The Orrery is an Astronomical Machine, made to represent the motions of the Planets. These machines are made of various sizes, some having more Planets than others; but I shall here confine myself to the description of that above-mentioned.
In the Introduction we gave a short account of the Order, Periods, Distances, and Magnitudes of the Primary Planets; and of the Distances and Periodical Resolutions of the Secondary Planets round their respective Primaries. We shall here explain their Stations, Regradations, Eclipses, Phases, &c. but first let us take a general view of the Orrery.
The frame which contains the wheel-work, &c. that regulates the whole Machine, is made of fine ebony, and is near four feet in diameter; the outside thereof is adorned with twelve pilasters, curiously wrought and gilt: Between these pilasters the twelve Signs of the Zodiac are neatly painted, with gilded frames. Above the frame is a broad ring, supported with twelve pillars: This ring represents the Plane of the Ecliptic, upon which there are two scales of degrees, and between those the names and characters of the twelve Signs. Near the outside is a scale of months and days, exactly corresponding to the Sun’s place at noon, each day throughout the year.
Above the ecliptic stands some of the principal circles of the sphere, according to their respective situations in the heavens, viz. N° 10, are the two Colures, divided into degrees, and half degrees; N° 11, is one half of the Equinoctial Circle, making an angle with the ecliptic of 23½ degrees. The Tropic of Cancer, and the Arctic Circle, are each fixed parallel, and at their proper distance from the equinoctial. On the Northern half of the ecliptic is a brass semicircle, moveable upon two points fixed in ♈ and ♎: This semicircle serves as a moveable horizon, to be put to any degree of latitude upon the North part of the meridian. The whole machine is also so contrived, as to be set to any latitude, without in the least affecting any of the inside motions: For this purpose there are two strong hinges (N° 13,) fixed to the bottom frame, upon which the instrument moves, and a strong brass arch, having holes at every degree, thro’ which a strong pin is to be put, according to the elevation. This arch and the two hinges, support the whole machine, when it is lifted up according to any latitude; and the arch at other times lies conveniently under the bottom frame.
When the machine is set to any latitude (which is easily done by two men, each taking hold of two handles, conveniently fixed for that purpose) set the moveable horizon to the same degree upon the meridian, and you may form an idea of the respective altitude, or depressions of the Planets, above or below the horizon, according to their respective positions, with regard to the meridian.
Within the ecliptic, and nearly in the same place thereof, stands the Sun, and all the Planets, both Primary and Secondary. The Sun (Nº 1.) stands in the middle of the whole system, upon a wire, making an angle with the plane of the ecliptic, of about 82 degrees; which is the inclination of the Sun’s axis, to the axis of the ecliptic. Next to the Sun is a Small ball (Nº 2.) representing Mercury: Next to Mercury is Venus (Nº 3.) represented by a larger ball (and both these stand upon wires,) so that the balls themselves may be more visibly perceived by the eye. The Earth is represented (Nº 4.) by an ivory ball, having some of the principal meridians and parallels, and a little sketch of a map described upon it. The wire which supports the Earth, makes an angle with the plane of the ecliptic 66½ degrees, which is the inclination of the Earth’s axis to that of the ecliptic. Near the bottom of the Earth’s axis is a Dial Plate (Nº 9.) having an index pointing to the hours of the day, as the Earth turns round its axis.
Round the Earth is a ring, supported by two small pillars, which ring represents the Orbit of the Moon, and the division upon it answers to the Moon’s latitude; the motion of this ring represents the motion of the Moon’s Orbit, according to that of the Nodes. Within this ring is the Moon (Nº 5.) having a black cap or case, which by its motion, represents the Phases of the Moon according to her age. Without the Orbits of the Earth and Moon is Mars (Nº 6.) The next in order to Mars is Jupiter, and his four Moons (Nº 7); each of these moons is supported by a crooked wire fixed in a socket, which turns about the pillar that supports Jupiter. These satellites may be turned by the hand to any position; and yet when the machine is put in motion, they will all move in their proper times. The outermost of all is Saturn, and his five Moons (Nº 8.) These moons are supported and contrived after the same manner with those of Jupiter. The whole machine is put into motion by turning a small winch (like the key of a clock, Nº 14.) and all the inside work is so truly wrought, that it requires but very small strength to put the whole motion.
Above the handle there is a cylindrical pin, which may be drawn a little out, or pushed in, at pleasure: when it is pushed in, all the Planets, both primary and Secondary, will move according to their respective periods, by turning the handle: When it is drawn out, the motions of the Satellites of Jupiter and Saturn will be stopped, while all the rest move without interruption. This is a very good contrivance to preserve the instrument from being clogged by the swift motions of the wheels belonging to the Satellites of Jupiter and Saturn, when the motions of the rest of the Planets are only considered.
