63. The nature of eclipses.—Every planet has a shadow which travels with the planet along its orbit, always pointing directly away from the sun, and cutting off from a certain region of space the sunlight which otherwise would fill it. For the most part these shadows are invisible, but occasionally one of them falls upon a planet or some other body which shines by reflected sunlight, and, cutting off its supply of light, produces the striking phenomenon which we call an eclipse. The satellites of Jupiter, Saturn, and Mars are eclipsed whenever they plunge into the shadows cast by their respective planets, and Jupiter himself is partially eclipsed when one of his own satellites passes between him and the sun, and casts upon his broad surface a shadow too small to cover more than a fraction of it.

But the eclipses of most interest to us are those of the sun and moon, called respectively solar and lunar eclipses. In Fig.33 the full moon, M', is shown immersed in the shadow cast by the earth, and therefore eclipsed, and in the same figure the new moon, M, is shown as casting its shadow upon the earth and producing an eclipse of the sun. From a mere inspection of the figure we may learn that an eclipse of the sun can occur only at new moon—i.e., when the moon is on line between the earth and sun—and an eclipse of the moon can occur only at full moon. Why? Also, the eclipsed moon, M', will present substantially the same appearance from every part of the earth where it is at all visible—the same from North America as from South America—but the eclipsed sun will present very different aspects from different parts of the earth. Thus, at L, within the moon's shadow, the sunlight will be entirely cut off, producing what is called a total eclipse. At points of the earth's surface near J and K there will be no interference whatever with the sunlight, and no eclipse, since the moon is quite off the line joining these regions to any part of the sun. At places between J and L or K and L the moon will cut off a part of the sun's light, but not all of it, and will produce what is called a partial eclipse, which, as seen from the northern parts of the earth, will be an eclipse of the lower (southern) part of the sun, and as seen from the southern hemisphere will be an eclipse of the northern part of the sun.

The moon revolves around the earth in a plane, which, in the figure, we suppose to be perpendicular to the surface of the paper, and to pass through the sun along the line M'M produced. But it frequently happens that this plane is turned to one side of the sun, along some such line as PQ, and in this case the full moon would cut through the edge of the earth's shadow without being at any time wholly immersed in it, giving a partial eclipse of the moon, as is shown in the figure.

In what parts of the earth would this eclipse be visible? What kinds of solar eclipse would be produced by the new moon atQ? In what parts of the earth would they be visible?64. The shadow cone.—The shape and position of the earth's shadow are indicated in Fig.33 by the lines drawn tangent to the circles which represent the sun and earth, since it is only between these lines that the earth interferes with the free radiation of sunlight, and since both sun and earth are spheres, and the earth is much the smaller of the two, it is evident that the earth's shadow must be, in geometrical language, a cone whose base is at the earth, and whose vertex lies far to the right of the figure—in other words, the earth's shadow, although very long, tapers off finally to a point and ends. So, too, the shadow of the moon is a cone, having its base at the moon and its vertex turned away from the sun, and, as shown in the figure, just about long enough to reach the earth.

