, and thence its volume for any other weight. It is important therefore to be able to measure satisfactorily at least two of the four quantities. In usual studies of the atmosphere the pressure and temperature are observed directly. The method and instruments employed for that purpose are too well known to require description here.

In some speculations the pressure and temperature of the atmosphere are assumed, and certain interesting conclusions drawn. For instance, if the temperature is assumed constant throughout a dry atmosphere, the fluid will obey Boyle’s law, and it can be easily shown that the height of such a medium is the same whether it comprise much gas or little.[58] Again assuming the temperature and pressure constant, the height of the normal homogeneous atmosphere can be computed by dividing the pressure per square unit by its weight per cubic unit. In this way the height of the normal homogeneous atmosphere has been found to be about five miles. But these are hypothetical cases, of purely theoretic interest. In practice the temperature may, on the average, be assumed to decrease 6° C. for each kilometer of ascent, and the pressures may then be computed for various elevations by use of Boyle’s law, as done for Table I.

This leads us to a study of the gaseous properties of moist air. By moist air is meant a mixture of dry air and aqueous vapor in the form of an invisible elastic gas. The definition does not comprise air containing visible steam, or mist, or cloud, but clear moist air such as one ordinarily breathes. The study of this mixture may be preceded by a brief account of the gaseous properties of the vapor alone.

If water in sufficiently small quantity be introduced in a vacuum bottle at any ordinary temperature, it will promptly evaporate, forming an invisible gas known as aqueous vapor, filling the bottle and exerting a uniform pressure on its walls, except for the minute difference at top and bottom due to gravity. The vapor weighs 0.622 as much as dry air having the same volume, temperature and pressure, or quite accurately ? as much. It obeys all the laws given above for ordinary gases and dry air. But it has one singularity; at ordinary atmospheric temperatures, it cannot be indefinitely compressed without condensing to a liquid. In this respect it differs from the chief components of the atmosphere, which at ordinary temperatures can endure indefinite pressure without liquefaction. The ammonia and carbon dioxide in the air can, it is true, be condensed by pressure at their usual temperatures, but not by such pressures as occur in the free atmosphere, thus still leaving aqueous vapor the one singular constituent.

Reverting to the behavior of the water in the assumed vacuum bottle at fixed temperature, it may be observed that the pressure of the invisible vapor is directly proportional to the amount of liquid evaporated. In other words, for any fixed temperature the vapor pressure is directly proportional to its density. When this density reaches a certain definite amount, dependent solely upon the temperature, no further evaporation will occur, unless some of the vapor condenses. The pressure of saturation for that temperature has been reached, and any attempt to increase the pressure, by diminishing the volume of the vapor, will cause liquefaction at constant temperature.

If, however, the space is not saturated, the mass of vapor present may be expressed as a percentage of the amount required for saturation at that temperature. This percentage is called the relative humidity. Thus if the relative humidity is seventy per cent, the actual mass of water vapor present at the observed temperature is seventy per cent of the maximum that can exist in the given space, at the given temperature. In other words, the relative humidity is the ratio of the actual to the possible humidity at a given temperature.

In like manner, for any given vapor pressure there is a definite saturation temperature, known as the dew-point. If with constant pressure the vapor is given various temperatures higher than the dew-point, it will remain gaseous and invisible; but if it falls in temperature to the dew-point, liquefaction occurs, and drops of water appear on the inner wall of the vessel. Further cooling will entail still further liquefaction and reduction of pressure; for the lower the temperature the less the possible mass and pressure of saturation. But for all temperatures, down to freezing and considerably below, some vapor exists, and obeys the same laws as at higher temperatures. When, however, saturation occurs below freezing, the vapor may be precipitated as snow instead of water. This is a familiar phenomenon in the free atmosphere.

The actual mass of water vapor present in a cubic unit of space is sometimes called the absolute humidity. A formula giving the absolute humidity f, in kilograms per cubic meter, for any observed temperature t, and vapor pressure e, may be written as follows:

f = 0.00106 e / (1 + 0.00367 t)

in which e is the vapor pressure in millimeters of mercury, and t is the common Centigrade reading. As an illustration of the actual values of the pressure, temperature and density of saturated water vapor, for various conditions, the following table is presented:

Temperature, Pressure and Density of Aqueous Vapor, in Metric Measures.

Now by Dalton’s law, each gas or vapor in a mixture of several behaves as if it were alone. Thus if the foregoing experiment be conducted in a bottle containing various gases chemically inert to water, the same mass of water will be evaporated, and exert the same uniform pressure, in addition to those exerted by the gases. Now the density of each gas or vapor present, will equal its mass divided by its volume, and the density of the mixture will equal the total mass divided by the volume. Furthermore, it is well known that aqueous vapor is less dense than dry air at the same temperature and pressure. From this it is at once evident that moist air, which is merely a mixture of dry air and aqueous vapor, must be lighter than dry air at the same temperature and pressure. This is true whether the two fluids compared be in closed vessels or in the free atmosphere.

Accordingly in all precise dealing with the free air, whether involving its buoyancy, its resistance, its energy or any other mass function, its density as affected by the humidity must be taken into account. This can be computed from the observed pressure, temperature and relative humidity as revealed by well known instruments, the barometer, thermometer and hygrometer. Thus from the observed temperature and relative humidity, the mass of vapor present per cubic meter is read from Table III, the reader, of course, multiplying the given tabulated mass by the observed percentage of humidity. To this aqueous mass must be added the mass of dry air present. Then the total mass per cubic meter is the density.

Various formulÆ are available for computing the density of moist air from the readings of the three instruments mentioned above. Also, tables have been worked out giving the density without further calculation. Moreover, the density of free air may be directly measured, accurately enough for most purposes, by means of a densimeter. A simple formula for finding the density of moist air is as follows:

? = 0.465 (b-e)/T

in which b, e, are the pressures in millimeters mercury respectively of the moist air and its vapor, as revealed by the barometer and hygrometer.

In practice no great error will be made in assuming the relative humidity to be fifty per cent. For the moisture content never exceeds five per cent of the mass of the moist air, and hence in assuming a fifty per cent relative humidity, when there is actually a maximum or minimum humidity, the greatest possible error in estimating the moisture content is 2.5 per cent of the mass of moist air. Now if 2.5 per cent of a mass of air be assumed to be aqueous vapor when all is really dry air, or conversely if 2.5 per cent of the whole mass be assumed as dry air when it is really aqueous vapor, an error of much less than 2.5 per cent is made in estimating the true density. No error at all would ensue if both air and vapor were of the same density; but since one is ? as heavy as the other, the possible error is ? of 2.5 per cent, or 0.6 per cent. This is a negligible quantity in all mechanical considerations, except where great accuracy is required.

When any gas changes density or volume it also changes temperature, unless there be transfer of heat between it and its environment. When change of volume occurs without such transfer of heat the expansion, or contraction, is called “adiabatic;” when it occurs at constant temperature, the expansion is called “isothermal,” the temperature being kept uniform by suitable transfer of heat; when it occurs at constant pressure it is called “isopiestic.” In either case work may be done by the enlarging gas, if it press against a moving piston, or yielding envelope of some kind; and conversely work may be spent on the gas in compressing it either isothermally, adiabatically or isopiestically.

If, for example, a balloon rises rapidly its contents will expand adiabatically, pushing the envelope out in all directions against the static pressure of the embracing atmosphere. Thus it will do work and rapidly cool. But if it rapidly sinks, it will contract adiabatically and grow warm, owing to the work done by the surrounding air in compressing it. A like thing occurs when a great volume of air rises or sinks quickly in the free atmosphere. In this case the change of temperature is about 6° C. for each kilometer change of level, so long as the air remains unsaturated. A familiar example of this effect in Nature is manifested when an uprushing column of moist air chills, and precipitates moisture, forming a cloud toward its top. Thus a lone thundercloud in a clear sky may mark the upper part of such a column, or upward vortex in the air. And contrarywise, a descending column may absorb its visible moisture, causing it to become clear aqueous vapor, and thus vanish from view.

Having thus briefly examined the composition and certain gaseous properties of free air, both dry and moist, we may now study the atmosphere as a whole. We wish particularly to know of its distribution of temperature and pressure; of its general and permanent circulation; of its great periodic currents; of its vertical movements, and its minor local winds with their pulsations of velocity and direction. Fortunately much information is available, due both to governmental and private research, though this was collected more for purposes of meteorology than of aËrial locomotion. Of late, however, attention has been given to the aËronautic study of the atmosphere, which will, it is hoped, prove valuable to the aËrial navigator.

The movements of the atmosphere are due mainly to the sun’s heat and to the rotation of the earth. The earth’s internal heat and the moon’s attraction are other minor agencies, but these may be neglected by comparison. The earth’s rotation also would be ineffectual in modifying the aËrial movements, except for the coÖperation of the sun. Without his influence the atmosphere, always stagnant, would simply rotate with the globe, at constant angular velocity and uniformly graded density at various levels. This evenness of density for any level is broken by the solar radiation increasing the temperature and moisture, otherwise the air would remain practically at a standstill.

Though the moisture by its lesser density causes some lightening of the air at fixed temperature, this at most is hardly one per cent, as already shown, and on the average is much less. Its effect, therefore, is equivalent to less than that caused by a rise of temperature of three degrees. But if precipitation occurs, an enormous amount of stored sunshine, or latent heat, is liberated and applied to warming the associated air. Thus each pound of vapor condensed may, by the release of its thermal store, heat more than a ton of air one degree in temperature, or more than half a ton of air two degrees, etc. The actual number of pounds of air at constant pressure, raised one degree Centigrade by the condensation of one pound of vapor at various temperatures, is given in the following table:

The sun then is father of the wind. By uneven heating of the atmosphere it disturbs the uniform density gradation that would otherwise exist. Thus abnormal pressures are generated which disturb the repose of the aËrial sea, causing the fluid to flow from regions of excessive to regions of defective pressure. Hence the study of insolation[59] and temperature distribution is fundamental to the science of the winds.

Without detailed study, we may note the aggregate insolation received by the earth, at various latitudes, and its general effect on terrestrial temperature. The sun emits a nearly constant stream of radiation, from year to year, which plays continuously upon the earth as a whole, with an intensity which varies but slightly from month to month, due to the slightly varying distances of the earth from the sun. Owing to the sun’s seasonal wandering across the equator, the insolation at any latitude varies considerably month by month, and the polar regions receive much more light than if no such wandering occurred. The total yearly insolation for every 5° of latitude is shown in the following table from Hann, in which the unit is the amount that the earth would receive in one day at the time of the equinox, if the sun were at its mean distance from the earth:

Annual Amounts of Insolation

From this it appears that the equator receives nearly 2.5 times as much heat yearly as the poles. Since, moreover, the equator enjoys nearly constant insolation, while the polar regions suffer great variations of heat, with the varying altitude of the sun, the equatorial atmosphere is both much hotter and more equable than the poles, and high latitudes generally. Thus at the equator the frost level stands constantly at 18,000 feet, while in the middle latitudes it varies greatly in height from season to season. If, for example, a circle be drawn to represent the earth, and above it a line to indicate the mean altitude of the frost level in July, the frost line starting at the equator at an elevation of 18,000 feet will decline north and south, finally touching the earth well toward the frigid zones. The levels for other temperatures, above and below freezing, are similarly inclined downward from the equator to north and south. Obviously these isothermal levels vary with the varying season, and at any fixed time differ on different longitudes. On the plane of any given latitude the frost line varies much less in altitude, and so for the other isothermals. This is particularly true at the poles and equator, and everywhere at considerable altitude. If one voyaged around the earth at the equator at an elevation of 5,000 feet, he should find the average temperature about 65° F. In the temperate zone, following a line of latitude at the same height, he should have a lower temperature, but still comparatively equable. The average annual temperature of the earth’s entire surface is about 60° F.

