Part 10

The lamp turns round in the same time with the Earth, and by means of the glasses cast a strong light upon her; and when the smaller Earth and Moon are placed on, it will be easy to shew when either of them may be eclipsed.

Having thus given a brief description of the outward part of this machine, I shall next give an account of the phænomena explained by it, when it is put into motion.

_Of the Motions of the Planets in general._

Having put on the handle, push in the pin which is just above it, and place a small black patch (or bit of wafer) upon the middle of the Sun (for instance) right against the first degree of ♈; you may also place patches upon _Venus_, _Mars_, and _Jupiter_, right against some noted point in the ecliptic. If you lay a thread from the Sun to the first degree of ♈, you may set a mark where it intersects the orbit of each Planet, and that will be a help to note the time of their revolutions.

One entire turn of the handle answers to the diurnal motion of the Earth round her axis, as may be seen by the motion of the hour index, which is placed at the foot of the wire on which the terella is fixed. When the index has moved the space of ten hours, you may observe that _Jupiter_ has made one revolution compleat round its axis; the handle being turned until the hour index has passed over 24 days, 8 hours, will bring the patch upon _Venus_ to its former situation with respect to the ecliptic, which shews that ♀ has made one entire revolution round her axis. _Mars_ makes one compleat revolution round its axis in 24 hours and about 40 minutes. When the handle is turned 25½ times round, the spot upon the Sun will point to the same degree of the ecliptic, as it did when the instrument was first put into motion. By observing the motions of the spots upon the surface of the Sun, and of the Planets in the heavens, their diurnal motion was discovered; after the same manner as we do here observe the motions of their representatives, by that of the marks placed upon them.

If while you turn the handle you observe the Planets, you will see them perform their motions in the same relative times as they really do in the heavens, each making its period in the times mentioned in the Tables, _Page_, 28, 27¼ turns of the handle will bring the Moon round the Earth, which is called a _Periodic_ Month; and all the while she keeps the same face towards the Earth; for the Moon’s annual and diurnal motion are performed both in the same time nearly, so that we always see the same face or side of the Moon.

If before the instrument is put into motion, the satellites of _Jupiter_ and _Saturn_ be brought into the same right line from their respective primaries, you will see them, as you turn the handle, immediately dispersed from one another, according to their different celerities. Thus one turn of the handle will bring the first of _Jupiter_’s Moons about ⁴/₇ part round _Jupiter_, while the second has described but ²/₇ part, the third but above ¹/₇, and the fourth not quite ¹/₁₆ part, each of its respective orbits. If you turn the handle until the hour index has moved 18½ hours more, the first satellite will then be brought into its former position, and so has made one entire revolution; the second at the same time will be almost diametrically opposite to the first, and so has made a little more than half of one revolution; the others will be in different aspects, according to the length of their periods, as will be plainly exhibited by the instrument. The same observations may be made with respect to the satellites of _Saturn_.

The machine is so contrived, that the handle may be turned either way; and, if before you put it into motion, you observe the aspect (or situation with respect to each other) of the Planets, and then turn the handle round any number of times; the same number of revolutions being made backwards, will bring all the Planets to their former situations. I shall next proceed to particulars.

_Of the Stations and Retrogradations of the Planets._

[Sidenote: _Retrograde Motion of the Planets._]

The primary Planets, as they all turn round the Sun, at different distances, and in different times, appear to us from the Earth to have different motions; as sometimes they appear to move from West to East, according to the order of the signs, which is called their _Direct Motion_; then by degrees they slacken their pace, until at last they lose all their motion, and become _Stationary_, or not to move at all; that is, they appear in the same place with respect to the fixed Stars for some time together; after which they again begin to move, but with a contrary direction, as from East to West, which is called their _Retrograde Motion_; then again they become stationary, and afterwards reassume their direct motion. The reason of all these appearances is very evidently shewn by the _Orrery_.

_Of the Stations_, &c. _of the Inferior Planets._

We shall instance in the Planet _Mercury_, because his motion round the Sun differs more from the Earth’s than that of _Venus_ does.