It is easily shown, by the theorem of similar triangles in connection with the known size of the earth and sun, that the distance from the center of the earth to the vertex of its shadow is always equal to the distance of the earth from the sun divided by 108, and, similarly, that the length of the moon's shadow is equal to the distance of the moon from the sun divided by 400, the moon's shadow being the smaller and shorter of the two, because the moon is smaller than the earth. The radius of the moon's orbit is just about 1/400th part of the radius of the earth's orbit—i.e., the distance of the moon from the earth is 1/400th part of the distance of the earth from the sun, and it is this "chance" agreement between the length of the moon's shadow and the distance of the moon from the earth which makes the tip of the moon's shadow fall very near the earth at the time of solar eclipses. Indeed, the elliptical shape of the moon's orbit produces considerable variations in the distance of the moon from the earth, and in consequence of these variations the vertex of the shadow sometimes falls short of reaching the earth, and sometimes even projects considerably beyond its farther side. When the moon's distance is too great for the shadow to bridge the space between earth and moon there can be no total eclipse of the sun, for there is no shadow which can fall upon the earth, even though the moon does come directly between earth and sun. But there is then produced a peculiar kind of partial eclipse called annular, or ring-shaped, because the moon, although eclipsing the central parts of the sun, is not large enough to cover the whole of it, but leaves the sun's edge visible as a ring of light, which completely surrounds the moon. Although, strictly speaking, this is only a partial eclipse, it is customary to put total and annular eclipses together in one class, which is called central eclipses, since in these eclipses the line of centers of sun and moon strikes the earth, while in ordinary partial eclipses it passes to one side of the earth without striking it. In this latter case we have to consider another cone called the penumbra—i.e., partial shadow—which is shown in Fig.33 by the broken lines tangent to the sun and moon, and crossing at the point V, which is the vertex of this cone. This penumbral cone includes within its surface all that region of space within which the moon cuts off any of the sunlight, and of course it includes the shadow cone which produces total eclipses. Wherever the penumbra falls there will be a solar eclipse of some kind, and the nearer the place is to the axis of the penumbra, the more nearly total will be the eclipse. Since the moon stands about midway between the earth and the vertex of the penumbra, the diameter of the penumbra where it strikes the earth will be about twice as great as the diameter of the moon, and the student should be able to show from this that the region of the earth's surface within which a partial solar eclipse is visible extends in a straight line about 2,100 miles on either side of the region where the eclipse is total. Measured along the curved surface of the earth, this distance is frequently much greater.

Is it true that if at any time the axis of the shadow cone comes within 2,100 miles of the earth's surface a partial eclipse will be visible in those parts of the earth nearest the axis of the shadow?65. Different characteristics of lunar and solar eclipses.—One marked difference between lunar and solar eclipses which has been already suggested, may be learned from Fig.33. The full moon, M', will be seen eclipsed from every part of the earth where it is visible at all at the time of the eclipse—that is, from the whole night side of the earth; while the eclipsed sun will be seen eclipsed only from those parts of the day side of the earth upon which the moon's shadow or penumbra falls. Since the point of the shadow at best but little more than reaches to the earth, the amount of space upon the earth which it can cover at any one moment is very small, seldom more than 100 to 200 miles in length, and it is only within the space thus actually covered by the shadow that the sun is at any given moment totally eclipsed, but within this region the sun disappears, absolutely, behind the solid body of the moon, leaving to view only such outlying parts and appendages as are too large for the moon to cover. At a lunar eclipse, on the other hand, the earth coming between sun and moon cuts off the light from the latter, but, curiously enough, does not cut it off so completely that the moon disappears altogether from sight even in mid-eclipse. The explanation of this continued visibility is furnished by the broken lines extending, in Fig.33, from the earth through the moon. These represent sunlight, which, entering the earth's atmosphere near the edge of the earth (edge as seen from sun and moon), passes through it and emerges in a changed direction, refracted, into the shadow cone and feebly illumines the moon's surface with a ruddy light like that often shown in our red sunsets. Eclipse and sunset alike show that when the sun's light shines through dense layers of air it is the red rays which come through most freely, and the attentive observer may often see at a clear sunset something which corresponds exactly to the bending of the sunlight into the shadow cone; just before the sun reaches the horizon its disk is distorted from a circle into an oval whose horizontal diameter is longer than the vertical one (see §50).

Query.—At a total lunar eclipse what would be the effect upon the appearance of the moon if the atmosphere around the edge of the earth were heavily laden with clouds?66. The track of the shadow.—We may regard the moon's shadow cone as a huge pencil attached to the moon, moving with it along its orbit in the direction of the arrowhead (Fig.34), and as it moves drawing a black line across the face of the earth at the time of total eclipse. This black line is the path of the shadow and marks out those regions within which the eclipse will be total at some stage of its progress. If the point of the shadow just reaches the earth its trace will have no sensible width, while, if the moon is nearer, the point of the cone will be broken off, and, like a blunt pencil, it will draw a broad streak across the earth, and this under the most favorable circumstances may have a breadth of a little more than 160 miles and a length of 10,000 or 12,000 miles. The student should be able to show from the known distance of the moon (240,000 miles) and the known interval between consecutive new moons (29.5 days) that on the average the moon's shadow sweeps past the earth at the rate of 2,100 miles per hour, and that in a general way this motion is from west to east, since that is the direction of the moon's motion in its orbit. The actual velocity with which the moon's shadow moves past a given station may, however, be considerably greater or less than this, since on the one hand when the shadow falls very obliquely, as when the eclipse occurs near sunrise or sunset, the shifting of the shadow will be very much greater than the actual motion of the moon which produces it, and on the other hand the earth in revolving upon its axis carries the spectator and the ground upon which he stands along the same direction in which the shadow is moving. At the equator, with the sun and moon overhead, this motion of the earth subtracts about 1,000 miles per hour from the velocity with which the shadow passes by. It is chiefly on this account, the diminished velocity with which the shadow passes by, that total solar eclipses last longer in the tropics than in higher latitudes, but even under the most favorable circumstances the duration of totality does not reach eight minutes at any one place, although it may take the shadow several hours to sweep the entire length of its path across the earth.

