252. By looking at the Moon with an ordinary telescope we perceive that her surface is diversified with long tracts of prodigious high mountains and deep cavities. Some of her mountains, by comparing their height with her diameter (which is 2180 miles) are found to be three times higher than the highest hills on our Earth. This ruggedness of the Moon’s surface is of great use to us, by reflecting the Sun’s light to all sides: for if the Moon were smooth and polished like a looking-glass, or covered with water, she could never distribute the Sun’s light all round; only in some positions she would shew us his image, no bigger than a point, but with such a lustre as would be hurtful to our eyes.
253. The Moon’s surface being so uneven, many have wondered why her edge appears not jagged, as well as the curve bounding the light and dark places. But if we consider, that what we call the edge of the Moon’s Disc is not a single line set round with mountains, in which case it would appear irregularly indented, but a large Zone having many mountains lying behind one another from the observer’s eye, we shall find that the mountains in some rows will be opposite to the vales in others; and so fill up the inequalities as to make her appear quite round: just as when one looks at an orange, although it’s roughness be very discernible on the side next the eye, especially if the Sun or a Candle shines obliquely on that side, yet the line terminating the visible part still appears smooth and even.
Plate VII.
J. Ferguson delin.
J. Mynde Sculp.
254. As the Sun can only enlighten that half of the Earth which is at any moment turned towards him, and being withdrawn from the opposite half leaves it in darkness; so he likewise doth to the Moon: only with this difference, that the Earth being surrounded by an Atmosphere, and the Moon having none, we have twilight after the Sun sets; but the Lunar Inhabitants have an immediate transition from the brightest Sun-shine to the blackest darkness § 177. For, let tkrsw be the Earth, and A, B, C, D, E, F, G, H the Moon in eight different parts of her Orbit. As the Earth turns round its Axis, from west to east, when any place comes to t the twilight begins there, and when it revolves from thence to r the Sun S rises; when the place comes to s the Sun sets, and when it comes to w the twilight ends. But as the Moon turns round her Axis, which is only once a month, the moment that any point of her surface comes to r (see the Moon at G) the Sun rises there without any previous warning by twilight; and when the same point comes to s the Sun sets, and that point goes into darkness as black as at midnight.
255. The Moon being an opaque spherical body, (for her hills take off no more from her roundness than the inequalities on the surface of an orange takes off from its roundness) we can only see that part of the enlightened half of her which is towards the Earth. And therefore, when the Moon is at A, in conjunction with the Sun S, her dark half is towards the Earth, and she disappears as at a, there being no light on that half to render it visible. When she comes to her first Octant at B, or has gone an eighth part of her orbit from her Conjunction, a quarter of her enlightened side is towards the Earth, and she appears horned as at b. When she has gone a quarter of her orbit from between the Earth and Sun to C, she shews us one half of her enlightened side as at c, and we say, she is a quarter old. At D she is in her second Octant, and by shewing us more of her enlightened side she appears gibbous as at d. At E her whole enlightened side is towards the Earth, and therefore she appears round as at e, when we say, it is Full Moon. In her third Octant at F, part of her dark side being towards the Earth, she again appears gibbous, and is on the decrease, as at f. At G we see just one half of her enlightened side, and she appears half decreased, or in her third Quarter, as at g. At H we only see a quarter of her enlightened side, being in her fourth Octant, where she appears horned as at h. And at A, having compleated her course from the Sun to the Sun again, she disappears; and we say, it is New Moon. Thus in going from A to E the Moon seems continually to increase; and in going from E to A, to decrease in the same proportion; having like Phases at equal distances from A or E, but as seen from the Sun S, she is always Full.
256. The Moon appears not perfectly round when she is Full in the highest or lowest part of her Orbit, because we have not a direct view of her enlightened side at that time. When Full in the highest part of her orbit, a small deficiency appears on her lower edge; and the contrary when Full in the lowest part of her Orbit.
