180". It follows from this theorem, that the first three satellites of Jupiter can never all be eclipsed together. For if it was possible, then l', l'", and "" would be equal, and consequently 1—31"' + 2 1"" = 0. When the second and third are eclipsed together, then "="", and consequently-1" 180; hence, when the second and third satellites of Jupiter are eclipsed at the same time, the first is always in conjunction with Jupiter. Various other interesting consequences of this theorem might be easily deduced; but we leave the ingenious reader to make them out for himself. The relative distances of the satellites from their primaries are shown in plate VII. fig.13.

128. Saturn, when viewed through a good telescope, makes a more remarkable appearance than any of the other planets. Galileo first discovered his uncommon shape, and from the discoveries made by him and other astronomers, it appears that this planet is surrounded by a broad thin ring, the edge of which reflects little, if any, of the sun's light to us, but the planes of the ring reflect the light in the same manner that the planet itself does. If we suppose the diameter of Saturn to be divided into three equal parts, the diameter of the ring is about seven of these parts. The ring is detached from the body of Saturn in such a manner, that the distance between the innermost part of the ring and the body is equal to its breadth. If we had a view of the planet and his ring with our eyes perpendicular to one of the planes of the latter, we should see them as in plate VII. fig. 12; but our eye is never so much elevated above either plane as to have the visual ray at right angles to it, nor indeed is it ever elevated more than about 30° above it; so that the ring being commonly viewed at an oblique angle, appears of an oval form, and through very good telescopes double, as represented, plate VII. fig. 13. and plate XI. fig. 3. When the ring appears most open, its longest diameter appears about twice the length of its shortest.

129. Both the outward and inward rim are projected into an ellipsis, more or less oblong, according to the different degrees of obliquity with which it is viewed. Sometimes our eye is in the plane of the ring, and then it becomes in visible; either because the outward edge is not fitted to reflect the sun's light, or more probably because it is too thin to be seen at such a distance. As the plane of this ring keeps always parallel to itself, that is, its situation in one part of the orbit is always parallel to that in any other part, it disappears twice in every evolution of the planet, that is about once in fifteen years; and the planet sometimes appears quite round for months together. At other times the distance betwixt the body of the planet and the ring is very perceptible; and Mr. Whiston tells us, that Dr. Clarke's father saw a star through the opening.

130. When Saturn appears round, if our eye be in the plane of the ring, it will appear as a dark line across the middle of the planet's disk; and if our eye be elevated above the plane of the ring, a shadowy belt will be visible, caused by the

shadow of the ring as well as by the interposition of part of it betwixt the eye and the planet. The shadow of the ring is broadest when the sun is most elevated, but its obscure parts appear broadest when our eye is most elevated above the plane of it. When it appears double, the ring next the body of the planet appears brightest; when the ring appears of an elliptical form, the parts about the ends of the largest axis are called the ansæ. These, a little before and after the disappearing of the ring, are of unequal magnitude: the largest ansæ is longer visible before the planet's round phase, and appears again sooner than the other. In the diagram, plate VII. fig. 2, are delineated the phases of the ring from its full appearance in 1825, to its disappearance in 1832, and its full re-appearance in 1839.

131. Dr. Herschel has found that the ring is double, or that there are two concentric rings; also that it has a motion of rotation in its own plane, its axis of motion being the same as that of Saturn himself, and its periodical time 10h. 32′ 15′′, 4: But he thinks it probable that the concentric rings may not revolve in the same period. Their dimensions, and the space between them, he states in the following proportion to each other:

:

132. Dr. Herschel concludes, from his observations on the ring, that its structure is such as to allow it to remain permanently in its present state; nor does he think it at all probable that the ring is of that changeable nature which some persons have imagined.

133. The same excellent astronomer, from a series of observations on the belts of Saturn, has concluded, that he revolves upon his axis in 10h. 16' 0", 4, that he has a dense atmosphere, and that his polar diameter is to his equatorial one as 10 to 11.

134. Saturn has, besides his ring, seven little secondary planets or satellites revolving round him. One of them, which till lately was reckoned the fourth in order from Saturn, was discovered by Huygens in 1655, by means of a telescope 100 feet long; and the others, viz. the first, second, third, and fifth, at different times by Cassini, between 1671 and 1684, by the help of glasses of 100 and 136 feet. The sixth and seventh have lately been discovered by Herschel, with his forty feet reflecting telescope, in 1787 and 1788. These he has called the sixth and seventh satellites, though they are nearer to Saturn than the other five; that the names may not be mistaken with regard to former observations

of them.

135. The periodical revolutions and distances of these satellites expressed in semidiameters of that planet, and in English miles are as follows:

136. The first four describe ellipses like those of the ring, and are in the same plane: their inclination to the orbit is from 30° to 31°. The fifth describes an orbit inclined from 17° to 18° to the orbit of Saturn, his plane lying between the ecliptic and those of the other satellites. Dr. Herschel observes, that the fifth satellite turns round its axis once, exactly in the time in which it revolves round the planet Saturn. In this respect, like the satellites of Jupiter, it resembles which does the same thing. The proportional distances of the seven satellites formerly known to astronomers, are shown in plate VII. fig. 13.

our moon,

137. The apparent form of the ring of Saturn, and the form of the orbits of his first four satellites, may easily be found by means of the following table:

planet's latitude, which correction is obtained by taking one-fourth of the latitude in minutes, and applying it to the number in the table, with the sign when the latitude is north, but when south.

Example. What is the shape of Saturn's ring on January 25, 1826?

By the Nautical Almanack, his longitude, on that day, is 28 15° 23′, and latitude 1° 26′ S. Now 28 15° 23′ + 13° 43′, is 2s 29° 6', with which, in the table, we find -521, which corrected by + 26, one-fourth of the latitude gives

495; or the shorter diameter is to the longer, as 495 to 1000. The sign + indicates that the most distant half of the ring is north, and — that the most distant half is south of the centre of the planet.

139. The Georgium Sidus, Herschel, or Uranus, was discovered by Herschel on March 13th 1781. From certain inequalities in the notion of Jupiter and Saturn, the existence of a planet of considerable size, without the orbit of either, had before been suspected. Its apparent magnitude, as seen from the earth, is about three seconds and a half; and as, from its distance from the sun, it shines but with a pale light, it cannot often be seen with the naked eye. Its diameter is about four times and a half that of the earth, and it revolves round the sun in 83 years, 150 days, 18 hours. The want of light in this planet, on account of its great distance from the sun, is supplied by no less than six moons, which revolve round it in different periods. But there is a remarkable peculiarity in the position of the orbits in which these moons revolve round their primary, and in the direction in which they revolve in their orbits. The orbits are nearly perpendicular to the plane of the ecliptic, and they revolve in them in a direction contrary to the order of the signs of the eciiptic. La Place, from theoretical considerations, concludes that this planet itself revolves on an axis very little inclined to the plane of the ecliptic; but there is little hope that this theoretical deduction will ever be either confirmed, or set aside, by observations on a body so very remote.

140. The periods of the revolution of the satellites, and the greatest angle of elongation of their orbits, as seen from the earth, are contained in the following table.

Signs.

O. VI.

+

+

4.

0.000

0.260

0.451

30

0.027

0.284

0.464 27

0.054

0.306

0.476 24

0.081

0.328

0.486

21