Popular Science Monthly/Volume 76/May 1910/The Circulations of the Atmospheres of the Earth and of the Sun

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THE CIRCULATIONS OF THE ATMOSPHERES OF THE EARTH AND OF THE SUN
By Professor FRANK H. BIGELOW

U. S. WEATHER BUREAU

The Two Causes of Circulation on a Non-Rotating Earth

Gravity, Temperature and Pressure

IT must seem rather ambitious to attempt to treat so great a subject as that of the circulation of the atmospheres of the earth and the sun in a single lecture. It is true that if it should be discussed fully, in the technical way, it would require a great many lectures, but of course there are at the same time certain fundamental principles which are common to all circulations that can easily be studied, and then illustrated by the known facts of the circulation in these two atmospheres. All circulation depends upon two primary causes, the first being the attraction of gravitation, by the laws of the action of the earth upon its atmosphere or the great body of the sun upon its atmosphere; and, secondly, the difference of temperature which exists in different parts of a given atmosphere. If we had an earth standing still in space without rotation upon its axis and the sun were withdrawn for a considerable time, the atmosphere of the earth would gradually settle down into a quiescent state, which may be described as consisting of a series of concentric shells, each shell having a certain fixed temperature passing around the earth at the same distance from a center, as if a balloon were floating at the same height above the surface, where will be found the same barometric pressure and the same temperature in all latitudes and longitudes. If the balloon falls from one shell to another it would pass into layers of greater density, and if it rises, into layers of less density. The boundary of each shell may be conceived as a surface having the same force of gravity acting upon it, and this is called the gravity level. In this case the surfaces of equal pressure or the isobars, and the surfaces of equal temperatures, isotherms, both coincide with their own gravity levels. Everything is quiescent and there is no circulation. It is quite important to secure a clear idea of the fact that the isobars, isotherms and gravity levels coincide wherever the layers in the atmosphere have the same temperature. As a matter of fact the earth is not without rotation, and the sun is shining upon it, sending enormous masses of heat which fall upon the tropics, and it is our problem to study the effect of this heat, at certain layers in the earth's atmosphere, upon the circulation of the entire mass.

To illustrate the series of causes and effects we can take a long box or canal containing air at a certain temperature. Now if heat be applied at one end, it is evident that the air at that end is displaced in proportion to the amount of heat. The effect of heating the bottom of a column of air is to expand the lower layers of it and this produces less density in each of the lower layers, while at the same time the entire mass is lifted, provided the bottom rests upon a solid surface. Take water in a tube, heat the lower part of the tube, and the whole column will seem to rise in the tube, but the lower parts, being hotter, will necessarily have a smaller density. A common case of the power that can be produced by heat is seen in its effects in the steam engine. Similarly, the air when heated in certain localities, as over the tropics, begins to work practically like the steam engine. The air is expanded, the upper part is elevated and the lower part is rarefied. Now the effect of lifting a column which is heated in the lower part is to raise the isobar above the gravity level which is occupied before heating, and in the lower part the isobar is depressed below the position which it had before it was heated. It is now readily seen that isobars, instead of coinciding with the gravity levels, have a slope, the upper ones trending downwards towards the cold end of the canal, and the lower one sloping downwards to the warm end of the canal. Under the action of gravity a liquid or a fluid which rests on a slope of any kind tends to run down hill, just like water in a brook or a railroad train on a grade. The part which is above the gravity levels tends to get down to it, in order to destroy the slopes which nature abhors among its gravity levels. The force of gravity tries to make all the temperature and pressure levels coincide with the gravity levels, and in order to do that it is clear that currents of circulation are set up. In this way there is an effort to destroy the differences in temperature which have been produced by the sun's radiation and reduce them to a uniformity; that is, a uniform temperature at the same distance above the surface of the earth.

It becomes, therefore, a fundamental point in meteorology that the air over the tropics is heated in the lower levels by the action of the sun's radiation falling upon the earth, and that the air in the tropics is also lifted above its natural gravity position; hence, in the upper levels the air flows from the tropics towards the poles, and in the lower levels from the poles towards the tropics. We will not attempt to trace out this general circulation more fully until certain other conditions have been described.

If the heat is applied at the center of a canal, instead of at one end, the same principles operate, so that the lower part, being heated, has its isobars depressed in the middle, while the upper part is lifted so that the higher isobars are elevated above their original position. In this case air flows from the center in both directions towards the cold ends of the canal in the upper levels, and from the cold ends towards the middle in the lower levels. In this figure we have therefore a general description of the primary motion of the air on the earth taken as a whole, by which the air flows from the tropics towards the north pole and the south pole of the earth, respectively, in the upper levels, and from the north pole towards the tropics and from the south pole towards the tropics in the lower levels. It should be remarked in passing that since the assumed canal is like a rectangular square box in our laboratory experiments, but as a matter of fact of a wedge shape in the earth's atmosphere, the circulation is not so easy as might be at first assumed. The meridians at the equator, which are one degree apart, converge to a point at the poles, so that the atmosphere when quiescent must be thought of as made up of a series of sectors or spherical wedges. Now the air in running from the tropics towards the poles runs from a broad end to a thin end of the wedge, and, since it can not congest, a very complex circulation is set up in order to enable it to escape unnatural compression. There are, however, many examples in the earth's atmosphere of masses of air which are arranged much more nearly in the form of a rectangular box canal, as shown when a long mass of cold air is pointing north and south, with a mass of warm air pointing from south to north and lying east of it, while another mass of cold air pointing from north to south is placed just east of the mass of warm air. While these masses may not in fact be very rectangular, yet we can study their action on the supposition that sections through them produce figures which are practically rectangular in shape. Suppose we have a warm mass lying between the cold masses, then the warm mass will be higher above and also lower below than the cold masses so far as their isobars are concerned. That is to say, at the upper surface of the sections if you want to get a mass of air at a certain density it will be necessary to go higher up in the atmosphere over the warm mass than over either of the undisturbed cold masses lying on the side, and furthermore, if one wants to get a mass of air of the same density as that lying on the under side of the cold section, it will be necessary to go down lower in the warmer mass, that is, nearer the surface of the ground, in order to find it. Applying now our principles of circulation, the action of gravity will tend to draw the upper part of the warm mass over upon the cold masses to either side, and thus tend to destroy the inequality in the elevation of the upper isobar. Similarly the cold masses will tend to flow under the warm mass from either side, and remove the discontinuity in the positions of the lower isobars. Not only do these masses of warm and cold air tend to overflow and underflow sidewise, but they seek to move, as it were, along the meridians, northward and southward at the same time; hence the long currents of circulating air are naturally produced so that the warm and cold begin to interflow among one another, as a matter of fact in very complicated curves, the purpose of this being to restore the coincidence between the isobars, isotherms and gravity levels, which had been disturbed primarily by the heat of the sun falling upon the tropics of the earth. Having considered thus briefly the general principles which would induce circulation on a non-rotating earth, we can take up somewhat more fully the effect produced upon this same circulation by the fact of the earth's rotation; that is to say, we can discuss the circulation upon a rotating earth.

