Part 11

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_.

[Sidenote: _Full Moon._]

[Sidenote: _Half Moon._]

[Sidenote: _New Moon._]

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.

_Of the Eclipses of the Sun and Moon._

[Sidenote: _Eclipse._]

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.

[Sidenote: _Fig. 4_.]

[Sidenote: _Lunar Eclipse._]

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.

[Sidenote: _Solar Eclipse._]

[Sidenote: _Fig. 5._]

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.

[Sidenote: _Fig. 6._]

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.

_Of the Eclipses of the_ Satellites _of_ Jupiter.

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.

[Sidenote: _Fig. 7._]

Let S be the Sun, ABT the Earth’s orbit; and C ♃ D, an arch of _Jupiter_’s orbit, in which let _Jupiter_ be in the point ♃; and let CFDH be the orbit of one of _Jupiter_’s satellites, which we will here suppose to be the farthest from him. These satellites, while they move thro’ the inferior parts of their orbs, _viz._ from D thro’ H, I, to C, seem from the Earth and the Sun to have a retrograde motion; but when they are in the superior part of their orbit, they are then seen to move from West to East, according to their true motion. Now while they describe the superior part of their orbits, they will be twice hid from the Earth, once in the shadow of ♃, and once behind his body. If _Jupiter_ be more Westerly than the Sun, that is, when the Earth is in A, they will be first hid in the shadow F, and afterwards behind the body of ♃ in G: But when the Earth is in B, then they are first hid behind ♃’s body in E, and afterwards fall into the shadow F. While the satellites describe the inferior parts of their orbit, they only once disappear, which may be either in I or H, according to the position of the Earth, in which places they cannot be distinguished from the body of _Jupiter_.

When the satellites seen from ♃ are in conjunction with the Sun, their shadows will then fall upon ♃, and some part of his body be involved in darkness, to which part the Sun will be totally eclipsed.

By observing the eclipses of _Jupiter_’s satellites, it was first discovered that light is not propogated instantaneously, though it moves with an incredible swiftness: For if light came to us in an instant, an observer in T will see an eclipse of one of the satellites, at the same time that another in K would. But it has been found by observations, that when the Earth is in K, at her nearest distance from _Jupiter_, these eclipses happen much sooner than when she is in T. Now having the difference of time betwixt these appearances in K and T, we may find the length of time the light takes in passing from K to T, which space is equal to the diameter of the Earth’s annual orb. By these kinds of observations it has been found, that light reaches from the Sun to us in the space of eleven minutes of time, which is at least at the rate of 100,000 miles in a second.

_FINIS._

AN INDEX OF THE ASTRONOMICAL TERMS Made Use of in this BOOK.

_Acronical_ Rising and Setting of the Stars Page 96 _Almacanthers_ 63 _Altitudes_ ib. ——— _Meridian Altitude_ 63 _Amplitude_ 62 _Amphiscians_ 91 _Annual Motion_ 7 _Antœci_ 92 _Antarctic Circle_ 53 ——— _Pole_ ib. _Antipodes_ 93 _Arctic Circle_ 52 _Arctic Pole_ 53 _Ascension_ 68 ——— _Right_ ib. ——— _Oblique_ 69 _Ascensional Difference_ ib. _Ascians_ 91 ——— _Heteroscians_ ib. _Asterisms_ 36 _Atmosphere_ 81 _Axis_ 43 ——— _of the World_ 49 _Azimuth_ 61

Babylonish _Hours_ 71 _Bissextile_ 78

_Circle_ 42 ——— Great _Circles_ ib. ——— Parallel, _or_ lesser _Circles_ 43 ——— Secondary _Circles_ ib. _Circles of the Sphere_ 47 _Climates_ 93 _Colures_ 53 ——— _Equinoctial Colure_ ib. ——— _Solstitial Colure_ 54 _Comets_ 29 _Conjunction_ 11, 207 _Constellations_ 36 _Cosmical_ rising and setting of the Stars 96 _Crepusculum_ 83

_Day_, Natural _and_ Artificial 69 _Declination_ 52 _Diurnal Motion_ 7 _Diurnal Arch_ 68 _Eclipses_ 208 ——— _Solar_ ib. ——— _Lunar_ ib. _Eclipses of_ Jupiter’s _Satellites_ 212 _Ecliptic_ 53 _Egyptian Year_ 75 _Elongation_ 18 _Equator, or Equinoctial_ 48 _Equinoctial Points_ 53 ——— _Precession of_ 55 ——— _Vernal and Autumnal_ 70 _Excentricity_ 4

_Galaxy, or Milky Way_ 38 _Geocentric Place_ 19 _Globe_ 42 ——— _Terrestrial_ 43 ——— _Celestial_ 44 Gregorian _Account_ 80

_Heliacal_ rising and setting of the Stars 96 _Heliocentric Place_ 19 _Hemisphere_ 42 ——— _Northern and Southern_ 49 _Heteroscians_ 91 _Horizon_ 58 ——— _Sensible_ ib. ——— _Rational_ 59 _Hour Circles_ 50

Italian _Hours_ 72

Jewish _Hours_ ib. Julian _Account_ 79

_Latitude, in Astronomy_ 56 ——— _in Geography_ 84 _Longitude in Astronomy_ 56 ——— _in Geography_ 87

_Meridian_ 50, 61

_Nadir_ 61 _Nodes_ 3, 202 _Nocturnal Arch_ 68

_Orbit_ 3

_Parallel of the_ Earth’s Semidiameter 23 ——— _of the Earth’s Annual Orb_ 20 _Periœci_ 92 _Periscians_ 91 _Periodical_ Month 74, 202 _Phases of the_ Moon 201 _Planets_ 1 ——— _Inferior and Superior_ 14 _Planetary Hours_ 72 _Poles_ 42 ——— _of the World_ 49 ——— _of the Ecliptic_ 56 _Polar Circles_ 52 _Points of the Compass_ 60 ——— _Cardinal Points_ 59 _Primary Planets_ 5

_Retrograde Motion of the_ Planets 187 ——— _of the Nodes_ 202

_Secondary Planets_ 5 _Sidereal Year_ 74 _Signs of the_ Zodiac 54 ——— _Northern and Southern_ ib. _Solstices_ 71 ——— _Summer and Winter Solstices_ ib. _Solstitial Points_ 53 _Sphere_ 42 ——— _Parallel and Right_ 67 ——— _Oblique_ 68 _Stationary_ 186 _Style_ Old 79 ——— New _Style_ 80 _Synodical Month_ 74, 202

_Tropics (of_ Cancer _and_ Capricorn) 52 _Twilights_ 83

_Vertical Circles_ 61 ——— _Prime Vertical_ 62

_Zenith_ 61 _Zenith Distance_ 63 _Zones, Torrid, Temperate, and Frigid_ 90

THE END

Directions to the Binder.

The great ORRERY to face the Title. Plate I. Page 2 Plate II. 28 The Globes 35 Plate III. 194 Plate IV. 200 Plate V. 214

A CATALOGUE

Of Mathematical, Philosophical, and Optical Instruments,

MADE and SOLD by _BENJAMIN COLE_,

At his Shop, the Sign of the _Orrery_, No. 136, in _Fleet street, London_.