In practical meteorology the temperature is observed at many points simultaneously over a wide stretch of the earth’s surface. These are then plotted on a weather chart, and through all points of like temperature are drawn lines known as isothermals. These lines not only map the earth’s surface into regions of equal temperature, but they also show the direction of fall or rise of temperature, and its space rate of change. This rate is called the “temperature gradient,” and when estimated straight across from isothermal to isothermal, that is in the direction of liveliest change of temperature, it is the maximum gradient. Such a map is very useful in forecasting the weather. It is but a particular instance of the more general map conceived by the physicist, exhibiting the thermal condition of the entire atmosphere by means of a series of equal temperature surfaces one above the other. Here, of course, the temperature gradient at any point is the space rate of change of temperature in any direction, being zero along the isothermal surface and greatest normal to it.

The vertical temperature gradient is of particular interest, since it determines the condition of fluid equilibrium at any point in the atmosphere when the level surfaces are isothermal. If, for example, a balanced balloon or portion of air, on starting upward from any level, cools faster than the environing stagnant air, it will become more dense, and cease to ascend, in which case the atmospheric equilibrium is stable. Again, if the ascending gas or air cools more slowly than the surrounding medium, it will become less dense, and so continue to ascend, in which case the atmospheric equilibrium at the point is unstable. Thirdly, if the rate of cooling be identical for the ascending gas and its surrounding medium, the equilibrium is neutral, and the motion will be stopped by friction but unaffected by change of buoyancy, since no such change can occur. Of these three states of equilibrium, the stable is dominant above the cirrus level, while below that level each state may be found, at various times, prevailing at random in all parts of the world, but more generally the stable and neutral states. When the unstable condition occurs at any locality and any level, it is usually followed ere long by a commotion or upheaval in the atmosphere, until the temperature gradient alters to the neutral or stable.

Many observations have been made to determine the variation of temperature along the verticle in various places and in different seasons. From the temperature records obtained in 722 balloon ascensions near Paris, France, the mean fall of temperature per 1000 feet up to 20,000 feet was found to be 2°.4 in winter, 2°.8 in spring, 2°.6 in summer, 2°.5 in autumn and 2°.6 for the year. Near Berlin 3°.1 for the year was found from 75 balloon ascensions, the rate being nearly the same for the halves of the year. Fig. 44 gives the average of 52 winter and 65 summer temperature gradients, taken at about 8 a.m. by means of sounding balloons sent up at Munich, Strassburg, Trappe and Uccle. It will be noted that in both summer and winter the temperature falls rapidly with increase of elevation, up to ten or eleven kilometers, but above twelve remains nearly constant for all altitudes. The difference in temperature summer and winter is interesting, also in its gradual diminution with altitude. Another striking feature is the inversion of gradient shown at twelve kilometers elevation, where the temperature ceases to diminish, and may even increase with altitude. This region is known as the upper inversion level of the atmosphere, as distinguished from other levels at or below three kilometers height, known as lower inversions, where the temperature gradient is sometimes reversed, though not so illustrated in the diagram.

Thus the atmosphere divides into three marked layers. The lower layer, three kilometers deep, is the region of turbulence and storm, the home of heavy rain clouds, lightning, wind gusts and irregular temperatures. The middle layer, some seven kilometers thick, bounded top and bottom by the upper and lower inversion levels, is a clear region of steady-falling temperature, for the most part frigid—a region of far reaching and rapid winds, sweeping eastwardly, except near the equator, and bearing on their backs the frosty cirrus clouds. The upper layer reaching from the cirri to the cosmic void, is always cloudless and very frigid, with temperature nearly constant, or maybe slightly increasing with elevation.

A striking peculiarity of these three regions is that the lower and middle layers may freely intermingle with each other, but never with the upper, or isothermal layer. Owing to its constant temperature, the upper layer floats on its neighbor like oil on water.[60] If a mass of dry air were forced up into it from below, with the natural cooling due to adiabatic expansion, such mass would be denser than the surrounding medium, and hence would promptly sink back to its initial position. Thus whatever turmoil may vex the middle or lower region, it can at most upheave the floor of the isothermal layer, leaving inviolate the crystal depths of the empyrean.

We may now turn to the distribution of barometric pressure in the atmosphere and the effect of its variation. In general, the distribution is not very uniform, but it can be graphically pictured by drawing a series of surfaces connecting all points of equal pressure. These are called isobaric surfaces. In a stagnant uniformly heated atmosphere, for example, these surfaces would lie one above the other parallel to the ocean face; but where turmoil exists, and irregular temperature distribution, the isobaric surfaces are bent into hills and hollows of varied form. These surfaces not only map the aËrial sea into regions of equal pressure, but they also show the direction of fall or rise of pressure, and its space rate of change. This rate is called the “pressure gradient.” When estimated straight across from surface to surface, that is, in the direction of the liveliest change of pressure, it is the maximum pressure gradient. Along this normal direction the air tends to flow with an acceleration proportional to the gradient. The velocity thus acquired by any portion of air in being pushed along the line of falling pressure, combined with its velocity due to other causes, gives its true velocity. A most important consideration, therefore, in a scientific study of the wind is the pressure distribution.

In practical meteorology, observations of the barometric pressure are made simultaneously at many points on the earth’s surface, and the readings then plotted on a map, after “reduction to sea level.” This reduction is made by adding to each barometric reading the weight of a column of air between the barometer level and the sea level, according to tables prepared for this purpose. Lines called “isobars”[61] are then drawn, at regular intervals, through all points of like sea-level pressure, the indicated change of pressure between consecutive isobars on the U. S. weather map being usually one-tenth of an inch of mercury. These exhibit at once, over the entire field of observation, the horizontal pressure gradient reduced to sea level, and commonly called the “barometric gradient.” In meteorology, the pressure normal to the isobar is called the gradient, and is expressed in millimeters of mercury per degree of a great circle. On the same weather chart are mapped the isothermal lines and wind directions for all the stations of the weather service. From these data and the reported moisture conditions, the meteorologist forecasts the probable weather some hours or days in advance.

No perfectly comprehensive formula can be given for the barometric pressure at any place and altitude, but certain general laws may be observed. Where, for example, the speed of the air is increased along any level of an air stream, the pressure is lessened, and conversely. Thus, if the wind blows squarely against the front of an isolated house, the speed will be greatly checked at the center front, and accelerated at both sides and over the roof, thereby increasing the apparent barometric pressure on the front, and lessening it on the sides and over the top. A similar effect may be observed when the air flows round the hull and framing of air craft.

Again, if the atmosphere over any locality is heated appreciably more than its environment, the heated column tends to expand upward and overflow aloft in all directions toward the cooler neighborhood, thus lessening the pressure throughout the heated column, and increasing the pressure throughout the environing atmosphere laterally. When this effect is marked the plotted isobars often form a series of closed curves about the heated region, manifesting a pressure gradient at the lower levels in all directions toward the heated area. This grouping of the isobars exhibits the familiar low pressure area of the weather map. On the other hand, if any locality be cooled appreciably more than its environment, the cooled column sinks, so that the surrounding warmer air aloft flows in over it, thereby increasing the pressure over the cooled area, and diminishing it throughout the environment. The isobars may then form a series of closed curves about the cooled region, with a pressure gradient along the higher levels in all directions away from the cooled area. Of course, if heat were the only agency disturbing the earth’s barometric pressure, there should be a parallelism between the heat and pressure gradients; but, as already noted, the speed or momentum of the aËrial currents is also a substantial agency in modifying the pressure lines.

It is well to remember that, while the base of a warm column of air may, due to the overflow aloft, have less pressure than the base of the cool environing column which receives the overflow, the high part of the column may have greater pressure than the equally high part of the cool. For if the columns be initially of the same temperature and pressure, heating one of them uplifts its levels of given pressure above those of its neighbor. When the overflow begins, a partial equalization of pressure levels occurs, but not a complete one so long as the flow has any head.

An interesting hygrometric feature of these highs and lows may here be observed in passing. As already explained, when a column of air ascends it cools by expansion, and tends to precipitate its water content as cloud or rain; and conversely, when the air sinks it heats by compression, thus acquiring greater moisture capacity and tending to clarify. As a consequence, the areas of low pressure and a rising atmosphere are usually marked by clouds and rainfall, while the areas of high pressure and falling atmosphere are marked by clear, or clearing weather. In the low, damp areas, then, the air feels heavy while it is really light; in the high and dry area the air feels light, while it is really dense, and most favorable to air men for carrying heavy loads in their balloons or flyers. Similarly when air flows over a mountain range the ascending stream precipitates moisture, due to cooling by expansion, while the descending stream, on the other side, comes down hot and dry, due to compression.

A characteristic mechanical feature of the high and low pressure areas is the closed circulation between them, involving practically the whole atmosphere below the isothermal layer. If we conceive the entire globe spotted with high and low areas, we may picture the air surging upward in the lows, flowing outward under the isothermal layer, descending in the highs, then flowing outward along the earth’s surface toward the lows in a continuous cycle. Thus, chiefly is maintained the vast and multifold circulation of the atmosphere over the entire world.

In general the motion is of a vortical nature, by which is meant that the masses of air as they flow along stream suffer more or less change of orientation in space, the rotation at times being so slight as to be undetectable, and again so marked as to excite wonder, as in the whirlwind. Many of these atmospheric vortices, even though varying in diameter from a few yards to hundreds of miles, resemble in their behavior the gyrating column of water in a common circular basin emptying through an orifice at its bottom. If the water is very still when the drain opens, the column descends with imperceptible, if any, rotation; but if the column has an initial whirl, or angular velocity, this is magnified as the water approaches the axis of the vortex, the tendency of the mass being to preserve its angular momentum, or fly wheel property. A like action obtains in the great atmospheric vortices, though here the motion far from the axis may seem like a straight-blowing wind, rather than part of a vast whirl covering thousands of square miles.

But even if all the air started directly for the axis of the ascending column, like still water in a basin, it would promptly acquire vortex motion, because it flows on the surface of a rotating sphere. The deflection so produced is evidently greatest at the poles, and for other places equals the polar value multiplied by the sine of the latitude. The effect is similar to what occurs when a basin, rotating about a vertical axis and carrying water with the same angular velocity, is opened at the bottom. In this case the water at once begins to gyrate within the basin, as the particles move toward its axis.

With these preliminary generalities we may proceed to study the more prominent movements in the atmosphere.

The winds of the world are commonly classified as the permanent, the periodic and the nonperiodic, according to their genesis and character. Their chief features may be briefly outlined.

The most conspicuous and important aËrial current on the globe is the permanent double vortex playing between the equator and the poles. The heated air of the equatorial belt, uplifted by expansion, overflows beneath the isothermal layer toward the north and south, thereby increasing the pressure in the higher latitudes sufficiently to generate a surface inflow along the earth, and thus maintaining a perpetual closed circulation which is felt all over the globe. The main features of this motion have been determined mathematically by Ferrel,[62] and summarized as follows:

“In the preceding part of this chapter it has been shown that, if all parts of the atmosphere had the same temperature, there would be a complete calm over all parts of the earth’s surface. But that, in consequence of the difference of temperature between the equatorial and polar regions of the globe, and the consequent temperature gradient, there arise pressure gradients and forces which give rise to and maintain a vertical circulation of the atmosphere, with a motion of the air of the upper strata of the atmosphere from the equator toward the poles, and a counter current in the lower part from the poles toward the equator, as represented by the arrows in the following figure, and that this of course requires a gradual settling down of the air from the higher to the lower strata in the middle and higher latitudes and the reverse in the lower latitudes. It has also been shown that in case the earth had no rotation on its axis, this would be exclusively a vertical circulation in the planes of the meridians without any east or west components of motion in any part; but that, in consequence of the deflecting forces arising from the earth’s rotation, the atmosphere at the earth’s surface has also an east component of motion in the middle and higher latitudes, and the reverse in the lower latitudes, and that the velocities of the east components increase with increase of elevation, so that at great altitudes they become very much greater than those at the earth’s surface; while those of the west components decrease with increase of altitude up to a certain altitude, where they vanish and change signs and become east velocities, now increasing with increase of altitude to the top of the atmosphere.

