158. Visitors in the solar system.—All of the objects—sun, moon, planets, stars—which we have thus far had to consider, are permanent citizens of the sky, and we have no reason to suppose that their present appearance differs appreciably from what it was 1,000 years or 10,000 years ago. But there is another class of objects—comets, meteors—which appear unexpectedly, are visible for a time, and then vanish and are seen no more. On account of this temporary character the astronomers of ancient and mediÆval times for the most part refused to regard them as celestial bodies but classed them along with clouds, fogs, Jack-o'-lanterns, and fireflies, as exhalations from the swamps or the volcano; admitting them to be indeed important as harbingers of evil to mankind, but having no especial significance for the astronomer.

The comet of 1618 A.D. inspired the lines—

which, according to White (History of the Doctrine of Comets), were to be taught in all seriousness to peasants and school children.

It was by slow degrees, and only after direct measurements of parallax had shown some of them to be more distant than the moon, that the tide of old opinion was turned and comets were transferred from the sublunary to the celestial sphere, and in more recent times meteors also have been recognized as coming to us from outside the earth. A meteor, or shooting star as it is often called, is one of the commonest of phenomena, and one can hardly watch the sky for an hour on any clear and moonless night without seeing several of those quick flashes of light which look as if some star had suddenly left its place, dashed swiftly across a portion of the sky and then vanished. It is this misleading appearance that probably is responsible for the name shooting star.

159. Comets.—Comets are less common and much longer-lived than meteors, lasting usually for several weeks, and may be visible night after night for many months, but never for many years, at a time. During the last decade there is no year in which less than three comets have appeared, and 1898 is distinguished by the discovery of ten of these bodies, the largest number ever found in one year. On the average, we may expect a new comet to be found about once in every ten weeks, but for the most part they are small affairs, visible only in the telescope, and a fine large one, like Donati's comet of 1858 (Fig.101), or the Great Comet of September, 1882, which was visible in broad daylight close beside the sun, is a rare spectacle, and as striking and impressive as it is rare.

Note in Fig.102 the great variety of aspect presented by some of the more famous comets, which are here represented upon a very small scale.

Fig.103 is from a photograph of one of the faint comets of the year 1893, which appears here as a rather feeble streak of light amid the stars which are scattered over the background of the picture. An apparently detached portion of this comet is shown at the extreme left of the picture, looking almost like another independent comet. The clean, straight line running diagonally across the picture is the flash of a bright meteor that chanced to pass within the range of the camera while the comet was being photographed.

A more striking representation of a moderately bright telescopic comet is contained in Figs.104 and105, which present two different views of the same comet, showing a considerable change in its appearance. A striking feature of Fig.105 is the star images, which are here drawn out into short lines all parallel with each other. During the exposure of 2h. 20m. required to imprint this picture upon the photographic plate, the comet was continually changing its position among the stars on account of its orbital motion, and the plate was therefore moved from time to time, so as to follow the comet and make its image always fall at the same place. Hence the plate was continually shifted relative to the stars whose images, drawn out into lines, show the direction in which the plate was moved—i.e., the direction in which the comet was moving across the sky. The same effect is shown in the other photographs, but less conspicuously than here on account of their shorter exposure times.

These pictures all show that one end of the comet is brighter and apparently more dense than the other, and it is customary to call this bright part the head of the comet, while the brushlike appendage that streams away from it is called the comet's tail.160. The parts of a comet.—It is not every comet that has a tail, though all the large ones do, and in Fig.103 the detached piece of cometary matter at the left of the picture represents very well the appearance of a tailless comet, a rather large but not very bright star of a fuzzy or hairy appearance. The word comet means long-haired or hairy star. Something of this vagueness of outline is found in all comets, whose exact boundaries are hard to define, instead of being sharp and clean-cut like those of a planet or satellite. Often, however, there is found in the head of a comet a much more solid appearing part, like the round white ball at the center of Fig.106, which is called the nucleus of the comet, and appears to be in some sort the center from which its activities radiate. As shown in Figs.106 and107, the nucleus is sometimes surrounded by what are called envelopes, which have the appearance of successive wrappings or halos placed about it, and odd, spurlike projections, called jets, are sometimes found in connection with the envelopes or in place of them. These figures also show what is quite a common characteristic of large comets, a dark streak running down the axis of the tail, showing that the tail is hollow, a mere shell surrounding empty space.

The amount of detail shown in Figs.106 and107 is, however, quite exceptional, and the ordinary comet is much more like Fig.103 or104. Even a great comet when it first appears is not unlike the detached fragment in Fig.103, a faint and roundish patch of foggy light which grows through successive stages to its maximum estate, developing a tail, nucleus, envelopes, etc., only to lose them again as it shrinks and finally disappears.

161. The orbits of comets.—It will be remembered that Newton found, as a theoretical consequence of the law of gravitation, that a body moving under the influence of the sun's attraction might have as its orbit any one of the conic sections, ellipse, parabola, or hyperbola, and among the 400 and more comet orbits which have been determined every one of these orbit forms appears, but curiously enough there is not a hyperbola among them which, if drawn upon paper, could be distinguished by the unaided eye from a parabola, and the ellipses are all so long and narrow, not one of them being so nearly round as is the most eccentric planet orbit, that astronomers are accustomed to look upon the parabola as being the normal type of comet orbit, and to regard a comet whose motion differs much from a parabola as being abnormal and calling for some special explanation.

