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The minor planets, commonly known as asteroids or planetoids, form a remarkable group of small planetary bodies, of which all the known members but three move between the orbits of Mars and Jupiter. Until recently they were all supposed to be contained within the region just mentioned; but the discovery of one, which at perihelion comes far within the orbit of Mars, and of two others, which at aphelion pass outside the orbit of Jupiter, shows that no well-defined limit can be set to the zone containing them. Before the existence of this group was known, the apparent vacancy in the region occupied by it, as indicated by the arrangement of the planets according to Bode's law, had excited remark and led to the belief that a planet would eventually be found there. Towards the end of the 18th century the conviction that such a planet existed was so strong that an association of astronomers was formed to search for it. The first discovery of the looked-for planet was not, however, made by any member of this association, but by Giuseppe Piazzi of Palermo. On the 1st of January 1801 he noted a small star in Taurus, which, two days later, had changed its place, thus showing it to be a planet. Shortly after Piazzi's discovery the body was lost in the rays of the sun, and was not again seen until near the following opposition in 1801-1802. The orbit was then computed by C. F. Gauss, who found its mean distance from the sun to correspond with Bode's law, thus giving rise to the impression that the gap in the system was filled up. The planet received the name Ceres.

On the 28th of March 1802 H. W. M. Olbers (1758-1840) discovered a second planet, which was found to move in an orbit a little larger than that of Ceres, but with a very large eccentricity and inclination. This received the name of Pallas. The existence of two planets where only one was expected led Olbers to his celebrated hypothesis that these bodies were fragments of a larger planet which had been shattered by an internal convulsion; and he proposed that search should be made near the common node of the two orbits to see whether other fragments could be found. Within the next few years two other planets of the group were discovered, making four. No others were found for more than a generation; then on the 8th of December 1845 a fifth, Astrea, was discovered by K. L. Hencke of Driesen. The same observer added a sixth in 1847. Two more were found by J. R. Hind of London during the same year, and from that time discovery has gone on at an increasing rate, until the number now known is more than six hundred and is growing at the rate of thirty or more annually.

Up to 1890 discoveries of these bodies were made by skilful search with the telescope and the eye. Among the most successful discoverers were Johann Palisa of Vienna, C. H. F. Peters (1813-1890) of Clinton, New York, and James Craig Watson (1838-1880) of Ann Arbor, Michigan. In recent times the discoveries are made almost entirely by photography. When a picture of the stars is taken with a telescope moved by clockwork, so as to follow the stellar sphere in its apparent diurnal rotation, the stars appear on the plates as minute dots. But if the image of a planet is imprinted on the plate it will generally appear as a short line, owing to its motion relative to the stars. Any such body can therefore be detected on the plate by careful examination much more expeditiously than by the old method of visual search. The number now known is so great that it is a question whether they can be much longer individually followed up so as to keep the run of their movements.

Among the distinctive features of the planets of this group one is their small size. None exists which approaches either Mercury or the moon in dimensions. The two largest, Ceres and Juno, present at opposition a visible disk about 1" in diameter, corresponding to about 400 miles. The successively discovered ones naturally have, in the general average, been smaller and smaller. Appearing only as points of light, even in the most powerful telescopes, nothing like a measure of their size is possible. It can only be inferred from their apparent magnitude that the diameters of those now known may range from fifteen or twenty miles upwards to three or four hundred, the great majority being near the lower limit. There is yet no

sign of a limit to their number or minuteness. From the increasing rate at which new ones approaching the limit of visibility are being discovered, it seems probable that below this limit the number of unknown ones is simply countless; and it may well be that, could samples of the entire group be observed, they would include bodies as small as those which form the meteors which so frequently strike our atmosphere. Such being the case, the question may arise whether the total mass of the group may be so great that its action on the major planets admits of detection. The computations of the probable mass of those known, based upon their probable diameter as concluded from the light which they reflect, have led to the result that their combined action must be very minute. But it may well be a question whether the total mass of the countless unknown planets may not exceed that of the known. The best answer that can be made to this question is that, unless the smaller members of the group are almost perfectly black, a number great enough to produce any observable effect by their attraction would be visible as a faintly illuminated band in the sky. Such a band is occasionally visible to very keen eyes; but the observations on it are, up to the present time, so few and uncertain that nothing can positively be said on the subject. On the other hand, the faint " Gegenschein" opposite the sun is sometimes regarded as an intensification of this supposed band of light, due to the increased reflection of the sun's light when thrown back perpendicularly (see Zodiacal Light). But this supposition, though it may be well founded, does not seem to fit with all the facts. All that can be said is that, while it is possible that the light reflected from the entire group may reach the. extreme limit of visibility, it seems scarcely possible that the mass can be such as to produce any measurable effect by its attraction.

