Chapter XXII: Part 22

Turn the Globe round eastward, or according to the order of Signs; and as the eastern edge of the Horizon comes right against the Sun, Moon, or any Planet, the Hour Index will shew the time of it’s rising; and the inner edge of the Ecliptic will cut it’s rising Amplitude in the Horizon. Turn on, and as the Quadrant of Altitude comes right against the Sun, Moon, or Planets, the Ecliptic cuts their meridian Altitudes in the Quadrant, and the Hour Index shews the times of their coming to the Meridian. Continue turning, and as the western edge of the Horizon comes right against the Sun, Moon, or Planets, their setting Amplitudes are cut in the Horizon by the Ecliptic; and the times of their setting are shewn by the Index on the Hour Circle.

PROBLEM II.

_To find the Altitude and Azimuth of the Sun, Moon, and Planets, at any
time of their being above the Horizon._

Turn the Globe till the Index comes to the given time in the Hour Circle; then keep the Globe steady, and moving the Quadrant of Altitude to each Planet respectively, the edge of the Ecliptic will cut the Planet’s mean Altitude on the Quadrant, and the Quadrant will cut the Planet’s Azimuth, or Point of Bearing on the Horizon.

PROBLEM III.

_The Sun’s Altitude being given at any time either before or after Noon, to find the Hour of the Day, and the Variation of the Compass, in any known Latitude._

With one hand hold the edge of the Quadrant right against the Sun; and, with the other hand, turn the Globe westward, if it be in the forenoon, or eastward if it be in the afternoon, until the Sun’s place at the inner edge of the Ecliptic cuts the Quadrant in the Sun’s observed Altitude; and then the Hour Index will point out the time of the day, and the Quadrant will cut the true Azimuth, or Bearing of the Sun for that time: the difference between which, and the Bearing shewn by the Azimuth Compass, shews the variation of the Compass in that place of the Earth.

[Sidenote: The TRAJECTORIUM LUNARE.

PL. VII. Fig. V.]

440. The _Trajectorium Lunare_. This Machine is for delineating the paths of the Earth and Moon, shewing what sort of Curves they make in the etherial regions; and was just mentioned in the 266th Article. _S_ is the Sun, and _E_ the Earth, whose Centers are 81 Inches distant from each other; every Inch answering to a Million of Miles § 47. _M_ is the Moon, whose Center is 24/100 parts of an Inch from the Earth’s in this Machine, this being in just proportion to the Moon’s distance from the Earth § 52. _AA_ is a Bar of Wood, to be moved by hand round the Axis _g_ which is fixed in the Wheel _Y_. The Circumference of this Wheel is to the Circumference of the small Wheel _L_ (below the other end of the Bar) as 365-1/4 days is to 29-1/2; or as a Year is to a Lunation. The Wheels are grooved round their edges, and in the Grooves is the cat-gut string _GG_ crossing between the Wheels at _X_. On the Axis of the Wheel _L_ is the Index _F_, in which is fixed the Moon’s Axis _M_ for carrying her round the Earth _E_ (fixed on the Axis of the Wheel _L_) in the time that the Index goes round a Circle of 29-1/2 equal parts, which are the days of the Moon’s age. The Wheel _Y_ has the Months and Days of the year all round it’s Limb; and in the Bar _AA_ is fixed the Index _I_, which points out the Days of the Months answering to the Days of the Moon’s age, shewn by the Index _F_, in the Circle of 29-1/2 equal parts at the other end of the Bar. On the Axis of the Wheel _L_ is put the piece _D_, below the Cock _C_, in which this Axis turns round; and in _D_ are put the Pencils _e_ and _m_, directly under the Earth _E_ and Moon _M_; so that _m_ is carried round _e_ as _M_ is round _E_.

[Sidenote: It’s use.]