The fact that comet orbits are parabolas, or differ but little from them, explains at once the temporary character and speedy disappearance of these bodies. They are visitors to the solar system and visible for only a short time, because the parabola in which they travel is not a closed curve, and the comet, having passed once along that portion of it near the earth and the sun, moves off along a path which ever thereafter takes it farther and farther away, beyond the limit of visibility. The development of the comet during the time it is visible, the growth and disappearance of tail, nucleus, etc., depend upon its changing distance from the sun, the highest development and most complex structure being presented when it is nearest to the sun.

Fig.108 shows the path of the Great Comet of 1882 during the period in which it was seen, from September 3, 1882, to May 26, 1883. These dates—IX, 3, and V, 26—are marked in the figure opposite the parts of the orbit in which the comet stood at those times. Similarly, the positions of the earth in its orbit at the beginning of September, October, November, etc., are marked by the Roman numerals IX, X, XI, etc. The line SV shows the direction from the sun to the vernal equinox, and SO is the line along which the plane of the comet's orbit intersects the plane of the earth's orbit—i.e., it is the line of nodes of the comet orbit. Since the comet approached the sun from the south side of the ecliptic, all of its orbit, save the little segment which falls to the left of SO, lies below (south) of the plane of the earth's orbit, and the part which would be hidden if this plane were opaque is represented by a broken line.

162. Elements of a comet's orbit.—There is a theorem of geometry to the effect that through any three points not in the same straight line one circle, and only one, can be drawn. Corresponding to this there is a theorem of celestial mechanics, that through any three positions of a comet one conic section, and only one, can be passed along which the comet can move in accordance with the law of gravitation. This conic section is, of course, its orbit, and at the discovery of a comet astronomers always hasten to observe its position in the sky on different nights in order to obtain the three positions (right ascensions and declinations) necessary for determining the particular orbit in which it moves. The circle, to which reference was made above, is completely ascertained and defined when we know its radius and the position of its center. A parabola is not so simply defined, and five numbers, called the elements of its orbit, are required to fix accurately a comet's path around the sun. Two of these relate to the position of the line of nodes and the angle which the orbit plane makes with the plane of the ecliptic; a third fixes the direction of the axis of the orbit in its plane, and the remaining two, which are of more interest to us, are the date at which the comet makes its nearest approach to the sun (perihelion passage) and its distance from the sun at that date (perihelion distance). The date, September 17th, placed near the center of Fig.108, is the former of these elements, while the latter, which is too small to be accurately measured here, may be found from Fig.109 to be 0.82 of the sun's diameter, or, in terms of the earth's distance from the sun, 0.008.

Fig.109 shows on a large scale the shape of that part of the orbit near the sun and gives the successive positions of the comet, at intervals of 2/10 of a day, on September 16th and 17th, showing that in less than 10 hours—17.0 to 17.4—the comet swung around the sun through an angle of more than 240°. When at its perihelion it was moving with a velocity of 300 miles per second! This very unusual velocity was due to the comet's extraordinarily close approach to the sun. The earth's velocity in its orbit is only 19 miles per second, and the velocity of any comet at any distance from the sun, provided its orbit is a parabola, may be found by dividing this number by the square root of half the comet's distance—e.g., 300 miles per second equals 19÷v0.004.

Most of the visible comets have their perihelion distances included between 1/3 and 4/3 of the earth's distance from the sun, but occasionally one is found, like the second comet of 1885, whose nearest approach to the sun lies far outside the earth's orbit, in this case half-way out to the orbit of Jupiter; but such a comet must be a very large one in order to be seen at all from the earth. There is, however, some reason for believing that the number of comets which move around the sun without ever coming inside the orbit of Jupiter, or even that of Saturn, is much larger than the number of those which come close enough to be discovered from the earth. In any case we are reminded of Kepler's saying, that comets in the sky are as plentiful as fishes in the sea, which seems to be very little exaggerated when we consider that, according to Kleiber, out of all the comets which enter the solar system probably not more than 2 or 3 per cent are ever discovered.

163. Dimensions of comets.—The comet whose orbit is shown in Figs.108 and109 is the finest and largest that has appeared in recent years. Its tail, which at its maximum extent would have more than bridged the space between sun and earth (100,000,000 miles), is made very much too short in Fig.109, but when at its best was probably not inferior to that of the Great Comet of 1843, shown in Fig.110. As we shall see later, there is a peculiar and special relationship between these two comets.

The head of the comet of 1882 was not especially large—about twice the diameter of the ball of Saturn—but its nucleus, according to an estimate made by Dr. Elkin when it was very near perihelion, was as large as the moon. The head of the comet shown in Fig.107 was too large to be put in the space between the earth and the moon, and the Great Comet of 1811 had a head considerably larger than the sun itself. From these colossal sizes down to the smallest shred just visible in the telescope, comets of all dimensions may be found, but the smaller the comet the less the chance of its being discovered, and a comet as small as the earth would probably go unobserved unless it approached very close to us.164. The mass of a comet.—There is no known case in which the mass of a comet has ever been measured, yet nothing about them is more sure than that they are bodies with mass which is attracted by the sun and the planets, and which in its turn attracts both sun and planets and produces perturbations in their motion. These perturbations are, however, too small to be measured, although the corresponding perturbations in the comet's motion are sometimes enormous, and since these mutual perturbations are proportional to the masses of comet and planet, we are forced to say that, by comparison with even such small bodies as the moon or Mercury, the mass of a comet is utterly insignificant, certainly not as great as a ten-thousandth part of the mass of the earth. In the case of the Great Comet of 1882, if we leave its hundred million miles of tail out of account and suppose the entire mass condensed into its head, we find by a little computation that the average density of the head under these circumstances must have been less than 1/1500 of the density of air. In ordinary laboratory practice this would be called a pretty good vacuum. A striking observation made on September 17, 1882, goes to confirm the very small density of this comet. It is shown in Fig.109 that early on that day the comet crossed the line joining earth and sun, and therefore passed in transit over the sun's disk. Two observers at the Cape of Good Hope saw the comet approach the sun, and followed it with their telescopes until the nucleus actually reached the edge of the sun and disappeared, behind it as they supposed, for no trace of the comet, not even its nucleus, could be seen against the sun, although it was carefully looked for. Now, the figure shows that the comet passed between the earth and sun, and its densest parts were therefore too attenuated to cut off any perceptible fraction of the sun's rays. In other cases stars have been seen through the head of a comet, shining apparently with undimmed luster, although in some cases they seem to have been slightly refracted out of their true positions.165. Meteors.—Before proceeding further with the study of comets it is well to turn aside and consider their humbler relatives, the shooting stars. On some clear evening, when the moon is absent from the sky, watch the heavens for an hour and count the meteors visible during that time. Note their paths, the part of the sky where they appear and where they disappear, their brightness, and whether they all move with equal swiftness. Out of such simple observations with the unaided eye there has grown a large and important branch of astronomical science, some parts of which we shall briefly summarize here.