“It has been further shown that the deflecting forces arising from the east components of motion of each hemisphere from the earth’s surface to the top of the atmosphere, in the middle and higher latitudes and of the upper part of the atmosphere in the lower latitudes, drives the atmosphere from the polar regions toward the equator, while those arising from the west components of motion in the lower part of the atmosphere in the lower latitudes, having a contrary effect, but small in comparison with the other on account of the weakness of these forces near the equator, tend to drive the air a little from the equator toward the poles. There is, therefore, a depression of the isobaric surfaces at all altitudes in the polar regions, especially in the southern hemisphere, a much smaller depression in the equatorial regions, and a bulging up of the isobaric surfaces in the vicinity of the parallel of 30° in the lower part of the atmosphere, the maximum being nearer the equator as the altitude increases, as represented in Fig. 45, but at high altitudes there is a minimum of barometric pressure at the poles and a maximum at the equator.

“In the accompanying figure the solid arrows in the interior part represent the resultant motions of the winds (longer arrows indicating greater velocities), in case of an earth with a homogeneous surface over both hemispheres, in which the motions would be symmetrical in both and the same at all longitudes, and the equatorial and tropical calm belts would be situated at equal distances from each pole. The dotted arrows indicate the strong, almost eastern motion of the air at all latitudes at some high altitude, as that of the cirrus clouds.

“The outline of the outer part of the figure represents an isobaric surface high up where the bulging up near the parallel of 30° disappears and the maximum pressure at the same altitude is transferred to the equator. For lower altitudes the isobaric surfaces have a bulging up at the parallel of 30°, and a slight depression at and near the equator. The arrows in this part represent the polar and equatorial components of motion, the former above and the latter below, except near the earth’s surface on the polar sides of the tropical calm-belts, where there is a polar component of motion arising from the air’s being pressed out from under the belt of high pressure. This, perhaps, does not extend beyond the polar circles, beyond which there can be little motion in any direction, except from abnormal disturbances.

“For reasons given in § 103, the actual mean position of the equatorial and tropical calm-belts are not precisely as here represented, but are all a little displaced toward the north pole, and the polar depression of the isobaric surfaces is greater in the southern than in the northern hemisphere.”

The conclusions from this approximate analysis are in the main supported by observation, except as modified by the heterogeneity of the earth’s surface. The sea-level distribution of barometric pressure between the equator and poles, as found by Ross’ long series of measurements, manifests a variation of about one inch of mercury, with maxima at about 30° of latitude, north and south, as required by Ferrel’s theory. As a further cause of the depression toward the poles, may be mentioned the greater speed of the permanent east wind with the consequent centrifugal lift in the atmosphere.

As to the general easterly direction of the winds at middle and higher latitudes, that is well known from observation of the motion of clouds and of the air near the earth. At the cirrus level the velocity in those latitudes is almost exactly eastward. But the flow in longitude, illustrated by the outer arrows in Fig. 45, has not been fully determined by observation. Moreover, as Ferrel himself showed, the unequal heating of continents and oceans sets up gradients in longitude, especially in the northern hemisphere, thus adding considerable disturbance to the general circulation. To this agency must be added also the latitudinal shifting of insolation, due to the annual march of the sun across the equator, entailing an oscillatory seasonal shift of the hot belt, and therefore of the twin-hemispheric cycle of the atmosphere.

Some currents of the general and permanent circulation are sufficiently prominent to have special names, such as the trade-winds, the antitrade-winds, the prevailing westerlies, and, in the lower latitudes, the calm belts, where the flow is exceptionally feeble. All these currents have been known to sailors since early times, and have been of considerable importance in marine navigation. Eventually, perhaps, they may be of like importance in aËrial navigation.

The trade-winds are mild tropical surface currents of remarkably steady speed and direction. Springing from the high-pressure belts in either hemisphere, at about latitude 30°, they blow toward the equator with increasing westerly trend. As shown in charts 46 and 47 for midwinter and midsummer, the trade winds cover a large portion of the tropical zones in both oceans, and shift slightly in latitude with the sun. They are separated at the heat equator by the equatorial calm belts, or doldrums, and are bounded north and south respectively by the calms of Cancer and of Capricorn. Particularly interesting are the trade-winds blowing from Spain to the West Indies, which favored Columbus on his westward voyage, and which certain adventurous Germans have proposed using to duplicate that memorable voyage, in air ships.

The antitrade-winds, or counter trades, are lofty winds blowing over and contrary to the trade winds. As some doubt regarding the direction of these counter trades had existed, an expedition was sent in 1905, by two distinguished meteorologists, Teisserenc de Bort of France, and A. Lawrence Rotch of America, to explore the atmosphere above the tropical Atlantic. Mr. Rotch has summarized their measurements and conclusions as follows:[63]

“Pilot balloons, dispatched from the island of Teneriffe and St. Vincent, were observed with theodolites at the ends of a base-line, and in this way the heights at which the balloons changed direction could be ascertained. Later the balloons were sent up from the yacht itself, which steamed after them, measurements being made of their angular elevation. The observations which are plotted in Fig. 46 prove conclusively the existence of the upper counter-trade. The courses of the balloons are represented as if projected upon the surface of the sea and show that the northeast trade-wind extended only to the height of 3,200 or 4,000 meters, and then gradually turned into a southerly current which, higher up, came from the southwest. The width of the dotted band represents approximately the varying velocity of the trade and counter-trade. Similar proofs of the northwest trade-wind, south of the equator were obtained by the same expedition during the following year, but the above suffices to show that it would be possible for an aËronaut in the ordinary balloon to start from the African coast, or from some of the islands in the trade-wind region, and, after drifting towards the southwest, to rise a few miles into the current, which would carry the balloon north and eventually northeast back to land. Nevertheless, it does happen in certain atmospheric situations over the tropical north Atlantic that the winds from the general northwesterly direction prevail up to great heights without any evidence of the return-trade. Near the equator the winds are easterly up to the greatest heights which have been attained.”

The prevailing westerlies are high-latitude surface winds of the permanent circulation. In the southern hemisphere they are particularly strong and steady owing to the comparatively unbroken stretch of ocean. In the north also they are strong and persistent, but variable in direction because of disturbances by local winds due to unequal heating of tracts of land and sea. These features are well illustrated in charts 47 and 48. Of particular interest in aËronautics is the prevailing wind blowing from the United States to Europe, which has been considered a suitable current for transoceanic balloon voyages.[64]

The periodic winds are those whose gradient alternates annually or daily, due to annual or daily fluctuations of temperature on sloping or on heterogeneous parts of the globe. The annually fluctuating winds due to alternate heating and cooling of continents, or large land areas, bear the general name of monsoon. Among diurnal winds the most prominent are the land-and-sea breezes, and the mountain-and-valley breezes. Both kinds are practically available in aËronautics; the monsoons for long-distance travel, the diurnal winds for local use.

The general motive cause is the same for all periodic winds. When any portion of the earth’s surface is periodically more heated above its normal temperature, or average for the year, than the neighboring region, the resulting abnormal temperature gradient causes a periodic surface wind tending toward the excessively heated place, and a counter wind above. That is, the cooler and heavier column of air sinking and uplifting the lighter, results in a lowering of the common center of gravity of the two columns of air, and thus furnishes the driving power of the wind. For example, an island or a peninsula may be considerably hotter by day and cooler by night than the surrounding water; a continent may be much hotter in summer and much colder in winter than the bordering ocean. Thus during the hot period a moist wind blows landward; during the cold period a dry wind blows seaward. If the land has vast and lofty slopes the uprush of air during the hot period and the downrush during the cool period may be very powerful. The currents so produced by the aggregate of local agencies, including the deviation caused by the earth’s rotation, combine with the general circulation of the atmosphere to form the actual wind of the place. Thus the periodic current may conspire with the general circulation, or oppose it; may intensify, weaken or obliterate it; may overmaster, reverse or mask it completely.

Of the various continental monsoons of the globe the most powerful spring from the annual flux and reflux of the atmosphere over the vast declivities and table-lands of Asia. Here the conditions are especially favorable. As the sun approaches Cancer, the burning deserts and high plateaus, combining their force with the draft on the mountain sides, generate a continental uprush that sucks in all the aËrial currents of the surrounding seas, hurling them aloft to the isothermal layer whence they radiate as the four winds of heaven; for here at this season the planetary circulation is disrupted, obliterated or reversed, appearing merely as a perturbation of the monsoon at its height. In India the force is particularly effective. Along the north the Himalayas stretch 1,300 miles in latitude, with an average height of 18,000 feet and with sunburned areas on either side. North of this range are the lofty plateaus of Thibet and Cashmere, south of it the desert of Gobi and the borders of the Indian Ocean. Over this watery tract from beyond the equatorial line, from the isles of Oceanica and from the wintry plains of Australia, the air flows in with accumulated strength, sweeping the Bay of Bengal and the Arabian Sea in a continuous gale bearing up the mountain slopes incredible floods of water. Over the Arabian Sea in summer the gale is so steady and swift that no ordinary ship can force a passage from Bombay to the Gulf of Aden. Above the Bay of Bengal the moist south winds, converging between the coast and headlands, pour cloud laden up the Himalayan slopes, precipitating their whole vapor in prodigious torrents seldom seen elsewhere. Khasia at this season sustains a Noachian deluge, the rain at times falling nearly a yard deep in one day and night.[65] Quite appropriately, therefore, the summer monsoon over India, especially its component southwest wind from the Arabian Sea, and southerly wind from the Bengal Bay and farther east, is called the wet monsoon.

The winter monsoon of Asia, is the reverse of the summer one, both in direction of gradient and in physical character. It is a cold flood of air pouring from the frigid table-lands and wintry depths of the desert, down the mountains and valleys in continual overflow on all sides of the continent, and then far out over the sea, where it reascends to complete its long cycle. In its descent all moisture vanishes by heating, and no intensive temperature gradient occurs, as in summer, to accelerate its gently modulated tide. In India the winds from Cashmere and Thibet pour down the Himalayas toward the Arabian Sea a clear current of air which unites with the trade-wind, increasing its force, and forming the moderate winter monsoon of that region, or as it is commonly called, from its lack of moisture, the dry monsoon.

The kinematic character, and the extent of both summer and winter currents, are well portrayed in charts 47 and 48 for all the south and southeast of Asia. Across the islands of Japan, it will be observed, the winds blow in opposite directions summer and winter. In Siberia the monsoon winds trend along her great rivers and valleys, generally northward in the winter and the reverse in the summer, combining in both seasons with the prevailing westerlies, due to the rotation of the earth.

All the other continents have their monsoons, though less powerful than those of Asia. In the great desert of Sahara, for example, there is an ascending hot current in the summer, causing a strong indraught from the Atlantic and the Mediterranean; but this is far less intense than if its action were fortified by lofty slopes and table-lands. In winter when the Sahara cools to nearly the oceanic temperature, little monsoon effect is perceptible, and the general circulation continues unperturbed. In Australia the monsoon influence is still feebler, owing to the limited extent of the country and to the general lowness and flatness of the land. Over parts of South America, the annual ebb and flow of the atmosphere is considerable, particularly along the northeastern coast, and in the whole Amazon Valley, whose aËrial currents in general conspire with the trade-winds, strengthening them materially in the southern summer, though it is less in winter when the continental temperature more nearly approximates that of the ocean. The monsoons of North America have been described in some detail by Ferrel as follows:

“On the continent of North America we have monsoon influences similar to those of Asia, but not nearly so strong, because the extent of the continent, and consequently the annual range of temperature, are not so great. They are, for the most part, not sufficiently strong to completely overcome and reverse the current of the general circulation of the atmosphere, and so to produce a real monsoon, but they cause great differences between the prevailing directions of the winter and summer winds.

“In the summer the whole interior of the continent becomes heated up to a temperature much above that of the oceans on the same latitudes on each side—indeed, above that of the Gulf of Mexico and the Pacific Ocean on its southern and southwestern borders. The consequence is that the air over the interior of the continent becomes more rare than over the oceans, rises up and flows out in all directions above while the barometric pressure is diminished, and the air from all sides, from the Atlantic on the east to Pacific Ocean on the west, the Gulf of Mexico on the south, and the polar sea on the north, flows in below to supply its place. On the east the tendency to flow in is not strong enough to counteract the general easterly motion of the air at the earth’s surface in the middle latitudes, and to cause a westerly current, but it simply retards the general easterly current and gives rise to a greater prevalence of easterly winds along the Atlantic sea-coast during the summer season....

