The size and mass of the asteroids do not admit of very accurate definition, for the reason that, with rare exceptions, they are seen in the telescopes only as points of light. Barnard has, however, succeeded in measur ing the apparent diameter of the first four, three of which are probably the largest of the group, with the great Lick telescope. The results are: Miles Diameter of Ceres 488 Diameter of Pallas 304 Diameter of Vesta 248 Diameter of Juno 118 Only the largest shows a diameter exceed ing one-twentieth that of the earth, and all the others are much smaller than this. Judging from the amount of light they reflect very few of them are 100 miles in diameter and most of those known may not exceed 10 or 12 miles in extent. Indeed, we have reason to believe that as we take smaller diameters the number increases without any limit. The same remark might apply in a still greater extent to the masses. The latter are so small that the attrac tion of the whole mass of all the asteroids does not produce any effect that has yet been ob served upon any planet or comet.
Of the total number of these bodies it is hardly possible to form any estimate, because the more powerful the means of research the more are found. We can hardly be supposing that thousands exist, and if we in clude those that must forever remain invisible to us, the number must be countless. Yet they are all so minute that the total mass cannot be as great as that of the planet Mercury.
The hypothesis already mentioned, that these bodies are fragments of a great planet, has been effectually disproved by modern research. Apart from the impossibility of an explosion which would rend a planet, we have the fact that in the event of a disruption all the orbits would pass through a single point. It is true that this coincidence would not continue indefinitely, be cause the orbits would change their positions by the attraction of the other planets; but their sizes are found to be such that they could not originally have passed through any single point. It is more probable that the asteroids are merely scattered meteoric material which formed a small part of the original nebula from which the solar system was developed but which was prevented from becoming aggregated into a single world, probably by the great disturb ances produced by the attraction of the nearby planet, Jupiter. There is a curious grouping of the orbits which seems to have some connec tion with the origin of the whole collection. Many years ago it was noticed by Kirkwood that, if the orbits were arranged according to their mean distance from the sun, there would be gaps in the series at those points where the time of revolution was commensurable with the period of Jupiter. For example, there are no known asteroids having a period one-third that of Jupiter, or one-half or two-fifths, al though there are plenty of orbits within and outside these peculiar limiting values. The sub sequent discovery of hundreds of these bodies has led to a slight modification of this law. The orbits not only seem to avoid these peculiar values, but to accumulate midway between them. To get an idea of the results suppose that every orbit stretched into a circle of a radius equal to its mean distance. Then treat ing these orbits as hoops, suppose that we ar range them all round on one centre. We should then find that the rings are divisible into four, five or six nearly distinct groups with vacant spaces between them. The explanation seems
to be that the material which might have been originally in these vacant zones could not long remain there, for the accumulating, periodic, planetary perturbations would speedily force it nearer or farther away from the sun.
Perhaps the most remarkable of the aster oids was one discovered in 1898. Some of its peculiarities have excited great attention on the part of the astronomical world. The orbits of all the other known asteroids are contained between the orbits of Mars and Jupiter, no known orbits approaching very near either of these planets. But, in the summer of 1898, Witt, of Berlin, found an asteroid which at perihelion came far inside the orbit of Mars, indeed within 13,500,000 miles of the orbit of the earth. Its orbit was found to be extremely eccentric and, which was more curious, it was interlinked with that of Mars, so that if the orbits were rings, they would have passed through each other and hung together like two links. What gives this planet especial interest is that on these rare occasions when it comes nearest to the earth its parallax can be meas ured with greater precision than that of any of the other planets. It therefore affords us the best possible method of directly measuring the solar system; but, most unfortunately, it is only at intervals of 37 years that the nearest approaches occur. What is most tantalizing, is that only six years before it was discovered, it is known to have passed at nearly the least distance from the earth, but it was then unseen by human eye. It was found to have been photographed a great number of times at the Harvard Observatory; but among the hun dreds of stars whose images were found on the plate, its image was completely lost after the discovery in 1898. It was recognized through the determination of its orbit which made pos sible the computation of its position in the heavens at former positions.
In the winter of 1900-01 there was as close an approach to the earth as would occur during the next 30 years, although the distance was then hut little less than 30,000,000 miles. A co operative effort was made to measure the paral lax on this occasion. No less than 58 observa tories took part, some making photographic and others micrometric measures of the planet, while many others co-operated by making meridian observations of reference stars. When the great mass of observational material was finally reduced, there resulted for the solar parallax the value, 8."806 with a probable error of but 0."004. This is the most accurate value thus far determined by any method. The next closest approach of Eros to the earth will occur in 1931 when the distance apart of the planets will be less than half as great as it was at the time of their closest approach in 1900. Soon after this date, therefore, the value of the fundamental unit of astronomy will become known with a far greater accuracy.
A curious property of this most remarkable body is a periodical variation in its light which was noticed during the opposition of 1900-01. It was found to go through a series of changes in the course of five hours quite similar to those of a variable star. The period was found to be two and one-half hours, but possibly the same brightness was not reproduced except in a period of five hours. It was yet more curi ous that these variations seemed to have nearly or quite ceased at the next opposition.