A particular meteor is a local phenomenon seen over only a small part of the earth's surface, although occasionally a very big and bright one may travel and be visible over a considerable territory. Such a one in December, 1876, swept over the United States from Kansas to Pennsylvania, and was seen from eleven different States. But the ordinary shooting star is much less conspicuous, and, as we know from simultaneous observations made at neighboring places, it makes its appearance at a height of some 75 miles above the earth's surface, occupies something like a second in moving over its path, and then disappears at a height of about 50 miles or more, although occasionally a big one comes down to the very surface of the earth with force sufficient to bury itself in the ground, from which it may be dug up, handled, weighed, and turned over to the chemist to be analyzed. The pieces thus found show that the big meteors, at least, are masses of stone or mineral; iron is quite commonly found in them, as are a considerable number of other terrestrial substances combined in rather peculiar ways. But no chemical element not found on the earth has ever been discovered in a meteor.166. Nature of meteors.—The swiftness with which the meteors sweep down shows that they must come from outside the earth, for even half their velocity, if given to them by some terrestrial volcano or other explosive agent, would send them completely away from the earth never to return. We must therefore look upon them as so many projectiles, bullets, fired against the earth from some outside source and arrested in their motion by the earth's atmosphere, which serves as a cushion to protect the ground from the bombardment which would otherwise prove in the highest degree dangerous to both property and life. The speed of the meteor is checked by the resistance which the atmosphere offers to its motion, and the energy represented by that speed is transformed into heat, which in less than a second raises the meteor and the surrounding air to incandescence, melts the meteor either wholly or in part, and usually destroys its identity, leaving only an impalpable dust, which cools off as it settles slowly through the lower atmosphere to the ground. The heating effect of the air's resistance is proportional to the square of the meteor's velocity, and even at such a moderate speed as 1 mile per second the effect upon the meteor is the same as if it stood still in a bath of red-hot air. Now, the actual velocity of meteors through the air is often 30 or 40 times as great as this, and the corresponding effect of the air in raising its temperature is more than 1,000 times that of red heat. Small wonder that the meteor is brought to lively incandescence and consumed even in a fraction of a second.167. The number of meteors.—A single observer may expect to see in the evening hours about one meteor every 10 minutes on the average, although, of course, in this respect much irregularity may occur. Later in the night they become more frequent, and after 2 A.M. there are about three times as many to be seen as in the evening hours. But no one person can keep a watch upon the whole sky, high and low, in front and behind, and experience shows that by increasing the number of observers and assigning to each a particular part of the sky, the total number of meteors counted may be increased about five-fold. So, too, the observers at any one place can keep an effective watch upon only those meteors which come into the earth's atmosphere within some moderate distance of their station, say 50 or 100 miles, and to watch every part of that atmosphere would require a large number of stations, estimated at something more than 10,000, scattered systematically over the whole face of the earth. If we piece together the several numbers above considered, taking 14 as a fair average of the hourly number of meteors to be seen by a single observer at all hours of the night, we shall find for the total number of meteors encountered by the earth in 24 hours, 14×5 ×10,000 ×24 =16,800,000. Without laying too much stress upon this particular number, we may fairly say that the meteors picked up by the earth every day are to be reckoned by millions, and since they come at all seasons of the year, we shall have to admit that the region through which the earth moves, instead of being empty space, is really a dust cloud, each individual particle of dust being a prospective meteor.

On the average these individual particles are very small and very far apart; a cloud of silver dimes each about 250 miles from its nearest neighbor is perhaps a fair representation of their average mass and distance from each other, but, of course, great variations are to be expected both in the size and in the frequency of the particles. There must be great numbers of them that are too small to make shooting stars visible to the naked eye, and such are occasionally seen darting by chance across the field of view of a telescope.168. The zodiacal light is an effect probably due to the reflection of sunlight from the myriads of these tiny meteors which occupy the space inside the earth's orbit. It is a faint and diffuse stream of light, something like the Milky Way, which may be seen in the early evening or morning stretching up from the sunrise or sunset point of the horizon along the ecliptic and following its course for many degrees, possibly around the entire circumference of the sky. It may be seen at any season of the year, although it shows to the best advantage in spring evenings and autumn mornings. Look for it.169. Great meteors.—But there are other meteors, veritable fireballs in appearance, far more conspicuous and imposing than the ordinary shooting star. Such a one exploded over the city of Madrid, Spain, on the morning of February 10, 1896, giving in broad sunlight "a brilliant flash which was followed ninety seconds later by a succession of terrific noises like the discharge of a battery of artillery." Fig.111 shows a large meteor which was seen in California in the early evening of July 27, 1894, and which left behind it a luminous trail or cloud visible for more than half an hour.