“In winter the thermal conditions over the continent are reversed. The interior of the continent is now the coldest part, and it is especially colder than the surrounding oceans at that season. It has also very high plateaus and mountain ranges. The air, therefore, of the lower strata, and especially those next the earth’s surface, now tends to flow out in all directions to the warmer oceans and the Gulf of Mexico, and especially to run down the long slope of plateau from the Rocky Mountains into the Mississippi Valley. The effect over the whole of the United States east of the Rocky Mountains is to cause the winds, which otherwise would be westerly and southwesterly, to become generally northwesterly winds, instead of southerly and southwesterly ones, as in summer. There is not a complete monsoon effect, but simply a great change between summer and winter in the prevailing directions of the winds. In Texas, however, and farther east along the northern border of the Gulf, the effect is somewhat that of a complete monsoon. In New England and farther south in the Eastern States the monsoon effect is to cause the prevailing winds to be from some point north of west, instead of south of west as in summer.

“In summer, Central America and Mexico have a much higher temperature than that of the adjacent tropical sea on the southwest, and having high mountain ranges and elevated plateaus, there is consequently a strong tendency to draw in air from the southwest at this season, which not only entirely counteracts the regular trade-winds of these latitudes, but even reverses them and causes southwest winds. The effect is to cause in midsummer a large area here, extending far westward, of calms and irregular and light winds, mostly southwesterly ones, and an apparent widening of the equatorial calm-belt at this season so as to make its northern limit reach up, along the coast, nearly to the parallel of 20°. The effect is similar to that in the Atlantic west of the Gulf of Guinea and Liberia, except that it here appears to be some greater, and causes a true monsoon effect, since during the winter the regular northeasterly trade-winds prevail, but strengthened by the reverse thermal conditions of the winter season. On the eastern side, and over the western end of the Gulf of Mexico, there is a somewhat regular monsoon effect, the prevailing winds being easterly, or blowing toward the land, during the summer, and the reverse in winter.

“Along the west coast of North America in the middle latitudes there is a strong monsoon influence; for the interior of the continent becomes heated in summer to a much higher temperature than that of the southwesterly ocean, and hence a strong current is drawn in from this direction, at right angles to the general trend of the coast which, combining with the general southwesterly winds of these latitudes in the general circulation of the atmosphere, causes the strong and steady westerly and southwesterly winds of this region during the summer. Farther north, up toward Alaska, the summer monsoon effect is combined with the current caused by the deflection of the continent as well as the general easterly current of high latitudes, so that the winds here are generally southerly, but still have somewhat of a monsoon character, being southerly and southwesterly in summer and easterly and southeasterly during the winter.

“Along the northern coast of America, as along that of Siberia, the monsoon tendency is to draw the air from the colder land to the warmer ocean in winter, and the reverse in summer; and these effects, combined with the general easterly motion of the atmosphere in these latitudes, gives rise to prevailing southwesterly winds in winter and northwesterly ones in summer. The winter monsoon influence, however, is small here—much more so than in Siberia, for the ocean contains so many large islands that it has rather a continental than an oceanic winter temperature; and besides, it has not the influence of a warm current—such as the continuation of a part of the Gulf Stream along the northern coast of Europe and Asia.”

Similar to the monsoons in essential nature are the diurnal winds of seacoast and mountain side. They begin with the heating of the land in the morning, attain their maximum intensity about mid afternoon, or during the hottest of the day, and finally are reversed at night. Besides being so much briefer than monsoons, they are also in general feebler and less extensive. They may be quite noticeable on calm days, especially in clear weather and in hot climates; but usually they are masked or entirely overwhelmed where other marked currents occur—currents due either to the general circulation or monsoons, or other powerful disturbing agencies.

In land-and-sea breezes, which usually extend not far inland, there is a surface inflow of sea air during the forenoon and early afternoon, balanced by an outflow of warm air above, rising from the heated soil. After sundown this is reversed, the chilled air from inland pouring out to sea, while overhead the warmer sea air is forced landward at a higher level. These currents are strongest where the diurnal range of temperature is greatest and where the local topography is of suitable configuration. Particularly favorable are steeply declining shores, narrow bays and inlets, girded by mountains or lofty hills. During the day heated air ascends such declivities with alacrity, like smoke through an inclined flue, while at night, when cooled by radiation and contact with the soil, it rushes torrentlike down the valleys and hillsides, passing out to sea, often in sudden squalls that embarrass, or endanger, small sailing craft. Circulatory currents like the above have sometimes been used by aËronauts to carry them out to sea and back again to land at a different level.

In like manner the mountain-and-valley winds may be used by the skillful aËronaut. It is well known that these flow up the courses of rivers, caÑons and land slopes generally by day, but at night reverse their course and pour down again with considerable force. For this reason experienced hunters place their camp fires below tent in a sloping valley. The strength of the breeze depends, of course, upon the daily range of temperature, and the steepness and expanse of the slope. Such winds are deftly used by the masters of soaring flight, the great robber and scavenger birds, and no doubt may be used by men in motorless aËroplanes, to gain elevation, and journey great distances without expenditure of energy.

Besides the periodic winds so far treated, there are prominent aËrial movements having no regular course or season. These are the nonperiodic winds which so exercise or perplex the weather forecaster and those who confide in him. In general such winds are of a temporary character, arising from an unstable condition of the air in some locality, or from unequal heating, either of which causes may generate, or briefly sustain, an updraught, with its attendant gyration. Owing to the whirling character of such ascending currents, they have received various significant names, such as cyclone, tornado, whirlwind; the three terms applying to vortices in decreasing order of magnitude. Each in turn may be treated briefly.

The cyclone is a temporary large gyratory wind. It may last a few hours or a few days. It may measure fifty to a hundred miles across, or it may measure more than a thousand miles. On the weather map it is in general marked by a group of closed isobars, showing a considerable pressure gradient toward a small internal area where the pressure is a minimum. To an observer looking about the earth’s surface and lower levels of the atmosphere, the cyclone appears merely as an ordinary wind, accompanied perhaps by rain or snow. It is not a swiftly rotating narrow column, or cone of air, like a tornado or whirlwind, full of gyrating dust and dÉbris.

The motive power of a cyclone, though in general due to the buoyancy of heated air, may spring from more than one set of conditions. Notice has already been taken of vortices due to a hot column of air at lower barometric pressure than its lateral environment. Take another case. If a dry atmosphere is of uniform temperature and pressure at various levels, but has a vertical temperature gradient a little greater than the normal cooling of an ascending gas, a portion of air started upward in any casual way becomes warmer than its lateral environment, and hence continues to rise until the unstable condition due to abnormal temperature gradient ceases. Again, while the surface stratum is in stable equilibrium, it may happen that the second mile of air is abnormally hot, and the third mile abnormally cold, and thus a vortex may occur in mid air, without disturbing the face of the earth.

Whatever be the initial atmospheric condition causing the vertical uprush, the nature of the resulting circulation is in general that of the cyclone, illustrated, in part, by the whirling vortex of water in a basin. As the current ascends, an indraught occurs in all the lower regions of air, and an outflow in all directions above, sometimes at the height of a mile or two, again in all the region next to the isothermal layer. As the earth has at all places above the equator a component of rotation about the vertical line, it follows that in northern latitudes all the air flowing toward the vortex is in a whirl opposite in motion to the hands of a watch lying face upward, and all the outflowing air above has a like angular motion, but gradually diminishing until it is reversed. At the lower portion of the vortex the air whirls inward and upward with increasing velocity, while above, it whirls outward and upward, with waning velocity, thus moving in a double-spiral path shaped like a cord wound on an hourglass. In the constricted part, or neutral plane of the vortex, the air moves neither outward nor inward, but spirals straight upward. To match the upflow, and complete the closed circulation, there must be a downflow on the exterior of the cyclone, and since the whirl is reversed in direction, this outer mass of downflowing reverse-whirling air embracing the cyclone is called the anticyclone.

Between the inner and outer vortex the air is comparatively calm and the pressure is a maximum, with steepest gradient toward the center of the cyclone. Also the air is calm just at the axis of the vortex, while for some distance away its speed increases as the radius of its whirl, so that the central mass rotates practically as a solid column, thus still further lowering the pressure near the axis. This solidly rotating central column of air is sometimes called the core of the vortex.

High above the center of the cyclone, where perhaps the air is sucked downward, clarified by compression, then whirled outward, the sky is usually clear, or thinly fogged, while without this central patch are heavy clouds. The obscure or clear central part is called the “eye[66] of the storm.” Through this the cirrus clouds may sometimes be seen high above, either stationary or radiating away, if the vortex extends so high. Sailors on the deck of a vessel passing through a cyclone have often noticed the eye of the storm overhead, perhaps ten or twelve degrees in diameter, and with special clearness in the tropics. To the white, feathery cirrus clouds, scurrying away radially from the top of the vortex, they have given the name “plumes of the storm,” or “mares’ tails.” In sailing their vessel through the center of a cyclone, they have observed the circulatory motion of the winds and clouds, and frequently have found the deck covered or surrounded with cyclone sweepings, such as land and water birds, insects, butterflies, etc., brought into the quiet core of the vortex from the incurving winds beyond. Further details of the motion in a cyclone vortex are given as follows by Ferrel, §178:

“In Fig. 49 is given a graphic representation of the resultant motions and of the barometric pressures for both the surface of the earth and for some level high up in the atmosphere and above the neutral plane, where the motions in the vertical circulation are outward from the center. The solid circles represent isobars at the earth’s surface and the solid arrows the directions, and in some measure, by their different lengths, the relative velocities of the wind. The heavy circle represents the circle of greatest barometric pressure at the earth’s surface, say 765 mm., while the pressure of the outer border is 760 mm., and the dividing line between the cyclone and the anticyclonic gyrations. Within this limit the pressure diminishes to the center, and the gyrations are cyclonic, and the direction of the resultant of motion inclines in toward the center, but beyond that limit the gyrations are anticyclonic, and the direction of resultant motion inclines toward the outer border of these gyrations. The heavy dotted circle represents the circle of maximum pressure at some high level, and is much nearer the center than that at the earth’s surface. It is also the dividing line between the cyclonic and anticyclonic gyrations at that level. The dotted arrows indicate the directions and in some measure the relative velocities, of the wind at this level. The arrows in the cyclonic part represent the direction of the wind as declining outward, because the plane here considered is supposed to be above the neutral plane, where the radial component of motion is outward, but for any level below the neutral plane the inclination is still inward. The arrows are shorter above in the cyclonic part and longer in the anticyclonic part than they are at the earth’s surface, since the cyclonic gyratory velocities decrease and the anticyclonic increase with increase of altitude.

“The upper part of the figure is a representation of a vertical section of the air, very much exaggerated in altitude, in which the solid curved line represents a section of an isobaric surface near the earth’s surface, say of 740 mm. barometric pressure. The lowest part corresponds with the center of the cyclone and the highest part with the heavy circle in the lower part of the figure, and the steepest gradients with the longest solid arrows, since the greater the gyratory velocities at the earth’s surface the greater the gradients, though they are not strictly proportional. The second dotted curved line from the top represents a section of the isobaric surface of high altitudes, in which the highest parts correspond with the heavy dotted circle below, since the highest pressure at all altitudes is very nearly where the cyclonic gyrations vanish and change to the anti-cyclonic. The depression here is smaller because the cyclonic area is smaller, and the gyratory velocities less, than at the earth’s surface. The upper dotted line belongs to an isobaric surface still higher, where the gyrations are supposed to be all anti-cyclonic, and here, consequently, the greatest pressure is in the center, as indicated by the curved line.