Lay the Machine on an even Floor, pressing gently on the Wheel _Y_ to cause its spiked Feet (of which two appear at _P_ and _P_, the third being supposed to be hid from sight by the Wheel) enter a little into the Floor to secure the Wheel from turning. Then lay a paper about four foot long under the Pencils _e_ and _m_, cross-wise to the Bar: which done, move the Bar slowly round the Axis _g_ of the Wheel _Y_; and, as the Earth _E_ goes round the Sun _S_, the Moon _M_ will go round the Earth with a duly proportioned velocity; and the friction Wheel _W_ running on the Floor, will keep the Bar from bearing too heavily on the Pencils _e_ and _m_, which will delineate the paths of the Earth and Moon, as in Fig. 2d, already described at large, § 266, 267. As the Index _I_ points out the Days of the Months, the Index _F_ shews the Moon’s age on these Days, in the Circle of 29-1/2 equal parts. And as this last Index points to the different Days in it’s Circle, the like numeral Figures may be set to those parts of the Curves of the Earth’s Path and Moon’s, where the Pencils _e_ and _m_ are at those times respectively, to shew the places of the Earth and Moon. If the Pencil _e_ be pushed a very little off, as if from the Pencil _m_, to about 1/40 part of their distance, and the Pencil _m_ pushed as much towards _e_, to bring them to the same distances again, though not to the same points of space; then as _m_ goes round _e_, _e_ will go as it were round the Center of Gravity between the Earth _e_ and Moon _m_ § 298: but this Motion will not sensibly alter the Figure of the Earth’s Path or the Moon’s.

If a Pin as _p_ be put through the Pencil _m_, with its head towards that of the Pin _q_ in the Pencil _e_, its head will always keep thereto as _m_ goes round _e_, or as the same side of the Moon is still obverted to the Earth. But the Pin _p_, which may be considered as an equatoreal Diameter of the Moon, will turn quite round the Point _m_, making all possible Angles with the Line of its progress or line of the Moon’s Path. This is an ocular proof of the Moon’s turning round her Axis.

[Sidenote: The TIDE DIAL.

PLATE IX. Fig. VII.

It’s use.]

441. The TIDE-DIAL. The outside parts of this Machine consist of, 1. An eight-sided Box, on the top of which at the corner is shewn the Phases of the Moon at the Octants, Quarters, and Full. Within these is a Circle of 29-1/2 equal parts, which are the days of the Moon’s age accounted from the Sun at New Moon round to the same again. Within this Circle is one of 24 hours divided into their respective Halves and Quarters. 2. A moving elliptical Plate painted blue to represent the rising of the Tides under and opposite to the Moon; and has the words, _High Water, Tide falling, Low Water, Tide rising_, marked upon it. To one end of this Plate is fixed the Moon _M_ by the Wire _W_, and goes along with it. 3. Above this elliptical Plate is a round one, with the Points of the Compass upon it, and also the names of above 200 places in the large Machine (but only 32 in the Figure to avoid confusion) set over those Points on which the Moon bears when she raises the Tides to the greatest heights at these Places twice in every lunar day: and to the North and South Points of this Plate are fixed two Indexes _I_ and _K_, which shew the times of High Water in the Hour Circle at all these places. 4. Below the elliptical Plate are four small Plates, two of which project out from below its ends at New and Full Moon; and so, by lengthening the Ellipse shew the Spring Tides, which are then raised to the greatest heights by the united attractions of the Sun and Moon § 302. The other two of these small Plates appear at low water when the Moon is in her Quadratures, or at the sides of the elliptic Plate, to shew the Nepe Tides; the Sun and Moon then acting cross-wise to each other. When any two of these small Plates appear, the other two are hid; and when the Moon is in her Octants they all disappear, there being neither Spring nor Nepe Tides at those times. Within the Box are a few Wheels for performing these Motions by the Handle or Winch _H_.

_J. Ferguson inv. et del._ _J. Mynde Sculp._]

Turn the Handle until the Moon _M_ comes to any given day of her age in the Circle of 29-1/2 equal parts, and the Moon’s Wire _W_ will cut the time of her coming to the Meridian on that day, in the Hour Circle; the XII under the Sun being Mid-day, and the opposite XII Mid-night: then looking for the name of any given place on the round Plate (which makes 29-1/2 rotations whilst the Moon _M_ makes only one revolution from the Sun to the Sun again) turn the Handle till _that_ place comes to the word _High Water_ under the Moon, and the Index which falls among the Afternoon Hours will shew the time of high water at that place in the Afternoon of the given day: then turn the Plate half round, till the same place comes to the opposite High Water Mark, and the Index will shew the time of High Water in the Forenoon at that place. And thus, as all the different places come successively under and opposite to the Moon, the Indexes shew the times of High Water at them in both parts of the day: and when the same places come to the Low Water Marks the Indexes shew the times of Low Water. For about two days before and after the times of New and Full Moon, the two small Plates come out a little way from below the High Water Marks on the elliptical Plate, to shew that the Tides rise still higher about these times: and about the Quarters, the other two Plates come out a little from under the Low Water Marks towards the Sun and on the opposite side, shewing that the Tides of Flood rise not then so high, nor do the Tides of Ebb fall so low, as at other times.