There is also a brass lamp having two convex glasses, to be put in the room of the Sun; and also a smaller Earth and Moon, made somewhat in proportion to their distance from each other, which may be put on at pleasure.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Let AB be an arch of the Earth’s orbit, and when the Earth is in T, let the Moon be in N, in conjunction with the Sun in S, while the Moon is describing her orbit NAFD, the Earth will describe the arch of her orbit T t; and when the Earth has got into the point t, the Moon will be in the point of her orbit n, having made one compleat revolution round the Earth. But the Moon, before she comes in conjunction with the Sun, must again describe the arch n o; which arch is similar to T t, because the lines FN, f n, are parallel; and because, while the Moon describes the arch n o, the Earth advances forward in the ecliptic; the arch described by the Moon, after she has finished her periodical month, before she makes a synodical month, must be somewhat greater than n o. To determine the mean length of a synodical month, find the diurnal motion of the Moon (or the space she describes round the Earth in one day) and likewise the diurnal motion of the Earth; then the difference betwixt the two motions, is the apparent motion of the Moon round the Earth in one day; then it will be, as this differential arch is to a whole circle; so is one day to that space of time wherein the Moon appears to describe a compleat circle round the Earth, which is about 29½ days. But this is not always a true Lunation, for the motion of the Moon is sometimes faster, and sometimes slower, according to the position of the Earth in her orbit.
In one synodical month the Moon has all manner of aspects with the Sun and Earth, and because she is opaque, that face of hers will only appear bright which is towards the Sun, while the opposite remains in darkness. But the inhabitants of the Earth can only see that face of the Moon which is turned towards the Earth; and therefore, according to the various positions of the Moon, in respect of the Sun and Earth, we observe different portions of her illuminated face, and so a continual change in her[7] Phases.
Let S be the Sun, RTV an arch of the Earth’s orbit, T the Earth, and the circle ABCD, &c. the Moon’s orbit, in which she turns round the Earth in the space of a month; and let A, B, C, &c. be the centers of the Moon in different parts of her orbit.
Now if with the lines S A, S B, &c. we join the centers of the Sun and Moon, and at right angles to these draw the lines H O; the said lines H O will be the circles that separate the illuminated part of the Moon from the dark and obscure. Again, if we conceive another line I L to be drawn at right angles to the lines TA, TB, &c. passing from the center of the Earth to the Moon, the said line I L will divide the visible hemisphere of the Moon, or that which is turned towards us, from the invisible, or that which is turned from us; and this circle may be called the Circle of Vision.
Now it is manifest, that whenever the Moon is in the position A, or in that point of her orbit which is opposite to the Sun, the circle of vision, and the circle bounding light and darkness, do coincide, and all the illuminated face of the Moon is turned towards the Earth, and is visible to us; and in this position the Moon is said to be full. But when the Moon arrives to B, all her illuminated face is then not towards the Earth, there being a part of it, HBI, not to be seen by us; and then her visible face is deficient from a circle, and appears of a gibbous form, as in B. Fig. 3. Again when she arrives to C, the two forementioned circles cut each other at right angles, and then we observe a half Moon, as in C, Fig. 3. And again the illuminated face of the Moon is more and more turned from the Earth, until she comes to the Point E, where the circle of vision, and that bounding light and darkness, do again coincide. Here the Moon disappears, the illuminated part being wholly turned from the Earth; and she is now said to be in Conjunction with the Sun, because she is in the same direction from the Earth that the Sun is in, which position we call a New Moon. When the Moon is arrived to F, she again assumes a horned figure, but her horns (which before the change were turned Westward) have now changed their position, and look Eastward. When she has arrived to a quadrate aspect at G, she will appear bissected, like a half Moon, afterwards she will still grow bigger, until at last she comes to A, where again she will appear in her full splendor.
The same appearances which we observe in the Moon are likewise observed by the Lunarians in the Earth, our Earth seeing a Moon to them, as their Moon is to us; and we are observed by them to be carried round in the space of time that they are really carried round the Earth. But the same phases of the Earth and Moon happen when they are in contrary position; for when the Moon is in conjunction to us, the Earth is then in opposition to the Moon, and the Lunarians have then a full Earth, as we in a similar position have a full Moon. When the Moon comes in opposition to the Sun, the Earth, seen from the Moon, will appear in conjunction with her, and in that position the Earth will disappear; afterwards she will assume a horned figure, and so shew the same phases to the inhabitants of the Moon as she does to us.
An Eclipse is that deprivation of light in a Planet, when another is interposed betwixt it and the Sun. Thus, an eclipse of the Sun is made by the interposition of the Moon at her conjunction, and an eclipse of the Moon is occasioned by the shadow of the Earth falling upon the Moon, when she is in opposition to the Sun.