Not infrequently large meteors are found traveling together, two or three or more in company, making their appearance simultaneously as did the California meteor of October 22, 1896, which is described as triple, the trio following one another like a train of cars, and Arago cites an instance, from the year 1830, where within a short space of time some forty brilliant meteors crossed the sky, all moving in the same direction with a whistling noise and displaying in their flight all the colors of the rainbow.

The mass of great meteors such as these must be measured in hundreds if not thousands of pounds, and stories are current, although not very well authenticated, of even larger ones, many tons in weight, having been found partially buried in the ground. Of meteors which have been actually seen to fall from the sky, the largest single fragment recovered weighs about 500 pounds, but it is only a fragment of the original meteor, which must have been much more massive before it was broken up by collision with the atmosphere.

170. The velocity of meteors.—Every meteor, big or little, is subject to the law of gravitation, and before it encounters the earth must be moving in some kind of orbit having the sun at its focus, the particular species of orbit—ellipse, parabola, hyperbola—depending upon the velocity and direction of its motion. Now, the direction in which a meteor is moving can be determined without serious difficulty from observations of its apparent path across the sky made by two or more observers, but the velocity can not be so readily found, since the meteors go too fast for any ordinary process of timing. But by photographing one of them two or three times on the same plate, with an interval of only a tenth of a second between exposures, Dr. Elkin has succeeded in showing, in a few cases, that their velocities varied from 20 to 25 miles per second, and must have been considerably greater than this before the meteors encountered the earth's atmosphere. This is a greater velocity than that of the earth in its orbit, 19 miles per second, as might have been anticipated, since the mere fact that meteors can be seen at all in the evening hours shows that some of them at least must travel considerably faster than the earth, for, counting in the direction of the earth's motion, the region of sunset and evening is always on the rear side of the earth, and meteors in order to strike this region must overtake it by their swifter motion. We have here, in fact, the reason why meteors are especially abundant in the morning hours; at this time the observer is on the front side of the earth which catches swift and slow meteors alike, while the rear is pelted only by the swifter ones which follow it.

A comparison of the relative number of morning and evening meteors makes it probable that the average meteor moves, relative to the sun, with a velocity of about 26 miles per second, which is very approximately the average velocity of comets when they are at the earth's distance from the sun. Astronomers, therefore, consider meteors as well as comets to have the parabola and the elongated ellipse as their characteristic orbits.171. Meteor showers—The radiant.—There is evident among meteors a distinct tendency for individuals, to the number of hundreds or even hundreds of millions, to travel together in flocks or swarms, all going the same way in orbits almost exactly alike. This gregarious tendency is made manifest not only by the fact that from time to time there are unusually abundant meteoric displays, but also by a striking peculiarity of their behavior at such times. The meteors all seem to come from a particular part of the heavens, as if here were a hole in the sky through which they were introduced, and from which they flow away in every direction, even those which do not visibly start from this place having paths among the stars which, if prolonged backward, would pass through it. The cause of this appearance may be understood from Fig.112, which represents a group of meteors moving together along parallel paths toward an observer at D. Traveling unseen above the earth until they encounter the upper strata of its atmosphere, they here become incandescent and speed on in parallel paths, 1, 2, 3, 4, 5, 6, which, as seen by the observer, are projected back against the sky into luminous streaks that, as is shown by the arrowheads, b, c, d, all seem to radiate from the point a—i.e., from the point in the sky whose direction from the observer is parallel to the paths of the meteors.

Such a display is called a meteor shower, and the point a is called its radiant. Note how those meteors which appear near the radiant all have short paths, while those remote from it in the sky have longer ones. Query: As the night wears on and the stars shift toward the west, will the radiant share in their motion or will it be left behind? Would the luminous part of the path of any of these meteors pass across the radiant from one side to the other? Is such a crossing of the radiant possible under any circumstances? Fig.113 shows how the meteor paths are grouped around the radiant of a strongly marked shower. Select from it the meteors which do not belong to this shower.

Many hundreds of these radiants have been observed in the sky, each of which represents an orbit along which a group of meteors moves, and the relation of one of these orbits to that of the earth is shown in Fig.114. The orbit of the meteors is an ellipse extending out beyond the orbit of Uranus, but so eccentric that a part of it comes inside the orbit of the earth, and the figure shows only that part of it which lies nearest the sun. The Roman numerals which are placed along the earth's orbit show the position of the earth at the beginning of the tenth month, eleventh month, etc. The meteors flow along their orbit in a long procession, whose direction of motion is indicated by the arrow heads, and the earth, coming in the opposite direction, plunges into this stream and receives the meteor shower when it reaches the intersection of the two orbits. The long arrow at the left of the figure represents the direction of motion of another meteor shower which encounters the earth at this point.

Can you determine from the figure answers to the following questions? On what day of the year will the earth meet each of these showers? Will the radiant points of the showers lie above or below the plane of the earth's orbit? Will these meteors strike the front or the rear of the earth? Can they be seen in the evening hours?