“As the interior of the whole cyclonic system is warmer than the exterior, and consequently the air less dense, the distances between the isobaric surfaces are necessarily greater in the interior than the exterior part, and so, however much the isobaric surface at or near the earth’s surface may be depressed by the cyclone gyration there, at a considerable altitude, if the temperature difference is great enough, it must become convex instead of concave.

“The track of any given particle of air in a cyclone, resulting from the vertical and gyratory circulation, is that of a large converging and ascending spiral in the lower part, but of a diverging and ascending spiral in the upper strata of the atmosphere, and the nearer the earth’s surface the more nearly horizontal is the motion, since the vertical component gradually decreases and vanishes at the surface.

“The whole energy of the system by which the inertia of the air and the frictional resistance are overcome and the motions maintained, is in the greater interior temperature and the temperature gradients, by which the circulation is maintained. This being kept up, the deflections and gyrations are merely the result of the modifying influence of the earth’s rotation, which is not a real force, since it does not give rise to kinetic energy, but merely to changes of direction.

“It must be borne in mind that the preceding is a representation of the motions and pressures of a cyclone resulting from perfectly regular conditions, in an atmosphere otherwise undisturbed, and having a uniform temperature, except so far as it is affected by the temperature disturbance arising from the cyclonic conditions. Accordingly results so regular are not to be found in Nature, but generally only rough approximations to them.

“Since the wind inclines less and less toward the center of the cyclone below the neutral plane and declines from the center above it, the upper currents above this plane in a cyclone are always from a direction, in the northern hemisphere, a little to the right of that of the lower currents, when not affected by abnormal circumstances.”

Observation of cyclones in Nature very well confirms the leading features set forth on theoretical grounds. If the vortex pass centrally over an observatory there is noted first a high barometer and calm air, attended perhaps by scurrying cirrus clouds; next a rapidly falling pressure and increasing wind, with dark clouds and precipitation, commonly accompanied by thunder and lightning; then the hushing of the storm to a dead calm, and low barometer and thinning or clearing of the clouds overhead; then a rising barometer with renewed winds in the reverse direction, and finally subsiding winds, rising barometer and clearing weather. These phenomena are the more definitely presented if the whirl is strong while its travel along the earth is slow. But owing to their progressive easterly motions, cyclones in the north have their moist hot southern masses elevated, chilled and precipitated on their eastern fronts and beyond, while their rear experiences the opposite action and is called the clearing side. Conversely in the tropics the westerly moving cyclones have cloudy and wet rears, because the easterly drift on high carries the precipitating masses toward the rear. The general hygrometric appearance of a centrally passing cyclone in middle latitude is thus described by Ferrel, §207:

“In the regular progression of a cyclone in the middle latitudes somewhat centrally over a place, the cloud and rain area of the front part, extending far toward the east, first passes over, occupying a half-day, or a day and more, and then the front part of the ring of dense cloud with a heavy shower of rainfall. After this there are indications of a clearing up, and even the sun may break through the cloud for an hour or two; but presently there is an apparent gathering and thickening of the cloud and a second shower. This is at the time of the passage of the rear side of the ring of denser cloud. After this there is the final clearing up.”

Except for special conditions, cyclones are never stationary, but drift along with the general march of the atmosphere, like dimpling eddies in a stately flowing river. In general, therefore, their trend is westward in lower latitudes, eastward in middle and higher latitudes, with a pace slow or swift according to the prevailing current. Notably also they have a poleward trend. Thus, if the path extends from tropic to temperate clime, it is frequently concave toward the east and sensibly parabolic in form. This is markedly true of those swift-whirling, small cyclones called hurricanes,[67] and particularly those vigorous ones blowing past the West Indies and the Philippines, and those that vex the Indian Ocean.

As to the speed of travel of cyclones, that may be judged, at least for northern latitudes, from the accompanying table, taken from Loomis,[68] and showing the average monthly rate of progression in miles per hour, of cyclone centers over the United States, the Atlantic Ocean and Europe. In general, beyond the tropics tall cyclones travel faster than short ones, owing to the faster drift of the higher strata.

To find the actual speed of the wind at a place, of course, the linear velocities of whirl and of translation must be combined; or, vice versa, if one of these be known it can be graphically subtracted from the observed wind velocity to find the other. This combination of two wind components to find their resultant, or, vice versa, can easily be done by laying off on paper, arrows of suitable length and direction to represent the two known velocities, placing the head of one arrow to the tail of the other, then completing the triangle, and taking its third side to represent the required wind velocity, in magnitude and direction. Obviously if the cyclone moves eastward, whirling oppositely to the hands of a watch, the swiftest wind is on its right side, which consequently is known as the dangerous side. In the northern hemisphere, therefore, the rule for dodging a great whirlwind is to run north, if that be practicable.

Stationary cyclones occur under favorable conditions. At least that name has been applied to columns of hot air streaming up from a fixed base, more or less circular. Every island in the ocean generates such a vortex on a clear, hot summer day, since its temperature far exceeds that of the surrounding water. All day long this uprush continues whatever be the humidity. And if the soil slopes upward steeply, the vortex is so much the stronger, particularly if the island be in a calm region. Above such a tract the gulls and vultures, and possibly even man, might soar all day without motive power. This condition and its interesting possibility deserve investigation.

Cyclones may occur at any season, but in general they are most abundant when the greatest temperature disturbances occur. The relative frequency of tropical cyclones for various localities and for the twelve months of the year is seen in the following table[69]:

The Yearly Periods of Cyclone Frequency in Several Seas

The tornado is a slender cyclone or hurricane. It is usually but a few yards or rods in diameter, and seldom exceeds one mile across its active column, whereas a cyclone may cover an area of any size from fifty to one or two thousand miles in diameter. Moreover, the cyclone requires for its inception an extensive pressure gradient marked by closed isobars, and once generated may last several days. A tornado per contra may spring into action where the lateral pressure is uniform, spend its force in a few moments, and leave a uniform barometric field in its wake. In shape the tornado is usually of greater height than width. The cyclone is far-flung laterally, but in height may not exceed the narrow tornado, since both must terminate beneath the isothermal layer, and commonly do not extend so high. Both vortices are caused by the ascensional force of hot air. In both the air spirals in and upward at the bottom, out and upward at the top, constantly cooling by expansion, and finally descends on the outside to complete the closed circulation. In general the tornado is the more violent and destructive, though limited to a brief and narrow path. More aptly, perhaps, the tornado may be called a slender hurricane of brief duration; both of them being small cyclones, or aËrial vortices, of minor size and concentrated intensity. The relation of the tornado and cyclone has been defined as follows, by Professor Moore:

“The cyclone is a horizontally revolving disk of air of probably 1,000 miles in diameter, while the tornado is a revolving mass of air of only about 1,000 yards in diameter, and is simply an incident of the cyclone, nearly always occurring in its southeast quadrant. The cyclone may cause moderate or high winds through a vast expanse of territory, while the tornado, with a vortical motion almost unmeasurable, always leaves a trail of destruction in an area infinitesimal in comparison with the area covered by the cyclone.”

Two initial conditions seem essential to the genesis of a substantial tornado. In the first place, the atmosphere of its immediate locality must have appreciable gyration. Of course, in all extra equatorial regions the air has some incipient whirl due to the earth’s rotation, and this whirl is magnified as the fluid is sucked into the vortex. But the magnification may be slight owing to the brief lateral displacement of the air feeding the tornado. If, however, the fluid be drawn from a considerable distance, and have from local conditions some additional whirl superadded to that due to the earth’s rotation, the gyratory flow in the medium near the vortical axis may be very swift. On the other hand, the additional whirl, due to local conditions, may tend to neutralize that due to the earth’s component, thereby leaving a very feeble gyration, if any. But in general the rotation of tornadoes is observed to be in the direction of the earth’s component; to the left north of the equator, to the right south of it. This observation is doubtless the more striking because when the accidental local spin conspires with the permanent terrestrial one, the resultant whirl is intensified, while in the opposite case it is so enfeebled as to attract scant, if any attention.

In the second place, the genesis of a tornado requires unstable equilibrium in the local atmosphere. This instability, as in cyclones, may arise from abnormal temperature gradation. Thus, if along any vertical the temperature falls more than six degrees Centigrade for one thousand meters ascent, a mass of air started upward will continue to rise, since it cools less rapidly than the environing medium. In this way there will ensue a continuous uprush of air so long as the unstable state endures; and the action may be very vigorous if a large stratum of air is greatly heated before it disrupts into the cold upper layers. In general, the loftier the tornado the more violent it is, just as the taller flue generates the stronger draft with the same temperature gradient.

Dynamically, the tornado may be treated as a rotating pillar of air in which each mass of fluid fairly retains its angular momentum. This means that for any mass of the whirling air the radius of its path, multiplied by its circular speed, remains a constant product; in other words, the velocity of whirl varies inversely as the radius. Accordingly, the circular velocity is exceedingly rapid where the radius is very small. Now, when any mass runs round a circle its centrifugal force is known to be directly as the square of the speed of its centroid and inversely as the radius. But by the above assumption the speed itself is inversely as the radius. Hence, the centrifugal force varies inversely as the cube of the radius of the inflowing mass of air. This centrifugal force, acting on the inner layers of air of the rotating column, must be supported by the pressure against them exerted by the outer layers as they pass inward. Thus there is a strong barometric gradient from the remote still air toward the swiftly whirling parts of the vortex.

It follows from the above argument that inside a tornado the barometric pressure may be much below the normal; and it is easy to see that if a barometer, starting from some point on the tornado base, be moved vertically upward it must show a declining pressure, but if moved upward and outward it may be made to show a constant pressure all the way to the upper portion of the vortex. The instrument would thus travel along an isobaric, bell-shaped surface opening upward. On a series, therefore, of concentric circles on the base of a tornado, we may erect a family of coaxial bell-shaped surfaces to mark the points of equal pressure, and thus map out the isobars of the vortex. Inside these coaxial surfaces reaching to earth, others of still lower pressure may be drawn tapering downward to a rounded point and terminating at various places on the axis. In an actual tornado one of these infinitely numerous funnel-shaped isobaric surfaces may become distinctly outlined and visible, if the air has sufficient moisture to start precipitation when it reaches a surface of suitably low pressure. This quite usually occurs in Nature, the funnel sometimes reaching to earth, sometimes only part way, according to the pressure at which precipitation begins, this pressure depending, of course, on the percentage of humidity of the uprushing air.

The form of the funnel-like cloud ere it reaches the earth is interesting. Being an isobaric surface, it would support in static equilibrium a free particle resting on it and sharing its rotatory motion. The lower rounded part of the funnel is parabolic, the upper outer part hyperbolic; the two together delineating the well-known Rankine double vortex of hydrodynamics. Students of hydrostatics know that when a glass of water is spun round its axis at a fixed velocity, the dimple observed is of parabolic form, and if frozen will sustain in repose a small shot resting on its surface and whirling with it. Similarly the lower part of the funnel is parabolic because in it the air rotates, as one solid body, while the broader part of the funnel is hyperbolic because in it the air has a speed inversely proportional to its radius of motion.

If everywhere in a tornado the circular velocity of the inflowing air were inversely proportional to the radius, as above assumed, the speed near the axis would be indefinitely great. This cannot be admitted. Practically, the inflow ceases when the centrifugal force of the gyrating stratum equals the pressure urging it toward the axis. Within this stratum is a column of air rotating everywhere with constant angular velocity about the vortical axis, and thus having quite calm air at its center. Outside this solidly rotating core the air spirals radially inward and upward. Some idea of the stream lines in such spiral flow may be obtained from Fig. 50 if a rapid circular motion be added to the inward and upward velocity represented by the arrows.

In the foregoing discussion no account of friction was taken. Near the earth’s surface this dampens the whirl and centrifugal force, so that the air flows more directly into the vortex, while farther aloft the centrifugal force near the axis so effectually checks the inflow as to allow the central core of air to rush up nearly unimpeded, as in a walled flue, taking its draught mostly from the lower part. As a consequence, the upward speed of the heated air in the tornado tube may be enormous, supporting in its stream objects of considerable mass.