By pulling the Handle a little way outward, it is disengaged from the Wheel-work, and then the upper Plate may be turned round quickly by hand so, as the Moon may be brought to any given day of her age in about a quarter of a minute.

[Sidenote: The inside work described.

Fig. VIII.]

On _AB_, the Axis of the Handle _H_, is an endless Screw _C_ which turns the Wheel _FED_ of 24 teeth round in 24 revolutions of the Handle: this Wheel turns another _ONG_ of 48 teeth, and on its Axis is the Pinion _PQ_ of four leaves which turns the Wheel _LKI_ of 59 teeth round in 29-1/2 turnings or rotations of the Wheel _FED_, or in 708 revolutions of the Handle, which is the number of Hours in a synodical revolution of the Moon. The round Plate with the names of Places upon it is fixed on the Axis of the Wheel _FED_; and the Elliptical or Tide-Plate with the Moon fixed to it is upon the Axis of the Wheel _LKI_; consequently, the former makes 29-1/2 revolutions in the time that the latter makes one. The whole Wheel _FED_ with the endless Screw _C_, and dotted part of the Axis of the Handle _AB_, together with the dotted part of the Wheel _ONG_, lie hid below the large Wheel _LKI_.

Fig. 9th represents the under side of the Elliptical or Tide-Plate _abcd_, with the four small Plates _ABCD_, _EFGH_, _IKLM_, _NOPQ_ upon it: each of which has two slits as _TT_, _SS_, _RR_, _UU_ sliding on two Pins as _nn_, fixed in the elliptical Plate. In the four small Plates are fixed four Pins at _W_, _X_, _Y_, and _Z_; all of which work in an elliptic Groove _oooo_ on the cover of the Box below the elliptical Plate; the longest Axis of this Groove being in a right line with the Sun and Full Moon. Consequently, when the Moon is in Conjunction or Opposition, the Pins _W_ and _X_ thrust out the Plates _ABCD_ and _IKLM_ a little beyond the ends of the elliptic Plate at _d_ and _b_, to _f_ and _e_; whilst the Pins _Y_ and _Z_ draw in the Plates _EFGH_ and _NOPQ_ quite under the elliptic Plate to _g_ and _h_. But, when the Moon comes to her first or third Quarter, the elliptic Plate lies across the fixed elliptic Groove in which the Pins work; and therefore the end Plates _ABCD_ and _IKLM_ are drawn in below the great Plate, and the other two Plates _EFGH_ and _NOPQ_ are thrust out beyond it to _a_ and _c_. When the Moon is in her Octants the Pins _V, X, Y, Z_ are in the parts _o, o, o, o_ of the elliptic Groove, which parts are at a mean between the greatest and least distances from the Center _q_, and then all the four small Plates disappear below the great one.

[Sidenote: The ECLIPSAREON.

Pl. XIII.]

442. The ECLIPSAREON. This Piece of Mechanism exhibits the Time, Quantity, Duration, and Progress of solar Eclipses, at all Parts of the Earth.

The principal parts of this Machine are, 1. A terrestrial Globe _A_ turned round its Axis _B_ by the Handle or Winch _M_; the Axis _B_ inclines 23-1/2 Degrees, and has an Index which goes round the Hour Circle _D_ in each rotation of the Globe. 2. A circular Plate _E_ on the Limb of which the Months and Days of the year are inserted. This Plate supports the Globe, and gives its Axis the same position to the Sun, or to a candle properly placed, that the Earth’s Axis has to the Sun upon any day of the year § 338, by turning the Plate till the given Day of the Month comes to the fixed Pointer or annual Index _G_. 3. A crooked Wire _F_ which points towards the middle of the Earth’s enlightened Disc at all times, and shews to what place of the Earth the Sun is vertical at any given time. 4. A Penumbra, or thin circular Plate of brass _I_ divided into 12 Digits by 12 concentric Circles, which represent a Section of the Moon’s Penumbra, and is proportioned to the size of the Globe; so that the shadow of this Plate, formed by the Sun, or a candle placed at a convenient distance, with it’s Rays transmitted through a convex Lens to make them fall parallel on the Globe, covers exactly all those places upon it that the Moon’s Shadow and Penumbra do on the Earth: so that the Phenomena of any solar Eclipse may be shewn by this Machine with candle-light, almost as well as by the light of the Sun. 5. An upright frame _HHHH_, on the sides of which are Scales of the Moon’s Latitude or Declination from the Ecliptic. To these Scales are fitted two Sliders _K_ and _K_, with Indexes for adjusting the Penumbra’s Center to the Moon’s Latitude, as it is North or South Ascending or Descending. 6. A solar Horizon _C_, dividing the enlightened Hemisphere of the Globe from that which is in the dark at any given time, and shewing at what places the general Eclipse begins and ends with the rising or setting Sun. 7. A Handle _M_, which turns the Globe round it’s Axis by wheel-work, and at the same time moves the Penumbra across the frame by threads over the Pullies _L, L, L_, with the velocity duly proportioned to that of the Moon’s shadow over the Earth, as the Earth turns on its Axis. And as the Moon’s Motion is quicker or slower, according to her different distances from the Earth, the penumbral Motion is easily regulated in the Machine by changing one of the Pullies.