From many of the radiants year after year, upon the same day or week in each year, there comes a swarm of shooting stars, showing that there must be a continuous procession of meteors moving along this orbit, so that some are always ready to strike the earth whenever it reaches the intersection of its orbit with theirs. Such is the explanation of the shower which appears each year in the first half of August, and whose meteors are sometimes called Perseids, because their radiant lies in the constellation Perseus, and a similar explanation holds for all the star showers which are repeated year after year.172. The Leonids.—There is, however, a kind of star shower, of which the Leonids (radiant in Leo) is the most conspicuous type, in which the shower, although repeated from year to year, is much more striking in some years than in others. Thus, to quote from the historian: "In 1833 the shower was well observed along the whole eastern coast of North America from the Gulf of Mexico to Halifax. The meteors were most numerous at about 5 A.M. on November 13th, and the rising sun could not blot out all traces of the phenomena, for large meteors were seen now and then in full daylight. Within the scope that the eye could contain, more than twenty could be seen at a time shooting in every direction. Not a cloud obscured the broad expanse, and millions of meteors sped their way across in every point of the compass. Their coruscations were bright, gleaming, and incessant, and they fell thick as the flakes in the early snows of December." But, so far as is known, none of them reached the ground. An illiterate man on the following day remarked: "The stars continued to fall until none were left. I am anxious to see how the heavens will appear this evening, for I believe we shall see no more stars."

An eyewitness in the Southern States thus describes the effect of this shower upon the plantation negroes: "Upward of a hundred lay prostrate upon the ground, some speechless and some with the bitterest cries, but with their hands upraised, imploring God to save the world and them. The scene was truly awful, for never did rain fall much thicker than the meteors fell toward the earth—east, west, north, and south it was the same." In the preceding year a similar but feebler shower from the same radiant created much alarm in France, and through the old historic records its repetitions may be traced back at intervals of 33 or 34 years, although with many interruptions, to October 12, 902, O.S., when "an immense number of falling stars were seen to spread themselves over the face of the sky like rain."

Such a star shower differs from the one repeated every year chiefly in the fact that its meteors, instead of being drawn out into a long procession, are mainly clustered in a single flock which may be long enough to require two or three or four years to pass a given point of its orbit, but which is far from extending entirely around it, so that meteors from this source are abundant only in those years in which the flock is at or near the intersection of its orbit with that of the earth. The fact that the Leonid shower is repeated at intervals of 33 or 34 years (it appeared in 1799, 1832-'33, 1866-'67) shows that this is the "periodic time" in its orbit, which latter must of course be an ellipse, and presumably a long and narrow one. It is this orbit which is shown in Fig.114, and the student should note in this figure that if the meteor stream at the point where it cuts through the plane of the earth's orbit were either nearer to or farther from the sun than is the earth there could be no shower; the earth and the meteors would pass by without a collision. Now, the meteors in their motion are subject to perturbations, particularly by the large planets Jupiter, Saturn, and Uranus, which slightly change the meteor orbit, and it seems certain that the changes thus produced will sometimes thrust the swarm inside or outside the orbit of the earth, and thus cause a failure of the shower at times when it is expected. The meteors were due at the crossing of the orbits in November, 1899 and 1900, and, although a few were then seen, the shower was far from being a brilliant one, and its failure was doubtless caused by the outer planets, which switched the meteors aside from the path in which they had been moving for a century. Whether they will be again switched back so as to produce future showers is at the present time uncertain.173. Capture of the Leonids.—But a far more striking effect of perturbations is to be found in Fig.115, which shows the relation of the Leonid orbit to those of the principal planets, and illustrates a curious chapter in the history of the meteor swarm that has been worked out by mathematical analysis, and is probably a pretty good account of what actually befell them. Early in the second century of the Christian era this flock of meteors came down toward the sun from outer space, moving along a parabolic orbit which would have carried it just inside the orbit of Jupiter, and then have sent it off to return no more. But such was not to be its fate. As it approached the orbit of Uranus, in the year 126 A.D., that planet chanced to be very near at hand and perturbed the motion of the meteors to such an extent that the character of their orbit was completely changed into the ellipse shown in the figure, and in this new orbit they have moved from that time to this, permanent instead of transient members of the solar system. The perturbations, however, did not end with the year in which the meteors were captured and annexed to the solar system, but ever since that time Jupiter, Saturn, and Uranus have been pulling together upon the orbit, and have gradually turned it around into its present position as shown in the figure, and it is chiefly this shifting of the orbit's position in the thousand years that have elapsed since 902 A.D. that makes the meteor shower now come in November instead of in October as it did then.

174. Breaking up a meteor swarm.—How closely packed together these meteors were at the time of their annexation to the solar system is unknown, but it is certain that ever since that time the sun has been exerting upon them a tidal influence tending to break up the swarm and distribute its particles around the orbit, as the Perseids are distributed, and, given sufficient time, it will accomplish this, but up to the present the work is only partly done. A certain number of the meteors have gained so much over the slower moving ones as to have made an extra circuit of the orbit and overtaken the rear of the procession, so that there is a thin stream of them extending entirely around the orbit and furnishing in every November a Leonid shower; but by far the larger part of the meteors still cling together, although drawn out into a stream or ribbon, which, though very thin, is so long that it takes some three years to pass through the perihelion of its orbit. It is only when the earth plunges through this ribbon, as it should in 1899, 1900, 1901, that brilliant Leonid showers can be expected.175. Relation of comets and meteors.—It appears from the foregoing that meteors and comets move in similar orbits, and we have now to push the analogy a little further and note that in some instances at least they move in identically the same orbit, or at least in orbits so like that an appreciable difference between them is hardly to be found. Thus a comet which was discovered and observed early in the year 1866, moves in the same orbit with the Leonid meteors, passing its perihelion about ten months ahead of the main body of the meteors. If it were set back in its orbit by ten months' motion, it would be a part of the meteor swarm. Similarly, the Perseid meteors have a comet moving in their orbit actually immersed in the stream of meteor particles, and several other of the more conspicuous star showers have comets attending them.

