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second satellites will also take place during the pre
sent month, viz.
1st Satellite, May 2, 38 after 2 in the morning.
1 after 11 in the evening.
50 after 2 in the morning.
5 after 2 in the morning,
The eclipses of satellites make known the instants of their oppositions to the Sun; the interval between two eclipses gives the synodic revolution of the satellite; from which astronomers conclude its angular motion, with respect to the axis of the shadow or the line which joins the centres of the planet and the Sun. Then the motion of the planet about the Sun being known, they deduce from this result the length of the sidereal revolution. In order to ensure a greater degree of accuracy, they employ those eclipses that were observed near the oppositions of the planet, when it is found nearly in the same right line with the earth and the Sun; and to compensate for the inequalities that may take place in the movements of the satellite and the planet, care is taken to compare such eclipses as are remote from each other.
Observation has shown that the orbits of the satellites are very nearly circular; and therefore their distances from the principal planet may be ascertained by measuring them with a micrometer at the time of their greatest elongation. Then, by comparing these distances with the times of their sidereal revolutions, it has been found that Kepler's law for the planets holds good for the satellites also, viz. that, in each system, the squares of their revolutions are as the cubes of their mean distances.
The frequent eclipses of Jupiter's satellites have furnished astronomers with the means of examining their motions with much greater accuracy than they could have done merely by observations of their dis
tances from the primary planet; for these distances are always extremely small, and their variations very difficult to be perceived.
The greater or less duration of the successive eclipses of the same satellite, and the series of positions in which they happen, make known the inclination of its orbit and the position of its nodes upon the plane of the orbit of the planet. Observations of Jupiter's satellites have also led to the discovery of another very remarkable phenomenon of nature; the successive transmission of light. By comparing the returns of these eclipses, it is seen that, when Jupiter is in opposition to the Sun, they happen sooner than they ought to do according to the calculations, from the sidereal revolutions of the satellites. On the contrary, towards the conjunctions, when Jupiter is beyond the Sun with respect to the earth, they take place after the calculated time; and these variations are exactly the same for all the satellites, and cannot be attributed to any inequalities in their movements; for, by the effect of Jupiter's motion, the conjunctions and oppositions answer successively to different points of the heavens. The same thing also takes place with respect to the eclipses of the satellites and their orbits. What presents itself as the most simple and easy explanation of this observed fact, is, that the light of the Sun reflected by these small bodies is not suddenly transmitted to the earth, but requires a sensible time to traverse the space between the satellite and us. Indeed, if the orbit of Jupiter be concentric with the Sun, and the phenomena of his movement leave no reason to doubt it, this planet is much nearer to us in his oppositions than in his conjunctions. Supposing, for the sake of greater simplicity, that the orbit of Jupiter is circular, we perceive that the difference is double the radius of the apparent orbit of the Sun; which is sufficient to account for the retardations which observation points
The eclipses which happen near the conjunctions take place about 16′ 26′′ after those which occur near the oppositions; hence light employs that time to traverse the solar orbit, and, consequently, it requires only half that interval to come from the Sun to us. Observations agree so well with hypothesis in this respect, that they answer as fully and completely as possible.
The observations of Jupiter's satellites are also extremely useful in finding the longitude at land. The rapid motion of these bodies causes frequent eclipses, the epochs of which are previously calculated, and entered in Ephemerides. The Tables of Jupiter's satellites, constructed by Delambre, according to the theory of Laplace, and after a great number of observations, leave little to be desired on this subject. By comparing the epochs caculated for the first me ridian with the results of immediate observations made in another place, at a determined time, the dif ference of longitude may be concluded for this time. The method is the same as for eclipses of the Moon; but, unfortunately, it cannot be employed at sea. The telescopes necessary for observing these small bodies are too long to be used on board a ship, on account of the instability of the vessel; but these observations may be very useful to the navigator when in harbour.
[Concluded from p. 105.]
FROM what has been previously stated, it is evident that the whole problem is reduced to that of determining the horizontal parallax; for it is easy to perceive, from an inspection of the triangle CS'O, that the sine of this parallax is CO r equal to
CSD where r is the terrestrial radius,
and D the distance of the body. If, therefore, this distance can be ascertained in terms of the radius, the parallax will be completely determined. The process for accomplishing this is at once simple and natural; and is nothing more than an application of the principles of trigonometry in precisely the same manner as in finding the distance of an inaccessible object, by taking the angles it makes with a given line at the two extremities of a known base.
observers, situated at O and O', fig. 3, at a known distance from each other, and under the same celestial meridian, observe, at the same instant, the altitude of the body S', or its zenith distance, then, in the quadrilateral S'OCO', there will be known the three angles O, C, and O', and the two equal sides OC and O'C, which are the radii of the earth. Hence the diagonal CS', which is the distance of the body, may readily be found by calculation; and the radius of the earth being divided by this distance, gives the horizontal parallax required.
The calculation which results from this method, and is necessary for finding the horizontal parallax, is stated by M. Biot in the following terms, and is remarkable for its simplicity :
The horizontal parallax is equal to the angle at the body, divided by the sum of the sines of the zenith distances, if the body be situated between the zeniths of the two observers; or by the difference of these sines, if the body be found on the same side of both theit zeniths.
Astronomers, however, frequently make use of another method of finding the parallax by observation; which is that of determining the angle OS'O' immediately from the differences of the observed declination of the same star and the heavenly body; and these, it should be remarked, are susceptible of being observed with great accuracy. The following explanation will enable the astronomical student to
understand this method. Let A be a star (fig. 5) which passes the meridian at the same time with the
body; and suppose two visual rays to be drawn from the observers to the star, which may be regarded as parallel to each other, since the parallax of the stars is insensible (see the preceding Note). Suppose, likewise, two other visual rays to be drawn through the body to meet these to the star in s and s', as in the figure; then the angles SOA and SO'λ are evidently the differences of the observed declination; and the angle OSO', being the exterior angle of the triangle SOs, will be equal to the sum of these differences. But if the body was on the same side of the zenith with respect to both the observers, the angle OSO' would be equal to the difference of the same angles, SOA and SO'λ.
In the above case, it has been supposed, for the sake of making the illustration more easy and simple, that the two bodies passed the meridian of the ob servers at the same time; but this is not necessary in practice, provided they be chosen very nearly on the same parallel, and their difference of declination taken with a simple micrometer.
The following is an example in which this method was put in practice by Lacaille and Wargentin, in