[Sidenote: To rectify it.]

_To rectify the Machine for use._ The true time of New Moon and her Latitude being known by the foregoing Precepts § 355, 363, if her Latitude exceeds the number of minutes or divisions on the Scales (which are on the side of the frame hid from view in the Figure of the Machine) there can be no Eclipse of the Sun at that Conjunction; but if it does not, the Sun will be eclipsed to some places of the Earth; and, to shew the times and various appearances of the Eclipse at those places, proceed in order as follows.

_To rectify the Machine for performing by the Light of the Sun._ 1. Move the Sliders _KK_ till their Indexes point to the Moon’s Latitude on the Scales, as it is North and South Ascending or Descending, at that time. 2. Turn the Month Plate _E_ till the day of the given New Moon comes to the annual Index _G_. 3. Unscrew the Collar _N_ a little on the Axis of the Handle, to loosen the contiguous Socket on which the threads that move the Penumbra are wound; and set the Penumbra by Hand till its Center comes to the perpendicular thread in the middle of the frame; which thread represents the Axis of the Ecliptic § 371. 4. Turn the Handle till the Meridian of _London_ on the Globe comes just under the point of the crooked Wire _F_; then stop, and turn the Hour Circle _D_ by Hand till XII at Noon comes to its Index. 5. Turn the Handle till the Hour Index points to the time of New Moon in the Circle _D_; and holding it there, screw fast the Collar _N_. Lastly, elevate the Machine till the Sun shines through the Sight-Holes in the small upright Plates _O_, _O_, on the Pedestal; and the whole Machine will be rectified.

_To rectify the Machine for shewing the Candle-Light_, proceed in every respect as above, except in that part of the last paragraph where the Sun is mentioned; instead of which place a Candle before the Machine, about four yards from it, so as the shadow of Intersection of the cross threads in the middle of the frame may fall precisely on that part of the Globe to which the crooked Wire _F_ points: then, with a pair of Compasses take the distance between the Penumbra’s Center and Intersection of the threads; and equal to that distance set the Candle higher or lower as the Penumbra’s Center is above or below the said Intersection. Lastly, place a large convex Lens between the Machine and Candle, so as the Candle may be in the Focus of the Lens, and then the Rays will fall parallel, and cast a strong light on the Globe.

[Sidenote: It’s use.]

These things done, which may be sooner than expressed, turn the Handle backward until the Penumbra almost touches the side _HF_ of the frame; then turning it gradually forward, observe the following Phenomena. 1. Where the eastern edge of the Shadow of the penumbral Plate _I_ first touches the Globe at the solar Horizon, those who inhabit the corresponding part of the Earth see the Eclipse begin on the uppermost edge of the Sun, just at the time of its rising. 2. In that place where the Penumbra’s Center first touches the Globe, the inhabitants have the Sun rising upon them centrally eclipsed. 3. When the whole Penumbra just falls upon the Globe, its western edge, at the solar Horizon, touches and leaves the place where the Eclipse ends at Sun-rise on his lowermost edge. Continue turning, and, 4. the cross lines in the Center of the Penumbra will go over all those places on the Globe where the Sun is centrally eclipsed. 5. When the eastern edge of the Shadow touches any place of the Globe, the Eclipse begins there: when the vertical line in the Penumbra comes to any place, then is the greatest obscuration at that place; and when the western edge of the Penumbra leaves the place, the Eclipse ends there; the times of all which are shewn on the Hour Circle: and from the beginning to the end, the Shadows of the concentric penumbral Circles shew the number of Digits eclipsed at all the intermediate times. 6. When the eastern edge of the Penumbra leaves the Globe at the solar Horizon _C_, the inhabitants see the Sun beginning to be eclipsed on his lowermost edge at its setting. 7. Where the Penumbra’s Center leaves the Globe, the inhabitants see the Sun set centrally eclipsed. And lastly, where the Penumbra is wholly departing from the Globe, the inhabitants see the Eclipse ending on the uppermost part of the Sun’s edge, at the time of its disappearing in the Horizon § 343.

