279. The planet Saturn is distinguished from all the other bodies of the solar system, in being surrounded by a detached ring which, receiving light from the sun on one of its faces, reflects that light to the earth. The plane of the ring coincides with that of the planet's equator, and this being oblique to the plane of the ecliptic, the ring, to an observer on the earth, appears of an elliptical form; its breadth being variable according to its position with respect to such observer. The phenomena which it presents indicate that its true figure is circular, and that the line in which it intersects the plane of the planet's orbit revolves in that plane, as the line of the moon's nodes revolves in the plane of the ecliptic: when that line, which is called the line of the ring's nodes, if produced, would pass through the earth, the ring is invisible, because its edge only is turned towards the spectator, and from this time the apparent breadth of the ring gradually enlarges till the line of section is perpendicular to one drawn from its centre to the earth, after which, as the line of section continues to revolve, the breadth as gradually diminishes, and so on. The ring is also invisible, or appears merely as a luminous thread, when the line of section passes through the sun; and it is evidently invisible when it presents towards the earth the surface which is not enlightened by the sun. It may be observed that when the enlightened surface of the ring is towards the earth, the part nearest the latter casts a distinct shadow on the body of the planet.

280. On account of the great distance of Saturn from the earth, when compared with the magnitude of the ring, rays of light passing to a spectator on the earth from every part of the circumference of the ring, may be considered as parallel to a line drawn to the spectator from its centre; and if a plane perpendicular to the last-mentioned line be imagined to cut the cylinder formed by the rays, the section will represent the visible figure of the ring. Now, if a time be chosen when the nodes of the ring are perpendicular to the axis of such cylinder, that is, when the breadth of the ring appears to be the greatest, to measure with a micrometer the lengths of the greatest and least diameters of the ring, the inclination of the ring to the plane passing through the earth and the ring's nodes may be found. For if E represent the earth, C the centre of the ring and planet, CA the semidiameter of the ring (equal to the greatest of the visible semidiameters so measured), and AB drawn perpendi

E

D

B

F

cular to EC produced, represent its visible projection or the

AB

least semidiameter; we have (sin. ACB) for the sine

CA

of the required inclination, which from such observations has been found to be between 25 and 30 degrees. Imagine now the semidiameter AC to be produced to meet the ecliptic EF, as in D; then if to the angle ACB or ECD there be added the angle CED or the geocentric latitude of Saturn, the sum will be equal to CDF, which expresses the inclination of the ring to the plane of the ecliptic. M. Struve makes this angle equal to 28° 6'. (Mem. Astr. Soc., vol. ii. part 2.)

281. The positions of the nodes of the ring are determined by observing the instants when the ring disappears in consequence of its plane passing through the sun; for then the heliocentric longitude of the nodes is the same as that of the planet. Those disappearances may be recognised by being such as are observed to take place regularly at intervals equal to half a sidereal revolution of Saturn about the sun; for the disappearances which are caused by the plane of the ring passing through the earth, occur at intervals which depend on the position of the earth: and, as the situations of the nodes of the ring always correspond to the same points in the orbit of the planet, it follows that the plane of the ring remains constantly parallel to itself. The line joining the nodes of the ring, if transferred parallel to itself on the ecliptic, makes a constant angle equal to about 59° 30' with the line joining the nodes of Saturn's orbit.

282. At the latter end of the seventeenth century, M. Römer, on comparing the recurrences of the eclipses of Jupiter's first satellite with the time of its sidereal revolution, ascertained that, between a conjunction of Jupiter with the sun and the next following opposition, the immersions and emersions were continually accelerated, with respect to the times at conjunction; and that between an opposition and the next following conjunction, they were continually retarded, with respect to the times at opposition. Now the difference between the two distances of Jupiter from the earth at the times of conjunction and opposition is equal to a diameter of the earth's orbit; and, in order to account for the differences between the observed and computed times of the phenomena, it was assumed as an hypothesis that the passage of light from the celestial body to the earth, instead of being instantaneous, as had been till then supposed, takes place in times which depend upon the distances. From the best observations, it is found that the whole acceleration of the eclipses at the time of the opposition, and the retardation at the time of the conjunction of Jupiter, is 16'27";

in which time, therefore, the particles of light are supposed to move through a diameter of the earth's orbit, and it follows that light should pass from the sun to the earth in half that time, or 8'13".5. What was at first observed with respect to the first satellite of Jupiter, is now known to take place with all the satellites, and the above hypothesis is fully confirmed by the phenomena of aberration; it is, therefore, universally admitted as just. Also, since the latter phenomena can be explained only on the supposition that the motion of light is progressive, and that the earth revolves about the sun, the fact of such revolution is to be considered as established.