When _Mercury_ is in his superior conjunction (or when he is in a direct line from the Earth beyond the Sun) fasten a string about the axis of the Earth, and extend it over _Mercury_ to the ecliptic; then turning the handle, keep the thread all the while extended over ☿, and you will find it move with a direct motion in the ecliptic, but continually slower, until _Mercury_ has the greatest elongation from the Earth. Near this position, the thread for some time will lay over _Mercury_ without being moved in the ecliptic, tho’ the Earth and _Mercury_ both continue their progressive motion in their respective orbits. When _Mercury_ has got a little past this place, you will find the thread must be moved backward in the ecliptic, beginning first with a slow motion, and then faster by degrees, until _Mercury_ is in his inferior conjunction, or directly between the Earth and the Sun. Next this position of ☿, his retrograde motion will be the swiftest; but he still moves the same way, tho’ continually slower, ’till he has again come to his greatest elongation, where he will appear the second time to be stationary; after which he begins to move forward, and that faster by degrees, until he is come to the same position with respect to the Earth, that he was in at first. The same observations may be made relating to the motions of _Venus_. In like manner the different motions observed in the superior Planets may be also explained by the _Orrery_. If you extend the thread over _Jupiter_, and proceed after the same manner as before we did in regard to _Mercury_, you will find that from the time _Jupiter_ is in conjunction with the Sun, his motion is direct, but continually slower, until the Earth is nearly in a quadrate aspect with _Jupiter_, near which position _Jupiter_ seems to be stationary: After which he begins to move, and continually mends his pace, until he comes in opposition to the Sun, at which time his retrograde motion is swiftest. He still seems to go backward, but with a slower pace, ’till the Earth and he are again in a quadrate aspect, where _Jupiter_ seems to have lost all his motion; after which he again resumes his direct motion, and so proceeds faster by degrees, ’till the Earth and he are again in opposition to each another.

[Sidenote: _Plate 3_. _Fig. 1_.]

These different motions observed in the Planets, are easily illustrated, as followeth: The lesser circle round the Sun is the orbit of _Mercury_, in which he performs his revolution round the Sun, in about three months, or while the Earth is going thro’ ¼ part of her orbit, or from A to N. The numbers 1, 2, 3, _&c._ in the orbit of _Mercury_, show the spaces he describes in a week nearly, and the distance AB, BC, DC, _&c._ in the Earth’s orbit, do likewise show her motion in the same time. The letters A, B, C, _&c._ in the great orb, are the motions of _Mercury_ in the Heavens, as they appear from the Earth. Now if the Earth be supposed in A, and _Mercury_ in 12, near his superior conjunction with the Sun; a spectator on the Earth will see ☿, as if he were in the point of the Heavens A, and while ☿ is moving from 12 to 1, and from 1 to 2, _&c._ the Earth in the same time also moves from A to B, and from B to C, _&c._ All which time ☿ appears in the Heavens to move in a direct motion from A to B, and from B to C, _&c._ but gradually slower, until he arrives near the point G; near this place he appears stationary, or to stand still; and afterwards (tho’ he still continues to move uniformly in his own orbit, with a progressive motion) yet in the sphere of the fixed Stars he will appear to be retrograde, or to go backwards, as from G to H, from H to I, _&c._ until he has arrived near the point L, where again he will appear to be stationary; and afterwards to move in a direct motion from L to M, and from M to N, _&c._

What has been here shewed concerning the motions of _Mercury_, is also to be understood of the motions of _Venus_; but the conjunctions of _Venus_ with the Sun do not happen so often as in _Mercury_; for _Venus_ moving in a larger orbit, and much slower than _Mercury_, does not so often overtake the Earth. But the retrogradations are much greater in _Venus_ than they are in _Mercury_, for the same reasons.

