110. Dependence of the earth upon the sun.—There is no better introduction to the study of the sun than Byron's Ode to Darkness, beginning with the lines—

and proceeding to depict in vivid words the consequences of this extinction. The most matter-of-fact language of science agrees with the words of the poet in declaring the earth's dependence upon the sun for all those varied forms of energy which make it a fit abode for living beings. The winds blow and the rivers run; the crops grow, are gathered and consumed, by virtue of the solar energy. Factory, locomotive, beast, bird, and the human body furnish types of machines run by energy derived from the sun; and the student will find it an instructive exercise to search for kinds of terrestrial energy which are not derived either directly or indirectly from the sun. There are a few such, but they are neither numerous nor important.111. The sun's distance from the earth.—To the astronomer the sun presents problems of the highest consequence and apparently of very diverse character, but all tending toward the same goal: the framing of a mechanical explanation of the sun considered as a machine; what it is, and how it does its work. In the forefront of these problems stand those numerical determinations of distance, size, mass, density, etc., which we have already encountered in connection with the moon, but which must here be dealt with in a different manner, because the immensely greater distance of the sun makes impossible the resort to any such simple method as the triangle used for determining the moon's distance. It would be like determining the distance of a steeple a mile away by observing its direction first from one eye, then from the other; too short a base for the triangle. In one respect, however, we stand upon a better footing than in the case of the moon, for the mass of the earth has already been found (ChapterIV) as a fractional part of the sun's mass, and we have only to invert the fraction in order to find that the sun's mass is 329,000 times that of the earth and moon combined, or 333,000 times that of the earth alone.

If we could rely implicitly upon this number we might make it determine for us the distance of the sun through the law of gravitation as follows: It was suggested in §38 that Newton proved Kepler's three laws to be imperfect corollaries from the law of gravitation, requiring a little amendment to make them strictly correct, and below we give in the form of an equation Kepler's statement of the Third Law together with Newton's amendment of it. In these equations—

T = Periodic time of any planet;

a = One half the major axis of its orbit;

m = Its mass;

M = The mass of the sun;

k = The gravitation constant corresponding to the particular set of units in which T, a, m, and M are expressed.

(Kepler) a³/T² = h; (Newton) a³/T² = k (M + m).

Kepler's idea was: For every planet which moves around the sun, a³ divided by T² always gives the same quotient, h; and he did not concern himself with the significance of this quotient further than to note that if the particular a and T which belong to any planet—e.g., the earth—be taken as the units of length and time, then the quotient will be1. Newton, on the other hand, attached a meaning to the quotient, and showed that it is equal to the product obtained by multiplying the sum of the two masses, planet and sun, by a number which is always the same when we are dealing with the action of gravitation, whether it be between the sun and planet, or between moon and earth, or between the earth and a roast of beef in the butcher's scales, provided only that we use always the same units with which to measure times, distances, and masses.

Numerically, Newton's correction to Kepler's Third Law does not amount to much in the motion of the planets. Jupiter, which shows the greatest effect, makes the circuit of his orbit in 4,333 days instead of 4,335, which it would require if Kepler's law were strictly true. But in another respect the change is of the utmost importance, since it enables us to extend Kepler's law, which relates solely to the sun and its planets, to other attracting bodies, such as the earth, moon, and stars. Thus for the moon's motion around the earth we write—

(240,000)³/(27.32)² = k (1 + 1/81),

from which we may find that, with the units here employed, the earth's mass as the unit of mass, the mean solar day as the unit of time, and the mile as the unit of distance—

k = 1830 × 10¹⁰.

If we introduce this value of k into the corresponding equation, which represents the motion of the earth around the sun, we shall have—

a³/(365.25)² = 1830 × 10¹⁰ (333,000 + 1),

where the large number in the parenthesis represents the number of times the mass of the sun is greater than the mass of the earth. We shall find by solving this equation that a, the mean distance of the sun from the earth, is very approximately 93,000,000 miles.113. Another method of determining the sun's distance.—This will be best appreciated by a reference to Fig.17. It appears here that the earth makes its nearest approach to the orbit of Mars in the month of August, and if in any August Mars happens to be in opposition, its distance from the earth will be very much less than the distance of the sun from the earth, and may be measured by methods not unlike those which served for the moon. If now the orbits of Mars and the earth were circles having their centers at the sun this distance between them, which we may represent by D, would be the difference of the radii of these orbits—

D = a'' - a',

where the accents'',' represent Mars and the earth respectively. Kepler's Third Law furnishes the relation—

(a'')³/(T'')² = (a')³/(T')²;

and since the periodic times of the earth and Mars, T', T'', are known to a high degree of accuracy, these two equations are sufficient to determine the two unknown quantities, a', a''—i.e., the distance of the sun from Mars as well as from the earth. The first of these equations is, of course, not strictly true, on account of the elliptical shape of the orbits, but this can be allowed for easily enough.