Let S be the Sun, T the Earth, and ABC its shadow; now if the Moon, when she is in opposition to the Sun, should come into the conical space ABC, she will then be deprived of the solar light, and so undergo an eclipse.
In the same manner, when the shadow of the Moon falls upon the Earth (which can never happen but when the Moon is in conjunction with the Sun) that part upon which the shadow falls will be involved in darkness, and the Sun eclipsed. But because the Moon is much less than the Earth, the shadow of the ☽ cannot cover the whole Earth, but only a part of it. Let S be the Sun, T the Earth, ABC the Moon’s orbit, and L the Moon in conjunction with the Sun: Here the shadow of the Moon falls only upon the part DE of the Earth’s surface, and there only the Sun is intirely hid: but there are other parts EF, DG, on each side of the shadow, where the inhabitants are deprived of part of the Solar rays, and that more or less, according to their distance from the shadow. Those who live at H and I will see half of the Sun eclipsed, but in the spaces FM, GN, all the Sun’s body will be visible, without any eclipse. From the preceding figure it appears, that an eclipse of the Sun does not reach a great way upon the superficies of the Earth; but the whole body of the Moon may sometimes be involved in the Earth’s shadow.
Although the Moon seen from the Earth, and the Earth seen from the Moon, are each alternately, once a month, in conjunction with the Sun; yet, by reason of the inclination of the Moon’s orbit to the ecliptic, the Sun is not eclipsed every new Moon, nor the Moon at every full. Let T be the Earth, DTE an arch of the ecliptic, ALBF, the Moon’s orbit, having the Earth T, in its center; and let AGBG be another circle coinciding with the ecliptic, and A, B, the nodes, or the two points where the Moon’s orbit and the ecliptic cut each other. A the ascending node, and B the descending node. The angle GAL equal to GBL is the inclination of the Moon’s orbit to the ecliptic, being about 5¼ degrees. Now a spectator from the Earth at T, will observe the Sun to move in the circle AGBC, and the Moon in her orbit ALBF; whence it is evident, that the Sun and Moon can never be seen in a direct line, from the center of the Earth, but when the Moon is in one of the nodes A or B; and then only will the Sun appear centrally eclipsed. But if the conjunction of the Moon happens when she is any where within the distance A c of the nodes, either North or South, the Sun will then be eclipsed, more or less, according to the distance from the node A, or B. If the conjunction happens when the Moon is in b, the Sun will be then one half eclipsed; and if it happens when she is in c, the Moon’s limb will just touch the Sun’s disk, without hiding any part of it.
The shadow of the Earth at the place where the Moon’s orbit intersects it, is three times as large as the Moon’s diameter, as in Fig. 4. and therefore it often happens that eclipses of the Moon are total, when they are not central: And for the same reason the Moon may sometimes be totally eclipsed for three hours together; whereas total eclipses of the Sun can scarcely ever exceed four minutes.
The eclipses of the Sun and Moon are very well explained by the Orrery: Thus having put the lamp in the place of the Sun, and the little Earth and the little Moon in their proper places, instead of the larger ones, let the room wherein the instrument stands be darkened; then turning the handle about, you will see when the conjunction of the Moon happens. When she is in or near one of the nodes, her shadow will fall upon the Earth, and so deprive that part upon which it falls of the light of the Sun: If the conjunction happens when the Moon is not near one of the nodes, the light of the lamp will fall upon the Earth, either above or below the Moon, according to her latitude at that time. In like manner, when the full Moon happens near one of the nodes, the shadow of the Earth will fall upon the Moon; and if the Moon’s latitude be but small, her whole face will be involved in darkness. At other times, when the full Moon happens when she is not near one of her nodes, the shadow of the Earth will pass either above or below the Moon, and so by that means the Moon will escape being eclipsed.
The apparent diameters of the inferior Planets are so small, that when they pass betwixt us and the Sun, they only appear like small spots upon the Sun’s surface, without depriving us of any sensible quantity of his light. The shadow of the Earth likewise terminates before it reaches any of the superior Planets, so that they are never eclipsed by us; and the Earth when she is in conjunction with the Sun, only appears like a black spot upon his surface.
But Jupiter and his Moons mutually eclipse each other, as our Earth and Moon do; as also doth Saturn and his Moons. The satellites of Jupiter become twice hid from us, in one circulation round ♃; viz. once behind the body of Jupiter, i. e. when they are in the right line joining the centers of the Earth and ♃; and again they become invisible when they enter the shadow of Jupiter, which happens when they are at their Full, as seen from ♃, at which times they also suffer eclipses; which eclipses happen to them after the same manner as they do to our Moon, by the interposition of the Earth betwixt her and the Sun.