_N.B._ If any given day of the year on the Plate _E_ be set to the annual Index _G_, and the Handle turned till the Meridian of any place comes under the point of the crooked Wire, and then the Hour Circle _D_ set by the hand till XII comes to its Index; in turning the Globe round by the Handle, when the said place touches the eastern edge of the Hoop or solar Horizon _C_, the Index shews the time of Sun-setting at that place; and when the place is just coming out from below the other edge of the Hoop _C_, the Index shews the time that the evening Twilight ends to it. When the place has gone through the dark part _A_, and comes about so to touch under the back of the Hoop _C_ on the other side, the Index shews the time that the Morning Twilight begins; and when the same place is just coming out from below the edge of the Hoop next the frame, the Index points out the time of Sun-rising. And thus, the times of Sun-rising and setting are shewn at all places in one rotation of the Globe, for any given day of the year: and the point of the crooked Wire _F_ shews all the places that the Sun passes vertically over on that day.

FINIS.

INDEX.

The numeral Figures refer to the Articles, and the small _n_ to the
Notes on the Articles.

A.

_Acceleration_ of the Stars, 221.

_Angle_, what, 185.

_Annual Parallax_ of the Stars, 196.

_Anomaly_, what, 239.

_Antients_, their superstitious notions of Eclipses, 329.
Their method of dividing the Zodiac, 398.

_Antipodes_, what, 122.

_Apsides_, line of, 238.

ARCHIMEDES, his ideal Problem for moving the Earth, 159.

_Areas_ described by the Planets, equal in times, 153.

_Astronomy_, the great advantages arising from it both in our religious
and civil concerns, 1 Discovers the laws by which the Planets move,
and are retained in their Orbits, 2
_Atmosphere_, the higher the thinner, 174.
It’s prodigious expansion, _ib._
It’s whole weight on the Earth, 175.
Generally thought to be heaviest when it is lightest, 176.
Without it the Heavens would appear dark in the day-time, 177.
Is the cause of twilight, _ib._
It’s height, _ib._
Refracts the Sun’s rays, 178.
Causeth the Sun and Moon to appear above the Horizon when they are
really below it, _ib._
Foggy, deceives us in the bulk and distance of objects, 185.

_Attraction_, 101-105.
Decreases as the square of the distance increases, 106.
Greater in the larger than in the smaller Planets, 158.
Greater in the Sun than in all the Planets if put together, _ib._

_Axes of the Planets_, what, 19.
Their different positions with respect to one another, 120.

_Axis of the Earth_, it’s parallelism, 302.
It’s position variable as seen from the Sun or Moon, 338.
the Phenomena thence arising, 340.

B.

_Bodies_, on the Earth, lose of their weight the nearer they are to the
Equator, 117.
How they might lose all their weight, 118,
How they become visible, 167.

C.

_Calculator_, (an Instrument) described, 436.

_Calendar_, how to inscribe the Golden Numbers rightly in it for
shewing the days of New Moons, 423.

_Cannon-Ball_, it’s swiftness, 89.
In what times it would fly from the Sun to the different Planets and
fixed Stars, _ib._

CASSINI, his account of a double Star eclipsed by the Moon, 58.
His Diagrams of the Paths of the Planets, 138.

_Catalogue_ of the Eclipses, 327.
Of the Constellations and Stars, 367.
Of remarkable _Æras_ and events, 433.

_Celestial Globe_ improved, 438.

_Centripetal and centrifugal forces_, how they alternately overcome
each other in the motions of the Planets, 152-154.

_Changes in the Heavens_, 403.

_Chords_, line of, how to make, 369.

_Circles_, of perpetual Apparition and Occultation, 128.
Of the Sphere, 198.
Contain 360 Degrees whether they be great or small, 207.

_Civil Year_, what, 411.

COLUMBUS (CHRISTOPHER) his story concerning an Eclipse, 330.