257. ’Tis plain by the Figure, that when the Moon changes to the Earth, the Earth appears Full to the Moon; and vice versâ. For when the Moon is at A, New to the Earth, the whole enlightened side of the Earth is towards the Moon: and when the Moon is at E, Full to the Earth, it’s dark side is towards her. Hence a New Moon answers to a Full Earth, and a Full Moon to a New Earth. The Quarters are also reversed to each other.
258. Between the third Quarter and Change, the Moon is frequently visible in the forenoon, even when the Sun shines; and then she affords us an opportunity of seeing a very agreeable appearance, wherever we find a globular stone above the level of the eye, as suppose on the top of a gate. For, if the Sun shines on the stone, and we place ourselves so as the upper part of the stone may just seem to touch the point of the Moon’s lowermost horn, we shall then see the enlightened part of the stone exactly of the same shape with the Moon; horned as she is, and inclining the same way to the Horizon. The reason is plain; for the Sun enlightens the stone the same way as he does the Moon: and both being Globes, when we put ourselves into the above situation, the Moon and stone have the same position to our eyes; and therefore we must see as much of the illuminated part of the one as of the other.
259. The position of the Moon’s Cusps, or a right line touching the points of her horns, is very differently inclined to the Horizon at different hours of the same days of her age. Sometimes she stands, as it were, upright on her lower horn, and then such a line is perpendicular to the Horizon: when this, happens, she is in what the Astronomers call the Nonagesimal Degree; which is the highest point of the Ecliptic above the Horizon at that time, and is 90 degrees from both sides of the Horizon where it is then cut by the Ecliptic. But this never happens when the Moon is on the Meridian, except when she is at the very beginning of Cancer or Capricorn.
260. The inclination of that part of the Ecliptic to the Horizon in which the Moon is at any time when horned, may be known by the position of her horns; for a right line touching their points is perpendicular to the Ecliptic. And as the Angle that the Moon’s orbit makes with the Ecliptic can never raise her above, nor depress her below the Ecliptic, more than two minutes of a degree, as seen from the Sun; it can have no sensible effect upon the position of her horns. Therefore, if a Quadrant be held up, so as one of it’s edges may seem to touch the Moon’s horns, the graduated side being kept towards the eye, and as far from the eye as it can be conveniently held, the arc between the Plumb-line and that edge of the Quadrant which seems to touch the Moon’s horns will shew the inclination of that part of the Ecliptic to the Horizon. And the arc between the other edge of the Quadrant and Plumb-line will shew the inclination of the Moon’s horns to the Horizon at that time also.
261. The Moon generally appears as large as the Sun; for the Angle vkA, under which the Moon is seen from the Earth, is the same with the Angle LkM, under which the Sun is seen from it. And therefore the Moon may hide the Sun’s whole Disc from us, as she sometimes does in solar Eclipses. The reason why she does not eclipse the Sun at every Change shall be explained afterwards. If the Moon were farther from the Earth as at a, she could never hide the whole of the Sun from us; for then she would appear under the Angle NkO, eclipsing only that part of the Sun which lies between N and O: were she still further from the Earth, as at X, she would appear under the small Angle TkW, like a spot on the Sun, hiding only the part TW from our sight.
262. The Moon turns round her Axis in the time that she goes round her orbit; which is evident from hence, that a spectator at rest, without the periphery of the Moon’s orbit, would see all her sides turned regularly towards him in that time. She turns round her Axis from any Star to the same Star again in 27 days 8 hours; from the Sun to the Sun again in 291⁄2 days: the former is the length of her sidereal day, and the latter the length of her solar day. A body moving round the Sun would have a solar day in every revolution, without turning on it’s Axis; the same as if it had kept all the while at rest, and the Sun moved round it: but without turning round it’s Axis it could never have one sidereal day, because it would always keep the same side towards any given Star.