In practice it is found better to apply this method of determining the sun's distance through observations of an asteroid rather than observations of Mars, and great interest has been aroused among astronomers by the discovery, in 1898, of an asteroid, or planet, Eros, which at times comes much closer to the earth than does Mars or any other heavenly body except the moon, and which will at future oppositions furnish a more accurate determination of the sun's distance than any hitherto available. Observations for this purpose are being made at the present time (October, 1900).

Many other methods of measuring the sun's distance have been devised by astronomers, some of them extremely ingenious and interesting, but every one of them has its weak point—e.g., the determination of the mass of the earth in the first method given above and the measurement of D in the second method, so that even the best results at present are uncertain to the extent of 200,000 miles or more, and astronomers, instead of relying upon any one method, must use all of them, and take an average of their results. According to Professor Harkness, this average value is 92,796,950 miles, and it seems certain that a line of this length drawn from the earth toward the sun would end somewhere within the body of the sun, but whether on the nearer or the farther side of the center, or exactly at it, no man knows.114. Parallax and distance.—It is quite customary among astronomers to speak of the sun's parallax, instead of its distance from the earth, meaning by parallax its difference of direction as seen from the center and surface of the earth—i.e., the angle subtended at the sun by a radius of the earth placed at right angles to the line of sight. The greater the sun's distance the smaller will this angle be, and it therefore makes a substitute for the distance which has the advantage of being represented by a small number, 8".8, instead of a large one.

The books abound with illustrations intended to help the reader comprehend how great is a distance of 93,000,000 miles, but a single one of these must suffice here. To ride 100 miles a day 365 days in the year would be counted a good bicycling record, but the rider who started at the beginning of the Christian era and rode at that rate toward the sun from the year 1 A.D. down to the present moment would not yet have reached his destination, although his journey would be about three quarters done. He would have crossed the orbit of Venus about the time of Charlemagne, and that of Mercury soon after the discovery of America.115. Size and density of the sun.—Knowing the distance of the sun, it is easy to find from the angle subtended by its diameter (32 minutes of arc) that the length of that diameter is 865,000 miles. We recall in this connection that the diameter of the moon's orbit is only 480,000 miles, but little more than half the diameter of the sun, thus affording abundant room inside the sun, and to spare, for the moon to perform the monthly revolution about its orbit, as shown in Fig.65.

In the same manner in which the density of the moon was found from its mass and diameter, the student may find from the mass and diameter of the sun given above that its mean density is 1.4 times that of water. This is about the same as the density of gravel or soft coal, and is just about one quarter of the average density of the earth.

We recall that the small density of the moon was accounted for by the diminished weight of objects upon it, but this explanation can not hold in the case of the sun, for not only is the density less but the force of gravity (weight) is there 28 times as great as upon the earth. The athlete who here weighs 175 pounds, if transported to the surface of the sun would weigh more than an elephant does here, and would find his bones break under his own weight if his muscles were strong enough to hold him upright. The tremendous pressure exerted by gravity at the surface of the sun must be surpassed below the surface, and as it does not pack the material together and make it dense, we are driven to one of two conclusions: Either the stuff of which the sun is made is altogether unlike that of the earth, not so readily compressed by pressure, or there is some opposing influence at work which more than balances the effect of gravity and makes the solar stuff much lighter than the terrestrial.116. Material of which the sun is made.—As to the first of these alternatives, the spectroscope comes to our aid and shows in the sun's spectrum (Fig.50) the characteristic line marked D, which we know always indicates the presence of sodium and identifies at least one terrestrial substance as present in the sun in considerable quantity. The lines marked C and F are produced by hydrogen, which is one of the constituents of water, E shows calcium to be present in the sun, b magnesium, etc. In this way it has been shown that about one half of our terrestrial elements, mainly the metallic ones, are present as gases on or near the sun's surface, but it must not be inferred that elements not found in this way are absent from the sun. They may be there, probably are there, but the spectroscopic proof of their presence is more difficult to obtain. Professor Rowland, who has been prominent in the study of the solar spectrum, says: "Were the whole earth heated to the temperature of the sun, its spectrum would probably resemble that of the sun very closely."