_Clocks_ and _Watches_, an easy method of knowing whether they go true
or false, 223.
Why they seldom agree with the Sun if they go true, 228-245.
How to regulate them by Equation Tables and a Meridian line, 225,
226.

_Cloudy Stars_, 402.

_Cometarium_ (an Instrument) described, 437.

_Constellations_, antient, their number, 396.
The number of Stars in each, according to different Astronomers, 399.

_Cycle_, Solar, Lunar, and _Romish_, 420.
Of _Easter_, 425.

D.

_Darkness_ at our SAVIOUR’s crucifixion supernatural, 352, 432.

_Day_, natural and artificial, what, 417.
And _Night_, always equally long at the Equator, 126.
Natural, not compleated in an absolute turn of the Earth on it’s
Axis, 222.

_Degree_, what, 207.

_Digit_, what, 321, _n._

_Direction_, (Number of) 426.

_Distances of the Planets from the Sun_, an idea thereof, 89.
A Table thereof, 98.
How found, 190.

_Diurnal_ and _annual Motions_ of the Earth illustrated, 200, 202.

_Dominical Letter_, 427.

_Double_ projectile force, a balance to a _Quadruple_ Power of Gravity,
153.
Star covered by the Moon, 58.

E.

_Earth_, it’s bulk but a point as seen from the Sun, 3 It’s Diameter,
annual Period, and Distance from the Sun, 47.
Turns round it’s Axis, _ib._
Velocity of it’s equatoreal Parts, _ib._
Velocity in it’s annual Orbit, _ib._
Inclination of it’s Axis, 48.
Proof of it’s being globular, or nearly so, 49, 314.
Measurement of it’s surface, 50, 51.
Difference between it’s Equatoreal and Polar Diameters, 76.
It’s motion round the Sun demonstrated by gravity, 108, 111.
by Dr. BRADLEY’s observations, 113.
by the Eclipses of Jupiter’s Satellites, 219.
It’s diurnal motion highly probable from the absurdity that must
follow upon supposing it not to move, 111. 120.
and demonstrable from it’s figure, 116.
this motion cannot be felt, 119.
Objections against it’s motion answered, 112, 121.
It has no such thing as an upper or under side, 122.
in what case it might, 123.
The swiftness of it’s motion in it’s Orbit compared with the velocity
of light, 197.
It’s diurnal and annual motions illustrated by an easy experiment,
200.
Proved to be less than the Sun and bigger than the Moon, 315.

_Easter Cycle_, 425.

_Eclipsareon_ (an Instrument) described, 442.

_Eclipses_, of Jupiter’s Satellites, how the Longitude is found by
them, 207-218.
they demonstrate the velocity of light, 216.
Of the Sun and Moon, 312-327.
Why they happen not in every month, 316.
When they must be, 317.
Their limits, _ib._
Their Period, 320, 326.
A dissertation on their progress, 321-324.
A large catalogue of them, 327.
Historical ones, 328.
More of the Sun than of the Moon, and why, 331.
The proper Elements for their calculation and projection, 353-390.

_Ecliptic_, it’s Signs, their names and characters, 91.
Makes different Angles with the Horizon every hour and minute, 275.
how these Angles may be estimated by the position of the Moon’s
horns, 260.
It’s obliquity to the Equator less now than it was formerly, 405.
How it’s Signs are numbered, 354.

_Elongations_, of the Planets, as seen by an observer at rest on the
outside of all their Orbits, 133.
Of Mercury and Venus as seen from the Earth, illustrated, 142.
it’s quantity, 143.
Of Mercury, Venus, the Earth, Mars, and Jupiter; it’s quantity as
seen from Saturn, 147.

_Epochas_ or _Æras_, 433.

_Equation_ of time, 224-245.
Of the Moon’s Place, 355.
Of the Sun’s Place, _ib._
Of the Nodes, 363.

_Equator_, day and night always equal there, 126.
Makes always the same Angle with the Horizon of the same place; the
Ecliptic not, 274, 275.

_Equinoctial Points_ in the Heavens, their precession, 246,
a very different thing from the recession or anticipation of the
Equinoxes on Earth, the one no ways occasioned by the other, 249.

_Excentricities_ of the Planets Orbits, 155.

F.

_Fallacies_ in judging of the bulk of objects by their apparent
distance, 185;
applied to the solution of the horizontal Moon, 187.

_First Meridian_, what, 207.

_Fixed Stars_, why they appear of less magnitude when viewed through a
telescope than by the bare eye, 391.
Their number, 392.
Their division into different Classes and Constellations, 395-399.