 

The Gyrations in the Atmosphere set up on a Rotating Earth

It will be desirable to define a few terms which occur in circulation that will enable us to speak more briefly of the subject in its advanced stages. Rotation will be confined to the motion of a mass of matter, as the sun or the earth, which is revolving about its center. The rotation of the earth takes place in 24 hours; the sun rotates on its axis in 27 days more or less. Revolution is the motion of a mass about a center from which it is separated by a radius, as the revolution of the moon about the earth, or the earth about the sun, or of an ideal particle of the atmosphere revolving about a center at a variable distance. Gyration is a more complicated motion. It consists of the revolution of a mass about its center at a given radius while the center itself is moving in some direction. If the moon revolves about the earth and the earth revolves about the sun, each particle of the moon will describe a series of gyrations forming a looped curve which describes this motion. If a particle of air in a tornado revolves about its axis while the axis is moving over the surface of the earth, the particle will gyrate or form a looped curve relatively to the surface of the earth. Vortex motion is more complex still. A vortex may be described as consisting of a series of concentric tubes. The motion of the tube is such that the inner tubes revolve about the axis faster than the outer tubes. A particle of an inner tube has a certain velocity which is greater than the velocity on an outer tube, but the velocity of the inner tube multiplied by its radius is equal to the velocity of the outer tube multiplied by its radius. If a particle moves from an outer tube to an inner tube in a vortex it can do so only by increasing its velocity of rotation. If the particle moves from the outer tube towards the inner tube and at the same time ascends along the axis, the particle will move in a helix. The helix may be contracting, with greater angular velocity, or expanding, with less angular velocity. In the latter case the particle moves from the inner tube to the outer tube of a vortex. A torque is a complicated motion which applies to a mass taken as a whole. The earth is covered by a shell of air and its actual motion may be described as a torque. Take a bundle of paper rolled up about a center line and grasp it in the two ends. Now twist the roll so that the ends move in opposite directions. At some point in the middle there will be no motion of the particles, while the upper particles of the paper move in one direction and the lower particles move in the opposite direction. In the case of the earth's atmosphere, in each hemisphere, there are two great currents each constituting a torque. In the northern hemisphere the northern current moves eastward and is called the eastward drift. In the northern tropic the great current moves westward and is called the westward drift. There are really two torques in the earth's atmosphere, one belonging to each hemisphere, so that in the tropics, as a whole, the movement is westward, while north of the Tropic of Cancer it is eastward, and south of the Tropic of Capricorn it is also eastward. Instead of the atmosphere running from the tropics towards the poles in the meridional wedges, as a matter of fact it circulates in these great torques. In the northern hemisphere north of the latitude of 33° there is a great eastward drift and between the latitudes of 33° there is a great westward drift. Along the latitude of 33° approximately there is no general motion either east or west, and this corresponds with the part of the paper bundle which does not get twisted when the upper and lower ends are moved in opposite directions.

When a current of air moves in any direction it tends to break up into two volutes or spiral branches. If one takes a dandelion stem and splits it along the center, the two pieces will curl over in opposite directions and form beautiful right and left handed spirals. If a warm current of air ascends from the ground and forms a cloud, it can be seen that the middle of the cloud is ascending while the edges are descending in a gentle spiral of an umbelliform shape. If a southerly current of air moves northward it will tend to open up in two branches to the right and left. If a northerly current moves southward it will tend to open up in two branches to the right and left. The left-hand branch of the southerly current and the right-hand branch of the northerly current will tend to interlock or intercurl. The great current in the tropics which moves westward, instead of proceeding due west around the earth, tends to break up into two great volutes, one curling into the northern hemisphere, and one curling into the southern hemisphere. The word curl has several meanings, the first is that in which it has already been used; namely, a spiral rolling about a center. The second is connected with vortex motion and is really a name for a part of the helix action. If a mass of air moves in a spiral towards a center, it is evident that it can not proceed long in this way without some provision for its escape. If it moves in a spiral on a given plane it must begin to escape along a line perpendicular to that plane. If a circle is taken as a boundary in a given plane, and a certain mass of air moves into this circle on spirals, then there will be a certain amount of the air moving perpendicular to the plane of the circle. This whole action of spiral movement inward and vertical motion from the plane is called a curl and it depends upon vortex laws. In a tornado or hurricane the curl is illustrated by air which ascends as a current while the air is moved inward along certain spirals. It is also illustrated in electricity and magnetism where an electric current passing around the helix surrounds a magnetic field perpendicular to the sections of the tube along which the electric current is flowing. Electric currents and magnetic fields are also related to each other by the law of the curl, and this evidently goes back to the idea of the helix or vertical spiral.

We may now resume our discussion of the circulation of the air on the rotating earth, repeating to some extent what has been said in defining these special terms. Take a globe and in the tropics place an arrow pointing westward between the equator and the latitude of 33° both north and south. To the north of 33° place an arrow pointing eastward, and in the southern hemisphere to the south of 33° place an arrow also pointing eastward. These represent in a general way the action of the atmosphere as consisting of two great whirls in each hemisphere, thus composing a torque on a hemispherical scale. Draw a ring around the earth in latitude 33°, cutting out a section of the atmosphere. If this ring moves northward it will evidently contract, and to have the same angular momentum, that is, mass energy, it must rotate faster about the axis as it approaches the pole. This constitutes in a way an illustration of vortex action whereby a particle passes from an outer to an inner tube and consequently revolves faster about the axis. Take another section south of latitude 33°, cutting out a ring of atmosphere. If this ring moves southward it must rotate slower because it is moving to a region at greater distance from the earth's axis if it is to retain the same momentum or energy of mass in motion. The importance of these great torques in the earth's atmosphere can be seen from this general fact that while the weight of the earth's atmosphere taken as a whole is very great, and is, generally speaking, in vigorous motion, yet the currents as a whole are so interbalanced that the mass energy moving eastward is exactly equal to the mass energy moving westward when the whole atmosphere is summed up. This is proved by the fact that the rotation of the earth on its axis does not change by the smallest fraction of a second from century to century, or at least astronomers have been unable to detect any change in the period of the earth's rotation so long as observations have been continued. If this balance of eastward and westward momentum were not perfect, it would immediately be shown by a change in the period of the rotation of the earth upon its axis.