CHAP. XII.

ROTATION OF THE SUN ON ITS AXIS, AND THE LIBRATIONS OF THE MOON.

283. On the surface of the sun are frequently seen a number of dark spots, which, entering at the eastern limb, appear to move across his disk, and occasionally, having disappeared at the western limb, they have been observed, after an interval of time equal to that of their passage over the disk, to re-appear on the eastern limb. It has been consequently concluded that they exist on the surface of the sun; and, as the time of performing a revolution is the same for all the spots (about 27 days 8 hours), it is further inferred that their apparent motion is caused by the rotation of the sun on an axis, in the same order as the earth and planets revolve about him. The paths which the spots appear to describe are generally of an oval figure, their convexities being towards the lower or upper part of the disk according as the northern extremity of the axis is directed towards, or from the earth; but twice in each year (in December and June) when the plane of the rotation, if produced, would pass through the earth, they appear to be straight lines.

In order to determine the apparent path of a spot it is necessary, with a transit or equatorial instrument, to find the difference between the right ascension of the spot and of the eastern or western limb of the sun, and with a micrometer, the difference between the declinations of the spot and of the upper or lower limb: the right ascension and declination of the sun's centre is known for the same instant; therefore a series of such observations being made during the time that a particular spot is on the disk, if AB be supposed to represent part of a parallel of declination passing through C the sun's centre; on making CM, CN, &c. equal to the differences of right ascension between the sun's centre and a spot in the situations s and s', and MS, NS', &c., perpendicular to AB, equal to the corresponding differences of declination, a line

A

D

บ

S

P

N

D/

Q

joining the points s, s', &c., will be an orthographical projection of the path described by the spot. The true path of the spot is the circumference of a circle whose plane is perpendicular to the axis of the sun's rotation, or parallel to what may be called the sun's equator; and therefore, from three observed right ascensions and declinations of a spot it is possible to determine by calculation the position of such circle with respect to the plane of the ecliptic, and the position of the line in which the sun's equator intersects that plane; but for these purposes it is necessary first to determine the centric longitude and latitude of the spot at the several times of observation.

geo

284. Let DD' represent a part of the ecliptic, and let fall S'R perpendicularly on it. Then, if the difference between the transit of A and s' be observed in sidereal time, and there be subtracted from it the time given in the Nautical Almanac, in which the sun's semidiameter AC passes the meridian, the remainder multiplied by 15 will express an arc of the equator corresponding to CN; and multiplying this by the cosine of the sun's declination, the product will be the value of CN in seconds of a great circle: S'N is the observed difference between the declinations of c and s', which is obtained by the micrometer in the same denomination; then in the right-angled triangle CNS', considered as plane, there may be found cs' and the angle s'CN. Now the angle D'CB is equal to the angle of the sun's position between the pole of the ecliptic and that of the equator, or the value of the angle p CP, where P is the pole of the equator and of the parallel AB, and p is the pole of the ecliptic. In the spherical triangle PPC we have pP, the obliquity of the ecliptic, pc equal to a quadrant, and the angle PPC the supplement (in the figure) of the angle CPQ, which last, since PPQ is the solsticial colure, is equal to the complement of the sun's right ascension: therefore

sin. PPC sin. pc (= radius) :: sin. Pp: sin. p CP, or sin. D'CB. Then, in the right-angled triangle s'CR, considered as plane, we have s'c, the angle s'CR (= S'CN - D'CB); to find CR and S'R: the former is the difference between the geocentric longitudes of the sun and spot, which may be represented by L-7 (L being the longitude of the sun's centre, and 7 the geocentric longitude of the spot), and the latter is the geocentric latitude (λ) of the spot.

285. Next, let E be the centre of the earth, s that of the sun, and through E imagine the rectangular co-ordinate axes EX, EY, EZ to be drawn, of which EX and EY are in the plane of the ecliptic, and the former passes through the equinoctial