Some of the common terrestrial elements found in the sun are:

Whatever differences of chemical structure may exist between the sun and the earth, it seems that we must regard these bodies as more like than unlike to each other in substance, and we are brought back to the second of our alternatives: there must be some influence opposing the force of gravity and making the substance of the sun light instead of heavy, and we need not seek far to find it in—117. The heat of the sun.—That the sun is hot is too evident to require proof, and it is a familiar fact that heat expands most substances and makes them less dense. The sun's heat falling upon the earth expands it and diminishes its density in some small degree, and we have only to imagine this process of expansion continued until the earth's diameter becomes 58 per cent larger than it now is, to find the earth's density reduced to a level with that of the sun. Just how much the temperature of the earth must be raised to produce this amount of expansion we do not know, neither do we know accurately the temperature of the sun, but there can be no doubt that heat is the cause of the sun's low density and that the corresponding temperature is very high.

Before we inquire more closely into the sun's temperature, it will be well to draw a sharp distinction between the two terms heat and temperature, which are often used as if they meant the same thing. Heat is a form of energy which may be found in varying degree in every substance, whether warm or cold—a block of ice contains a considerable amount of heat—while temperature corresponds to our sensations of warm and cold, and measures the extent to which heat is concentrated in the body. It is the amount of heat per molecule of the body. A barrel of warm water contains more heat than the flame of a match, but its temperature is not so high. Bearing in mind this distinction, we seek to determine not the amount of heat contained in the sun but the sun's temperature, and this involves the same difficulty as does the question, What is the temperature of a locomotive? It is one thing in the fire box and another thing in the driving wheels, and still another at the headlight; and so with the sun, its temperature is certainly different in different parts—one thing at the center and another at the surface. Even those parts which we see are covered by a veil of gases which produce by absorption the dark lines of the solar spectrum, and seriously interfere both with the emission of energy from the sun and with our attempts at measuring the temperature of those parts of the surface from which that energy streams.

In view of these and other difficulties we need not be surprised that the wildest discordance has been found in estimates of the solar temperature made by different investigators, who have assigned to it values ranging from 1,400° C. to more than 5,000,000° C. Quite recently, however, improved methods and a better understanding of the problem have brought about a better agreement of results, and it now seems probable that the temperature of the visible surface of the sun lies somewhere between 5,000° and 10,000° C., say 15,000° of the Fahrenheit scale.118. Determining the sun's temperature.—One ingenious method which has been used for determining this temperature is based upon the principle stated above, that every object, whether warm or cold, contains heat and gives it off in the form of radiant energy. The radiation from a body whose temperature is lower than 500° C. is made up exclusively of energy whose wave length is greater than 7,600 tenth meters, and is therefore invisible to the eye, although a thermometer or even the human hand can often detect it as radiant heat. A brick wall in the summer sunshine gives off energy which can be felt as heat but can not be seen. When such a body is further heated it continues to send off the same kinds (wave lengths) of energy as before, but new and shorter waves are added to its radiation, and when it begins to emit energy of wave length 7,500 or 7,600 tenth meters, it also begins to shine with a dull-red light, which presently becomes brighter and less ruddy and changes to white as the temperature rises, and waves of still shorter length are thereby added to the radiation. We say, in common speech, the body becomes first red hot and then white hot, and we thus recognize in a general way that the kind or color of the radiation which a body gives off is an index to its temperature. The greater the proportion of energy of short wave lengths the higher is the temperature of the radiating body. In sunlight the maximum of brilliancy to the eye lies at or near the wave length, 5,600 tenth meters, but the greatest intensity of radiation of all kinds (light included) is estimated to fall somewhere between green and blue in the spectrum at or near the wave length 5,000 tenth meters, and if we can apply to this wave length Paschen's law—temperature reckoned in degrees centigrade from the absolute zero is always equal to the quotient obtained by dividing the number 27,000,000 by the wave length corresponding to maximum radiation—we shall find at once for the absolute temperature of the sun's surface 5,400° C.

Paschen's law has been shown to hold true, at least approximately, for lower temperatures and longer wave lengths than are here involved, but as it is not yet certain that it is strictly true and holds for all temperatures, too great reliance must not be attached to the numerical result furnished by it.