According to Whitmell the greatest possible duration of a total solar eclipse is 7m. 40s., and it can attain this limit only when the eclipse occurs near the beginning of July and is visible at a place 5° north of the equator.

The duration of a lunar eclipse depends mainly upon the position of the moon with respect to the earth's shadow. If it strikes the shadow centrally, as at M', Fig.33, a total eclipse may last for about two hours, with an additional hour at the beginning and end, during which the moon is entering and leaving the earth's shadow. If the moon meets the shadow at one side of the axis, as at P, the total phase of the eclipse may fail altogether, and between these extremes the duration of totality may be anything from two hours downward.

67. Relation of the lunar nodes to eclipses.—To show why the moon sometimes encounters the earth's shadow centrally and more frequently at full moon passes by without touching it at all, we resort to Fig.34, which represents a part of the orbit of the earth about the sun, with dates showing the time in each year at which the earth passes the part of its orbit thus marked. The orbit of the moon about the earth, MM', is also shown, with the new moon, M, casting its shadow toward the earth and the full moon, M', apparently immersed in the earth's shadow. But here appearances are deceptive, and the student who has made the observations set forth in ChapterIII has learned for himself a fact of which careful account must now be taken. The apparent paths of the moon and sun among the stars are great circles which lie near each other, but are not exactly the same; and since these great circles are only the intersections of the sky with the planes of the earth's orbit and the moon's orbit, we see that these planes are slightly inclined to each other and must therefore intersect along some line passing through the center of the earth. This line, N'N'', is shown in the figure, and if we suppose the surface of the paper to represent the plane of the earth's orbit, we shall have to suppose the moon's orbit to be tipped around this line, so that the left side of the orbit lies above and the right side below the surface of the paper. But since the earth's shadow lies in the plane of its orbit—i.e., in the surface of the paper—the full moon of March, M', must have passed below the shadow, and the new moon, M, must have cast its shadow above the earth, so that neither a lunar nor a solar eclipse could occur in that month. But toward the end of May the earth and moon have reached a position where the line N'N'' points almost directly toward the sun, in line with the shadow cones which hide it. Note that the line N'N'' remains very nearly parallel to its original position, while the earth is moving along its orbit. The full moon will now be very near this line and therefore very close to the plane of the earth's orbit, if not actually in it, and must pass through the shadow of the earth and be eclipsed. So also the new moon will cast its shadow in the plane of the ecliptic, and this shadow, falling upon the earth, produced the total solar eclipse of May 28, 1900.

N'N'' is called the line of nodes of the moon's orbit (§39), and the two positions of the earth in its orbit, diametrically opposite each other, at which N'N'' points exactly toward the sun, we shall call the nodes of the lunar orbit. Strictly speaking, the nodes are those points of the sky against which the moon's center is projected at the moment when in its orbital motion it cuts through the plane of the earth's orbit. Bearing in mind these definitions, we may condense much of what precedes into the proposition: Eclipses of either sun or moon can occur only when the earth is at or near one of the nodes of the moon's orbit. Corresponding to these positions of the earth there are in each year two seasons, about six months apart, at which times, and at these only, eclipses can occur. Thus in the year 1900 the earth passed these two points on June 2d and November 24th respectively, and the following list of eclipses which occurred in that year shows that all of them were within a few days of one or the other of these dates:

Eclipses of the Year 1900

68. Eclipse limits.—If the earth is exactly at the node at the time of new moon, the moon's shadow will fall centrally upon it and will produce an eclipse visible within the torrid zone, since this is that part of the earth's surface nearest the plane of its orbit. If the earth is near but not at the node, the new moon will stand a little north or south of the plane of the earth's orbit, and its shadow will strike the earth farther north or south than before, producing an eclipse in the temperate or frigid zones; or the shadow may even pass entirely above or below the earth, producing no eclipse whatever, or at most a partial eclipse visible near the north or south pole. Just how many days' motion the earth may be away from the node and still permit an eclipse is shown in the following brief table of eclipse limits, as they are called:

Solar Eclipse Limits

Lunar Eclipse Limits

From this table of eclipse limits we may draw some interesting conclusions about the frequency with which eclipses occur.69. Number of eclipses in a year.—Whenever the earth passes a node of the moon's orbit a new moon must occur at some time during the 2×16 days that the earth remains inside the limits where some kind of eclipse is certain, and there must therefore be an eclipse of the sun every time the earth passes a node of the moon's orbit. But, since there are two nodes past which the earth moves at least once in each year, there must be at least two solar eclipses every year. Can there be more than two? On the average, will central or partial eclipses be the more numerous?

A similar line of reasoning will not hold true for eclipses of the moon, since it is quite possible that no full moon should occur during the 20 days required by the earth to move past the node from the western to the eastern limit. This omission of a full moon while the earth is within the eclipse limits sometimes happens at both nodes in the same year, and then we have a year with no eclipse of the moon. The student may note in the list of eclipses for 1900 that the partial lunar eclipse of June 12th occurred 10 days after the earth passed the node, and was therefore within the doubtful zone where eclipses may occur and may fail, and corresponding to this position the eclipse was a very small one, only a thousandth part of the moon's diameter dipping into the shadow of the earth. By so much the year 1900 escaped being an illustration of a year in which no lunar eclipse occurred.

A partial eclipse of the moon will usually occur about a fortnight before or after a total eclipse of the sun, since the full moon will then be within the eclipse limit at the opposite node. A partial eclipse of the sun will always occur about a fortnight before or after a total eclipse of the moon.

70. Eclipse maps.—It is the custom of astronomers to prepare, in advance of the more important eclipses, maps showing the trace of the moon's shadow across the earth, and indicating the times of beginning and ending of the eclipses, as is shown in Fig.35. While the actual construction of such a map requires much technical knowledge, the principles involved are simple enough: the straight line passed through the center of sun and moon is the axis of the shadow cone, and the map contains little more than a graphical representation of when and where this cone meets the surface of the earth. Thus in the map, the "Path of Total Eclipse" is the trace of the shadow cone across the face of the earth, and the width of this path shows that the earth encountered the shadow considerably inside the vertex of the cone. The general direction of the path is from west to east, and the slight sinuousities which it presents are for the most part due to unavoidable distortion of the map caused by the attempt to represent the curved surface of the earth upon the flat surface of the paper. On either side of the Path of Total Eclipse is the region within which the eclipse was only partial, and the broken lines marked Begins at 3h., Ends at 3h., show the intersection of the penumbral cone with the surface of the earth at 3 P.M., Greenwich time. These two lines inclose every part of the earth's surface from which at that time any eclipse whatever could be seen, and at this moment the partial eclipse was just beginning at every point on the eastern edge of the penumbra and just ending at every point on the western edge, while at the center of the penumbra, on the Path of Total Eclipse, lay the shadow of the moon, an oval patch whose greatest diameter was but little more than 60 miles in length, and within which lay every part of the earth where the eclipse was total at that moment.

The position of the penumbra at other hours is also shown on the map, although with more distortion, because it then meets the surface of the earth more obliquely, and from these lines it is easy to obtain the time of beginning and end of the eclipse at any desired place, and to estimate by the distance of the place from the Path of Total Eclipse how much of the sun's face was obscured.

Let the student make these "predictions" for Washington, Chicago, London, and Algiers.

The points in the map marked First Contact, Last Contact, show the places at which the penumbral cone first touched the earth and finally left it. According to computations made as a basis for the construction of the map the Greenwich time of First Contact was 0h. 12.5m. and of Last Contact 5h. 35.6m., and the difference between these two times gives the total duration of the eclipse upon the earth—i.e., 5 hours 23.1 minutes.

