73. The Orbits of these Moons are represented in the Scheme of the Solar System by four small circles marked 1. 2. 3. 4. on Jupiter’s Orbit ♃; but are drawn fifty times too large in proportion to it. The first Moon, or that nearest to Jupiter, goes round him in 1 day 18 hours and 36 minutes of our time; and is 229 thousand miles distant from his center: The second performs it’s revolution in three days 13 hours and 15 minutes, at 364 thousand miles distance: The third in 7 days three hours and 59 minutes, at the distance of 580 thousand miles: And the fourth, or outermost, in 16 days 18 hours and 30 minutes, at the distance of one million of miles from his center. The Periods of these Moons are so incommensurate to one another, that if ever they were all in a right line between Jupiter and the Sun, it will require more than 3,000,000,000,000 years from that time to bring them all into the same right line again, as any one will find who reduces all their periods into seconds, then multiplies them into one another, and divides the product by 432; which is the highest number that will divide the product of all their periodical times, namely 42,085,303,376,931,994,955,904 seconds, without a remainder. [Sidenote: Parallax of their Orbits, and distances from Jupiter. PLATE I. How he appears to his nearest Moon.] 74. The Angles under which the Orbits of Jupiter’s Moons are seen from the Earth, at it’s mean distance from Jupiter, are as follow: The first, 3ʹ 55ʺ; the second, 6ʹ 14ʺ; the third, 9ʹ 58ʺ; and the fourth, 17ʹ 30ʺ. And their distances from Jupiter, measured by his semidiameters, are thus: The first, 5-2/3; the second, 9; the third. 14-23/60; and the fourth, 25-18/60[15]. This Planet, seen from it’s nearest Moon, appears 1000 times as large as our Moon does to us; waxing and waneing in all her monthly shapes, every 42-1/2 hours. [Sidenote: Two grand discoveries made by the Eclipse of Jupiter’s Moons.] 75. Jupiter’s three nearest Moons fall into his shadow, and are eclipsed in every Revolution: but the Orbit of the fourth Moon is so much inclined, that it passeth by Jupiter, without falling into his shadow, two years in every six. By these Eclipses, Astronomers have not only discovered that the Sun’s light comes to us in eight minutes; but have also determined the longitudes of places on this Earth with greater certainty and facility than by any other method yet known; as shall be explained in the eleventh Chapter. [Sidenote: The great difference between the Equatoreal and Polar diameters of Jupiter. The difference little in those of our Earth.]