263. If the Earth had no annual motion, the Moon would go round it so as to compleat a Lunation, a sidereal, and a solar day, all in the same time. But, because the Earth goes forward in it’s orbit while the Moon goes round the Earth in her orbit, the Moon must go as much more than round her orbit from Change to Change in compleating a solar day as the Earth has gone forward in it’s orbit during that time, i. e. almost a twelfth part of a Circle.
264. The Moon’s periodical and synodical revolution may be familiarly represented by the motions of the hour and minute hands of a watch round it’s dial-plate, which is divided into 12 equal parts or hours, as the Ecliptic is divided into 12 Signs, and the year into 12 months. Let us suppose these 12 hours to be 12 months, the hour hand the Sun, and the minute hand the Moon; then will the former go round once in a year, and the latter once in a month; but the Moon, or minute hand must go more than round from any point of the Circle where it was last conjoined with the Sun, or hour hand, to overtake it again: for the hour hand being in motion, can never be overtaken by the minute hand at that point from which they started at their last conjunction. The first column of the annexed Table shews the number of conjunctions which the hour and minute hand make whilst the hour hand goes once round the dial-plate; and the other columns shew the times when the two hands meet at every conjunction. Thus, suppose the two hands to be in conjunction at XII, as they always are; then, at the first following conjunction it is 5 minutes 27 seconds 16 thirds 21 fourths 491⁄11 fifths past I where they meet; at the second conjunction it is 10 minutes 54 seconds 32 thirds 43 fourths 381⁄2 fifths past II; and so on. This, though an easy illustration of the motions of the Sun and Moon, is not precise as to the times of their conjunctions; because, while the Sun goes round the Ecliptic, the Moon makes 121⁄3 conjunctions with him; but the minute hand of a watch or clock makes only 11 conjunctions with the hour hand in one period round the dial-plate. But if, instead of the common wheel-work at the back of the dial-plate, the Axis of the minute hand had a pinion of 6 leaves turning a wheel of 40, and this last turning the hour hand, in every revolution it makes round the dial-plate the minute hand would make 121⁄3 conjunctions with it; and so would be a pretty device for shewing the motions of the Sun and Moon; especially, as the slowest moving hand might have a little Sun fixed on it’s point, and the quickest a little Moon. Besides, the plate, instead of hours and quarters, might have a Circle of months, with the 12 Signs and their Degrees; and if a plate of 291⁄2 equal parts for the days of the Moon’s age were fixed to the Axis of the Sun-hand, and below it, so as the Sun always kept at the 1⁄2 day of that plate, the Moon-hand would shew the Moon’s age upon that plate for every day pointed out by the Sun-hand in the Circle of months; and both Sun and Moon would shew their places in the Ecliptic: for the Sun would go round the Ecliptic in 365 Days and the Moon in 271⁄3 days, which is her periodical revolution; but from the Sun to the Sun again, or from Change to Change, in 291⁄2 days, which is her synodical revolution.
| Conj. | H. | M. | S. | ʺʹ | ʺʺ | v pts. |
|---|---|---|---|---|---|---|
| 1 | I | 5 | 27 | 16 | 21 | 491⁄11 |
| 2 | II | 10 | 54 | 32 | 43 | 382⁄11 |
| 3 | III | 16 | 21 | 49 | 5 | 273⁄11 |
| 4 | IIII | 21 | 49 | 5 | 27 | 164⁄11 |
| 5 | V | 27 | 16 | 21 | 49 | 55⁄11 |
| 6 | VI | 32 | 43 | 38 | 10 | 546⁄11 |
| 7 | VII | 38 | 10 | 54 | 32 | 437⁄11 |
| 8 | VIII | 43 | 38 | 10 | 54 | 328⁄11 |
| 9 | IX | 49 | 5 | 27 | 16 | 219⁄11 |
| 10 | X | 54 | 32 | 43 | 38 | 1010⁄11 |
| 11 | XII | 0 | 0 | 0 | 0 | 0 |
265. If the Earth had no annual motion, the Moon’s motion round the Earth, and her track in absolute space, would be always the same[58]. But as the Earth and Moon move round the Sun, the Moon’s real path in the Heavens is very different from her path round the Earth: the latter being in a progressive Circle, and the former in a curve of different degrees of concavity, which would always be the same in the same parts of the Heavens, if the Moon performed a compleat number of Lunations in a year.