G.

_General Phenomena_ of a superior Planet as seen from an inferior, 149.

_Gravity_, demonstrable, 101-104.
Keeps all bodies on the Earth to it’s surface, or brings them back
when thrown upward; and constitutes their weight, 101, 122.
Retains all the Planets in their Orbits, 103.
Decreases as the square of the distance increases, 106.
Proves the Earth’s annual motion, 108.
Demonstrated to be greater in the larger Planets than in the smaller;
and stronger in the Sun than in all the Planets together, 158.
Hard to understand what it is, 160.
Acts every moment, 162.

_Globe_, improved celestial, 438.

_Great Year_, 251.

H.

_Harmony_ of the celestial motions, 111.

_Harvest-Moon_, 273-293.
None at the Equator, 273.
Remarkable at the Polar Circles, 285.
In what years most and least advantageous, 292.

_Heat_, decreases as the square of the distance from the Sun increases,
169.
Why not greatest when the Earth is nearest the Sun, 205.
Why greater about three o’Clock in the afternoon than when the Sun is
on the Meridian, 300.

_Heavens_, seem to turn round with different velocities as seen from
the different Planets; and on different Axes as seen from most of
them, 120.
Only one Hemisphere of them seen at once from any one Planet’s
surface, 125.
The Sun’s Center the only point from which their true Motions could
be seen, 135.
Changes in them, 403.

_Horizon_, what, 125, _n._

_Horizontal-Moon_ explained, 187.

_Horizontal Parallax_, of the Moon, 190;
of the Sun, 191;
best observed at the Equator, 193.

_Hour-Circles_, what, 208.

_Hour_ of time equal to 15 degrees of motion, _ib._
How divided by the _Jews_, _Chaldeans_, and _Arabians_, 419.

HUYGENIUS, his thoughts concerning the distance of some Stars, 5

I. J.

_Inclination_ of Venus’s Axis, 29.
Of the Earth’s, 48.
Of the Axis or Orbit of a Planet only relative, 201.

_Inhabitants_ of the Earth (or any other Planet) stand on opposite
sides with their feet toward one another, yet each thinks himself on
the upper side, 122.

_Julian Period_, 430.

_Jupiter_, it’s distance, diameter, diurnal and annual revolutions,
67-69.
The Phenomena of it’s Belts, 70.
Has no difference of seasons, 71.
Has four Moons, 72,
their grand Period, 73,
the Angles which their Orbits subtend as seen from the Earth, 74,
most of them are eclipsed in every revolution, 75.
The great difference between it’s equatoreal and polar Diameters, 76.
The inclination of it’s Orbit, and place of it’s Ascending Node, 77.
The Sun’s light 3000 times as strong on it as Full Moon-light is on
the Earth, 85.
Is probably inhabited, 86.
The amazing strength required to put it in motion, 158.
The figures of the Paths described by it’s Satellites, 269.

L.

_Light_, the inconceivable smallness of it’s particles, 165,
and the dreadful mischief they would do if they were larger, 166.
It’s surprising velocity, 166,
compared with the swiftness of the Earth’s annual motion, 197.
Decreases as the square of the distance from the luminous body
increases, 169.
Is refracted in passing through different Mediums, 171-173.
Affords a proof of the Earth’s annual motion, 197, 219.
In what time it comes from the Sun to the Earth, 216,
this explained by a figure, 217.

_Limits_ of Eclipses, 317.

_Line_, of the Nodes, what, 317;
has a retrograde motion, 319.
Of Sines and Chords, how to make, 369.

LONG (Rev. Dr.) his method of comparing the quantity of the surface of
dry land with that of the Sea, 51.
His glass sphere, 126.

_Longitude_, how found, 207-213.

_Lucid Spots_ in the Heavens, 401.

_Lunar Cycle_ deficient, 422.

M.

_Magellanic Clouds_, 402.

_Man_, of a middle size, how much pressed by the weight of the
Atmosphere, 175;
why this pressure is not felt, _ib._

_Mars_, it’s Diameter, Period, Distance, and other Phenomena, 64-67.

_Matter_, it’s properties, 99.

_Mean Anomaly_, what, 239.

_Mercury_, it’s Diameter, Period, Distance, &c. 22.
Appears in all the shapes of the Moon, 23.
When it will be seen on the Sun, 24.
The inclination of it’s Orbit and Place of it’s Ascending Node, _ib._
It’s Path delineated, 138.
Experiment to shew it’s Phases and apparent Motion, 142.