[Sidenote: _Fig. 2._]

The innermost circle represents the Earth’s orbit, divided into 12 parts, answering to her monthly motion; the greatest circle is in the orbit of _Jupiter_, which he describes in about 12 years; and therefore the ¹/₁₂ thereof, from A to N, defines his motion, in one of our years nearly; and the intermediate divisions, A, B, C, _&c._ his monthly motion. Let us suppose the Earth to be in the point of her orbit 12, and _Jupiter_ in A, in his conjunction with the Sun; it is evident that from the Earth _Jupiter_ will be seen in the great orb, or in the point of the Heavens A, and while the Earth is moving from 12 to 1, 2, _&c._ ♃ also moves from A to B, _&c._ all which time he appears in the Heavens to move with a direct motion from A to B, C, _&c._, until he comes in opposition to the Earth near the point of the Heavens E, where he appears to be stationary; after which ♃ again begins to move (tho’ at first with a slow pace) from E through F, H, I to K, where again he appears to stand still, but afterwards he reassumes his direct motion from I thro’ K, to M, _&c._

From the construction of the preceding figure it appears, that when the superior Planets are in conjunction with the Sun, their direct motion is much quicker than at other times; and that because they really move from West to East, while the Earth in the opposite part of the Heavens is carried the same way, and round the same center. This motion afterwards continually slackens until the Planet comes almost in opposition to the Sun, when the line joining the Earth and Planet, will continue for some time nearly parallel to itself, and so the Planet seems from the Earth to stand still; after which, it begins to move with a slow motion backward, until it comes into a quartile aspect with the Sun, when again it will appear to be stationary, for the above reasons; after that it will resume its direct motion, until it comes into a conjunction with the Sun, then it will proceed as above explained. Hence it also appears, that the retrogradations of the superior Planets are much slower than their direct motions, and their continuance much shorter; for the Planet, from its last quarter, until it comes in opposition to the Sun, appears to move the same way with the Earth, by whom it is then overtaken: After which it begins to go backwards, but with a slow motion, because the Earth being in the same part of the Heavens, and moving the same way that the Planet really does, the apparent motion of the Planet backwards, must thereby be lessened.

What has been here said concerning the motions of _Jupiter_, is also to be understood of _Mars_ and _Saturn_. But the retrogradations of _Saturn_ do oftener happen than those of _Jupiter_, because the Earth oftener overtakes _Saturn_; and for the same reason, the regressions of _Jupiter_ do oftener happen than those of _Mars_. But the retrogradations of _Mars_ are much greater than those of _Jupiter_, whose are also much greater than those of _Saturn_.

In either of the satellites of _Jupiter_ or _Saturn_, these different appearances in the neighbouring Worlds are much oftener seen than they are by us in the primary Planets.

We never observe these different motions in the Moon, because she turns round the Earth as her center; neither do we observe them in the Sun, because he is the center of the Earth’s motion; whence the apparent motion of the Sun always appears the same way round the Earth.

_Of the Annual and Diurnal Motion of the Earth, and of the increase and decrease of Days and Nights._

The Earth in her annual motion round the Sun, has her axis always in the same direction, or parallel to itself; that is, if a line be drawn parallel to the axis, while the Earth is in any point of her orbit, the axis in all other positions of the Earth will be parallel to the said line. This parallelism of the axis, and the simple motion of the Earth in the ecliptic, solves all the phænomena of different seasons. These things are very well illustrated by the _Orrery_.

If you put on the lamp in the place of the Sun, you will see how one half of our globe is always illuminated by the Sun, while the other hemisphere remains in darkness; how Day and Night are formed by the revolution of the Earth round her axis; for as she turns from West to East, the Sun appears to move from East to West. And while the Earth turns in her orbit, you may observe that her axis always points the same way, and the several seasons of the year continually change.

To make these things plainer, we will take a view of the Earth in different parts of her orbit.

When the Earth is in the first point of _Libra_ (which is found by extending a thread from the Sun, and over the Earth, to the ecliptic) we have the _Vernal Equinox_, and the Sun at that time appears in the first point of ♈. In this position of the Earth, two Poles of the world are in the line separating light and darkness; and as the Earth turns round her axis, just one half of the equator, and all its parallels, will be in the light, and the other half in the dark; and therefore the days and nights must be every where equal.