266. Let a nail in the end of the axle of a chariot-wheel represent the Earth, and a pin in the nave the Moon; if the body of the chariot be propped up so as to keep that wheel from touching the ground, and the wheel be then turned round by hand, the pin will describe a Circle both round the nail and in the space it moves through. But if the props be taken away, the horses put to, and the chariot driven over a piece of ground which is circularly convex; the nail in the axle will describe a circular curve, and the pin in the nave will still describe a circle round the progressive nail in the axle, but not in the space through which it moves. In this case, the curve described by the nail will resemble in miniature as much of the Earth’s annual path round the Sun, as it describes whilst the Moon goes as often round the Earth as the pin does round the nail: and the curve described by the nail will have some resemblance of the Moon’s path during so many Lunations.
Let us now suppose that the Radius of the circular curve described by the nail in the axle is to the Radius of the Circle which the pin in the nave describes round the axle as 3371⁄2 to 1; which is the proportion of the Radius or Semidiameter of the Earth’s Orbit to that of the Moon’s; or of the circular curve A 1 2 3 4 5 6 7 B &c. to the little Circle a; and then, whilst the progressive nail describes the said curve from A to E, the pin will go once round the nail with regard to the center of it’s path, and in doing so, will describe the curve abcde. The former will be a true representation of the Earth’s path for one Lunation, and the latter of the Moon’s for that time. Here we may set aside the inequalities of the Moon’s Moon, and also the Earth’s moving round it’s common center of gravity and the Moon’s: all which, if they were truly copied in this experiment, would not sensibly alter the figure of the paths described by the nail and pin, even though they should rub against a plain upright surface all the way, and leave their tracks visible. And if the chariot should be driven forward on such a convex piece of ground, so as to turn the wheel several times round, the track of the pin in the nave would still be concave toward the center of the circular curve described by the pin in the Axle; as the Moon’s path is always concave to the Sun in the center of the Earth’s annual Orbit.
In this Diagram, the thickest curve line ABCD, with the numeral figures set to it, represents as much of the Earth’s annual Orbit as it describes in 32 days from west to east; the little Circles at a, b, c, d, e shew the Moon’s Orbit in due proportion to the Earth’s; and the smallest curve abcdef represents the line of the Moon’s path in the Heavens for 32 days, accounted from any particular New Moon at a. The machine, Fig. 5th is for delineating the Moon’s path, and will be described, with the rest of my Astronomical machinery, in the last Chapter. The Sun is supposed to be in the center of the curve A 1 2 3 4 5 6 7 B &c. and the small dotted Circles upon it represent the Moon’s Orbit, of which the Radius is in the same proportion to the Earth’s path in this scheme, that the Radius of the Moon’s Orbit in the Heavens bears to the Radius of the Earth’s annual path round the Sun; that is, as 240,000 to 81,000,000, or as 1 to 3371⁄2.
When the Earth is at A the New Moon is at a; and in the seven days that the Earth describes the curve 1 2 3 4 5 6 7, the Moon in accompanying the Earth describes the curve ab; and is in her first Quarter at b when the Earth is at B. As the Earth describes the curve B 8 9 10 11 12 13 14 the Moon describes the curve bc; and is opposite to the Sun at c, when the Earth is at C. Whilst the Earth describes the curve C 15 16 17 18 19 20 21 22 the Moon describes the curve cd; and is in her third Quarter at d when the Earth is at D. Once more, whilst the Earth describes the curve D 23 24 25 26 27 28 29 the Moon describes the curve de; and is again in conjunction at e with the Sun when the Earth is at E, between the 29th and 30th day of the Moon’s age, accounted by the numeral Figures from the New Moon at A. In describing the curve abcde, the Moon goes round the progressive Earth as really as if she had kept in the dotted Circle A, and the Earth continued immoveable in the center of that Circle.