119. The sun's surface.—A marked contrast exists between the faces of sun and moon in respect of the amount of detail to be seen upon them, the sun showing nothing whatever to correspond with the mountains, craters, and seas of the moon. The unaided eye in general finds in the sun only a blank bright circle as smooth and unmarked as the surface of still water, and even the telescope at first sight seems to show but little more. There may usually be found upon the sun's face a certain number of black patches called sun spots, such as are shown in Figs.66 to69, and occasionally these are large enough to be seen through a smoked glass without the aid of a telescope. When seen near the edge of the sun they are quite frequently accompanied, as in Fig.69, by vague patches called faculÆ (Latin, facula =a little torch), which look a little brighter than the surrounding parts of the sun. So, too, a good photograph of the sun usually shows that the central parts of the disk are rather brighter than the edge, as indeed we should expect them to be, since the absorption lines in the sun's spectrum have already taught us that the visible surface of the sun is enveloped by invisible vapors which in some measure absorb the emitted light and render it feebler at the edge where it passes through a greater thickness of this envelope than at the center. See Fig.70, where it is shown that the energy coming from the edge of the sun to the earth has to traverse a much longer path inside the vapors than does that coming from the center.

Examine the sun spots in the four photographs, Figs.66 to69, and note that the two spots which appear at the extreme left of the first photograph, very much distorted and foreshortened by the curvature of the sun's surface, are seen in a different part of the second picture, and are not only more conspicuous but show better their true shape.

120. The sun's rotation.—The changed position of these spots shows that the sun rotates about an axis at right angles to the direction of the spot's motion, and the position of this axis is shown in the figure by a faint line ruled obliquely across the face of the sun nearly north and south in each of the four photographs. This rotation in the space of three days has carried the spots from the edge halfway to the center of the disk, and the student should note the progress of the spots in the two later photographs, that of August 21st showing them just ready to disappear around the farther edge of the sun.

Plot accurately in one of these figures the positions of the spots as shown in the other three, and observe whether the path of the spots across the sun's face is a straight line. Is there any reason why it should not be straight?

These four pictures may be made to illustrate many things about the sun. Thus the sun's axis is not parallel to that of the earth, for the letters NS mark the direction of a north and south line across the face of the sun, and this line, of course, is parallel to the earth's axis, while it is evidently not parallel to the sun's axis. The group of spots took more than ten days to move across the sun's face, and as at least an equal time must be required to move around the opposite side of the sun, it is evident that the period of the sun's rotation is something more than 20 days. It is, in fact, rather more than 25 days, for this same group of spots reappeared again on the left-hand edge of the sun on September 5th.

121. Sun spots.—Another significant fact comes out plainly from the photographs. The spots are not permanent features of the sun's face, since they changed their size and shape very appreciably in the few days covered by the pictures. Compare particularly the photographs of August 14th and August 18th, where the spots are least distorted by the curvature of the sun's surface. By September 16th this group of spots had disappeared absolutely from the sun's face, although when at its largest the group extended more than 80,000 miles in length, and several of the individual spots were large enough to contain the earth if it had been dropped upon them. From Fig.67 determine in miles the length of the group on August 14th. Fig.71 shows an enlarged view of these spots as they appeared on August 17th, and in this we find some details not so well shown in the preceding pictures. The larger spots consist of a black part called the nucleus or umbra (Latin, shadow), which is surrounded by an irregular border called the penumbra (partial shadow), which is intermediate in brightness between the nucleus and the surrounding parts of the sun. It should not be inferred from the picture that the nucleus is really black or even dark. It shines, in fact, with a brilliancy greater than that of an electric lamp, but the background furnished by the sun's surface is so much brighter that by contrast with it the nucleus and penumbra appear relatively dark.

The bright shining surface of the sun, the background for the spots, is called the photosphere (Greek, light sphere), and, as Fig.71 shows, it assumes under a suitable magnifying power a mottled aspect quite different from the featureless expanse shown in the earlier pictures. The photosphere is, in fact, a layer of little clouds with darker spaces between them, and the fine detail of these clouds, their complicated structure, and the way in which, when projected against the background of a sun spot, they produce its penumbra, are all brought out in Fig.72. Note that the little patch in one corner of this picture represents North and South America drawn to the same scale as the sun spots.

