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 t11ose 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 eithe1 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 180º 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 orbit of Jupiter. The statistical law governing these may be seen from fig. 1.
Fig. 1.
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 plane told. 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 ls 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 planetoids, while SC represents its actual but varying eccentricity,