And thus we see, that although the Moon goes round the Earth in a Circle, with respect to the Earth’s center, her real path in the Heavens is not very different in appearance from the Earth’s path. To shew that the Moon’s path is concave to the Sun, even at the time of Change, it is carried on a little farther into a second Lunation, as to f.
267. The Moon’s absolute motion from her Change to her first Quarter, or from a to b, is so much slower than the Earth’s, that she falls 240 thousand miles (equal to the Semidiameter of her Orbit) behind the Earth at her first Quarter in b, when the Earth is in B; that is, she falls back a space equal to her distance from the Earth. From that time her motion is gradually accelerated to her Opposition or Full at c, and then she is come up as far as the Earth, having regained what she lost in her first Quarter from a to b. From the Full to the last Quarter at d her motion continues accelerated, so as to be just as far before the Earth at D, as she was behind it at her first Quarter in b. But, from d to e her motion is retarded so, that she loses as much with respect to the Earth as is equal to her distance from it, or to the Semidiameter of her Orbit; and by that means she comes to e, and is then in conjunction with the Sun as seen from the Earth at E. Hence we find, that the Moon’s absolute motion is slower than the Earth’s from her third Quarter to her first; and swifter than the Earth’s from her first Quarter to her third: her path being less curved than the Earth’s in the former case, and more in the latter. Yet it is still bent the same way towards the Sun; for if we imagine the concavity of the Earth’s Orbit to be measured by the length of a perpendicular line Cg, let down from the Earth’s place upon the straight line bgd at the Full of the Moon, and connecting the places of the Earth at the end of the Moon’s first and third Quarters, that length will be about 640 thousand miles; and the Moon when New only approaching nearer to the Sun by 240 thousand miles than the Earth is, the length of the perpendicular let down from her place at that time upon the same straight line, and which shews the concavity of that part of her path, will be about 400 thousand miles.
268. The Moon’s path being concave to the Sun throughout, demonstrates that her gravity towards the Sun, at her conjunction, exceeds her gravity towards the Earth. And if we consider that the quantity of matter in the Sun is almost 230 thousand times as great as the quantity of matter in the Earth, and that the attraction of each body diminishes as the square of the distance from it increases, we shall soon find, that the point of equal attraction where these two powers would be equally strong, is about 70 thousand miles nearer the Earth than the Moon is at her Change. It may now appear surprising that the Moon does not abandon the Earth when she is between it and the Sun, because she is considerably more attracted by the Sun than by the Earth at that time. But this difficulty vanishes when we consider, that the Moon is so near the Earth in proportion to the Earth’s distance from the Sun, that she is but very little more attracted by the Sun at that time than the Earth is; and whilst the Earth’s attraction is greater upon the Moon than the difference of the Sun’s attraction upon the Earth and her (and that it is always much greater is demonstrable) there is no danger of the Moon’s leaving the Earth; for if she should fall towards the Sun, the Earth would follow her almost with equal speed. The absolute attraction of the Earth upon a drop of falling rain is much greater than the absolute attraction of the particles of that drop upon each other, or of it’s center upon all parts of it’s circumference; but then the side of the drop next the Earth is attracted with so very little more force than it’s center, or even it’s opposite side; that the attraction of the center of the drop upon it’s side next the Earth is much greater than the difference of force by which the Earth attracts it’s nearer surface and center: on which account the drop preserves it’s round figure, and might be projected about the Earth by a strong circulating wind so as to be kept from falling to the Earth. It is much the same with the Earth and Moon in respect to the Sun; for if we should suppose the Moon’s Orbit to be filled with a fluid Globe, of which all the parts would be attracted towards the Earth in it’s center, but the whole of it much more attracted by the Sun; one part of it could not fall to the Sun without the other, and a sufficient projectile force would carry the whole fluid Globe round the Sun. A ship, at the distance of the Moon, sailing round the Earth on the surface of the fluid Globe, could no more be taken away by the Sun when it is on the side next him, than the Earth could be taken away from it when it is on the opposite side; which could never happen unless the Earth’s projectile motion were stopt; and if it were stopt, the Ship with the whole fluid Globe, Earth and all together, would as naturally fall to the Sun as a drop of rain in calm air falls to the Earth. Hence we may see, that the Earth is in no more danger of 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.