The picture which is presented by these ideal rings starting from latitude 33° in each hemisphere and moving respectively towards the poles and towards the equator is not very complete, because the rings do not continue to move as a whole with an increase or decrease of velocity. If we examine the actual velocity of the air in a given latitude, as over the city of Washington or again in the tropics, as over the Barbadoes, we shall find the following facts: At the ground in Washington the wind averages about six meters per second eastward; at an elevation of 2,000 meters the eastward velocity is about eighteen meters per second; at 4,000, it is about twenty-four meters per second; at 6,000, it is about twenty-eight meters per second; and at 10,000, it is about thirty-four meters per second.

Above this level the air moves eastward at a rate of about forty meters per second; that is, ninety miles per hour. That is to say the eastward velocity or the eastward drift increases upwards with the distance from the ground. Now these velocities are maintained throughout the year with certain seasonal variations, though, of course, they are at times disturbed by certain local circulations as when storms disturb the normal movements of the air. The gyrating rings then which we first considered may be more accurately described as sheets of air parallel with the earth's surface which flow over each other at different speeds, the upper sheets flowing faster than the lower sheets. This may be practically seen in the cirrus clouds which are higher than the cumulus clouds, and move eastward as a whole with twice as great velocity. It is evident that we have here another type of vortex motion. What we first considered in the course of our definition was a vortex in which the inner rings rotate faster than the outer rings, but in this case of the torque in the northern hemisphere, for example, we have the upper rings moving faster than the lower rings. This apparent inconsistency may be reconciled by assuming that the axis of the upper rings instead of being a line, as in the other case, is really a spherical surface high above the ground outside the earth's surface, to which the actual motion has to be referred. Mathematically considered such a spherical sheet is in certain aspects equivalent to a line so far as the reference of motion is concerned; that is, the motion may be a maximum along a spherical sheet in one case, or a maximum around an axial line in the other case.

Turning now to the tropics and examining the motion of the air in a vertical section just as we did in the north temperate zone, we find that the westward motion is distributed very differently. At the surface the westward motion is greatest, and it decreases gradually on going upwards from the ground till at 10,000 meters or so it has decreased to zero, and above that region an eastward motion sets in, gradually increasing with the height. The westward branch of the torque then, is strongest at the surface and decreases upwards. The eastward branch of the torque is a minimum at the surface and increases upwards. We have several times referred to the latitude of 33° north and south of the equator as separating the eastward branch from the westward branch of the torque, but it has now been indicated that at about 10,000 meters above the tropics the westward branch changes into an eastward branch of the torque. As a matter of fact the surface which separates the westward branch from the eastward branch spans the tropics in an arch resting on the ground at 33° of latitude and crossing the equator at 10,000 or 12,000 meters above it. Beneath this arch the western torque is included with its maximum motion at the bottom; above this arch with a broad base in each temperate zone rises the eastward torque in which the velocity increases upward and gradually overspreads the tropics in the higher elevations, the northern branch reaching southward, and the southern branch reaching northward in a comparatively thin shell till they touch somewhere above the equator. All this circulation therefore constitutes a complex vortex which can be referred to distinct mathematical laws. If the atmosphere were willing to circulate in this simple manner it would not be difficult to adapt our mathematical analysis to it, but unfortunately, instead of moving so that the branches of this torque remain intact and retain their theoretical individuality, there is a continual interchange or passage of currents from one branch to the other in a rather irregular way which it will be necessary more closely to examine.

 

The Circulation on the Rough Rotating Earth

The circulation which we have been describing might possibly be set up on a perfectly smooth globe having the size and shape of the earth, but the presence of continents and ocean areas, the mountain ranges stretching north and south on the American and east and west on the Euro-Asiatic continent, facilitate the breaking of these theoretical branches of the torque into great circulating masses which interplay among each other. It is evident that the Rocky Mountains of North America and the Cordilleras of South America tend to stop the westward currents in the tropics and the eastward currents in the temperate zones. On the other hand, the Himalaya range in Asia tends to hold the westward current in the tropical zone and the eastward current in the temperate zone. There are thus certain places, that is, certain longitudes, where the currents tend to curl from the tropics into the temperate zones. A conspicuous instance of this occurs in the United States, where there is a continual outpouring of warm air from the Gulf of Mexico over the Mississippi and central valleys of the United States. While the trade winds in the tropics tend to blow from the northeast, it is known that immense masses of air move from the tropics over the United States from the south, quite contrary to the general principle; and similarly, though not so conspicuously, a case is found in South America and south Africa. On the contrary, the warm air in the lower levels over the Indian Ocean, whose winds are called monsoons, simply beats upon the great mountain ranges to the northward of India without penetrating the temperate zone in Siberia. In this way certain great circulations called centers of action form in each hemisphere. There is one over the middle Atlantic Ocean; another over the middle Pacific Ocean of the northern hemisphere; and there are other corresponding centers of action in the southern hemisphere. These are especially well marked during the summer time when the ocean is cool and the land air is warm. In the winter time the tendency is to form centers of action over the land areas instead of over the ocean areas, but the process is much more irregular, and in the United States it is exhibited chiefly by a succession of cold waves which traverse the United States from west to east. Referring to the center of action over the middle Atlantic Ocean in summer, we know that the winds near the American side are from the south or southwest. On the Atlantic Ocean in latitude 35° to 40° north the winds are blowing eastward, and in latitudes 25° to 30° they are blowing westward; on the European side they are blowing from the northwest and north. The consequence is that the United States is bathed during the summer with warm, moist winds in the eastern half, and with warm, dry winds in the western half of the continent. In Europe, on the contrary, the northerly winds prevail, and it follows that the American continent is warm during the summer while Europe is cool, and this is the cause of the annual migration of tourists from America to Europe instead of from Europe to America. The control of the climate of Europe by the American Gulf Stream is a myth. As a matter of fact the European climate is controlled by the great currents of circulation referred to these centers of action.

More generally, warm masses of air find their way from the tropics into the temperate zones by very irregular paths, and cold masses find their way from the northern latitudes into the temperate zones by very irregular paths. A similar statement applies to the circulations of the southern hemisphere. The disturbances in the general circulation which are produced by the land and ocean areas make it well-nigh impossible to reduce meteorology to any simple scientific system. The irregularities produced by the interaction of these warm and cold masses are so great that the problem of forecasting seems to bid defiance to any clear classification. The eastward drift over the United States is, of course, the basis of any possible forecasts, and the irregularities caused by the interpenetration of the warm and cold masses, one after the other under the action of gravitation, produce what we call our storms, but technically are called cyclones and anticyclones. It would be beyond my province to attempt to analyze the technical side of the theories of cyclones and anticyclones, and yet the subject of circulation would be so incomplete without at least alluding to the prominent attempts which have been made to solve these great questions that I shall venture a few remarks along this line.

