ecliptic 59°. 42', and 61°. 18'. to its orbit; and the north pole to be directed to 17°. 47′ of Pisces upon the ecliptic, and 19°. 28'. on its orbit. He makes the ratio of the diameters of Mars to be as 16: 15. Dr. MASKELYNE has carefully observed Mars at the time of opposition, but could not perceive any difference in its diameters. Dr. HERSCHEL Observes, that Mars has a consi derable atmosphere. 404. GALILEO first discovered the phases of Venus in 1611, and sent the discovery to WILLIAM de' MEDICI, to communicate it to KEPLER. He sent it in this cypher, Hæc immaturæ a me frustra leguntur, o, y, which put in order, is, Cynthia figuras æmulatur mater amorum, that is, Venus emulates the phases of the moon. He afterwards wrote a letter to him, giving an account of the discovery, and explaining the cypher. In 1666, M. CASSINI, at a time when Venus was dichotomised, discovered a bright spot upon it at the straight edge, like some of the bright spots upon the moon's surface; and by observing its motion, which was upon the edge, he found the sidereal time of rotation to be 23h. 16. In the year 1726, BIANCHINI made some observations upon the spots of Venus, and asserted the time of rotation to be 24 days; that the north pole answered to the 20th degree of Aquarius, and was elevated 15°. or 20°. above its orbit; and that the axis continued parallel to itself. The small angle which the axis of Venus makes with its orbit, is a singular circumstance; and must cause a very great variety in the seasons. M. CASSINI, the Son, has vindicated his Father, and shown from BIANCHINI'S observations being interrupted, that he might easily mistake different spots for the same; and he concludes, that if we suppose the periodic time to be 23h. 20', it agrees equally with their observations; but if we take it 24 days, it will not at all agree with his Father's observations. M. SCHROETER has endeavoured to show that Venus has an atmosphere, from observing that the illuminated limb, when horned, exceeds a semicircle; this he supposes to arise from the refraction of the sun's rays through the atmosphere of Venus at the cusps, by which they appear prolonged. The cusps appeared sometimes to run 15°. 19'. into the dark hemisphere; from which he computes that the height of the atmosphere to refract such a quantity of light must be 15156 Paris feet. But this must depend on the nature and density of the atmosphere, of which we are ignorant. Phil. Trans. 1792. He makes the time of rotation to be 23h. 21', and concludes, from his observations, that there are considerable mountains upon this planet. Phil. Trans. 1795. Dr. HERSCHEL agrees with M. SCHROETER, that Venus has a considerable atmosphere; but he has not made any observations, by which he can determine, either the time of rotation, or the position of the axis. Phil. Trans. 1793. 405. The phases of Mercury are easily distinguished to be like those of Venus; but no spots have yet been discovered by which we can ascertain whether it has any rotation. 8 406. There is reason to believe that the satellites of Jupiter and Saturn revolve about their axes; for the satellites of the former appear at different times to be of very different magnitudes and brightness. The fifth satellite of Saturn was observed by M. CASSINI for several years as it went through the eastern part of its orbit to appear less and less, till it became invisible; and in the western part to increase again. These phænomena can hardly be accounted for, but by supposing some parts of the surfaces to be unfit to reflect light, and therefore when such parts are turned towards the earth, they appear to grow less, or to disappear. As the same appearances of this satellite returned again when it came to the same part of its orbit, it affords an argument that the time of the rotation about its axis is equal to the time of its revolution about its primary, a circumstance similar to the case of the moon and earth. See Dr. HERSCHEL'S account of this in the Phil. Trans. 1792. The appearance of this satellite of Saturn is not always the same, and therefore it is probable that the dark parts are not permanent. CHAP. XX. ON THE SATELLITES. Art. 407. ON January 8, 1610, GALILEO discovered the four satellites of Jupiter, and called them Medicea Sidera, or Medicean Stars, in honor of the family of the MEDICI, his patrons. This was a discovery, very important in its consequences, as it furnished a ready method of finding the longitudes of places, by means of their eclipses; the eclipses led M. ROEMER to the discovery of the progressive motion of light; and hence Dr. BRADLEY was enabled to solve an apparent motion in the fixed stars, which could not otherwise have been accounted for. 408. The satellites of Jupiter in going from the west to the east are eclipsed by the shadow of Jupiter, and as they go from east to west are observed to pass .over its disc; hence they revolve about Jupiter, and in the same direction as Jupiter revolves about the sun. The three first satellites are always eclipsed, when they are in opposition to the sun, and the lengths of the eclipses are found to be different at different times; but sometimes the fourth satellite passes through opposition without being eclipsed. Hence it appears, that the planes of the orbits do not coincide with the plane of Jupiter's orbit, for in that case, they would always pass through the center of Jupiter's shadow, and there would always be an eclipse, and of the same, or very nearly the same duration, at every opposition to the sun. As the planes of the orbits which they describe sometimes pass through the pass through the eye, they will then appear to describe straight lines passing through the center of Jupiter; but at all other times they will appear to describe ellipses, of which Jupiter is the center. On the Periodic Times, and Distances of Jupiter's Satellites. 