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.
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 421⁄2 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.
Having drawn their Orbits on a Card, in proportion to their relative distances from Jupiter, I measured the radius of the Orbit of the fourth Satellite, which was an inch and a tenth part; then multiplied this by 424 for the radius of Jupiter’s Orbit, because Jupiter is 424 times as far from the Sun’s center as his fourth Satellite is from his center; and the product thence arising was 4664⁄10 inches. Then taking a small cord of this length, and fixing one end of it to the floor of a long room by a nail, with a black lead pencil at the other end I drew the curve ABCD &c. and set off a degree and an half thereon, from A to T; because Jupiter moves only so much, whilst his outermost Satellite 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 AT into 18 equal parts, as AB, 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 it’s synodical period round Jupiter. Then drawing a right line through the center of the Card, as a diameter to all the 4 Orbits upon it, I put the card upon the line of Jupiter’s motion, and transferred it to every horary division thereon, keeping always the said 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 etc. 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 center 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 Satellites as can be desired. And in the same manner might those for Saturn’s Satellites be delineated.
270. It appears by the scheme, that the three first Satellites come almost into the same line or position every seventh day; the first being only a little behind with the second, and the second behind with the third. But the period of the fourth Satellite is so incommensurate to the periods of the other three, that it cannot be guessed at by the diagram when it would fall again into a line of conjunction with them, between Jupiter and the Sun. And no wonder; for supposing them all to have been once in conjunction, it will require 3,087,043,493,260 years to bring them in a conjunction again: See § 73.
271. In Fig. 4th we have the proportions of the Orbits of Saturn’s five Satellites, and of Jupiter’s four, to one another, to our Moon’s Orbit, and to the Disc of the Sun. S is the Sun; M m the Moon’s Orbit (the Earth supposed to be at E;) J Jupiter; 1. 2. 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 211⁄4 yards, of Jupiter’s orbit 112⁄3, and of the Earth’s 21⁄4, 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 whilst they describe the inferior parts of their Orbits, and direct whilst they describe the superior. This is the case with Jupiter’s first and second Satellites, and with Saturn’s first. But those Satellites whose velocities 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. There is a table of this sort in De la Caile’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 Satellites | Proportion of the Radius of the Planet’s Orbit to the Radius of the Orbit of each Satellite. | Proportion of the Time of the Planet’s Revolution to the Revolution of each Satellite. | Proportion of the Velocity of each Satellite to the Velocity of its primary Planet. | ||||
|---|---|---|---|---|---|---|---|
| of Saturn | 1 | As 5322 | to 1 | As 5738 | to 1 | As 5738 | to 5322 |
| 2 | 4155 | 1 | 3912 | 1 | 3912 | 4155 | |
| 3 | 2954 | 1 | 2347 | 1 | 2347 | 2954 | |
| 4 | 1295 | 1 | 674 | 1 | 674 | 1295 | |
| 5 | 432 | 1 | 134 | 1 | 134 | 432 | |
| of Jupiter | 1 | As 1851 | to 1 | As 2445 | to 1 | As 2445 | to 1851 |
| 2 | 1165 | 1 | 1219 | 1 | 1219 | 1165 | |
| 3 | 731 | 1 | 604 | 1 | 604 | 731 | |
| 4 | 424 | 1 | 258 | 1 | 258 | 424 | |
| The Moon | As 3371⁄2 | to 1 | As 121⁄3 | to 1 | As 121⁄3 | to 3371⁄2 | |