The circulation of the air is classified as general and local, "general" applying to the whole hemisphere, of which some description has been given, and "local" as applying to the individual storms and their accompaniments. The local storms are known as cyclones and anticyclones, hurricanes, tornadoes and water spouts. They are all features or phases of the circulation and can be referred back to a few simple mathematical laws. Two attempts were made to solve the question of the general circulation, but the year 1896–7, which represents a new era in meteorology, when the international cloud observations were established under the leadership of Dr. Hildebrandsson, marks an epoch in the theory of the subject. I refer to those of Ferrel and Oberbeck regarding the general circulation. They had one picture in mind, namely, that of the simple canal, heated at one end, to which allusion was made in the early paragraphs of this lecture. They conceived the air to flow from the tropics northward towards the poles in the upper levels, and from the poles towards the equator in the lower levels, the northward current being separated from the southward current by a neutral plane along which there was no motion. Ferrel discussed the equations of motion adapted to the general hemisphere, and threw considerable light upon the subject. He conceived the rings of parallel 33° to move towards the poles with increasing velocity, and he made serious efforts to account for the fact that the velocity in higher latitudes is comparatively moderate instead of excessively great, as his equations demanded. If Ferrel derived an excessive velocity near the poles, Oberbeck, as a result of his complex integration, derived an excessive velocity in the upper levels over the tropics. Neither of these authors accounted for the reversal of direction from west to east at a moderate elevation, as 10,000 meters over the tropics, nor did they attempt to take into account the great irregularities in the circulation in an east and west direction, which we have described in discussing the centers of action. The result of the work of the Weather Bureau in the international cloud observations in the year 1896–7, was to destroy this theory of a neutral plane separating the upper northward current from the lower southward current. In place of that it was explained that these interchanging currents, instead of passing over each other at different levels, really interpenetrate and pass by each other on the same level; that is to say, warm air moves from the tropics towards the poles in all levels, and cold air from the poles towards the tropics in all levels. The first theory can be illustrated by sliding the fingers of the smooth hands over each other in opposite directions, while the second theory can be illustrated by sliding the fingers between one another on the same level; the fingers of the one hand will represent the warm currents and the fingers of the other hand the cold currents. This new view is really revolutionary because it renders inapplicable the integrations which were attempted by previous authors. Unfortunately the problem has become in this way so very complicated, that no one of sufficient ability has yet been found to carry out the necessary mathematical analysis with anything like fullness or precision. At present meteorologists are engaged, by means of balloon and kite ascensions, in determining the nature of the currents from the south and from the north which prevail in different localities. Europe has already done a great deal of work in this direction, and the United States has recently made a beginning. A few soundings have also been made over the Atlantic Ocean. Generally speaking, however, this is a great field of research which it will require much money and time to adequately complete. The circulation of the atmosphere, therefore, is a great and fascinating problem for future development, and indeed it may require more than one generation of scientists to bring it into subjection.

We have described the cold and warm currents as interpenetrating on the same levels like the fingers of the two opposite hands. Gravitation takes these warm and cold masses and seeks to make them interpenetrate yet more intimately, so that the warm masses will become more cooled, and the cold masses more warmed, and the isobars and isotherms coincide with each other and the gravity levels. It is a curious fact that masses of warm and cold air having any size are exceedingly reluctant to mix with one another; that is to say, the interchange of heat is a molecular process which naturally goes on slowly, and in accomplishing it, in the atmosphere, a great deal of energy must be expended. The great masses are first torn into shreds along their edges, and are gradually fritted away in the local cyclonic circulation. The energy that is felt in storms of any kind is merely an illustration of this thermodynamic process of interchanging temperature.

 

The Local Circulations

Historically speaking, the year 1896–7 marks the beginning of a period of transition in the history of local as well as general theoretical meteorology. There have been two schools of meteorology: one American, whose head is Ferrel, and one German, of which Guldberg and Mohn, Sprung, Oberbeck, Margules and Pockels are leaders. These two schools agreed in one particular, namely, in that they assumed that the cyclonic and anticyclonic circulations are symmetrical about a center. The first break in this theory was also made by Professor Bigelow in the cloud work of the international year, when it was shown that the distribution of warm and cold masses in the anticyclone was not symmetrical but asymmetrical. In the symmetrical theory the center of motion coincides with the center of heat or center of cold; in the asymmetrical theory the center of motion is located near the edge of the warm and cold masses. The actual cyclone is warm on the one side and cold on the other side of the center, and likewise the anticyclone is cold on one side of it and warm on the other side of it. The northerly cold current, therefore, has a cyclonic center on the east side of it and an anticyclonic center on the west side of it, while the southerly warm current has an anticyclonic center on the east side of it and a cyclonic center on the west side of it. These differences are also fundamental. Ferrel treated the equation of motion by one solution, quite similar to that which he applied to the general circulation of the hemisphere, and he found the vortical torque for the cyclone clockwise on the outer part, anticlockwise on the inner part, with complex lines of flow connecting them. The theoretical difficulties are quite obvious when we consider that such a vortex as Ferrel worked out is applicable only to a fixed mass of air; for example, put a mass of water in a cylindrical vessel and sprinkle sawdust in it so that the stream lines can be followed by the eye. If now heat is applied to the center it will boil along the stream lines indicated by Ferrel's vortex, and especially so if the glass vessel is rotating on its axis. This would make our cyclones storms in which the same mass of air is boiling over and over again along these fixed lines, whereas we have shown that the cyclonic circulation is simply built up by currents of air which are streaming through it in a very irregular way, and, anticipating the conclusion which we have reached in our research, it may be asserted that the cyclone, besides being asymmetrical, conforms only loosely to any known type of theoretical vortex. The German school of meteorologists also discussed the symmetrical vortex, but by another mathematical process. There are two other solutions of the second equation of motion, one of which was assumed to apply to the outer part and the other to the inner part of a cyclone. The solution for the outer part has no vertical current, while the circulation for the inner has a vertical current, quite like that in the vortical helix, such as may be illustrated by the ordinary tornado tube. Many attempts were made to join the outer part and inner part in a single set of equations, the results conforming very loosely to the observed facts in nature regarding the velocity and angular directions. It is not too much to say that neither of these systems of solution will find more than a very small application in practical meteorology. Ferrel discussed the three equations of motion, one by one, giving certain practical inferences which he found more or less illustrated in nature, but he never succeeded in uniting the three equations in one comprehensive system. The Germans approached more nearly a satisfactory solution, but as already stated, the assumption that cyclones and anticyclones are symmetrical, respectively, about warm and cold centers, is no longer tenable. We have already made the assertion that the asymmetrical cyclone, as it occurs in nature, does not conform satisfactorily to any homogeneous vortex. It will be possible to show how this is by giving a few details regarding waterspouts, tornadoes and hurricanes, which will lead up to this conclusion.