The true horizontal speed anywhere in a tornado is compounded of the velocities of gyration and of translation, as in the cyclone. Hence the advancing side may be considerably the swifter and more destructive, particularly more destructive since the impact of air increases as the square of the velocity. If the vortex were stationary it would be equally dangerous on all sides, standing erect and symmetrical; but it drifts with the whole mass of air, sometimes quite swiftly and often with varying speed of travel at different levels; thus, in its slenderest forms, appearing bent and not infrequently twisted, as it advances writhing serpentlike through the sky. Furthermore, the intensity of whirl may fluctuate momentarily, with consequent shifting of the isobaric surface, including that one whose form is visible by reason of incipient condensation; and thus the funnel-like misty tongue appears to dart earthward as a foggy downshoot from the cloud above, whereas its parts are really rushing upward at all times very swiftly, whether visible or not. This agile protrusion of the nimbus, now a tongue, now a dark and mighty tower, is the strenuous part of the storm, the abominated “twister” which the Kansan farmer sedulously shuns, or peeps at from a hole in the ground. Unwelcome, indeed, are its visitations, when, with mickle and multitudinous roar, it claps his house in sudden darkness, hurls it aloft and sows its sacred relics over all the adjoining township, “that with the hurly-burly hell itself awakes.”

Theory, as well as experience, accredits the tornado with vast energy and power. For, suppose a surface stratum of air one mile in area and one thousand feet thick to increase in absolute temperature one per cent, thus uplifting the superincumbent atmosphere ten feet. The total energy stored in this way equals the weight lifted multiplied by its upward displacement. The weight is a ton per square foot and the displacement is ten feet; hence the stored energy is ten-foot tons per square foot of the heated tract, or about 280,000,000 foot tons for the square mile of heated air. This is equivalent to the work of one million horses for over a quarter of an hour. A goodly percentage of this stored work may be converted into kinetic energy in the active part of the dry tornado. It is the energy of a vast reservoir suddenly gushing through a tall penstock. It is a colossal upward cataract, an aËrial Niagara, a Johnstown flood suddenly liberated and quickly spent.

A vortex of that description possesses enormous devastating power, for it is endowed with four destructive elements: rapid onset for razing, violent spin for distorting, swift uprush for lifting, low pressure for disrupting. These four grim powers may operate at once and in accord. When, for example, they assault a house, the horizontal blasts push and wrench it on the foundation, the cellar air suddenly expanding puffs it aloft, the internal air bursts its walls or windows, the uprush carries its members on high and scatters them wantonly to the four winds. These powers are abundantly attested by authentic reports from many localities.

When the tornado appears as a misty column it is familiarly called a “waterspout,” particularly if it appears over a sea or lake. As already explained, the visible and cloudy portion of the column is due to condensation of the aqueous vapor in the air, as it rushes expanding and cooling into the low pressure part of the vortex. From the lashed and rippling sea surface, where it upcones into the base of the spout, some water is carried aloft as spray mingling with the mist of the chilled vapor, but not necessarily in very large proportion, and never rising in solid body to the cloud, as popularly supposed. On the contrary, waterspouts, however massive and formidable looking, are very tenuous, and may occur on land or water indifferently. Doubtless they are better defined, more regular and more familiar over water, and hence their name; but essentially they are vapor spouts, though mingled at times with dust or spray. Owing to rapid precipitation of the uprushing aqueous vapor, there may be heavy rainfall on all sides of the waterspout, so that at sea it may be difficult for the observer to ascertain how much of the downpour is salt water and how much is fresh. On land the downpour is sometimes mingled with dÉbris, and even with live fish and frogs caught up from neighboring bodies Of water. Copious hail also may fall with the rain, if the vortex be a lofty one.

The following description and analysis of a representative spout is due to Professor Bigelow of the U. S. Weather Bureau:[70]

“The tornado may be illustrated by the St. Louis storm of May 27, 1896. It is a truncated dumbbell vortex out off at the ground on the plane where the inflowing angle is about 30°. This vortex is much smaller than the hurricane, although of the same type. It is about 1,200 meters high and about 2,000 meters in diameter on the surface. The vortex tubes are shown in Figs. 51 and 52. In these figures can be seen the vortex tubes, geometrically spaced, through each of which the same amount of air rises. The rotating velocity is greatest about 300 meters above the ground, but the dimensions are such as to produce enormous velocities in the lower levels. The radius in the outer tube is taken to be 960 meters, and the inner tube 55 meters. The radial inward velocity on the outer tube is—8 meters per second; on the outer tube the tangential velocity is 13 meters per second, and on the inner 224 meters per second; on the outer tube the vertical velocity is 0.27, and on the inner tube it is 80 meters per second. On the outer tube the total velocity is 15 meters per second, and on the inner tube 270 meters per second. The volume of air ascending in each tube is 774,500 cubic meters per second. On account of the distortion of the theoretical vortex, due to the cutting of the lower portion by the truncated plane, and to the progressive motion of the whole system that constitutes the tornado, there is difficulty in computing the pressure to fit these observed velocities and radii.

“Tornadoes occur in the southern and southeastern quadrants of areas of low pressure, along the borders of the cold and the warm masses which entered into the structure of the cyclone. When a cold mass is superposed upon a warm mass, as was the case at St. Louis, a tornado will occur if the difference in specific gravity be sufficient to inaugurate a violent mixing, and the rotation be about a vertical axis, instead of about a horizontal axis, as in the case of thunderstorms.”

The size and form of waterspouts alter greatly with the state of the atmosphere. As Ferrel observes, they may vary “from that of a cloud brought down over a large area of the earth’s surface in a tornado where the air is nearly saturated with vapor and the general base of the clouds very low, somewhat as represented in Fig. 53, to that which occurs when the air is very dry, and when the tornadic action is barely able to bring the cloud down from a great height into a slender spout of small diameter, somewhat as represented in Fig. 54. Horner says that their diameters range from 2 to 200 feet, and their heights from 30 to 1,500 feet. Dr. Reye states that their diameters on land, at base, are sometimes more than 1,000 feet. Oersted puts the usual height of waterspouts from 1,500 feet to 2,000 feet, but states that in some rare cases they cannot be much less than 5,000 or 6,000 feet. On the 14th of August, 1847, Professor Loomis observed a waterspout on Lake Erie, the height of which, by a rough estimate, was a half mile, and the diameter about 10 rods at the base and 20 rods above.

“Judge Williams, in speaking of the tornado of Lee’s Summit, where he saw it, says: ‘It seemed to be about the size of a man’s body where it touched the clouds above, and then tapered down to the size of a mere rod.’”

When the tornado vortex is so tall and strong as to carry raindrops up to freezing strata it is commonly known as a hailstorm. The congealing occurs usually in those isobaric surfaces which dip down in the center of the vortex, but reach only part way to the earth. As indicated in Fig. 55, the clear aqueous vapor near the earth is condensed to cloud on crossing an isobaric surface of sufficiently low pressure and temperature; then it proceeds as mingled cloud and rain till it crosses the freezing isobar into the region of snow and hail formation; thence finally curves outwardly to stiller air and descends as a cloud of mingled vapor, rain and frozen parts. Of this frozen shower one part may come to earth as hail or rain, the snow and sleet melting on the way; while another part may be redrawn into the swift uprush, and carried aloft till its frozen drops, or pellets, have grown so large by accretion as to plunge to earth by sheer bulk, even though they must traverse a furious ascending wind. A good illustration from Nature of this cycle in the center of a hailstorm is presented in the following by Mr. John Wise, America’s adventurous pioneer balloonist:

“This storm originated over the town of Carlisle, Pa., on the 17th of June, 1843. I entered it just as it was forming. The nucleus cloud was just spreading out as I entered the vortex unsuspectingly. I was hurled into it so quickly that I had no opportunity of viewing the surroundings outside, and must therefore confine this relation to its internal action. On entering it the motions of the air swung the balloon to and fro and around in a circle, and a dismal, howling noise accompanied the unpleasant and sickening motion, and in a few minutes thereafter was heard the falling of heavy rain below, resembling in sound a cataract. The color of the cloud internally was of a milky hue, somewhat like a dense body of steam in the open air, and the cold was so sharp that my beard became bushy with hoar frost. As there were no electric explosions in this storm during my incarceration, it might have been borne comfortably enough but for the seasickness occasioned by the agitated air-storm. Still, I could hear and see, and even smell, everything close by and around. Little pellets of snow (with an icy nucleus when broken) were pattering profusely around me in promiscuous and confused disorder, and slight blasts of wind seemed occasionally to penetrate this cloud laterally, notwithstanding there was an upmoving column of wind all the while. This upmoving stream would carry the balloon up to a point in the upper clouds, where its force was expended by the outspreading of its vapor, whence the balloon would be thrown outward, fall down some distance, then be drawn into the vortex, again be carried upward to perform the same revolution, until I had gone through the cold furnace seven or eight times; and all this time the smell of sulphur, or what is now termed ozone, was perceptible, and I was sweating profusely from some cause unknown to me, unless it was from undue excitement. The last time of descent in this cloud brought the balloon through its base, where, instead of pellets of snow, there was encountered a drenching rain, with which I came into a clear field, and the storm passed on.”

As might be expected the hailstones vary much in form, size and quantity. If by chance any stones become slightly flattened they ride level in the ascending current, and hence by aggelation grow most rapidly on the periphery which is a line of diminished pressure. At times they are more or less oval, and again they appear as fragments of considerable masses of ice, broken perhaps by collision in the violent parts of the tornado tube. Their great variety in shape and bulk may be appreciated from the following extracts taken from the records of the Signal Service:

In Professional Paper of the Signal Service No. 4, describing the tornadoes of May 29th and 30th, 1879, in Kansas, Nebraska, Missouri, and Iowa, this passage occurs relative to a tornado at Delphos, Mo.:

“On the farm of Mr. Peter Bock, in the adjoining township of Fountain, about 4 miles W. of the storm’s centre, and during the hailstorm that preceded the tornado, masses of ice fell as large as a man’s head, breaking in pieces as they struck the earth. One measured 13 inches in circumference, another 15, and a hole made by one that fell near the place of Mr. J. H. Kams measured 7 inches across one way and 8 the other. This immense fragment of aËrial ice broke into small pieces, so that its exact size could not be determined.”

The following description is given of the tornado that visited Lincoln County, Neb., at that time:

“At first the hailstones were about the size of marbles, but they rapidly increased in diameter until they were as large as hens’ eggs and very uniform in shape. After the precipitation had continued about fifteen minutes, the wind ceased and the small hail nearly stopped, when there commenced to fall perpendicularly large bodies of frozen snow and ice, some round and smooth and as large as a pint bowl, others inclined to be flat, with scalloped edges, and others resembled rough sea-shells. One of the latter, after being exposed an hour to the sun, measured fourteen inches in circumference.”

The following was reported by the Signal Service observer at Fort Elliott, Tex., 1888:

“A thunder-storm began at 4.10 p.m. and ended at 7.40 p.m., moving from southwest to northwest. Hail began at 5.18 p.m. and ended at 5.26 p.m., the hailstones being spheroidal in shape and about two inches in diameter; formation, solid snow. The ‘break’ (hills) at the foot of the plains several miles northwest of station were absolutely white with hailstones for three hours after the storm. This was observed by everybody at the station; on the morning of the 26th I walked down to the Sweetwater Creek, three fourths of a mile distant, and saw great banks of hailstones which had been washed down during the night. The bottoms along the Sweetwater were literally covered with banks of hailstones from six to eight feet in depth. It was estimated that there was enough hail to cover ten acres to a depth of six feet. The hailstones killed five horses which were out on the prairie on a ranch six miles north of station. The Sweetwater Creek was higher than ever known before, the freshet destroying nearly the entire post garden. The high water is supposed to have been caused by a ‘cloud-burst’ at or near the foot of the plains, where the Sweetwater has its source; there was only 0.36 inch of rainfall at the station. On Sunday, May 27th, hailstones were collected on the banks of the Sweetwater, which had been washed down and lay in drifts 6 feet deep, actual measurement by the observer.”

