parent latitude + parallax in latitude = (when an eclipse barely takes place,) sum of the semi-diameters + parallax in latitude. Therefore, at the ecliptic limits the parallax in altitude is the greatest possible, that is, when it is equal to the horizontal parallax. Hence, CL=semi-diameter moon + semi-diam. sun + hor. par. moon. Therefore, CL, (when greatest,) = 33′ +61' = 1° 34 nearly. And Fig.A because sin. NC = cot. NX tan. LC, L rad. we find NC = 170 12' nearly; an eclipse may happen withinthis limit; but if we take CL N C =30+54' (the least diameters and least parallax) = 10 24', we find NC = 15° 19', and an eclipse must happen within this limit. 9. There must be two eclipses, at least, of the sun every year, because the sun is above a month in moving through the solar ecliptic limits. But there may be no eclipse of the moon in the course of a year, because the sun is not a month in moving through the lunar ecliptic limits. When a total aud central eclipse of the moon happens, there may be solar eclipses at the new moon preceding and following; because, between new and full moon, the sun moves only about 150, and therefore the preceding and following conjunctions will be at less distances from the node than the limit for eclipses of the sun. As the same may take place at the opposite node, there may be six eclipses in a year. Also when the first eclipse happens early in January, another eclipse of the sun may take place near the end of the year, as the nodes retrograde nearly 200 in a year. Hence, there may be seven eclipses in one year, five of the sun, and two of the moon. 10. Thus more solar than lunar eclipses happen, but few solar are visible at a given place. A total eclipse of the sun, April 22d, 1715, was seen in most parts of the south of Europe. A total eclipse of the sun has not been seen in London since the year 1140. The eclipse of 1715 was a very remarkable one; during the total darkness, which lasted in London 3'23", the planets Jupiter, Mercury, and Venus, were seen; also the fixed stars Cape'la and Aldebaran. Dr. Halley has given a very interesting account of this eclipse, which is said by Maclaurin to be the best description of an eclipse that astronomical history affords. A particular account is also given in the Phil. Trans. by Maclaurin, of an annular eclipse of the sun, observed in Scotland, February 18, 1737. He remarks that this phenomenon is so rare, that he could not meet with any particular description of an annular eclipse recorded. This eclipse was annular at Edinburgh during 5' 48". The beginning and end of a solar eclipse can be observed with considerable exactness, and are of great use in determining the longitudes of places; but the computation is complex and tedious, from the necessary allowances to be made for parallax. 11. When Jupiter and any of his satellites are in a line with the sun, and Jupiter between the satellite and the sun, the satellite disappears, being then eclipsed, or involved in Jupiter's shadow. When the satellite comes into a position between Jupiter and the sun, it sometimes casts a shadow on the disc of that planet, which is seen by a spectator on the earth as an obscure round spot. And when the satellite is in a line between Jupiter and the earth, it appears on his disc as a round black spot, and a transit of the satellite takes place. The instant of the disappearance of the satellite by entering into the shadow of Jupiter, is called the immersion of that satellite; and the emersion signifies the first instant of its appearance at coming out of the same. Obs. 1. Before the opposition, the immersions only of the first satellite are visible; and after the opposition, the emersions only. 2. The first three satellites are always eclipsed, when they are in opposition; but sometimes the fourth satellite, like our moon, passes through opposition without being eclipsed. 9. As these phenomena appear at the same moment of absolute time at all places on the earth to which Jupiter is then visible, but at different hours of relative time, according to the distance between the meridians of the places at which observations are made; it follows that this difference of time converted into degrees, will be the difference of longitude between those places. 4. The instant of immersion or emersion, is more precisely defined than the beginning or end of a lunar eclipse; and, therefore, the longitude is more accurately found by the former. 5. For this purpose all the eclipses of the four satellites of Jupiter, that are visible in any part of the world, are given in the Nautical Almanac. The times of the immersions and emersions are calculated with great accuracy, for the meridian of Greenwich, from the very excellent tables of De Lambre. 6. The first satellite is the most proper for finding the longitude, its motions being best known, and its eclipses occuring most frequent. : 7. When Jupiter is at such a distance from conjunction with the sun as to be more than eight degrees above the horizon, when the sun is 80 below, an eclipse of the satellites will be visible at any place; this may be determined near enough by the celestial globe. 