Another feature of the group is the generally large inclinations and eccentricities of the orbits. Comparatively few of these are either nearly circular or near any common plane. Considering the relations statistically, the best conception of the distribution of the planes of the orbits may be gained by considering the position of their poles on the celestial sphere. The pole of each orbit is defined as the point in which an axis perpendicular to the plane intersects the celestial sphere. When the poles are marked as points on this sphere it is found that. they tend to group themselves around a certain position, not. far from the pole of the invariable plane of the planetary system, which again is very near that of the orbit of Jupiter. This. statistical result of observation is also inferred from theory,. which shows that the pole of each orbit revolves around a point near the pole of the invariable plane with an angular motion varying with the mean distance of the body. This would result in a tendency toward an equal scattering of the poles around. that of Jupiter, the latter being the centre of position of the. whole group. From this it would follow that, if we referred. the planes of the orbit to that of Jupiter, the nodes upon the orbit of that planet should also be uniformly scattered. Examination, however, shows a seeming tendency of the nodes. to crowd into two nearly opposite regions, in longitudes of about 180 and 330°. But it is difficult to regard this as anything but the result of accident, because as the nodes move along at unequal rates they must eventually scatter, and must have been scattered in past ages. In other words it does not seem that any other than a uniform distribution can be a permanent feature of the system.

A similar law holds true of the eccentricities and the perihelia.. These may both be defined by the position of the centre of the orbit relative to the sun. If a be the mean distance and e the eccentricity of an orbit, the geometry of the ellipse shows that the centre of the orbit is situated at the distance ae from the sun, in the direction of the aphelion of the body. When the centres of the orbits are laid down on a diagram it is found that they are not scattered equally around the sun but around a point lying in the direction of the centre of the A orbit of Jupiter. The statistical law j governing these may be seen from fig. I. Here S represents the position of the sun, and J that of the centre of the orbit of Jupiter. The direction JS produced is that of the perihelion of Jupiter, which is now near longitude 12 °. As the perihelion. moves by its secular variation, the line SJ revolves around S. Theory then shows that for every asteroid there will be a certain point A near the line SJ and moving with it. Let C be the actual position of the centre of the planetoid. Theory shows that C is in motion around A as a centre in the direction shown by the arrow, the linear eccentricity ae being represented by the line SC. It follows that e will be at a minimum when AC passes through S, and at a maximum when in the opposite direction. The position of A is different in the case of different planetoids, but is generally about two-thirds of the way from S to J. The lines AC for different bodies are at any time scattered miscellaneously around the region A as a centre. AC may be called the constant of eccentricity of the planetoid, while SC represents its actual but varying eccentricity,.

S C FIG. I.

Grouping of the Planetoids

A curious feature of these bodies is that when they are classified according to their distances from the sun a tendency is seen to cluster into groups. Since the mean distance and mean motion of each planet are connected by Kepler's third law, it follows that this grouping may also be described as a tendency toward certain times of revolution or certain values of the mean motion around the sun. This feature was first noticed by D. Kirkwood in 1870, but at that time the number of planetoids known was not sufficient to bring out its true nature. The seeming fact pointed out by Kirkwood was that, when these bodies are arranged in the order of their mean motions, there are found to be gaps in the series at those points where the mean motion is commensurable with that of Jupiter; that is to say, there seem to be no mean daily motions near the values 598", 748" and 898", which are respectively 2, 22 and 3 times that of Jupiter. Such mean motions are nearly commensurable with that of Jupiter, and it is shown in celestial mechanics that when they exist the perturbations of the planet by Jupiter will be very large. It was therefore supposed that if the commensurability should be exact the orbit of the planet would be unstable. But it is now known that such is not the case, and that the only effect of even an exact commensurability would be a libration of long period in the mean motion of the planetoid. The gaps cannot therefore be accounted for on what seemed to be the plausible supposition that the bodies required to fill these gaps originally existed but were thrown out of their orbits by the action of Jupiter. The fact can now be more precisely stated by saying that we have not so much a broken series as a tendency to an accumulation of orbits between the points of commensurability. The law in question can be most readily shown in a graphical form. In fig. 2 the horizontal line represents distances from the sun, limits of the groups shown in the figure. Eros is so near the sun, and its orbit is so eccentric, that at perihelion it is only about 0.16 outside the orbit of the earth. On those rare occasions when the earth is passing the perihelion point of the orbit at nearly the same time with Eros itself, the parallax of the latter will be nearly six times that of the sun. Measurements of parallax made at these times will therefore afford a more precise value of the solar parallax than can be obtained by any other purely geometrical measurement. An approach almost as close as the nearest geometrically possible one occurred during the winter of 1893-1894. Unfortunately the existence of the planet was then unknown, but after the actual discovery it was found that during this opposition its image imprinted itself a number of times upon the photographs of the heavens made by the Harvard Observatory. The positions thus discovered have been extremely useful in determining the elements of the orbit. The next near approach occurred in the winter of 1900-1901, when the planet approached within 0 . 32 of the earth. A combined effort was made by a number of observatories at this time to determine the parallax, both by micrometric measures and by photography. Owing to the great number of stars with which the planet had to be compared, and the labour of determining their positions and reducing the observations, only some fragmentary results of this work are now available. These are mentioned in the article Parallax. So far as can yet be seen, no other approach so near as this will take place until January 1931.