 

Local Vortices in the Earth's Atmosphere

A large waterspout was seen at Cottage City, Mass., in the Vineyard Sound, on August 19, 1896, about eight miles distant from Cottage City. Fortunately a series of good photographs was secured of the waterspout and its cloud, which together with the meteorological data, have enabled us to compute the dimensions and the velocities of motion in all parts of it by means of the vortex formulas. It happens that the same cloud developed two types of vortex, at short intervals of time between them. One is the funnel-shaped vortex and the other is the dumbbell-shaped vortex. Fig. 1 gives an illustration of a section

PSM V76 D453 Funnel shaped vortex.png

Fig. 1. Funnel-shaped Vortex.

through the funnel-shaped vortex, and shows the boundary of the several vortex tubes. The horizontal dimensions are multiplied by ten for the sake of showing the relative dimensions more plainly which exist from one tube to another. It will be noted that the distances between the successive tubes get smaller and smaller in a geometric ratio towards the axis. They concentrate at the lower part, and expand so that the lines become parallel to a horizontal plane in a region at the level corresponding to the base of the cloud. Fixing attention upon any one of these tubes, as the first or outer one, the theory indicates that a particle of air which is lying on that tube in the lowest level continues throughout its motion to follow the same tube. This particle rotates in a spiral about a central axis gradually rising from the ocean towards the cloud, and, rotating in larger and larger spirals, at last it flows out from the axis parallel to the surface of the cloud itself. PSM V76 D454 Dumbbell shaped vortex.pngFig. 2. Dumbbell-shaped Vortex. On this outer tube the particle at the sea is moved with a velocity of 22 meters per second and gradually rises upwards and changes its velocity through 20, 18, 15, 12, 7, 5, 2 meters per second quite near the surface of the cloud, and finally the velocity falls to zero. At the sea level the velocity is in a circular direction around the axis; at the cloud level it is moving in a radial direction directly away from the axis. On the outer tube having a large radius the velocities as already given are small, but on the same levels on tube No. 5 quite near the axis the velocities on the same levels become, respectively, 182, 159, 136, 110, 80, 44, 31, 14 meters per second near the cloud level, and they finally run out to zero. With such enormous velocities as 182 meters per second at the sea level, the causes of the turmoil and destructive effects which are always found in the case of waterspouts and tornadoes passing over the land are readily appreciated. Illustrations of the destructive effects of tornadoes are commonly accessible. The purpose of such a vortex is to lift a mass of air, as in a suction pump, from the surface of the ocean to the cloud, and in this case it is computed that 2,468 cubic meters of air are lifted in each second through each section of this vortex tube. These natural lifting pumps are evidently of great efficiency.

The dumbbell-shaped vortex operates on substantially the same principles, though the details are different. In this vortex the air begins at the sea level to flow inwards towards the axis in a spiral which contracts up to about 500 or 600 meters above the surface of the sea, and then it begins to expand as in the funnel-shaped vortex. The dumbbell-shaped vortex is really composed of two funnel-shaped vortices, the lower one pointing upward and the upper one pointing downward, meeting half way between the two planes of reference. This vortex is really a more efficient lifting pump than the other one just described, and it is found that 16,452 cubic meters of air are moved upwards through each tube per second, so that the dumbbell-shaped vortex is carrying 6.7 times as much air upward as the funnel-shaped vortex. A careful examination of this dumbbell-shaped vortex at Cottage City shows that the lowest sections are not fully developed. The outward curvature of the tube is plainly shown on the picture, but at sea level it is cut off or truncated by the friction of the tube against the water of the ocean. The cutting off of these vortices at some section above their theoretical lowest plane seems to play an important part in practical meteorology.

On May 27, 1896, a violent tornado of large dimensions passed over the city of St. Louis, causing great destruction in Lafayette Park and thence to the bridge over the Mississippi River. The enormous power of the forces which accompanied this vortex is shown on many pictures which were secured at that time. Large trees were twisted off

PSM V76 D455 Truncated dumbbell shaped vortex.png

Fig. 3. Truncated Dumbbell-shaped Vortex.

and stripped of their branches; buildings were overturned and destroyed in every conceivable way; heavy iron girders and stone work of the bridge were destroyed; and in short almost limitless powers seem to have been at the disposal of this great vortex. Fig. 3 shows a section of this vortex, the relative distance apart of the tubes, and the part which has been cut off or truncated at about one third of the distance from its lower plane of reference, several hundred meters below the surface of the ground. It has been shown that this St. Louis tornado was about 47 times as efficient as the large Cottage City waterspout in its lifting power, and that at the surface of the ground it developed somewhere between 150 and 250 meters per second; that is, 340 to 560 miles per hour. While it is not probable that these enormous theoretical velocities can develop near the center of a great tornado on account of the retarding effects of friction where the wind moves over a rough region like a city, yet it does show where the enormous power resides that is always observed in these conditions. It might develop, therefore, a pressure of 5,000 or 6,000 pounds per square foot. This is, of course, very much more than would be necessary to make all the destruction that has been noted.

Hurricanes such as are observed in the neighborhood of the West Indies, and the typhoon, which is the name of a hurricane in the neighborhood of the Philippine Islands and China Sea, are truncated dumbbell-shaped vortices built on exactly the same principles as the St. Louis tornado, only they are very much larger in their dimensions.

PSM V76 D456 Half section of a hurricane vortex.png

Fig. 4. Half Section of a Hurricane Vortex.

The tornado generally ends at a level something like 1,200 meters above the ground, and it is usually much less than half a mile in diameter. The hurricane, however, is probably 12,000 meters thick, and it extends several hundred miles in diameter. This makes the hurricane a very thin mass of air of broad extent, as compared with the word tornado, which is a relatively high mass of air and narrow in extent. We can construct the velocities in the hurricane from our meteorological data, and show that the winds blow at a certain angle, which conforms to the section that cuts off or truncates the vortex at a certain plane. These angles should be more fully explained. On the lowest plane the wind flows radially and directly towards the axis; on the uppermost plane it flows radially and directly away from the axis; at a middle section, half way between these two planes, it flows in circles tangentially around the axis. In passing from the lower plane to the upper plane the wind gradually makes a larger angle with the radius; first 10°, then 20°, then 30°, and so on up to 90° at the middle plane half way up the tube; then 100°, 110°, and so on up to 180°, which represents the wind flowing radially away from the axis. If now a vortex is truncated at a certain plane, all the winds on that plane will make a given angle with the radius. If a truncated plane is one third the distance up the axis then the wind will make an angle of 60° with the radius; that is, it will blow in at an angle of 30° from a circle. This is about the angle of the wind which observers have recorded in the case of hurricanes, and hence it is proper to infer that the truncated section should be drawn at about the distance indicated from the lower plane.