71. Future eclipses.—An eclipse map of a different kind is shown in Fig.36, which represents the shadow paths of all the central eclipses of the sun, visible during the period 1900-1918 A.D., in those parts of the earth north of the south temperate zone. Each continuous black line shows the path of the shadow in a total eclipse, from its beginning, at sunrise, at the western end of the line to its end, sunset, at the eastern end, the little circle near the middle of the line showing the place at which the eclipse was total at noon. The broken lines represent similar data for the annular eclipses. This map is one of a series prepared by the Austrian astronomer, Oppolzer, showing the path of every such eclipse from the year 1200 B.C. to 2160 A.D., a period of more than three thousand years.

If we examine the dates of the eclipses shown in this map we shall find that they are not limited to the particular seasons, May and November, in which those of the year 1900 occurred, but are scattered through all the months of the year, from January to December. This shows at once that the line of nodes, N'N'', of Fig.34, does not remain in a fixed position, but turns round in the plane of the earth's orbit so that in different years the earth reaches the node in different months. The precession has already furnished us an illustration of a similar change, the slow rotation of the earth's axis, producing a corresponding shifting of the line in which the planes of the equator and ecliptic intersect; and in much the same way, through the disturbing influence of the sun's attraction, the line N'N'' is made to revolve westward, opposite to the arrowheads in Fig.34, at the rate of nearly 20° per year, so that the earth comes to each node about 19 days earlier in each year than in the year preceding, and the eclipse season in each year comes on the average about 19 days earlier than in the year before, although there is a good deal of irregularity in the amount of change in particular years.72. Recurrence of eclipses.—Before the beginning of the Christian era astronomers had found out a rough-and-ready method of predicting eclipses, which is still of interest and value. The substance of the method is that if we start with any eclipse whatever—e.g., the eclipse of May 28, 1900—and reckon forward or backward from that date a period of 18 years and 10 or 11 days, we shall find another eclipse quite similar in its general characteristics to the one with which we started. Thus, from the map of eclipses (Fig.36), we find that a total solar eclipse will occur on June 8, 1918, 18 years and 11 days after the one illustrated in Fig.35. This period of 18 years and 11 days is called saros, an ancient word which means cycle or repetition, and since every eclipse is repeated after the lapse of a saros, we may find the dates of all the eclipses of 1918 by adding 11 days to the dates given in the table of eclipses for 1900 (§67), and it is to be especially noted that each eclipse of 1918 will be like its predecessor of 1900 in character—lunar, solar, partial, total, etc. The eclipses of any year may be predicted by a similar reference to those which occurred eighteen years earlier. Consult a file of old almanacs.

The exact length of a saros is 223 lunar months, each of which is a little more than 29.5 days long, and if we multiply the exact value of this last number (see §60) by 223, we shall find for the product 6,585.32 days, which is equal to 18 years 11.32 days when there are four leap years included in the 18, or 18 years 10.32 days when the number of leap years is five; and in applying the saros to the prediction of eclipses, due heed must be paid to the number of intervening leap years. To explain why eclipses are repeated at the end of the saros, we note that the occurrence of an eclipse depends solely upon the relative positions of the earth, moon, and node of the moon's orbit, and the eclipse will be repeated as often as these three come back to the position which first produced it. This happens at the end of every saros, since the saros is, approximately, the least common multiple of the length of the year, the length of the lunar month, and the length of time required by the line of nodes to make a complete revolution around the ecliptic. If the saros were exactly a multiple of these three periods, every eclipse would be repeated over and over again for thousands of years; but such is not the case, the saros is not an exact multiple of a year, nor is it an exact multiple of the time required for a revolution of the line of nodes, and in consequence the restitution which comes at the end of the saros is not a perfect one. The earth at the 223d new moon is in fact about half a day's motion farther west, relative to the node, than it was at the beginning, and the resulting eclipse, while very similar, is not precisely the same as before. After another 18 years, at the second repetition, the earth is a day farther from the node than at first, and the eclipse differs still more in character, etc. This is shown in Fig.37, which represents the apparent positions of the disks of the sun and moon as seen from the center of the earth at the end of each sixth saros, 108 years, where the upper row of figures represents the number of repetitions of the eclipse from the beginning, marked 0, to the end, 72. The solar eclipse limits, 10, 16, 19 days, are also shown, and all those eclipses which fall between the 10-day limits will be central as seen from some part of the earth, those between 16 and 19 partial wherever seen, while between 10 and 16 they may be either total or partial. Compare the figure with the following description given by Professor Newcomb: "A series of such eclipses commences with a very small eclipse near one pole of the earth. Gradually increasing for about eleven recurrences, it will become central near the same pole. Forty or more central eclipses will then recur, the central line moving slowly toward the other pole. The series will then become partial, and finally cease. The entire duration of the series will be more than a thousand years. A new series commences, on the average, at intervals of thirty years."

