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, 2½ 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 lib ration of long period in the mean motion of the planetoids. 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,
Fig. 2.
increasing toward the left, of which certain equidistant numerical values are given below the line. Points on the line corresponding to each 0·01 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 0·01. 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 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 micro metric 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 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 planetoids in a list, while the name serves for more certain identification. (S. N.)
PLANK, a flat piece of timber, sawn and planed; it is technically distinguished from a “board” by its greater thickness, and should measure from 2 to 4 in. in thickness and from 10 to 11 in.
