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described the curve a 2, from its conjunction, his PLATE second the curve b 2, his third the curve c 2, and his fourth the curve d 2, 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 passed 3, and is twice stationary and once retrograde between 3 and 4.-The path of this satellite intersects itself every 4.2 hours, 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 its path every 3 days 13 hours; as at 4. 7. 11. 14. 18. making only 5 loops and as
5 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 its next conjunction. The fourth satellite d is always progressive, making neither loops nor angles in the heavens ; but comes to its next conjunction at e between Fig. III. the numeral figures 16 and 17, or in 16 days 18 hours. In order to have a tolerable good figure of the paths of these satellites, I took the following method.
Having drawn their orbits on a card, in proportion to their relative distances from Jupiter, I mea- Fig. IV. sured the radius of the orbit of the fourth satellite, which was an inch and í parts of an inch; then multiplied this by 424 for the radius of Jupiter's orbit, because Jupiter is 424 times as far from the Sun's centre as his fourth satellite is from his centre, and the product thence arising was 483
inches. Then taking a small cord of this length,
and fixing one end of it to the floor of a long room How to by a nail, with a black-lead pencil at the other end delineate I'drew the curve ABCD, &c. and set off a degree the paths of Jupi
and a half thereon, from A to T'; because Jupiter
moves only so much, while his outermost satellite Moons,
goes once round him, and somewhat more: so that this small portion of so large a circle differs but very little from a straight line. This done I divided the space A T into 18 equal parts, as A B, BC, &c. for the daily progress of Jupiter; and each part into 24 for his hourly progress. The orbit of each satellite was also divided into as many equal parts as the satellite is hours in finishing its synodical period round Jupiter. Then drawing a right line through the centre of the card, as a diameter to all the four orbits upon it, I put the card upon the line of Jupiter's motion, and transferred it to ev. ery horary division thereon, keeping always the same diameter-line on the line of Jupiter's path; and running a pin through each horary division in the orbit of each satellite as the card was gradually transferred along the line ABCD, &c. of Jupiter's motion, I marked points for every hour through the card for the curves described by the satellites, as the primary planet in the centre of the card was carried forward on the line; and so finished the figure, by drawing the lines of each satellite's motion through those (almost innumerable) points: by which means,
this is, perhaps, as true a figure of the paths of these and Sa.
satellites as can be desired. And in the same man
ner might those of Saturn's satellites be delineated. The grand
270. It appears by the scheme, that the three first periods of satellites come almost into the same line of position Jupiter's
every seventh day; the first being only a little behind with the second, and the second behind with the 3d. But the period of the 4th satellite is so incommensurate to the periods of the other three, that it cannot
be guessed at by the diagram when it would fall PLATE again into a line of conjunction with them between Jupiter and the Sun. And no wonder; for suppos. ing them all to have been once in conjunction, it will require 3,087,043,493,260 years to bring them in conjunction again. See 73.
§ 271. In Fig. 4th, we have the proportions of the Fig. IV. orbits of Saturn's five satellites, and of Jupiter's four, to one another, to our Moon's orbit, and to the disc the orbits
portions of of the Sun. S is the Sun; M m the Moon's orbit of the pla
nets and (the Earth supposed to be at E); J Jupiter ; 1. 2. satellites. 3.4, the orbits of his four moons or satellites; Sat. Saturn; and 1. 2. 3. 4. 5, the orbits of his five moons. Hence it appears, that the Sun would much
. more than fill the whole orbit of the Moon; for the Sun's diameter is 763,000 miles, and the diameter of the Moon's orbit only 480,000. In proportion to all these orbits of the satellites, the radius of Saturn's annual orbit would be 211 yards, of Jupiter's orbit ll}, and of the Earth's 24, taking them in round numbers. 272. The annexed table shews at once what
proportion the orbits, revolutions, and velocities of all the satellites bear to those of their primary planets, and what sort of curves the several satellites describe. For those satellites, whose velocities round their primaries are greater than the velocities of their primaries in open space, make loops at their conjunctions, $ 269; appearing retrograde as seen from the Sun while they describe the inferior parts of their orbits, and direct while they describe the superior. This is the case with Jupiter's first and second satellites, and with Saturn's first. But those satellites, whose velo. cities are less than the velocities of their primary planets, move direct in their whole circumvolutions ; which is the case of the third and fourth satellites of Jupiter, and of the second, third, fourth, and fifth satellites of Saturn, as well as of our satellite the Moon : but the Moon is the only satellite whose motion is always concave to the Sun.
(Proportion of Proportion of Proportion of
1 As 5322 to 1 As 5738 to 1 As 5738 to 5322
4155 1 3912 1 3912 4155 3 2954 1 2347 1 2347 2954 1295 1 674 1
674 1295 432 1 134 1 134 432
As 1851 to 1jAs 2445 to 1 As 2445 to 1851
731 424 1 258 1 258 424
Then As 3374 to 1 As 124 to 1 As 124 to 337} 1|
There is a table of this sort in De la Caille's Astronomy, but it is very different from the above, which I have computed from our English accounts of the periods and distances of these planets and satellites.
The Phenomena of the Harvest-Moon explained by
a common Globe. The Years in which the Har.
T is generally believed that the Moon rises No Har. about 50 minutes later every day than on vest moon
the preceding: but this is true only with regard to equator : places on the equator. In places of considerable latitude there is a remarkable difference, especially in the harvest time, with which farmers were better acquainted than astronomers, till of late; and gratefully ascribed the early rising of the full moon at that time of the year to the goodness of God, not doubting that he had ordered it so on purpose to give them an immediate supply of moon-light after sun-set, for their greater conveniency in reaping the fruits of the Earth.
In this instance of the harvest-moon, as in many others discoverable by astronomy, the wisdom and beneficence of the Deity is conspicuous, who really ordered the course of the Moon so, as to bestow more or less light on all parts of the Earth as their several circumstances and seasons render it more or less serviceable. About the equator, where there is no variety of seasons, and the weather changes sel. dom, and at stated times, moon-light is not necessary for gathering in the produce of the ground; and there the Moon rises about 50 minutes later every day or night ihan on the former. At considerable distances from the equator, where the weather and seasons are more uncertain, the autumnal full Moon rises very soon after sun-set for several evenings to