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. In order to have a tolerably good figure of the paths of
these Satellites, I took the following method.
[Sidenote: Fig. IV.