The ocean cyclone is a mass of air still larger than the hurricane, circulating on practically the same vortical laws, but unfortunately it shows indications of not being able to follow the law strictly, especially in the inner portions of it. The outer part of a strong ocean cyclone, where the barometer drops to 28 inches of pressure at the center, is very much like an enormous hurricane in its formation, but near the center the angles and the velocities begin to break away from the pure vortex law. This is probably due to the great extent of the wind areas, and consequently the congestion, and to the fact that the ocean cyclone is not deep enough, although it may be 3 or 4 miles high, to carry out fully the requirements of so large a vortex of a pure type. It is known that hurricanes are vortices which are 6 or 7 miles deep. The large ocean cyclone is probably not more than 4 miles deep, and the great land cyclone is rarely more than 2 or 3 miles deep.

The land cyclones in the United States conform to the pure vortex law less perfectly than does the ocean cyclone. The pressure in the land cyclone usually stops at about 29 inches near the center. Its depth is usually about 2 or 3 miles. It may cover a diameter of 2,000 miles. These dimensions are evidently unfavorable for the development of a pure vortex. Furthermore, the distribution of the temperature in the land cyclone is entirely different from that in the pure hurricane, and this too prevents the land cyclone from developing according to the perfect law. Furthermore, the cyclones of the temperate zone develop in the lower levels of the great eastward drift. In these lower levels the eastward velocity of the drift is not very high; something like ten meters per second. At the height of two or three miles the eastward drift is something like twenty to forty meters per second. It becomes evident, then, that a vortex which develops in the lower levels, from any set of causes, must lift its head into a rapidly flowing stream of air, and this necessarily will tend to break down the intruding head by stripping off portions of it and detaching the upper portions of the vortex from the lower portions. Now a vortex can not develop except as a complete individual. If it is intruded upon by cutting off the lower section, as in the hurricane over the ocean, or by the upper sections thrusting themselves into the stream of the rapidly flowing eastward drift, it is evident that this is a sufficient cause for the partial destruction of the vortex system. In the theoretical vortex, above the middle section, the wind has an outward component increasing with the height, as already explained. Below this section it has in every cyclone an inward component. Now as a result of the cloud observations which were undertaken by the U. S. Weather Bureau during the international cloud year 1896–7, in which between 6,000 and 7,000 observations were made by means of theodolites upon the direction of motion in the different cloud levels, it was found that there was an inward component over the cyclones in all levels from the ground up to four or five miles high. The strongest inward component was in the strata cumulus levels about two miles above the ground. Above this level and below it there was a radial inward velocity of a certain value corresponding to each level. There was no clear indication that the inward component in the lower levels reversed to an outward component in the upper levels, and it looked as if the intruding vortex of the lower levels did not succeed in reaching the middle plane where theoretically the outward component begins to develop. It looked as if this vortical system was so stripped of its natural features, by the action of its intrusion into the eastward drift, that only the lower half of the vortex really survived, and that there was an insistent struggle of the rotating cyclone with this eastward drift for the mastery. In a word, the upper sections of the vortex were stripped bare, and they gradually died out at the height of three or four miles within the eastward drift. What remains then is a set of stream lines in the lower levels which have certain features in harmony with the pure vortex system, though only roughly conforming to them, and which in the upper levels is broken down into a very imperfect kind of vortex. It should be said in passing that it is very difficult, on account of the prevailing clouds which occur in the cyclones of the United States, to get satisfactory measures of the cloud motions in the upper levels. Cumulus clouds develop strongly below the one-mile level, and above them it is possible to get the cloud motions in the higher levels only through the more or less occasional rifts in the lower cloud sheets. It is therefore very desirable that an extensive campaign of theodolite measurements of cloud motions in the upper levels of cyclones be instituted, in order to carry out much more fully the details of the discussion which have been suggested in this fundamental research.

 

Temperature Distribution

Having now described the general and local circulations in the temperate and tropical zones, it is important to make some further remarks regarding the distribution of temperature in those regions, also including the distribution of temperature in the sun itself. The circulations which take place are accompanied by certain changes of temperature in a vertical direction, called temperature gradients, which are characteristic of them. If a cubic centimeter of air at the sea level is lifted up to higher levels, so that it cools simply by the expansion of its own mass, and there is no mixture of warmer or colder air with it from the outside, then the temperature will fall 9.87° Centigrade for every 1,000 meters. Now it is found by balloon observations that the temperature gradients in different regions do not conform to this fundamental rule, which is called the law of adiabatic expansion. In the tropics in the lower levels this rate is very nearly approached, but there is a considerable deviation from it in the upper levels. In the temperate zones the normal vertical temperature gradient is only about 5.40° Centigrade, though it may be considerably more or considerably less according to the circumstances. It may be generally said that, except in restricted regions, the air does not cool as fast in going upwards as it should if it were caused by mere vertical expansion. The upper levels of the air are too warm; warmer than they should be if that law prevailed. In the temperate zones they are very much too warm, and that is why the vertical gradient is less than it should be according to that law. The fact is that the warm masses of air which flow from the tropics towards the poles retain their heat above what they should have for the given latitude, and in that way the upper levels of the atmosphere are maintained at a considerably higher heat than would be expected. When the air has once cooled to about 70° below zero, Centigrade, it seems disinclined to cool much further, and in the levels from 12,000 to 16,000 meters high there has been discovered a tendency for the air to be somewhat warmer than it is in the levels below, say from 8,000 to 12,000 meters high. It is generally thought that this phenomenon is due to radiation in some of its effects, but it is still a subject of discussion. If we should assume as the average vertical gradient for the entire atmosphere a rate of about 7° Centigrade per 1,000 meters then we should find that the temperatures in the tropics fall off too fast, and in the temperate zones too slow to conform to this average gradient. Now the mathematical law shows that if the lower levels of the atmosphere are relatively too warm for the upper levels there will be a westward drift as in the tropics, and if the upper levels are too warm relatively for the lower levels there will be an eastward drift as in the temperate zones. Speaking a little more broadly still, in order to avoid discontinuity, that is to say, changes by jumps in the atmosphere as regards the barometric pressure at the different levels, since the warm air has less density than the cold air, it follows that the warm air must move faster over the surface of the earth than does the cold air. Hence it is that in the tropics the air is too warm for its altitude, and it must move off faster than it otherwise would in the tropics. The westward drift in the lower levels compensates for this excessive temperature, and in the upper levels of the temperate zones the excess of motion compensates for the higher temperature. We find exactly the same principle working in the formation of hurricanes and tornadoes. Hurricanes develop in the northern hemisphere in the late summer and early autumn, and this is the season when the cool air of the northern latitudes begins to spread southward towards the equator as the sun begins its southward march into the southern hemisphere. At first the cool air flows over the warm air in the higher levels. This in a general way increases the vertical temparature gradient, and induces a more lively movement in the lower levels. In certain localities, in order to keep up the vertical continuity of barometric pressure, the warm air slides out radially in all directions, where conditions are right, and this movement first induces the vortical action in the upper sections of the hurricane which is gradually propagated, when it is highly developed, to the surface. Tornadoes are formed in somewhat a similar way, but in this case the cold and warm masses lie side by side on the same level, though there is a tendency for the cold air to overflow the warm air. The sliding action of the warm air against the cold sheet is the first incentive to the curling-up process which culminates in a tornado. In the ordinary cyclones the temperature distribution is such that the vertical gradient is about the same in the cold as in the warm mass, taken separately, though there are moderate variations in the different quadrants surrounding the high and the low areas of pressure. The warm air then overflows the cold air in two branches, and the cold air underflows the warm air in two branches. This tends to induce vortical action, but as already explained it is retarded, and the development is very imperfect on account of its intrusion into the eastward drift.