When, after imprisonment and long sustention in a powerful tornadic vortex, the accumulated rain or hail finally breaks through and pours down to earth, in solid cataract, the phenomenon is commonly called a cloud-burst. The foregoing example is a partial illustration. The following is quoted from Espy, describing a cloud-burst near Hollidaysburg, Penn., in which the water seems to have poured down nearly in a solid stream:

“On examining the northern side of this ridge, large masses of gravel and rocks and trees and earth, to the number of 22, were found lying at the base on the plain below, having been washed down from the side of the ridge by running water. The places from which these masses started could easily be seen from the base, being only about 30 yards up the side. On going to the head of these washes they were found to be nearly round basins from 1 to 6 feet deep, without any drains leading into them from above. The old leaves of last year’s growth, and other light materials, were lying undisturbed above, within an inch of the rim of these basins, which were generally cut down nearly perpendicularly on the upper side, and washed out clean on the lower. The greater part of these basins were nearly of the same diameter, about 20 feet, and the trees that stood in their places were all washed out. Those below the basin were generally standing, and showed by the leaves and grass drifted on their upper side how high the water was in running down the side of the ridge; on some it was as high as three feet. It probably, however, dashed up on the trees above its general level.”

Dry whirlwinds of moderate size, but sometimes of considerable violence, frequently occur in clear weather when the percentage of humidity is small and when the vertical temperature gradient is unusually pronounced. In this case there may be strong agitation of the air, rendered visible at the earth’s surface by light dÉbris on land, or boiling of the water at sea; but the main body of the tube is invisible and free from mist except high up where precipitation begins, capped by a growing patch of white cloud in a clear sky, and which may gradually broaden and condense sufficiently to cause a shower of rain. On land the dry whirlwind may be delineated as a tall column, by whirling dust or sand. In this case, if the gyration is violent, the central core may appear clean and clear owing to the centrifugal force which keeps the grains out where they are balanced by the pressure of the inrushing air. In such vortices the sand spout may appear to be hollow as in the case of waterspouts whose interior cores are free from cloud or condensed vapor. On the other hand, myriads of mild transparent whirlwinds unmarked, except by down or humanly invisible dust, or dim aËrial refractions, may frisk and play in the boundless sky unnoticed by the blunt eyes of men, yet constantly engaged in generating or marshaling the clouds and in buoying upward the ponderous eagles, the vultures and the whole brood of passive flyers whom we have not yet learned to emulate. Thus when we remember that an upward trend of air of scarcely one yard per second, and too feeble to support a falling hair, is yet sufficient to carry the condor and albatross without wing beat, it seems important to explore these minor vortices and to ascertain their availability and practical usefulness for human soaring.

Still another interesting kind of aËrial disturbance is the familiar heat thunderstorm. This is not synonymous with those electrified tornadoes and cyclones which are accompanied by thunder and lightning, sometimes of great violence. Most tornadoes are thunderstorms, but not vice versa. The thunderstorm is not essentially a vortex, but rather a wind squall marked by sudden changes of temperature and pressure, bearing with it massive clouds fraught with rain, or hail, and disruptive electric charges flashing frequently to earth, or from point to point in the sky. Its approach is usually announced by rumbling thunder and heavy black clouds along the horizon. Its duration is brief, varying from a few minutes to an hour or two. Further characteristics are thus expressed by Moore:

“On land, thunderstorms occur most frequently at specific hours of the day or night, such as 3 to 5 in the afternoon or 9 to 10 in the evening and sometimes even at 2 or 3 a.m., but no such diurnal period is observed in midocean. The phenomena usually occur in a pretty regular order of succession. After several hours of fair weather, with gentle winds, there comes a calm; the cumulus clouds grow larger, the lower stratum of clouds is seen to be moving rapidly; gusts of wind start up with clouds of dust, rain is seen to be falling at a distance; the movement of rain and dust shows that the wind is blowing out from this rain cloud near the ground no matter which way the rainy region is advancing; a few large drops fall from slight clouds and then suddenly the heavy rain begins. Lightning that may have occurred during the preceding few minutes becomes more frequent and more severe as the rain increases. After the maximum severity of rain and wind, the lightning also diminishes or entirely ceases, and we are soon able to say that the storm has passed by. If we watch its retreat from us in the afternoon we shall see the rear of a great cumulus on which the sun is shining, but through whose dark-blue curtain of cloud and rain nothing save occasional lightning is visible. After the storm has passed, the lower atmosphere soon becomes appreciably cooler and drier, the sky is nearly clear of clouds, and the wind has shifted to some other point of the compass than that which prevailed before the storm.”

The genesis of thunderstorms is varied and manifold. In one simple type, a large tract of heated air in the unstable state and with a high percentage of humidity swells upward at the center, the ascending moist air forming, at the precipitation altitude, a growing cloud which may become very broad, dark and bulky, drifting along over the earth with the prevailing current. Eventually rain begins to form, or may be hail or snow, if the heated column reaches to a great height. The falling shower cools the air from the cloud down to the earth, increasing its density and materially weighting it with the descending liquid or solid particles. The showery column then sinks, especially along its inner part where it is maturest, thus causing an outrush of cool air along the earth, the immediate forerunner and herald of the rain. This outrushing current pushes upward the environing clear moist air, thus forming new margins of massive cumuli around the older nimbus widening within, showering, cooling and sinking. Thus the rain area is broadened and propagated, sometimes with nearly equal speed in all directions, but generally fastest in the direction of the most unstable condition, or of the then prevailing drift of the atmosphere. Indeed, the forward cloud ranks may far outspeed the wind, seeming by their imperious bluster and gigantic gloom to commandeer new recruits, as if by magic, out of the clear sky. Before this solemn mustering and turbulent front of the storm the black vapors suddenly startled into visible shape, rush buoyantly upward in ragged shreds, like smoke from unseen fires, and quickly blend with the general array of compact cloud expanding across the sky. Again, several thunderstorms, merged like a mountain range in solid phalanx, may sweep abreast over a continent, with long horizontal[71] roll, ever rising in front and upheaving the sultry air, thus replenishing perpetually the ponderous cumuli which form the vanguard of this far-flung and titanic march of the clouds. Such a storm is usually powerful and persistent, commonly enduring until the sun’s decline and the shades of night have cooled the lower air, and thus allayed the commotion by enfeebling the forces that favor its progress.

The speed of rise of the air beneath the base of the thunderhead is a question of some interest in aËronautics. If the ascent be so much as a foot or two per second, one may expect the vultures to prefer soaring beneath the thundercloud during its formative period. Here also the aËroplanist might attempt a record flight, if the cloud were high enough to be out of his way. But if he ventured to penetrate the base of the thunderhead, he might find the turmoil too irregular and strenuous for his comfort.

Of like interest is the long aËrial swell that leads the advancing storm. When will aviators make this the theater of their adventurous frolic, careering playfully before the brow of the tempest and the harmless rage of the lightning, gay-winged heralds of the coming tumult, sailing perhaps with slackened motive power, yet swift and secure as the storm-riding petrels at sea?

Besides the winds and aËrial currents commonly studied by meteorologists, are the minor disturbances which affect more particularly the wayfarers of the sky, whether birds or men. The atmosphere quite usually is vexed with invisible turmoils; most sensible, indeed, over rough territory, but conspicuous also above the smooth terrene, and at all elevations from earth to the highest cloudland. Before sunrise, and generally in weather uniformly overcast, these miscellaneous and nondescript movements of the air are least active, for any given speed of the general drift of the atmosphere; but when the sun shines and the soil is nonuniformly heated, the disturbances become most pronounced. A whole troop of playful zephyrs rise and set with the sun, in addition to the diurnal winds already studied. Over the dusty plain they reveal their presence and shape in those coiling columns that constitute the safety vents of the atmosphere, and obviate the disruptive violence of the uprush that would occur should a considerable region of surface air become excessively heated. Over the city, particularly in winter, the local turmoils of the atmospheric surf are revealed in the play of a thousand smoky columns, and better still, when it snows, by the incessant swell and veering of the flaky flood whose surges and eddies bewilder the vision by their complexity. Over the water the clouds of fog and steaming vapor are the best index of the local zephyrs, where, it must be remembered, the rising and veering of the vapor wreaths accompany like motions in the atmosphere. Over the forest, field and meadow the interminable wandering of thistle down and gauzy shreds of vegetation, now fast, now slow, now high aloft, then sheer earthward, indicate what erratic and perpetual motions prevail throughout the open country even on the stillest days. In the deep bosom of the atmosphere, the parallel ranks of the cirri all across the sky mark the crests of undulations quite as regular and tumultuous as the billows of a wind-swept sea; while the fierce seething and upsurging of the separate cumuli manifest the operation of vortices of prodigious energy. These visible billows and whirlwinds suggest an infinitude of transparent ones hardly less powerful, at the various levels unmarked by clouds. For wherever two streams of abnormally graded densities neighbor each other, a readjustment may occur agitating the entire region with a host of pulsations, squalls, cataracts and fountains which the bird and navigator must parry with proportionate care and skill.

And it is because of the amazing resistance of these wandering zephyrs, waves and eddies that they demand the attention of aËronauts; nay, more, it is because of the substantial labor they can perform when adroitly encountered and duly employed. For the simplest elements of aËrodynamic science make clear that a rising zephyr hardly strong enough to support a falling leaf is adequate to sustain the heaviest soaring birds and aËroplanes gliding swiftly through it. In fact, the sailors of fast air ships feel a heavy impulse and distinct shock in plowing those mild cross winds which, to the fixed observer, seem not like blasts, but rather as gentle swells or harmless currents. These, therefore, have been made the subject of investigation by various students of aËronautics.

The first incentive to the instrumental study of the fluctuations of the wind in speed and direction seems to have been the hope to furnish a quantitative basis for various theories of soaring flight. PÉnaud,[72] in 1875, had explained this phenomenon by postulating an upward current. Lord Rayleigh,[73] in 1883, had made the more general assumption of a wind having either a variable speed or a variable direction as a necessary and sufficient condition for such flight. Marey,[74] in 1889, and Langley,[75] in 1893, gave elementary qualitative explanations of soaring in a horizontal wind of variable velocity, though neither adduced concrete data to prove that the feat could be performed in an actual wind. Each and all of those theories may be sound enough in the abstract, but to show that they represent realities of art or Nature they should be applied to a concrete instance of soaring of a machine or a bird of known resistance, in a wind of known variability.

To such end the writer in 1892 devised an anemograph for recording simultaneously the speed of the wind and its horizontal and vertical components of direction, while Dr. Langley devised a very light and delicate cup anemometer for recording the variations of wind speed in a horizontal plane, but not the changes of direction. Both instruments were set up in January, 1893, and both investigations were published with the Proceedings of the International Conference on AËrial Navigation of that year; but neither investigation was pushed far enough to prove conclusively the possibility of a particular bird or model soaring in the particular wind recorded. The two together did, however, reveal quite astonishing fluctuations of the wind in both speed and direction, results that have since received ample exemplification in the more extended records of other observers.

Fig. 56 shows the recording anemometer for speed and double direction constructed by the writer in 1892. A large weather vane was firmly strapped to a vertical pipe which turned freely on ball bearings and, by means of a small crank actuating a chronograph pencil, recorded its fluctuations on a long sheet of paper winding on the drum from a roll behind. On top of the pipe and about fifteen feet from the ground, was mounted a carefully balanced horizontal vane, from which a fine steel wire ran down the axis of the pipe to a fixed pulley, thence to a second recording pencil. A third pencil recorded the beats of a pendulum, thus standardizing the speed of the paper. A fourth pencil, not shown, was designed to record the turns of an anemometer mounted near the top of the pipe. The records of the wind speed thus secured are omitted for lack of standardization, as the experiments were prematurely terminated.