122. FaculÆ.—We have seen in Fig.69 a few of the bright spots called faculÆ. At the telescope or in the ordinary photograph these can be seen only at the edge of the sun, because elsewhere the background furnished by the photosphere is so bright that they are lost in it. It is possible, however, by an ingenious application of the spectroscope to break up the sunlight into a spectrum in such a way as to diminish the brightness of this background, much more than the brightness of the faculÆ is diminished, and in this way to obtain a photograph of the sun's surface which shall show them wherever they occur, and such a photograph, showing faintly the spectral lines, is reproduced in Fig.73. The faculÆ are the bright patches which stretch inconspicuously across the face of the sun, in two rather irregular belts with a comparatively empty lane between them. This lane lies along the sun's equator, and it is upon either side of it between latitudes 5° and 40° that faculÆ seem to be produced. It is significant of their connection with sun spots that the spots occur in these particular zones and are rarely found outside them.

123. Invisible parts of the sun. The Corona.—Thus far we have been dealing with parts of the sun that may be seen and photographed under all ordinary conditions. But outside of and surrounding these parts is an envelope, or rather several envelopes, of much greater extent than the visible sun. These envelopes are for the most part invisible save at those times when the brighter central portions of the sun are hidden in a total eclipse.

Fig.74 is from a drawing, and Figs.75 and76 are from eclipse photographs showing this region, in which the most conspicuous object is the halo of soft light called the corona, that completely surrounds the sun but is seen to be of differing shapes and differing extent at the several eclipses here shown, although a large part of these apparent differences is due to technical difficulties in photographing, and reproducing an object with outlines so vague as those of the corona. The outline of the corona is so indefinite and its outer portions so faint that it is impossible to assign to it precise dimensions, but at its greatest extent it reaches out for several millions of miles and fills a space more than twenty times as large as the visible part of the sun. Despite its huge bulk, it is of most unsubstantial character, an airy nothing through which comets have been known to force their way around the sun from one side to the other, literally for millions of miles, without having their course influenced or their velocity checked to any appreciable extent. This would hardly be possible if the density even at the bottom of the corona were greater than that of the best vacuum which we are able to produce in laboratory experiments. It seems odd that a vacuum should give off so bright a light as the coronal pictures show, and the exact character of that light and the nature of the corona are still subjects of dispute among astronomers, although it is generally agreed that, in part at least, its light is ordinary sunlight faintly reflected from the widely scattered molecules composing the substance of the corona. It is also probable that in part the light has its origin in the corona itself. A curious and at present unconfirmed result announced by one of the observers of the eclipse of May 28, 1900, is that the corona is not hot, its effective temperature being lower than that of the instrument used for the observation.

124. The chromosphere.—Between the corona and the photosphere there is a thin separating layer called the chromosphere (Greek, color sphere), because when seen at an eclipse it shines with a brilliant red light quite unlike anything else upon the sun save the prominences which are themselves only parts of the chromosphere temporarily thrown above its surface, as in a fountain a jet of water is thrown up from the basin and remains for a few moments suspended in mid-air. Not infrequently in such a fountain foreign matter is swept up by the rush of the water—dirt, twigs, small fish, etc.—and in like manner the prominences often carry along with them parts of the underlying layers of the sun, photosphere, faculÆ, etc., which reveal their presence in the prominence by adding their characteristic lines to the spectrum, like that of the chromosphere, which the prominence presents when they are absent. None of the eclipse photographs (Figs.74 to76) show the chromosphere, because the color effect is lacking in them, but a great curving prominence may be seen near the bottom of Fig.75, and smaller ones at other parts of the sun's edge.125. Prominences.—Fig.77 shows upon a larger scale one of these prominences rising to a height of 160,000 miles above the photosphere; and another photograph, taken 18 minutes later, but not reproduced here, showed the same prominence grown in this brief interval to a stature of 280,000 miles. These pictures were not taken during an eclipse, but in full sunlight, using the same spectroscopic apparatus which was employed in connection with the faculÆ to diminish the brightness of the background without much enfeebling the brilliancy of the prominence itself. The dark base from which the prominence seems to spring is not the sun's edge, but a part of the apparatus used to cut off the direct sunlight.

Fig.78 contains a series of photographs of another prominence taken within an interval of 1 hour 47 minutes and showing changes in size and shape which are much more nearly typical of the ordinary prominence than was the very unusual change in the case of Fig.77.

The preceding pictures are from photographs, and with them the student may compare Fig.79, which is constructed from drawings made at the spectroscope by the German astronomer Zoellner. The changes here shown are most marked in the prominence at the left, which is shaped like a broken tree trunk, and which appears to be vibrating from one side to the other like a reed shaken in the wind. Such a prominence is frequently called an eruptive one, a name suggested by its appearance of having been blown out from the sun by something like an explosion, while the prominence at the right in this series of drawings, which appears much less agitated, is called by contrast with the other a quiescent prominence. These quiescent prominences are, as a rule, much longer-lived than the eruptive ones. One more picture of prominences (Fig.80) is introduced to show the continuous stretch of chromosphere out of which they spring.