Perhaps the most remarkable case of this character is that of a shower which comes in the latter part of November from the constellation Andromeda, and which from its association with the comet called Biela (after the name of its discoverer) is frequently referred to as the Bielid shower. This comet, an inconspicuous one moving in an unusually small elliptical orbit, had been observed at various times from 1772 down to 1846 without presenting anything remarkable in its appearance; but about the beginning of the latter year, with very little warning, it broke in two, and for three months the pieces were watched by astronomers moving off, side by side, something more than half as far apart as are the earth and moon. It disappeared, made the circuit of its orbit, and six years later came back, with the fragments nearly ten times as far apart as before, and after a short stay near the earth once more disappeared in the distance, never to be seen again, although the fragments should have returned to perihelion at least half a dozen times since then. In one respect the orbit of the comet was remarkable: it passed through the place in which the earth stands on November 27th of each year, so that if the comet were at that particular part of its orbit on any November 27th, a collision between it and the earth would be inevitable. So far as is known, no such collision with the comet has ever occurred, but the Bielid meteors which are strung along its orbit do encounter the earth on that date, in greater or less abundance in different years, and are watched with much interest by the astronomers who look upon them as the final appearance of the dÉbris of a worn-out comet.176. Periodic comets.—The Biela comet is a specimen of the type which astronomers call periodic comets—i.e., those which move in small ellipses and have correspondingly short periodic times, so that they return frequently and regularly to perihelion. The comets which accompany the other meteor swarms—Leonids, Perseids, etc.—also belong to this class as do some 30 or 40 others which have periodic times less than a century. As has been already indicated, these deviations from the normal parabolic orbit call for some special explanation, and the substance of that explanation is contained in the account of the Leonid meteors and their capture by Uranus. Any comet may be thus captured by the attraction of a planet near which it passes. It is only necessary that the perturbing action of the planet should result in a diminution of the comet's velocity, for we have already learned that it is this velocity which determines the character of the orbit, and anything less than the velocity appropriate to a parabola must produce an ellipse—i.e., a closed orbit around which the body will revolve time after time in endless succession. We note in Fig.115 that when the Leonid swarm encountered Uranus it passed in front of the planet and had its velocity diminished and its orbit changed into an ellipse thereby. It might have passed behind Uranus, it would have passed behind had it come a little later, and the effect would then have been just the opposite. Its velocity would have been increased, its orbit changed to a hyperbola, and it would have left the solar system more rapidly than it came into it, thrust out instead of held in by the disturbing planet. Of such cases we can expect no record to remain, but the captured comet is its own witness to what has happened, and bears imprinted upon its orbit the brand of the planet which slowed down its motion. Thus in Fig.115 the changed orbit of the meteors has its aphelion (part remotest from the sun) quite close to the orbit of Uranus, and one of its nodes, ?, the point in which it cuts through the plane of the ecliptic from north to south side, is also very near to the same orbit. It is these two marks, aphelion and node, which by their position identify Uranus as the planet instrumental in capturing the meteor swarm, and the date of the capture is found by working back with their respective periodic times to an epoch at which planet and comet were simultaneously near this node.

Jupiter, by reason of his great mass, is an especially efficient capturer of comets, and Fig.116 shows his group of captives, his family of comets as they are sometimes called. The several orbits are marked with the names commonly given to the comets. Frequently this is the name of their discoverer, but often a different system is followed—e.g., the name 1886, IV, means the fourth comet to pass through perihelion in the year 1886. The other great planets—Saturn, Uranus, Neptune—have also their families of captured comets, and according to Schulhof, who does not entirely agree with the common opinion about captured comets, the earth has caught no less than nine of these bodies.

177. Comet groups.—But there is another kind of comet family, or comet group as it is called, which deserves some notice, and which is best exemplified by the Great Comet of 1882 and its relatives. No less than four other comets are known to be traveling in substantially the same orbit with this one, the group consisting of comets 1668, I; 1843, I; 1880, I; 1882, II; 1887, I. The orbit itself is not quite a parabola, but a very elongated ellipse, whose major axis and corresponding periodic time can not be very accurately determined from the available data, but it certainly extends far beyond the orbit of Neptune, and requires not less than 500 years for the comet to complete a revolution in it. It was for a time supposed that some one of the recent comets of this group of five might be a return of the comet of 1668 brought back ahead of time by unknown perturbations. There is still a possibility of this, but it is quite out of the question to suppose that the last four members of the group are anything other than separate and distinct comets moving in practically the same orbit. This common orbit suggests a common origin for the comets, but leaves us to conjecture how they became separated.

The observed orbits of these five comets present some slight discordances among themselves, but if we suppose each comet to move in the average of the observed paths it is a simple matter to fix their several positions at the present time. They have all receded from the sun nearly on line toward the bright star Sirius, and were all of them, at the beginning of the year 1900, standing nearly motionless inside of a space not bigger than the sun and distant from the sun about 150 radii of the earth's orbit. The great rapidity with which they swept through that part of their orbit near the sun (see §162) is being compensated by the present extreme slowness of their motions, so that the comets of 1668 and 1882, whose passages through the solar system were separated by an interval of more than two centuries, now stand together near the aphelion of their orbits, separated by a distance only 50 per cent greater than the diameter of the moon's orbit, and they will continue substantially in this position for some two or three centuries to come.