As the Earth moves along in her orbit, you will perceive the North Pole advances by degrees into the illuminated hemisphere, and at the same time the South Pole recedes into darkness; and in all places to the Northward of the equator, the days continually lengthen, while the contrary happens in the Southern parts, until at length the Earth is arrived in _Capricorn_. In this position of the Earth all the space included within the arctic circle falls wholly within the light, and all the opposite part lying within the antarctic circle, is quite involved in darkness. In all places between the equator and the arctic circle, the days are now at the longest, and are gradually longer, as the place are more remote from the equator. In the Southern hemisphere there is a contrary effect. All the while the Earth is travelling from _Capricorn_ towards _Aries_, the North Pole gradually recedes from the light, and the South Pole approaches nearer to it; the days in the Northern hemisphere gradually decrease, and in the Southern hemisphere they increase in the same proportion, until the Earth be arrived in ♈; then the two Poles of the world lie exactly in the line separating light and darkness, and the days are equal to the nights in all places of the world. As the Earth advances towards _Cancer_, the North Pole gradually recedes from the light, while the Southern one advances into it, at the same rate. In the Northern hemisphere the days decrease, and in the Southern one they gradually lengthen, until the Earth being arrived in _Cancer_, the North frigid Zone is all involved in darkness, and the South frigid Zone falls intirely within the light; the days every where in the Northern hemisphere are now at the shortest, and to the Southward they are at the longest. As the Earth moves from hence towards _Libra_, the North Pole gradually approaches the light, and the other recedes from it; and in all places to the Northward of the equator, the days now lengthen, while in the opposite hemisphere they gradually shorten, until the Earth has gotten into ♎; in which position the days and nights will again be of equal length in all parts of the world.

You might have observed that in all positions of the Earth, one half of the equator was in the light, and the other half in darkness; whence under the equator, the days and nights are always of the same length: And all the while the Earth was going from ♎ towards ♈, the North Pole was constantly illuminated, and the South Pole all the while in darkness; and for the other half year, the contrary. Sometimes there is a semicircle exactly facing the Sun, fixed over the middle of the Earth, which may be called the horizon of the disk: This will do instead of the lamp, if that half of the Earth which is next the Sun be considered, as being the illuminated hemisphere, and the other half, to be that which lies in darkness.

[Sidenote: _Plate 4._]

The great circle ♈, ♉, ♊ &_c._ represent the Earth’s annual orbit; and the four lesser circles ESQC, the ecliptic, upon the surface of the Earth, coinciding with the great ecliptic in the Heavens. These four lesser figures represent the Earth in the four cardinal points of the ecliptic, P being the North Pole of the equator, and _p_ the North Pole of the ecliptic; SPC, the solstitial colure which is always parallel to the great solstitial colure ♋ ☉ ♑ in the Heavens; EPQ the equinoctial colure. The other circles passing thro’ P, are meridians at two hours distance from one another; the semicircle EÆQ is the Northern half of the equator; the parallel circle touching the ecliptic in S, is the tropic of _Cancer_; the dotted circle, the parallel of _London_, and the small circle, touching the Pole of the ecliptic, is the _Arctic Circle_. The shaded part, which is always opposite to the Sun, is the obscure hemisphere, or that which lies in darkness; and that which is next the Sun, is the illuminated hemisphere.

If we suppose the Earth in ♎, she will then see the Sun in ♈ (which makes our vernal equinox) and in this position the circle bounding light and darkness, which here is SC, passes thro’ the Poles of the World, and bisects all the parallels of the equator; and therefore the diurnal and nocturnal arches, or the length of the days and nights, are equal in all places of the world.