8. The immersion or emersion of any satellite being carefully observed at any place according to mean time, the longitude from Greenwich is found immediately, by taking the difference of the observation from the corresponding time shown in the ephemeris, which must be converted into degrees, &c., by allowing 150 for every hour: and will be east or west of Greenwich, as the time observed is more or less than that of the ephemeris. CHAPTER XVII. 1. Comets are planetary bodies moving about the sun in elliptic orbits, and following the same laws as the planets; so that the areas described by their radii vectores are equal in equal times. When a comet appears, the observations to be made for ascertaining its orbit are of its declinations and right ascensions, from which the geocentric latitudes and longitudes are obtained. These observations of right ascension and declination must be made with an equatorial instrument, or by measuring with a micrometer, the differences of the declination and right ascension of the comet, and a neighbouring fixed star. The observations, according to Dr. Brinkley, ought to be made with the utmost care, as a small error may occasion a considerable one in the orbit. From the beginning of the christian era to the present time, there has appeared not less than 500 comets; but the elements of not more than 99 have been computed, and of the latter number, 22 passed between the sun and Mercury in their perihelia; 40 between Mercury and Venus; 17 between Venus and the earth; 16 between the earth and Mars; and 4 between Mars and Jupiter. The appearance of one comet has been several times recorded in history, viz. the comet of 1680. The period of this comet is 575 years. It exhibited at Paris a tail 620 long, and at Constantinople one of 900. When nearest the sun, it was only one-sixth part of the diameter of the sun distant from his surface; when farthest, its distance exceeded 138 times the distance of the sun from the earth. 2. As the orbits of the comets are very eccentric, the aphelion distance of a comet is so great, compared with its perihelion distance, that the small portion of the ellipse which it describes near its perihelion, or during its appearance, may, without any sensible error, be supposed to coincide with a parabola, and thus its motion during a short interval may be calculated as if that portion of the orbit was parabolical. Dr. Halley makes the perihelion distance of the comet of 1680 to be to its aphelion distance, nearly as 1 to 22412; so that this comet was twenty-two thousand four hundred and twelve times farther from the sun in its aphelion than in its perihelion. According to the laws of Kepler, the sectors described in the same time by two planets, are to each other as the areas of their ellipses divided by the square of the times of the revolution, and these squares are as the cubes of their semimajor axes. It is easy to conclude, that if we imagine a planet moving in a circular orbit, of which the radius is equal to the perihelion distance of a comet; the sector described by the radius vector of the comet, will be to the corresponding sector described by the radius vector of the planet, as the square root of the aphelion distance of the comet is to the square root of the semi-major axis of its orbit, a relation which, when the ellipse changes to a parabola, becomes that of the square root of 2 to unity. The relation of the sector of the comet to that of the imaginary planet is thus obtained, and it is easy by what has been already said, to get the proportion of this last sector, to that which the radius vector of the earth describes in the same time. The area described by the radius vector of the comet may then be determined for any instant whatever, setting out from the moment of its passage through the perihelion, and its position may be fixed in the parabola, which it is supposed to describe. Nothing more is necessary, but to deduce from observation the elements of the parabolic motions. 3. The elements of a comet are, the perihelion distance of the comet, the position of the perihelion, the instant of its passage through the perihelion, the inclination of its orbit to the plane of the ecliptic, and the position of its nodes. Elements of the Comet of 1811. Time of Comet's passage through its perihelion, Sep. Place of the perihelion, Place of the ascending node 4 12d. 9h. 48m. 74° 12′ 00′′ 1 .02241 Inclination of the orbit to the plane of the ecliptic Its heliocentric motion retrograde. The investigation of these five elements presents much greater difficulties than that of the elements of the planets, which being always visible, and having been observed during a long succession of years may be compared when in the most favourable position for determining these elements, instead |