being left by the Moon at the Change, than the Moon is of being left by the Earth at the Full: the diameter of the Moon’s Orbit being so small in comparison of the Sun’s distance, that the Moon is but little more or less attracted than the Earth at any time. And as the Moon’s projectile force keeps her from falling to the Earth, so the Earth’s projectile force keeps it from falling to the Sun. [Sidenote: Fig. III.] 269. All the curves which Jupiter’s Satellites describe, are different from the path described by our Moon, although these Satellites go round Jupiter, as the Moon goes round the Earth. Let _ABCDE_ &c. be as much of Jupiter’s Orbit as he describes in 18 days from _A_ to _T_; and the curves _a_, _b_, _c_, _d_ will be the paths of his four Moons going round him in his progressive motion. [Sidenote: The absolute Path of Jupiter and his Satellites delineated. Fig. III.] Now let us suppose all these Moons to set out from a conjunction with the Sun, as seen from Jupiter. When Jupiter is at _A_ his first or nearest Moon will be at _a_, his second at _b_, his third at _c_, and his fourth at _d_. At the end of 24 terrestrial hours after this conjunction, Jupiter has moved to _B_, his first Moon or Satellite has described the curve _a1_, his second the curve _b1_, his third _c1_, and his fourth _d1_. The next day when Jupiter is at _C_, his first Satellite has described the curve _a2_ from its conjunction, his second the curve _b2_, his third the curve _c2_, and his fourth the curve _d2_, and so on. The numeral Figures under the capital letters shew Jupiter’s place in his path every day for 18 days, accounted from _A_ to _T_; and the like Figures set to the paths of his Satellites, shew where they are at the like times. The first Satellite, almost under _C_, is stationary at + as seen from the Sun; and retrograde from + to _2_: at _2_ it appears stationary again, and thence it moves forward until it has past _3_, being twice stationary, and once retrograde between _3_ and _4_. The path of this Satellite intersects itself every 42-1/2 hours of our time, making such loops as in the Diagram at _2._ _3._ _5._ _7._ _9._ _10._ _12._ _14._ _16._ _18_, a little after every Conjunction. The second Satellite _b_, moving slower, barely crosses it’s path every 3 days 13 hours; as at _4._ _7._ _11._ _14._ _18_, making only five loops and as many conjunctions in the time that the first makes ten. The third Satellite _c_ moving still slower, and having described the curve _c 1. 2. 3. 4. 5. 6. 7_, comes to an Angle at _7_ in conjunction with the Sun at the end of 7 days 4 hours; and so goes on to describe such another curve _7. 8. 9. 10. 11. 12. 13. 14_, and is at _14_ in it’s next conjunction. The fourth Satellite _d_ is always progressive, making neither loops nor angles in the Heavens; but comes to it’s next conjunction at _e_ between the numeral figures _16_ and _17_, or in 16 days 18 hours.