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ASTRONOMY

perturbations produced by Jupiter would be greatly exaggerated in the course of centuries. It was therefore supposed that if there ever had been planets with these mean motions, their orbits would have been unstable and subjected to large and unknown changes. This conclusion, however, is misleading. The result in question follows when the integration of the equations of motion of the planet is only approximate, but a rigorous integration shows that commensurability of the kind in question does not lead to any instability. When Kirkwood made his investigation, only about 100 of these bodies were known, but a study of the 400 members of the group whose mean motions are fairly well determined shows the matter in another and more striking light. In the preceding table is shown the distribution of those members in zones of mean motion and mean distance. A study of this table shows that what we see in the group are not gaps in an otherwise uniform series, but a tendency to cluster into zones, which are condensed near the middle of the regions between the lines of commensurability and thin out gradually towards those lines. For the most part there is no absolute dividing line between the zones, the number being merely less near the line of commensurability. This, however, is not the case with the two outer zones. In the region 3’24 to 3-34 no planets are yet known, while in the next zone, 0 18 in breadth, there are ten. Then follows a zone 0-36 in breadth, without any, outside of which there are five. That there is a causal connexion between this system of grouping and the lines of commensurability with Jupiter can scarcely be doubted, but, as already remarked, we cannot attribute the paucity of planets approaching to commensurability to any want of stability in their motion. One cannot but suspect that the phenomenon has a cosmogonical origin, and arose from the formation of zones of different degrees of density in the original revolving nebulous mass from which these bodies were formed. The laws of secular variation of elements show that there is a certain mean plane around which the nodes of these bodies tend to be uniformly scattered, and a certain mean longitude towards which the perihelia tend (Astronom. Nach. Iviii. S. 210). The position of the mean plane is: longitude of node, 91°; inclination to eliptic, 1° 3'. The eccentricity and perihelion of the mean orbit are : eccentricity, 0-0321 ; longitude of perihelion, 3°. This last result does not imply that we have here the mean of all the eccentricities, but that the mean value of the e sin tt and e cos tt for all the orbits will be very near the products of the eccentricity just given into the sine and cosine of 3°. The result may be otherwise expressed by saying that the action of each planet tends to bring the mean plane of the orbits of the small planets into its own plane, and to elongate the orbits in the direction of its own aphelion. As Jupiter exerts the most powerful action on the minor planets, a tendency thus arises among the latter to coincidence of their nodes and perihelia with the node and perihelion of Jupiter. The most notable addition to our recent knowledge of the Jovian system consists in the discovery of a minute Jovian additional satellite by Barnard in September system. 1892, with the 36-inch telescope of the Lick Observatory. It is much nearer the planet than the four previously known, and the only designation which it has thus far received is that of “ fifth satellite,” the order of distances of the satellites thus being the fifth, first, second, &c. As regards visibility it is one of the most difficult objects—perhaps the most difficult—in the solar system, and has been seen only with a few of the largest telescopes. Its mean synodic period of revolution is 11 h. 51 m. 27‘635 s. It has been assiduously observed by its original discoverer, who finds a quite appreciable eccentricity in its orbit. From his observations, combined with a consideration of the theoretical effect of the ellipticity of Jupiter, its pericentre is found to revolve with a more rapid, motion than that of any other known celestial body, making more than an entire revolution in a year. The four satellites formerly known have been found by Barnard and W. H. Pickering to exhibit singular anomalies of apparent form while in transit across the disc of Jupiter. The first sometimes appeared double on such occasions, although no such form had been seen at other times, and it became a question whether it could really consist of two bodies. After a careful study of the subject, Barnard reached the conclusion that the appearance was due to a bright band around the equatorial

region of the satellite, while the poles were of a darker tint, the varied shading of the belts of Jupiter on which it was seen projected during the transit resulting sometimes in only the polar regions being visible. Anomalies of form noticed in the other satellites have not been confirmed by the observations of Barnard {Monthly Notices E. A. S. liv. 1894, p. 134). The ease with which the complex cloud-forms on Jupiter can be observed has led to a careful study of its surface by many observers. The British Astronomical Association has a special section devoted to this study. Although a great mass of observations has thus been collected, illustrative of the changes continually going on at the surface of the planet, it cannot be said that any radically new views respecting its constitution have been gained, nor that the observations have yet led to any researches that would throw much additional light on the subject. The most noteworthy phenomenon of late years has been the garnet spot which appeared in middle southern latitude in 1878. For ten years no great changes were noticed in it; then it gradually began to fade away. About 1892 it brightened up again, then again began to fade, and has been seen only occasionally and with difficulty since 1897. The most careful investigation of its motion has been made by Lohse, whose work embraced the entire period of visibility from 1878 to 1897. His most remarkable conclusion is that the period of revolution of the spot has been undergoing a fairly continuous change. For several years before and after 1891, it was 9 h. 55 m. 41 s. But if with this motion its position is computed back during previous years, it will be found to have wandered over more than two-thirds the circumference of the parallel on which it is situated. This result emphasizes the fact already known, that if Jupiter has any solid nucleus it is invisible to us; for had the spot in question been connected with such, a nucleus, had it even been in the nature of an eruption from a volcano, its period of revolution would necessarily have been uniform. Granting—as seems to be unavoidable —that the visible surface of the planet is either liquid or gaseous, the persistence of the spot through twenty years is remarkable. The most plausible hypothesis is that it is in the nature of an island floating upon a liquid surface, but it does not seem at all probable that any formation floating in an atmosphere could have lasted through such an interval. Still, it is an open question whether the socalled belts of Jupiter indicate a liquid or gaseous condition of the visible surface. The great difficulty in the way of the liquid hypothesis is the very great difference in the times of rotation of the equatorial portions of the planet and the spots in middle latitudes. It is now found that while the latter, like the red spot, rotate in 9 h. 55 m. and a somewhat variable number of seconds, the equatorial markings make a revolution in about five minutes less time, or 9 h. 50 m. plus a varying number of seconds. In this respect Jupiter resembles the sun, whose rotation follows the same law. In the case of the planet, however, it is very remarkable that no intermediate times of rotation seem to have been well made out. Whether this arises from the fact that observers have not devoted to this subject the attention which it deserves, or whether the line between the two times of rotations is a narrow one, is a question which cannot yet be decisively answered. The important point is that the difference between the /two times corresponds to a difference of about 7-5° in the motion round the planet during a terrestrial day. This corresponds to a linear motion on the surface of the planet of more than 30,000 miles per day, a motion which it seems difficult to reconcile with liquidity of the visible surface.