Prominences are seen only at the edge of the sun, because it is there alone that the necessary background can be obtained, but they must occur at the center of the sun and elsewhere quite as well as at the edge, and it is probable that quiescent prominences are distributed over all parts of the sun's surface, but eruptive prominences show a strong tendency toward the regions of sun spots and faculÆ as if all three were intimately related phenomena.126. The sun as a machine.—Thus far we have considered the anatomy of the sun, dissecting it into its several parts, and our next step should be a consideration of its physiology, the relation of the parts to each other, and their function in carrying on the work of the solar organism, but this step, unfortunately, must be a lame one. The science of astronomy to-day possesses no comprehensive and well-established theory of this kind, but looks to the future for the solution of this the greatest pending problem of solar physics. Progress has been made toward its solution, and among the steps of this progress that we shall have to consider, the first and most important is the conception of the sun as a kind of heat engine.

In a steam engine coal is burned under the boiler, and its chemical energy, transformed into heat, is taken up by the water and delivered, through steam as a medium, to the engine, which again transforms and gives it out as mechanical work in the turning of shafts, the driving of machinery, etc. Now, the function of the sun is exactly opposite to that of the engine and boiler: it gives out, instead of receiving, radiant energy; but, like the engine, it must be fed from some source; it can not be run upon nothing at all any more than the engine can run day after day without fresh supplies of fuel under its boiler. We know that for some thousands of years the sun has been furnishing light and heat to the earth in practically unvarying amount, and not to the earth alone, but it has been pouring forth these forms of energy in every direction, without apparent regard to either use or economy. Of all the radiant energy given off by the sun, only two parts out of every thousand million fall upon any planet of the solar system, and of this small fraction the earth takes about one tenth for the maintenance of its varied forms of life and action. Astronomers and physicists have sought on every hand for an explanation of the means by which this tremendous output of energy is maintained century after century without sensible diminution, and have come with almost one mind to the conclusion that the gravitative forces which reside in the sun's own mass furnish the only adequate explanation for it, although they may be in some small measure re-enforced by minor influences, such as the fall of meteoric dust and stones into the sun.

Every boy who has inflated a bicycle tire with a hand pump knows that the pump grows warm during the operation, on account of the compression of the air within the cylinder. A part of the muscular force (energy) expended in working the pump reappears in the heat which warms both air and pump, and a similar process is forever going on in the sun, only in place of muscular force we must there substitute the tremendous attraction of gravitation, 28 times as great as upon the earth. "The matter in the interior of the sun must be as a shuttlecock between the stupendous pressure and the enormously high temperature," the one tending to compress and the other to expand it, but with this important difference between them: the temperature steadily tends to fall as the heat energy is wasted away, while the gravitative force suffers no corresponding diminution, and in the long run must gain the upper hand, causing the sun to shrink and become more dense. It is this progressive shrinking and compression of its molecules into a smaller space which supplies the energy contained in the sun's output of light and heat. According to Lord Kelvin, each centimeter of shrinkage in the sun's diameter furnishes the energy required to keep up its radiation for something more than an hour, and, on account of the sun's great distance, the shrinkage might go on at this rate for many centuries without producing any measurable effect in the sun's appearance.127. Gaseous constitution of the sun.—But Helmholtz's dynamical theory of the maintenance of the sun's heat, which we are here considering, includes one essential feature that is not sufficiently stated above. In order that the explanation may hold true, it is necessary that the sun should be in the main a gaseous body, composed from center to circumference of gases instead of solid or liquid parts. Pumping air warms the bicycle pump in a way that pumping water or oil will not.