While our knowledge of the distribution of velocity and temperature in the atmosphere of the sun is much less perfect than it is of the atmosphere of the earth, we have yet definite knowledge regarding several important features. Apparently the sun's atmosphere does not operate in the same way that we have found to be the method of the circulation of the atmosphere of the earth. It is quite easy to see that these two atmospheres should work in a very different way. The atmosphere of the earth is really a thin shell of air heated in one zone by the solar radiation falling upon it, and then this thin shell simply slides around over the surface of the earth according to the laws which have been described. In the case of the atmosphere of the sun we have no definite knowledge as to its depth. It is proper to infer, from the law of pressure and mass, that the density near the center is such that the interior of the solar mass consists of a nucleus in a highly viscous or even solid state. Such a nucleus may be only one third of the diameter of the sun, but as the radius of the sun is 694,800 kilometers it would make a nucleus of about 400,000 or 500,000 kilometers in diameter. Above this the shell of the sun would be something like 400,000 kilometers thick, that is, about 250,000 miles. Our observations can not penetrate below the surface of the solar photosphere, and of course it is impossible to trace out the great currents which are undoubtedly operating within this enormously thick mass. On the surface we know from various sources that at the equator the solar mass drifts from east to west as we look at the sun's disc with a velocity such that the sun turns on its axis, as we see it, once in 26.68 days. This rotation of velocity falls off gradually towards the poles, until at the poles it takes something like 30 days to turn around. There is evidence to show that in the polar zones or near the poles there are certain variable velocities of rotation. These may belong to different sections in the sun's atmosphere. Our observations at the poles cut through the sun's atmosphere, as it were, parallel to the surface. At the equator our observations look down vertically through the sun's atmosphere. We can therefore near the poles get the same kind of observations at different solar levels. However this may be, the turbulence of motion seems to be much greater near the poles than near the equator. Within the sun's mass we can well imagine that many different periods of rotation, or of the daily angular velocity, actually exist. Looking at the solar surface as a unit, it consists of a huge wave whose crest advances around the equatorial regions at a considerably greater speed than in the polar regions. Now our mathematical analysis indicates that such a circulation can be maintained if the solar temperatures are greater in the polar regions than in the equatorial regions. That is a form of vortex, applicable to the solar mass, in which the velocities and temperatures are so connected together that the polar regions are warmer and have a slower angular velocity than the equatorial regions which are cooler with a greater angular velocity. This, therefore, is a condition of affairs practically the inverse of what we have been describing in the atmosphere of the earth. It is of course in some way associated with the great heat cauldron which is boiling inside the solar surface, where the heat accumulates and congests and finally works its way to the surface by means of this gigantic solar vortex. Within the great vortex there are innumerable minor vortices. These vortical tubes generally stretch from north to south perpendicular to the plane of the equator. These vortex tubes may be very irregular and broken up, but as a whole the sun may be described as a polarized mass throughout which the minor motions are nearly parallel to the plane of the equator.

 

Solar Phenomena

The different levels in the sun's atmosphere have received the following names: The lowest one which is visible is called the photosphere, and consists of mottled shapes like cumulus cloud forms, bright and dark areas being interspersed. Above this is the chromosphere, a layer of hydrogen and calcium and other gases 5,000 or 6,000 miles thick. The lower surface of the chromosphere is a reversing layer, so called, and is the level at which the dark lines of the solar spectrum are formed. Through these layers are projected jets of hydrogen and calcium flames which stretch out beyond the visible edge of the sun called prominences, and far beyond the region of the prominences extends the solar corona which reaches enormous distances into space. The corona is apparently composed of minute dust particles and ionized atoms and molecules held in certain positions by the action of electric and magnetic forces. The photosphere is penetrated in certain regions by solar spots which extend from the upper levels of the photosphere into the interior. It has been shown by recent photographs taken at the Mount Wilson Observatory that the sun spots are closely associated with motions so like those pertaining to the sections in a dumbbell-shaped vortex that the analogy appears to be very complete. If this is so, then terrestrial meteorology becomes intimately connected with solar meteorology in many of its features, in spite of the great differences of temperature. The average temperature of the earth's atmosphere may be taken as about 15° Centigrade below zero. The surface of the photosphere is apparently between 7,000° and 8,000° Centigrade, and the sun's temperature increases to more than 10,000° near the nucleus, though the gradient is not yet known. Taking the sun spot region as a whole, the sun spot belts form near latitude 30° north and south of the equator and they gradually drift towards the equator in the course of about eleven years, when new spot belts begin to form. The same is true of the faculæ which are closely associated with sun spots. The circulation within the sun spot belt is from the surface downwards, while the spots drift as a whole towards the equator. This indicates, therefore, descent into the sun from the surface in the neighborhood of the equatorial regions, and, of course, to compensate this, material must be projected from the interior outwards in the higher latitudes.