The slowness with which these bodies move when far from the sun is strikingly illustrated by an equation of celestial mechanics which for parabolic orbits takes the place of Kepler's Third Law—viz.:

r³ / T² = 178,

where T is the time, in years, required for the comet to move from its perihelion to any remote part of the orbit, whose distance from the sun is represented, in radii of the earth's orbit, by r. If the comet of 1668 had moved in a parabola instead of the ellipse supposed above, how many years would have been required to reach its present distance from the sun?178. Relation of comets to the solar system.—The orbits of these comets illustrate a tendency which is becoming ever more strongly marked. Because comet orbits are nearly parabolas, it used to be assumed that they were exactly parabolic, and this carried with it the conclusion that comets have their origin outside the solar system. It may be so, and this view is in some degree supported by the fact that these nearly parabolic orbits of both comets and meteors are tipped at all possible angles to the plane of the ecliptic instead of lying near it as do the orbits of the planets; and by the further fact that, unlike the planets, the comets show no marked tendency to move around their orbits in the direction in which the sun rotates upon his axis. There is, in fact, the utmost confusion among them in this respect, some going one way and some another. The law of the solar system (gravitation) is impressed upon their movements, but its order is not.

But as observations grow more numerous and more precise, and comet orbits are determined with increasing accuracy, there is a steady gain in the number of elliptic orbits at the expense of the parabolic ones, and if comets are of extraneous origin we must admit that a very considerable percentage of them have their velocities slowed down within the solar system, perhaps not so much by the attraction of the planets as by the resistance offered to their motion by meteor particles and swarms along their paths. A striking instance of what may befall a comet in this way is shown in Fig.117, where the tail of a comet appears sadly distorted and broken by what is presumed to have been a collision with a meteor swarm. A more famous case of impeded motion is offered by the comet which bears the name of Encke. This has a periodic time less than that of any other known comet, and at intervals of forty months comes back to perihelion, each time moving in a little smaller orbit than before, unquestionably on account of some resistance which it has suffered.

179. The development of a comet.—We saw in §174 that the sun's action upon a meteor swarm tends to break it up into a long stream, and the same tendency to break up is true of comets whose attenuated substance presents scant resistance to this force. According to the mathematical analysis of Roche, if the comet stood still the sun's tidal force would tend first to draw it out on line with the sun, just as the earth's tidal force pulled the moon out of shape (§42), and then it would cause the lighter part of the comet's substance to flow away from both ends of this long diameter. This destructive action of the sun is not limited to comets and meteor streams, for it tends to tear the earth and moon to pieces as well; but the densities and the resulting mutual attractions of their parts are far too great to permit this to be accomplished.

As a curiosity of mathematical analysis we may note that a spherical cloud of meteors, or dust particles weighing a gramme each, and placed at the earth's distance from the sun, will be broken up and dissipated by the sun's tidal action if the average distance between the particles exceeds two yards. Now, the earth is far more dense than such a cloud, whose extreme tenuity, however, suggests what we have already learned of the small density of comets, and prepares us in their case for an outflow of particles at both ends of the diameter directed toward the sun. Something of this kind actually occurs, for the tail of a comet streams out on the side opposite to the sun, and in general points away from the sun, as is shown in Fig.109, and the envelopes and jets rise up toward the sun; but an inspection of Fig.106 will show that the tail and the envelope are too unlike to be produced by one and the same set of forces.

It was long ago suggested that the sun possibly exerts upon a comet's substance a repelling force in addition to the attracting force which we call gravity. We think naturally in this connection of the repelling force which a charge of electricity exerts upon a similar charge placed on a neighboring body, and we note that if both sun and comet carried a considerable store of electricity upon their surfaces this would furnish just such a repelling force as seems indicated by the phenomena of comets' tails; for the force of gravity would operate between the substance of sun and comet, and on the whole would be the controlling force, while the electric charges would produce a repulsion, relatively feeble for the big particles and strong for the little ones, since an electric charge lies wholly on the surface, while gravity permeates the whole mass of a body, and the ratio of volume (gravity) to surface (electric charge) increases rapidly with increasing size. The repelling force would thrust back toward the comet those particles which flowed out toward the sun, while it would urge forward those which flowed away from it, thus producing the difference in appearance between tail and envelopes, the latter being regarded from this standpoint as stunted tails strongly curved backward. In recent years the Russian astronomer Bredichin has made a careful study of the shape and positions of comets' tails and finds that they fit with mathematical precision to the theories of electric repulsion.180. Comet tails.—According to Bredichin, a comet's tail is formed by something like the following process: In the head of the comet itself a certain part of its matter is broken up into fine bits, single molecules perhaps, which, as they no longer cling together, may be described as in the condition of vapor. By the repellent action of both sun and comet these molecules are cast out from the head of the comet and stream away in the direction opposite to the sun with different velocities, the heavy ones slowly and the light ones faster, much as particles of smoke stream away from a smokestack, making for the comet a tail which like a trail of smoke is composed of constantly changing particles. The result of this process is shown in Fig.118, where the positions of the comet in its orbit on successive days are marked by the Roman numerals, and the broken lines represent the paths of molecules m^I, m^II, m^III, etc., expelled from it on their several dates and traveling thereafter in orbits determined by the combined effect of the sun's attraction, the sun's repulsion, and the comet's repulsion. The comet's attraction (gravity) is too small to be taken into account. The line drawn upward from VI represents the positions of these molecules on the sixth day, and shows that all of them are arranged in a tail pointing nearly away from the sun. A similar construction for the other dates gives the corresponding positions of the tail, always pointing away from the sun.