The high temperature of the sun itself furnishes sufficient reason for supposing the solar material to be in the gaseous state, but the gas composing those parts of the sun below the photosphere must be very different in some of its characteristics from the air or other gases with which we are familiar at the earth, since its average density is 1,000 times as great as that of air, and its consistence and mechanical behavior must be more like that of honey or tar than that of any gas with which we are familiar. It is worth noting, however, that if a hole were dug into the crust of the earth to a depth of 15 or 20 miles the air at the bottom of the hole would be compressed by that above it to a density comparable with that of the solar gases.128. The sun's circulation.—It is plain that under the conditions which exist in the sun the outer portions, which can radiate their heat freely into space, must be cooler than the inner central parts, and this difference of temperature must set up currents of hot matter drifting upward and outward from within the sun and counter currents of cooler matter settling down to take its place. So, too, there must be some level at which the free radiation into outer space chills the hot matter sufficiently to condense its less refractory gases into clouds made up of liquid drops, just as on a cloudy day there is a level in our own atmosphere at which the vapor of water condenses into liquid drops which form the thin shell of clouds that hovers above the earth's surface, while above and below is the gaseous atmosphere. In the case of the sun this cloud layer is always present and is that part which we have learned to call the photosphere. Above the photosphere lies the chromosphere, composed of gases less easily liquefied, hydrogen is the chief one, while between photosphere and chromosphere is a thin layer of metallic vapors, perhaps indistinguishable from the top crust of the photosphere itself, which by absorbing the light given off from the liquid photosphere produces the greater part of the Fraunhofer lines in the solar spectrum.

From time to time the hot matter struggling up from below breaks through the photosphere and, carrying with it a certain amount of the metallic vapors, is launched into the upper and cooler regions of the sun, where, parting with its heat, it falls back again upon the photosphere and is absorbed into it. It is altogether probable that the corona is chiefly composed of fine particles ejected from the sun with velocities sufficient to carry them to a height of millions of miles, or even sufficient to carry them off never to return. The matter of the corona must certainly be in a state of the most lively agitation, its particles being alternately hurled up from the photosphere and falling back again like fireworks, the particles which make up the corona of to-day being quite a different set from those of yesterday or last week. It seems beyond question that the prominences and faculÆ too are produced in some way by this up-and-down circulation of the sun's matter, and that any mechanical explanation of the sun must be worked out along these lines; but the problem is an exceedingly difficult one, and must include and explain many other features of the sun's activity of which only a few can be considered here.129. The sun-spot period.—Sun spots come and go, and at best any particular spot is but short-lived, rarely lasting more than a month or two, and more often its duration is a matter of only a few days. They are not equally numerous at all times, but, like swarms of locusts, they seem to come and abound for a season and then almost to disappear, as if the forces which produced them were of a periodic character alternately active and quiet. The effect of this periodic activity since 1870 is shown in Fig.81, where the horizontal line is a scale of times, and the distance of the curve above this line for any year shows the relative number of spots which appeared upon the sun in that year. This indicates very plainly that 1870, 1883, and 1893 were years of great sun-spot activity, while 1879 and 1889 were years in which few spots appeared. The older records, covering a period of two centuries, show the same fluctuations in the frequency of sun spots and from these records curves (which may be found in Young's, The Sun) have been plotted, showing a succession of waves extending back for many years.

The sun-spot period is the interval of time from the crest or hollow of one wave to the corresponding part of the next one, and on the average this appears to be a little more than eleven years, but is subject to considerable variation. In accordance with this period there is drawn in broken lines at the right of Fig.81 a predicted continuation of the sun-spot curve for the first decade of the twentieth century. The irregularity shown by the three preceding waves is such that we must not expect the actual course of future sun spots to correspond very closely to the prediction here made; but in a general way 1901 and 1911 will probably be years of few sun spots, while they will be numerous in 1905, but whether more or less numerous than at preceding epochs of greatest frequency can not be foretold with any approach to certainty so long as we remain in our present ignorance of the causes which make the sun-spot period.

Determine from Fig.81 as accurately as possible the length of the sun-spot period. It is hard to tell the exact position of a crest or hollow of the curve. Would it do to draw a horizontal line midway between top and bottom of the curve and determine the length of the period from its intersections with the curve—e.g., in 1874 and 1885?