Typical records of the wind direction are shown in Fig. 57 in which the circles represent the paths swept by the wind-vane cranks that operated the corresponding pencils. Both vanes, as shown by their diagrams, veered quite frequently ten degrees in a short interval of time, and not seldom twenty to thirty degrees. Frequently, also, it was observed, in scanning the various records, that a rise or lull in the wind speed was accompanied by a corresponding variation in direction; but the observations were not sufficiently numerous and extended to establish this phenomenon as a general occurrence. But as it can be shown theoretically that a horizontal stream of air of constant cross section and uniform velocity at each section, can not greatly fluctuate in velocity from point to point, without more pronounced changes of density than the barometer records, it naturally follows that the stream must broaden where the air speed lags, and narrow where it accelerates; in other words, it follows that there must be some change in direction. The records were taken in the middle of a clear open space of two hundred acres at Notre Dame University on a sunless day in January, 1893, when the temperature was 24° F., and the wind eight to twelve miles per hour. Their application to the theory of soaring need not be considered here.

Further studies of the wind pulsations were made by use of a toy balloon attached to a long thread. The first trials are thus recounted in the paper above cited:

“After some preliminary tests from the top of the Physical Laboratory of the Johns Hopkins University, during the Easter vacation of 1893, I ascended the Washington Monument at Baltimore, where I paid out the exploring line at a height of 200 feet. The wind was blowing toward the southeast at the speed of 25 to 35 miles per hour, and the sky, which had remained clear till 3 o’clock, was rapidly darkening, with indications of approaching rain. The balloon, when let forth, immediately fell to a depth of 30 or 40 feet, being caught in the eddy of the monument, then presently encountering the unbiased current, sailed in it toward the southeast, approximately level with the spool end of the thread. After the balloon had drawn out 100 feet of thread I checked it to observe the behavior of this much of the exploring line. The balloon rose and fell with the tossing of the wind, but did not flutter like a flag, as it would do if formed of irregular outline. Neither did the thread flutter, nor do I believe there is ever a tendency in a line greatly to flutter in a current as does a flag or sail. Presently I paid out 300 feet of the exploring line, whereupon the waves in the thread became quite remarkable. The thread then, as a rule, was never approximately straight. Sometimes it was blown into the form of a helix of enormous pitch; at other times into the form of a wavy figure lying nearly in a single vertical plane; and again, the entire exploring line should veer through an angle of 40° to 60°, either vertically or horizontally. The balloon, of course, seldom remained quiet for more than a few seconds at a time, but tossed about on the great billows like a ship in a storm. Quite usually the billows could be seen running along the line from the spool to the balloon, and, as a rule, several different billows occupied the string at one time.

“The observations just delineated, however curious they may be, afford no adequate conception of the behavior of the air currents over an open plane, nor at a great height above the earth, because the Washington Monument at Baltimore stands but 100 feet above the surrounding buildings, which undoubtedly send disturbances to a greater height than 200 feet. To supplement these explorations, therefore, I determined to have them repeated from the top of the Washington Monument at Washington and the Eiffel Tower at Paris.”

Some months later in the year, the experiment was repeated at the top of the Washington Monument in Washington, at a height of five hundred feet. The balloon, with a stone attached, was paid out from the north window of the monument till it reached the ground. Then the stone was removed by an assistant who drew the balloon well away from the huge eddy of the great shaft, and let it fly toward the east, drawing the thread after it like a mariner’s log in the wake of a ship. When six hundred feet of the thread had been let out, it was observed to veer in all directions under the varying surges of the wind. These variations seemed larger than could be expected from the wake of the shaft alone near its summit, where it measures about thirty feet in thickness.

Such qualitative observations, though interesting and suggestive, are not wholly satisfactory. The same may be said of the study of air currents by aid of smoke from tall chimneys. The eddy about such columns may extend to a considerable height above them, and the wake is farreaching. The experiments would therefore best be made from high open-work towers above plane country or a broad sheet of water.

A better method perhaps would be to liberate a pilot balloon, or discharge a bomb giving a bright compact cloud, and to trace its path by means of two cameras, as it floats from point to point in the aËrial current. The instruments, if suitably stationed, would give the continuous space history of the floating object; that is, its actual path and the speed at each part thereof, or, in other words, the magnitude and direction of the velocity at each point. But, of course, this method would not reveal the wind’s history at any given fixed point, as recorded by the anemograph above described.

Fig. 58 is a typical wind-speed record obtained by Langley in January, 1893, by means of a very light cup anemometer mounted eleven feet above the north tower of the Smithsonian Institution, and 153 feet from the ground. The abscissÆ represent time in minutes, the ordinates wind speed in miles per hour. The records were taken in cloudy weather and in a south-southeast wind. Other records were taken during the month of February, showing like deviations from the mean, though at times more pronounced; for Dr. Langley noted that “the higher the absolute velocity of the wind, the greater the relative fluctuations which occur in it.”

It will be observed from this record that, when the average speed was about twelve miles an hour, the extreme fluctuation was rarely one third greater or less than that, and on the average varied hardly one sixth. It must be further added that the air on approaching the anemometer had traversed a mile of the lower residential section of the city, then crossed the body of the Smithsonian building, which itself is half as high as the tower. It should be expected, therefore, that this wind was, other things equal, naturally more turbulent than if flowing in from a level plain. This surmise is justified by the more extensive records of wind speeds shown in meteorological records taken respectively in clear and in obstructed places. On the other hand, even in level places where no obstruction is visible for several miles, the wind, though it may be steady at one time, can at another time be gustier than that shown in Langley’s record, according to the state of the weather; for the gusts are not all due to neighboring obstacles, but may be transmitted from afar, even from the depths of the atmosphere.

Assuming the wind speed at any instant to vary by one sixth of the mean, its impactual pressure will then vary by thirty-six per cent of the pressure of the mean wind, remembering that the pressure varies as the square of the speed. This fluctuation of the impactual pressure tallies fairly well with that found by Professor Marvin at the top of Mount Washington, in 1890, by means of a pressure plate.[76] He found the variation to be approximately thirty-five per cent of the mean pressure. Professor Hazen, however, reports but little variation in the wind speed in the free atmosphere well above the earth. In several balloon ascensions he suspended from the basket a lead weight by means of a cord to which was looped the thread of a toy balloon. He found that the little balloon sometimes moved ahead if the weight sometimes followed it, but that in general the relative motion was very feeble, thus indicating that the fluctuations of the velocity in the depth of the atmosphere at those times were very slight.[77] However this be for such distances from the earth and its protuberances, the fluctuations of wind speed found at meteorological stations sufficiently resemble those reported by Dr. Langley. As corroborative evidence, the reader may be referred to the wind records published in the Interim Report for 1909, of the British Advisory Committee for AËronautics.

Without the material evidence of commotion in the atmosphere, a moment’s reflection will make clear that such turmoil must exist, even over a vast, smooth plain, especially in bright weather, and more particularly over bare ground in dry weather. For it is well known that clear, dry air transmits radiation with very slight absorption, when the sun is well toward the zenith, and hence that the temperature in the depth of the atmosphere is but little changed from moment to moment, due to the passage of sunlight. At the earth’s surface, however, the air by contact with heating or cooling soil may change temperature rapidly. The direct sunlight falling perpendicularly upon a perfectly absorbent material transmits nearly two calories of heat per minute to each square centimeter of the receiving surface. It would, therefore, under favorable circumstances, elevate by nearly two degrees C. per minute a layer of water one centimeter deep, or a layer of air something over a hundred feet thick, if all the heat falling on the assumed surface were communicated to the neighboring air stratum. In practice, a large percentage of the incident sunlight is reflected and radiated by the soil, into sidereal space without heating the air. But every one per cent of it caught up by the air in contact with the earth is sufficient to heat a layer roughly one foot thick one degree per minute. Hence, unless the heated air streamed upward continually, the layer next the earth would quickly be raised to a very abnormal temperature, which would result in a violent uprush. The gradual ascension of the surface air may take place in large or small columns, or in both kinds at once. In either case, the composition of the ascensional motion with the general movement of the wind due to barometric gradient must cause gustiness and marked irregularity of speed and direction.

Various causes have been assigned for the gustiness of the winds. Ferrel and many other writers assume that the air, especially near the earth, is full of small vortices rotating about axes of various inclination. These whirls, on passing squarely across a weather vane, cause it to point one way for a moment, then presently the opposite way, while if they cross obliquely they cause a like sudden veering of the vane, but less extensive.

Helmholtz has proved that in the atmosphere strata of different densities come at regular intervals to be contiguous one above the other, and thus to beget conditions favorable to the formation of aËrial waves, sometimes so large as to set the lower regions of air into violent commotion and thereby generate the so-called gusty weather. He has summarized as follows some of the important conclusions of his dynamic analysis.[78]

“As soon as a lighter fluid lies above a denser one with well-defined boundary, then evidently the conditions exist at this boundary for the origin and regular propagation of waves, such as we are familiar with on the surface of water. This case of waves, as ordinarily observed on the boundary surfaces between water and air, is only to be distinguished from the system of waves that may exist between different strata of air, in that in the former the difference of density of the two fluids is much greater than in the latter case. It appeared to me of interest to investigate what other differences result from this in the phenomena of air waves and water waves.

“It appears to me not doubtful that such systems of waves occur with remarkable frequency at the bounding surfaces of strata of air of different densities, even although in most cases they remain invisible to us. Evidently we see them only when the lower stratum is so nearly saturated with aqueous vapor that the summit of the wave, within which the pressure is less, begins to form a haze. Then there appear streaky, parallel trains of clouds of very different breadths, occasionally stretching over the broad surface of the sky in regular patterns. Moreover, it seems to me probable that this, which we thus observe under special conditions that have rather the character of exceptional cases, is present in innumerable other cases when we do not see it.

“The calculations performed by me show, further, that for the observed velocities of the wind there may be formed in the atmosphere not only small waves, but also those whose wave lengths are many kilometers which, when they approach the earth’s surface to within an altitude of one or several kilometers, set the lower strata of air into violent motion and must bring about the so-called gusty weather. The peculiarity of such weather (as I look at it) consists in this, that gusts of wind often accompanied by rain are repeated at the same place, many times a day, at nearly equal intervals and nearly uniform order of succession.”

Commandant Le Clement de Saint-Marcq has drawn some interesting conclusions from the hypothesis that an ordinary wind consists of a uniform current on which is superposed periodic motions in the wind’s main direction and also at right angles thereto. But he has not established his hypothesis by adequate observations. He assumes the pulsations to be simple harmonic motions, which of course they would be if they were plane compressional waves; but at the same time he shows that the fluctuations are too large to be compressional waves, with the concurrent slight variations of the barometric pressure.

It is still a question whether the pulsations of the natural wind be harmonic. If so, the speed records should be sine curves, and the to and fro acceleration of any mass of moving air should be variable for any given pulsation. But the few records available show in many parts a constant acceleration of the wind speed throughout a particular swell or lull of velocity, indicating that the pulsations are not generally simple harmonic ones.

In scanning the wind-speed records published by Langley, so many instances of uniform wind acceleration are noticed that one naturally inquires whether the rate of gain of velocity be sufficient to sustain in soaring flight an aËroplane or bird held to the wind solely by its inertia, as Langley believed to be possible. The total forward resistance of a well-formed aËrial glider, or bird, may be taken as one eighth of its weight; hence, if poised stationary in its normal attitude of flight, it will just be sustained by a direct head wind having a horizontal acceleration of one eighth that of gravity, or four feet per second. Now, the most favorable parts of the record here shown (Fig. 58) exhibit nowhere an acceleration so great as four feet per second, and on the average far less than that, as may be proved by sealing the diagram. Hence, the wind here recorded was wholly inadequate to support by its pulsative force either bird or man. But as this record is a fair representative of all those published by Dr. Langley, it follows that such pulsations can at best merely aid in soaring when happily and adroitly encountered; but that they cannot fully sustain soaring at any level, much less during ascensional flight to great altitudes, or migrational flight to vast distances. It still remains, therefore, to ascertain what kind of aËrial currents are adequate to sustain those marvelous feats of soaring on passive pinions which for ages have been the delight and wonder of all keen observers, and which are of such enduring interest to mankind. This investigation, however, appertains more particularly to the science of applied aËrodynamics.