409. To get the times of their mean synodic revolutions, or of their revolu tions in respect to the sun, observe, when Jupiter is in opposition, the passage of a satellite over the body of Jupiter, and note the time when it appears to be exactly in conjunction with the center of Jupiter, and that will be the time of conjunction with the sun. After a considerable interval of time, repeat the same observation, Jupiter being in opposition, and divide the interval of time by the number of conjunctions with the sun in that interval, and you get the FIG. 94. time of a synodic revolution of the satellite. This is the revolution which we have occasion principally to consider, it being that on which the eclipses depend. But owing to the equation of Jupiter's orbit, this will not give the mean time of a synodic revolution, unless Jupiter was at the same point of its orbit at both observations; if not, we must proceed thus. 410. Let AIPR be the orbit of Jupiter, S the sun in one focus, and F the other focus; and as the excentricity of the orbit is small, the motion may be considered (227) as uniform about F. Let Jupiter be in its aphelion at A in opposition to the earth at T, and L a satellite in conjunction; and let I be the place of Jupiter at its next opposition with the earth at D, and the satellite in conjunction at G. Then if the satellite had been at O, it would have been in conjunction with F, or in mean conjunction; therefore it wants the angle FIS of being come to the mean conjunction, which angle is (227) the equation of the orbit according to the simple elliptic hypothesis, which may be here used, as the excentricity of the orbit is but small; the angle FIS therefore measures the difference between the mean synodic revolutions in respect to F, and the synodic revolutions in respect to the sun S. If therefore n be the number of revolutions which the satellite has made in respect to the sun, n × 360°- SIF= the revolutions in respect to F; hence, n x 360° - SIF: 360°:: the time between the two oppositions: the time of a mean synodic revolution about the sun. 411. As the satellite is at O at the mean conjunction, and at G when in conjunction with the sun, it is manifest, that if the angle FIS continued the same, the time of a revolution in respect to Swould be equal to the time in respect to F, or to the time of a mean synodic revolution; hence, the difference between the times of any two successive revolutions in respect to S and F respectively is as the variation of the angle FIS, or variation of the equation of the orbit. When Jupiter is at A the equation vanishes, and the times of the two conjunctions at F and S coincide. When Jupiter comes to I, the mean conjunction at O happens after the true conjunction at G, by the time of describing the angle SIF, the equation of Jupiter's orbit. This is the first inequality, and has for its argument a number called A, which is the mean anomaly of Jupiter, calculated to hundredths of a degree. By this inequality of the intervals of the conjunctions, the returns of the eclipses are affected. 412. But as it may not often happen that there will be a conjunction of the satellite exactly at the time when Jupiter is in opposition, the time of a mean revolution may be found, out of opposition, thus. Let H be the earth when the satellite is at Z in conjunction with Jupiter at R; and let V be another position of the earth when the satellite is at C in conjunction with Jupiter at I; and produce RH, IV to meet in M; then the motion of Jupiter about the earth in this interval is the same as if the earth had been fixed at M. Now the difference between the true and mean motions of Jupiter is RFI-RMI=FIM + FRM, which shows how much the number of mean revolutions in respect to Fexceeds the same number of apparent revolutions in respect to the earth; hence, n× 360° — MIF-MRF: 360°:: the time between the observations : the time of a mean synodic revolution of the satellite. If C and Z lie on the other side of O and Y, the angles MIF, MRF must be added to n × 360°; and if one lie on one side and the other on the other, one must be added and the other subtracted, according to the circumstances. 413. As it is difficult, from the great brightness of Jupiter, to determine accurately the time when the satellite is in conjunction with the center of Jupiter as it passes over its disc, the time of conjunction is determined by observing its entrance upon the disc, and its going off; but as this cannot be determined with so much accuracy as the time of immersion into the shadow of Jupiter, and emersion from it, the time of conjunction can be most accurately determined from the eclipses. 414. Let I be the center of Jupiter's shadow FG, Nmt the orbit of a satellite, N the node of the satellite upon the orbit of Jupiter; draw Iv perpendicular to IN, and Ic to Nt; and when the satellite comes to v it is in conjunction with the sun. * with the sun. Now both the immersion at m and emersion at t of the second, third, and fourth satellites may sometimes be observed, the middle point of time between which gives the time of the middle of the eclipse at c, and by calculating cv, from knowing the angle N and NI, we get the time of conjunction at v. If both the immersion and emersion cannot be observed, take the time of either, and after a very long interval of time, when an eclipse happens as nearly as possible in the same situation in respect to the node, take the time of the same phænomenon, and from the interval of these times you will get the time of a revolution. By these different methods, M. CASSINI found the times of the mean synodic revolutions of the four satellites to be as follows; FIG. 95. First Second Third 1d. 18h. 28'. 36" 3d. 13". 17. 54" 7. 3". 59'. 36" Fourth 415. Hence it appears, that 247 revolutions of the first satellite are performed in 437d. 3h. 44'; 123 revolutions of the second, in 437d. 3h. 41′; 61 revolutions of the third, in 437d. 3h. 35', and 26 revolutions of the fourth, in * A Satellite is said to be in conjunction, both when it is between the Sun and Jupiter, and when it is opposite to the Sun; the latter may be called Superior, and the former Inferior. |