A similar figure may be constructed to represent the recurrence of lunar eclipses; but here, in consequence of the smaller eclipse limits, we shall find that a series is of shorter duration, a little over eight centuries as compared with twelve centuries, which is the average duration of a series of solar eclipses.

One further matter connected with the saros deserves attention. During the period of 6,585.32 days the earth has 6,585 times turned toward the sun the same face upon which the moon's shadow fell at the beginning of the saros, but at the end of the saros the odd 0.32 of a day gives the earth time to make about a third of a revolution more before the eclipse is repeated, and in consequence the eclipse is seen in a different region of the earth, on the average about 116° farther west in longitude. Compare in Fig.36 the regions in which the eclipses of 1900 and 1918 are visible.

Is this change in the region where the repeated eclipse is visible, true of lunar eclipses as well as solar?73. Use of eclipses.—At all times and among all peoples eclipses, and particularly total eclipses of the sun, have been reckoned among the most impressive phenomena of Nature. In early times and among uncultivated people they were usually regarded with apprehension, often amounting to a terror and frenzy, which civilized travelers have not scrupled to use for their own purposes with the aid of the eclipse predictions contained in their almanacs, threatening at the proper time to destroy the sun or moon, and pointing to the advancing eclipse as proof that their threats were not vain. In our own day and our own land these feelings of awe have not quite disappeared, but for the most part eclipses are now awaited with an interest and pleasure which, contrasted with the former feelings of mankind, furnish one of the most striking illustrations of the effect of scientific knowledge in transforming human fear and misery into a sense of security and enjoyment.

But to the astronomer an eclipse is more than a beautiful illustration of the working of natural laws; it is in varying degree an opportunity of adding to his store of knowledge respecting the heavenly bodies. The region immediately surrounding the sun is at most times closed to research by the blinding glare of the sun's own light, so that a planet as large as the moon might exist here unseen were it not for the occasional opportunity presented by a total eclipse which shuts off the excessive light and permits not only a search for unknown planets but for anything and everything which may exist around the sun. More than one astronomer has reported the discovery of such planets, and at least one of these has found a name and a description in some of the books, but at the present time most astronomers are very skeptical about the existence of any such object of considerable size, although there is some reason to believe that an enormous number of little bodies, ranging in size from grains of sand upward, do move in this region, as yet unseen and offering to the future problems for investigation.

But in other directions the study of this region at the times of total eclipse has yielded far larger returns, and in the chapter on the sun we shall have to consider the marvelous appearances presented by the solar prominences and by the corona, an appendage of the sun which reaches out from his surface for millions of miles but is never seen save at an eclipse. Photographs of the corona are taken by astronomers at every opportunity, and reproductions of some of these may be found in ChapterX.

Annular eclipses and lunar eclipses are of comparatively little consequence, but any recorded eclipse may become of value in connection with chronology. We date our letters in a particular year of the twentieth century, and commonly suppose that the years are reckoned from the birth of Christ; but this is an error, for the eclipses which were observed of old and by the chroniclers have been associated with events of his life, when examined by the astronomers are found quite inconsistent with astronomic theory. They are, however, reconciled with it if we assume that our system of dates has its origin four years after the birth of Christ, or, in other words, that Christ was born in the year 4 B.C. A mistake was doubtless made at the time the Christian era was introduced into chronology. At many other points the chance record of an eclipse in the early annals of civilization furnishes a similar means of controlling and correcting the dates assigned by the historian to events long past.