130. The sun-spot zones.—It has been already noted that sun spots are found only in certain zones of latitude upon the sun, and that faculÆ and eruptive prominences abound in these zones more than elsewhere, although not strictly confined to them. We have now to note a peculiarity of these zones which ought to furnish a clew to the sun's mechanism, although up to the present time it has not been successfully traced out. Just before a sun-spot minimum the few spots which appear are for the most part clustered near the sun's equator. As these spots die out two new groups appear, one north the other south of the sun's equator and about 25° or 30° distant from it, and as the period advances toward a maximum these groups shift their positions more and more toward the equator, thus approaching each other but leaving between them a vacant lane, which becomes steadily narrower until at the close of the period, when the next minimum is at hand, it reaches its narrowest dimensions, but does not altogether close up even then. In Fig.82 these relations are shown for the period falling between 1879 and 1890, by means of the horizontal lines; for each year one line in the northern and one in the southern hemisphere of the sun, their lengths being proportional to the number of spots which appeared in the corresponding hemisphere during the year, and their positions on the sun's disk showing the average latitude of the spots in question. It is very apparent from the figure that during this decade the sun's southern hemisphere was much more active than the northern one in the production of spots, and this appears to be generally the case, although the difference is not usually as great as in this particular decade.131. Influence of the sun-spot period.—Sun spots are certainly less hot than the surrounding parts of the sun's surface, and, in view of the intimate dependence of the earth upon the solar radiation, it would be in no way surprising if their presence or absence from the sun's face should make itself felt in some degree upon the earth, raising and lowering its temperature and quite possibly affecting it in other ways. Ingenious men have suggested many such kinds of influence, which, according to their investigations, appear to run in cycles of eleven years. Abundant and scanty harvests, cyclones, tornadoes, epidemics, rainfall, etc., are among these alleged effects, and it is possible that there may be a real connection between any or all of them and the sun-spot period, but for the most part astronomers are inclined to hold that there is only one case in which the evidence is strong enough to really establish a connection of this kind. The magnetic condition of the earth and its disturbances, which are called magnetic storms, do certainly follow in a very marked manner the course of sun-spot activity, and perhaps there should be added to this the statement that auroras (northern lights) stand in close relation to these magnetic disturbances and are most frequent at the times of sun-spot maxima.

Upon the sun, however, the influence of the spot period is not limited to things in and near the photosphere, but extends to the outermost limits of the corona. Determine from Fig.81 the particular part of the sun-spot period corresponding to the date of each picture of the corona and note how the pictures which were taken near times of sun-spot minima present a general agreement in the shape and extent of the corona, while the pictures taken at a time of maximum activity of the sun spots show a very differently shaped and much smaller corona.132. The law of the sun's rotation.—We have seen in a previous part of the chapter how the time required by the sun to make a complete rotation upon its axis may be determined from photographs showing the progress of a spot or group of spots across its disk, and we have now to add that when this is done systematically by means of many spots situated in different solar latitudes it leads to a very peculiar and extraordinary result. Each particular parallel of latitude has its own period of rotation different from that of its neighbors on either side, so that there can be no such thing as a fixed geography of the sun's surface. Every part of it is constantly taking up a new position with respect to every other part, much as if the Gulf of Mexico should be south of the United States this year, southeast of it next year, and at the end of a decade should have shifted around to the opposite side of the earth from us. A meridian of longitude drawn down the Mississippi Valley remains always a straight line, or, rather, great circle, upon the surface of the earth, while Fig.83 shows what would become of such a meridian drawn through the equatorial parts of the sun's disk. In the first diagram it appears as a straight line running down the middle of the sun's disk. Twenty-five days later, when the same face of the sun comes back into view again, after making a complete revolution about the axis, the equatorial parts will have moved so much faster and farther than those in higher latitudes that the meridian will be warped as in the second diagram, and still more warped after another and another revolution, as shown in the figure.

At least such is the case if the spots truly represent the way in which the sun turns round. There is, however, a possibility that the spots themselves drift with varying speeds across the face of the sun, and that the differences which we find in their rates of motion belong to them rather than to the photosphere. Just what happens in the regions near the poles is hard to say, for the sun spots only extend about halfway from the equator to the poles, and the spectroscope, which may be made to furnish a certain amount of information bearing upon the case, is not as yet altogether conclusive, nor are the faculÆ which have also been observed for this purpose.

The simple theory that the solar phenomena are caused by an interchange of hotter and cooler matter between the photosphere and the lower strata of the sun furnishes in its present shape little or no explanation of such features as the sun-spot period, the variations in the corona, the peculiar character of the sun's rotation, etc., and we have still unsolved in the mechanical theory of the sun one of the noblest problems of astronomy, and one upon which both observers and theoretical astronomers are assiduously working at the present time. A close watch is kept upon sun spots and prominences, the corona is observed at every total eclipse, and numerous are the ingenious methods which are being suggested and tried for observing it without an eclipse in ordinary daylight. Attempts, more or less plausible, have been made and are now pending to explain photosphere, spots and the reversing layer by means of the refraction of light within the sun's outer envelope of gases, and it seems altogether probable, in view of these combined activities, that a considerable addition to our store of knowledge concerning the sun may be expected in the not distant future.

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