A few of the minor planets are of such special interest that some pains will doubtless be taken to determine their orbits and continue observations upon them at every available opposition. To this class belong those of which the orbits are so eccentric that they either pass near that of Jupiter or approach 3 6 3?5 3.4 33 3.2311 3TO 2928 FIG. 2.

2 7 216 215 2.4 2.3 2.2 21 2.O increasing toward the left, of which certain equidistant numerical values are given below the line. Points on the line corresponding to each o

oi of the distances are then taken, and at each point a perpendicular line of dots is drawn, of which the number is equal to that of the planetoids having this mean distance, no account being taken of fractions less than o

oi. The accumulations between the points of close commensurability with the mean motion of Jupiter may be seen by inspection. For example, at the point 2.59 the mean motion is three times that of Jupiter; at the point 2.81 twice the mean motion is equal to five times that of Jupiter; at 3.24 the mean motion is twice that of Jupiter. It will be seen that there is a strong tendency toward grouping near the values 2.75, and a lesser tendency toward 3.1 and 2.4. It is probable that the grouping had its origin in the original formation of these bodies and may be plausibly attributed to the formation of three or more separate rings which were broken up to form the group.

Continuing the question beyond these large collections, it will be seen that between the values 3.22 and 3.33 there are no orbits at all. Then between 3 . 3 and 3.5 there are nine orbits. The space between 3.5 and 3.9 is thus far a complete blank; then there are three orbits between 3.90 and 3.95, not shown in the diagram.

A group of great interest, of which only three members are yet known, was discovered during the years 1906-1907. The mean distance of each member of this group, and therefore its time of revolution, is so near that of Jupiter that the relations of the respective orbits are yet unknown. The case thus offered for study is quite unique in the solar system, but its exact nature cannot be determined until several more years of observation are available.

Several planetoids of much interest are situated without the near that of the earth. With most of the others little more can be done than to compute their elements with a view of subsequently identifying the object when desired. Unless followed up at several oppositions after discovery, the planet is liable to be quite lost. Of those discovered before 1890 about fifteen have not again been found, so that if discovered, as they doubtless will be, identification will be difficult.

The system of nomenclature of these bodies is not free from difficulty. When discoveries began to go on at a rapid rate, the system was introduced of assigning to each a number, in the order of its discovery, and using as its symbol its number enclosed in a circle. Thus Ceres was designated by the symbol(); Pallas by ®, &c., in regular order. This system has been continued to the present time. When photography was applied to the search it was frequently doubtful whether the planet of which the image was detected on the plates was or was not previously known. This led to the use. of capital letters in alphabetical order as a temporary designation. When the alphabet was exhausted a second letter was added. Thus there are planetoids temporarily designated as A, B, &c., and AB, AC, &c. The practice of applying a name to be selected by the discoverer has also been continued to the present time. Originally the names were selected from those of the gods or goddesses of classical mythology, but these have been so far exhausted that the name is now left to the discretion of the person selecting it. At present it is customary to use both the number and the name, the former being necessary to the ready finding of the planetoid in a list, while the name serves for more certain identification. (S. N.)