The prominences are hydrogen flames going through a periodic drift. They may be said to appear first in largest numbers in middle latitudes, and they seem to divide into two branches so far as the number of them is concerned. One branch drifts southward in the eleven-year period along with the spots and the faculæ. The other branch drifts poleward to the north and to the south, respectively. A study of the number of these prominences in different latitudes indicates that there is a periodic change in the apparent velocity of the rotation in the polar regions, fluctuating back and forth in about a mean value. Since the prominences have different elevations, and different levels in the sun have different velocities, it may well be that in the polar regions the prominences develop sometimes in the higher levels and sometimes in the lower levels, so that they actually drift eastward at different angular velocities according to their elevation. The spectroscope apparently indicates a certain angular velocity pertaining to special spectrum lines, which look like a fixed value for a given elevation, and at the same time it has been shown that hydrogen lines have different values from iron lines, and therefore the entire subject is open to an extensive investigation.

The atmosphere of the earth is filled with what is called atmospheric electricity. This consists of positive and negative charges of electricity distributed in a very complex way, depending upon temperature, vapor contents and barometric pressure. The distribution of electricity changes with the season of the year, and with the hour of the day, and differs from latitude to latitude, and from elevation to elevation above the same place. Similarly the sun's atmosphere is filled with electric charges. Every electric charge in motion produces magnetic field. If particles of electricity rotate about an axis, and parallel to a given plane, there will be a magnetic field perpendicular to that plane. These magnetic fields may occur at any temperature, provided the charge of electricity and the motion in a closed curve is at hand. If a ray of light in a strong magnetic field is looked at along the lines of force of the field, a single ray is split up into two lines slightly displaced and circularly polarized in opposite directions. If the line of light in the magnetic field is looked at perpendicular to the lines of the magnetic force, a single is split up into three or more lines. In the case of three lines the outside lines are displaced and polarized in one direction, while the middle line is not displaced but is polarized at right angles to the two side lines. These effects of the magnetic field upon a ray of light are called the Zeeman effect, and if these effects are seen it is strong evidence if not proof that the magnetic field has been acting upon the ray of light. The Mount Wilson Observatory has been able to show that the light which comes from the interior of the sun spot or vortex produces both types of the Zeeman effect, the two circularly polarized lines when one looks at the spot near the center of the solar disc; that is down the tube of the vortex; and the three plane polarized lines when one looks at the sun spot near the edge of the sun, that is, nearly at right angles to the sun spot vortex tube. At any rate enough has been shown to make it more than probable that magnetic field exists certainly in the solar spots, and probably throughout the mass of the sun where gyrations and internal vortices doubtless take place. If the sun spot produces a magnetic field strong enough to show the Zeeman effect at a distance of 93,000,000 miles, it is entirely reasonable to suppose that magnetic fields occur through the solar mass wherever there is actual circulation. It has already been intimated that the entire body of the sun consists of an enormous number of circulating tubes directed more or less perpendicular to the equator, and as a corollary the entire mass of the sun would be a magnetized sphere. The ends of these polarized circulations at the solar surface should develop an outside magnetic field to correspond with the interior. In my early researches of nearly twenty years ago it was shown that the lines in the solar corona are so distributed, especially at the time of minimum sun spot activity, as to indicate strongly that they were arranged around the sun as a magnetized sphere. It is not necessary here to review the many details which pointed to that conclusion. The great objection to that theory at the time in the minds of scientists consisted in the fact that the sun was too hot to be a magnetized sphere. It was pointed out by me that the earth is certainly a magnetized sphere, and that its interior has a very high temperature. Since those days the discovery of the ionization of matter, whereby dynamic forces of one kind or another disintegrate the atoms, of which molecules are composed, into their primal constituents, which are pure charges of electricity, and the demonstration that the free ions, positive or negative, as the case may be, wander about from place to place and produce magnetic field, have made this theory of the sun much more intelligible. The additional discovery of the Zeeman effect of magnetic field in the sun spots greatly strengthens my theory, and in fact it is not easy to see how solar phenomena can now be discussed on any other general basis.

The solar output shows itself in an irruption of prominences, in a very extended corona, and in an invisible radiation stretching out to almost unlimited distances in space. The polar magnetic field of the sun, of which the corona is an evidence, will expand to great distances from the center, and its strength may perhaps be detected as far as to the distance of the earth. Electromagnetic radiation stretches out over the solar sphere radially in every direction, a small pencil of the same falls upon the earth in its different positions along the orbit from day to day, and sets the circulation up in the earth's atmosphere which has been described. This solar radiation falling upon the earth's atmosphere is in part absorbed by it, so that the molecules and atoms yield up their ions, which by redistribution produce the observed phenomena of the earth's electric field, and also certain well-known variations in the strength of the earth's magnetic field. The entire subject is full of difficulties, but at the same time it possesses a fascination to the student such as pertains to very few branches of modern science. This same radiation of the sun falling upon the earth produces the temperatures which vary from place to place, from season to season, and from year to year, in a very complex series of changes which, taken as a whole, constitute what is called the earth's climate. There are many indications that this solar radiation, that is to say, the electromagnetic energy which the sun sends forth into space, is not exactly constant. The sun seems to be a variable star, the variation in its heat and light is the natural consequence of the incessant changes of temperature and pressure, in the circulation, the electricity and magnetism, which are going on within the solar mass. We have already been able to show from our studies of the barometric pressure, temperature and vapor pressure in different parts of the earth, especially of the United States, that there is a definite though complicated synchronism, which connects the variations of the solar action with the variation in the terrestrial climatic effects. This is a large subject which can not be properly undertaken in this lecture. It may be said in general that as the sun gets more energetic in some parts of its period, the temperatures in the earth's tropics are higher, and simultaneously in the temperate zones they are lower. At the same time the barometric pressures in the atmosphere of the earth centered around the Indian Ocean are higher, while in North and South America they are lower. In the Pacific states the temperatures increase with the solar energy, and in the central and eastern states they decrease. The solar impulse which produces these effects tends to precede the terrestrial exhibit which depends upon the solar impulse by some months, possibly by a year under certain conditions, and this anticipation of course promises an opportunity to develop what may become a rational ground for a seasonal forecast for terrestrial weather. The entire field of operations is very complicated, the circulation in both atmospheres tends to mask and make more complex the pure variation of the solar radiation, so that we must be very cautious in attempting to pronounce for or against certain tentative conclusions regarding this subject. It will probably require more than one generation of men to make practicable and popularize the result of this research. Mathematicians as well as laymen are cautioned to withhold negative evidence based upon half understood phenomena, because it is in fact very difficult to disentangle the net which nature has spread before us. The threads should not be torn and distorted by the bungling hands of those who have not the training required to unravel the several skeins which lead to the center of the great mesh. It is certainly not saying too much to assert that there is good ground for proceeding positively and firmly along this line of research, and the fact that it has attracted the attention of many commissions, international committees, scientific societies, observatories and institutions shows to what an extent the great problem has already commended itself to the favor of scientific men.