But while the Earth in her annual course, moves through ♏, ♐, to ♑, the line SC, keeping still parallel to itself, or to the place where it was at first, the Pole P will, by this motion, gradually advance into the illuminated hemisphere; and also the diurnal arches of the parallels gradually increase, and consequently the nocturnal ones decrease in the same proportion, until the Earth has arrived into ♑; in which position the Pole P, and all the space within the arctic circle, fall wholly within the illuminated hemisphere, and the diurnal arches of all the parallels that are without this circle, will exceed the nocturnal arches more or less, as the places are nearer to, or farther off from it, until the distance from the Pole is as far as the equator, where both these arches are always equal.

Again, while the Earth is moving from ♑ through ♒, ♓, to ♈, the Pole P begins to incline to the line, distinguishing light and darkness, in the same proportion that before it receded from it; and consequently the diurnal arches gradually lessen, until the Earth has arrived into ♈ where the Pole P will again fall on the horizon, and so cause the days and nights to be every where equal. But when the Earth has passed ♈, while she is going thro’ ♉, and ♊, _&c._ the Pole P will begin to fall in the obscure hemisphere, and so recede gradually from the light, until the Earth is arrived in ♋; in which position not only the Pole, but all the space within the arctic circle, are involved in darkness, and the diurnal arches of all the parallels, without the arctic circle, are equal to the nocturnal arches of the same parallels, when the Earth was in the opposite point ♑; and it is evident that the days are now at the shortest, and the nights the longest. But when the Earth has past this point, while she is going through ♌ and ♏, the Pole P will again gradually approach the light, and so the diurnal arches of the parallels gradually lengthen, until the Earth is arrived in ♎; at which time the days and nights will again be equal in all places of the World, and the Pole itself just see the Sun.

Here we only considered the phænomena belonging to the Northern parallels; but if the Pole P be made the South Pole, then all the parallels of latitude will be parallels of South latitude, and the days, every where, in any position of the Earth, will be equal to the nights of those who lived in the opposite hemisphere, under the same parallels.

_Of the Phases of the Moon, and of her Motion in her Orbit._

[Sidenote: _Nodes._]

[Sidenote: _Dragon’s Head._]

[Sidenote: _Dragon’s Tail._]

[Sidenote: _Retrograde Motion of the Nodes._]

The orbit of the Moon makes an angle with the plane of the ecliptic, of above 5¼ degrees, and cuts it into two points, diametrically opposite (after the same manner as the equator and the ecliptic cut each other upon the globe, in ♈ and ♎) which points are called the _Nodes_; and a right line joining these points, and passing through the center of the Earth, is called the _Line of the Nodes_. That node where the Moon begins to ascend Northward above the plane of the ecliptic, is called the _Ascending Node_, and the _Head of the Dragon_, and is thus commonly marked [Symbol]. The other node from whence the Moon, descends to the Southward of the ecliptic, is called the _Descending Node_, and the _Dragon’s Tail_, and is thus marked [Symbol]. The line of nodes continually shifts itself from East to West, contrary to the order of the signs; and with this _retrograde_ motion, makes one revolution round the Earth, in the space of about 19 years.

[Sidenote: _Periodical Month._]

[Sidenote: _Synodical Month._]

The Moon describes its orbit round the Earth in the Space of 27 days and 7 hours, which space of time is called a _Periodical Month_; yet from one conjunction to the next, the Moon spends 29 days and a half, which is called a _Synodical Month_; because while the Moon in her proper _Orbit_ finishes her course, the Earth advances near a whole sign in the ecliptic; which space the Moon has still to describe, before she will be seen in conjunction with the Sun.

When the Moon is in conjunction with the Sun, note her place in the ecliptic; then turning the handle, you will find that 27 days and 7 hours will bring the Moon to the same place; and after you have made 2¼ revolutions more, the Moon will be exactly betwixt the Sun and the Earth.

[Sidenote: _Phases of the Moon._]

The Moon all the while keeps in her orbit, and so the wire that Supports her continually rises or falls in a socket, as she changes her latitude; the black cap shifts itself, and so shews the phases of the Moon, according to her age, or how much of her enlightened part is seen from the Earth. In one synodical month, the line of the nodes moves about 1½ degree from West to East, and so makes one entire revolution in 19 years.