Only the lightest kind of molecules—e.g., hydrogen—could drift away from the comet so rapidly as is here shown. The heavier ones, such as carbon and iron, would be repelled as strongly by the electric forces, but they would be more strongly pulled back by the gravitative forces, thus producing a much slower separation between them and the head of the comet. Construct a figure such as the above, in which the molecules shall recede from the comet only one eighth as fast as in Fig.118, and note what a different position it gives to the comet's tail. Instead of pointing directly away from the sun, it will be bent strongly to one side, as is the large plume-shaped tail of the Donati comet shown in Fig.101. But observe that this comet has also a nearly straight tail, like the theoretical one of Fig.118. We have here two distinct types of comet tails, and according to Bredichin there is still another but unusual type, even more strongly bent to one side of the line joining comet and sun, and appearing quite short and stubby. The existence of these three types, and their peculiarities of shape and position, are all satisfactorily accounted for by the supposition that they are made of different materials. The relative molecular weights of hydrogen, some of the hydrocarbons, and iron, are such that tails composed of these molecules would behave just as do the actual tails observed and classified into these three types. The spectroscope shows that these materials—hydrogen, hydrocarbons, and iron—are present in comets, and leaves little room for doubt of the essential soundness of Bredichin's theory.181. Disintegration of comets.—We must regard the tail as waste matter cast off from the comet's head, and although the amount of this matter is very small, it must in some measure diminish the comet's mass. This process is, of course, most active at the time of perihelion passage, and if the comet returns to perihelion time after time, as the periodic ones which move in elliptic orbits must do, this waste of material may become a serious matter, leading ultimately to the comet's destruction. It is significant in this connection that the periodic comets are all small and inconspicuous, not one of them showing a tail of any considerable dimensions, and it appears probable that they are far advanced along the road which, in the case of Biela's comet, led to its disintegration. Their fragments are in part strewn through the solar system, making some small fraction of its cloud of cosmic dust, and in part they have been carried away from the sun and scattered throughout the universe along hyperbolic orbits impressed upon them at the time they left the comet.

But it is not through the tail only that the disintegrating process is worked out. While Biela's comet is perhaps the most striking instance in which the head has broken up, it is by no means the only one. The Great Comet of 1882 cast off a considerable number of fragments which moved away as independent though small comets and other more recent comets have been seen to do the same. An even more striking phenomenon was the gradual breaking up of the nucleus of the same comet, 1882, II, into a half dozen nuclei arranged in line like beads upon a string, and pointing along the axis of the tail. See Fig.119, which shows the series of changes observed in the head of this comet.182. Comets and the spectroscope.—The spectrum presented by comets was long a puzzle, and still retains something of that character, although much progress has been made toward an understanding of it. In general it consists of two quite distinct parts—first, a faint background of continuous spectrum due to ordinary sunlight reflected from the comet; and, second, superposed upon this, three bright bands like the carbon band shown at the middle of Fig.48, only not so sharply defined. These bands make a discontinuous spectrum quite similar to that given off by compounds of hydrogen and carbon, and of course indicate that a part of the comet's light originates in the body itself, which must therefore be incandescent, or at least must contain some incandescent portions.

By heating hydrocarbons in our laboratories until they become incandescent, something like the comet spectrum may be artificially produced, but the best approximation to it is obtained by passing a disruptive electrical discharge through a tube in which fragments of meteors have been placed. A flash of lightning is a disruptive electrical discharge upon a grand scale. Now, meteors and electric phenomena have been independently brought to our notice in connection with comets, and with this suggestion it is easy to frame a general idea of the physical condition of these objects—for example, a cloud of meteors of different sizes so loosely clustered that the average density of the swarm is very low indeed; the several particles in motion relative to each other, as well as to the sun, and disturbed in that motion by the sun's tidal action. Each particle carries its own electric charge, which may be of higher or lower tension than that of its neighbor, and is ready to leap across the intervening gap whenever two particles approach each other. To these conditions add the inductive effect of the sun's electric charge, which tends to produce a particular and artificial distribution of electricity among the comet's particles, and we may expect to find an endless succession of sparks, tiny lightning flashes, springing from one particle to another, most frequent and most vivid when the comet is near the sun, but never strong enough to be separately visible. Their number is, however, great enough to make the comet in part self-luminous with three kinds of light—i.e., the three bright bands of its spectrum, whose wave lengths show in the comet the same elements and compounds of the elements—carbon, hydrogen, and oxygen—which chemical analysis finds in the fallen meteor. It is not to be supposed that these are the only chemical elements in the comet, as they certainly are not the only ones in the meteor. They are the easy ones to detect under ordinary circumstances, but in special cases, like that of the Great Comet of 1882, whose near approach to the sun rendered its whole substance incandescent, the spectrum glows with additional bright lines of sodium, iron, etc.183. Collisions.—A question sometimes asked, What would be the effect of a collision between the earth and a comet? finds its answer in the results reached in the preceding sections. There would be a star shower, more or less brilliant according to the number and size of the pieces which made up the comet's head. If these were like the remains of the Biela comet, the shower might even be a very tame one; but a collision with a great comet would certainly produce a brilliant meteoric display if its head came in contact with the earth. If the comet were built of small pieces whose individual weights did not exceed a few ounces or pounds, the earth's atmosphere would prove a perfect shield against their attacks, reducing the pieces to harmless dust before they could reach the ground, and leaving the earth uninjured by the encounter, although the comet might suffer sadly from it. But big stones in the comet, meteors too massive to be consumed in their flight through the air, might work a very different effect, and by their bombardment play sad havoc with parts of the earth's surface, although any such result as the wrecking of the earth, or the destruction of all life upon it, does not seem probable. The 40 meteors of §169 may stand for a collision with a small comet. Consult the Bible (Joshuax, 11) for an example of what might happen with a larger one.