_Jupiter._—Galileo’s discovery of Jupiter’s satellites was followed by the discovery of his belts. Zucchi and Torricelli seem to have seen them. Fontana, in 1633, reported three belts. In 1648 Grimaldi saw but two, and noticed that they lay parallel to the ecliptic. Dusky spots were also noticed as transient. Hooke[5] measured the motion of one in 1664. In 1665 Cassini, with a fine telescope, 35-feet focal length, observed many spots moving from east to west, whence he concluded that Jupiter rotates on an axis like the earth. He watched an unusually permanent spot during twenty-nine rotations, and fixed the period at 9h. 56m. Later he inferred that spots near the equator rotate quicker than those in higher latitudes (the same as Carrington found for the sun); and W. Herschel confirmed this in 1778-9. Jupiter’s rapid rotation ought, according to Newton’s theory, to be accompanied by a great flattening at the poles. Cassini had noted an oval form in 1691. This was confirmed by La Hire, Römer, and Picard. Pound measured the ellipticity = 1/(13.25). W. Herschel supposed the spots to be masses of cloud in the atmosphere—an opinion still accepted. Many of them were very permanent. Cassini’s great spot vanished and reappeared nine times between 1665 and 1713. It was close to the northern margin of the southern belt. Herschel supposed the belts to be the body of the planet, and the lighter parts to be clouds confined to certain latitudes. In 1665 Cassini observed transits of the four satellites, and also saw their shadows on the planet, and worked out a lunar theory for Jupiter. Mathematical astronomers have taken great interest in the perturbations of the satellites, because their relative periods introduce peculiar effects. Airy, in his delightful book, _Gravitation_, has reduced these investigations to simple geometrical explanations. In 1707 and 1713 Miraldi noticed that the fourth satellite varies much in brightness. W. Herschel found this variation to depend upon its position in its orbit, and concluded that in the positions of feebleness it is always presenting to us a portion of its surface, which does not well reflect the sun’s light; proving that it always turns the same face to Jupiter, as is the case with our moon. This fact had also been established for Saturn’s fifth satellite, and may be true for all satellites. In 1826 Struve measured the diameters of the four satellites, and found them to be 2,429, 2,180, 3,561, and 3,046 miles.