_Mercury_ (Quicksilver) in the Barometer, why not affected by the
Moon’s raising Tides in the Air, 311.

_Meridian_, first, 207.
Line, how to draw one, 226.

_Milky Way_, what, 400.

_Months_, _Jewish_, _Arabian_, _Egyptian_, and _Grecian_, 415.

_Moon_, her Diameter and Period, 52.
Her phases, 53, 255.
Shines not by her own light, 54.
Has no difference of seasons, 55.
The Earth is a Moon to her, 56.
Has no Atmosphere of any visible Density, 58;
nor Seas, 59.
How her inhabitants may be supposed to measure their year, 62.
Her light compared with day-light, 85.
The excentricity of her Orbit, 98.
Is nearer the Earth now than she was formerly, 163.
Appears bigger in the Horizon than at any considerable height above
it, and why, 187;
yet is seen much under the same Angle in both cases, 188.
Her surface mountainous, 252:
if smooth she could give us no light, _ib._
Why no hills appear round her edge, 253.
Has no Twilight, 254.
Appears not always quite round when full, 256.
Her phases agreeably represented by a globular Stone viewed in
Sun-shine when she is above the Horizon, and the observer placed
as if he saw her on the top of the Stone, 258.
Turns round her Axis, 262.
The length of her Solar and Sidereal Day, _ib._
Her periodical and synodical revolution represented by the motions of
the hour and minute hands of a Watch, 264.
Her Path delineated, and shewn to be always concave to the Sun,
265-268.
Her motion alternately retarded and accelerated, 267.
Her gravity toward the Sun greater than toward the Earth at her
Conjunction, and why she does not then abandon the Earth on that
account, 268.
Rises nearer the time of Sun-set when about the full in harvest for a
whole week than when she is about the full at any other time of
the year, and why, 273-284:
this rising goes through a course of increasing and
decreasing benefit to the farmers every 19 years, 292.
Continues above the Horizon of the Poles for fourteen of our natural
Days together, 293.
Proved to be globular, 314.
and to be less than the Earth, 315.
Her Nodes, 317.
ascending and descending, 318.
their retrograde motion, 319.
Her acceleration proved from antient Eclipses, 322, _n._
Her Apogee and Perigee, 336.
Not invisible when she is totally eclipsed, and why, 346.
How to calculate her Conjunctions, Oppositions, and Eclipses,
355-390.
How to find her age in any Lunation by the Golden Number, 423.

_Morning_ and _Evening Star_, what, 145.

_Motion_, naturally rectilineal, 100.
Apparent, of the Planets as seen by a spectator at rest on the
outside of all their Orbits, 133;
and of the Heavens as seen from any Planet, 154.

N.

_Natural Day_, not compleated in the time that the Earth turns round
it’s Axis, 222.

_New_ and _Full Moon_, to calculate the times of 355.

_New Stars_, 403,
cannot be Comets, 404.

_New Style_, it’s original, 414.

NICIAS’s Eclipse, 328.

_Nodes_, of the Planet’s Orbits, their places in the Ecliptic, 20.
Of the Moon’s Orbit, 317.
their retrograde motion, 319.

_Nonagesimal Degree_, what, 259.

_Number of Direction_, 426.

O.

_Objects_, we often mistake their bulk by mistaking their distance,
185.
Appear bigger when seen through a fog than through clear Air, and
why, _ib._
this applied to the solution of the Horizontal Moon, 187.

_Oblique Sphere_, what, 131.

_Olympiads_, what, 323. _n._

_Orbits_ of the Planets not solid, 21.

_Orrery_ described, 434, 435, 436.

P.

_Parallax_, Horizontal, what, 190.

_Parallel Sphere_, what, 131.

_Path_ of the Moon, 265, 266, 267.
Of Jupiter’s Moons, 269.

_Pendulums_, their vibrating slower at the Equator than near the Poles
proves that the Earth turns on it’s Axis, 117.

_Penumbra_, what, 336.
It’s velocity on the Earth in Solar Eclipses, 337.

_Period of Eclipses_, 320, 326.

_Phases of the Moon_, 252-268.

_Planets_, much of the same nature with the Earth, 11.
Some have Moons belonging to them, 12.
Move all the same way as seen from the Sun, but not as seen from one
another, 18.
Their Moons denote them to be inhabited, 86.
The proportional breadth of the Sun’s Disc as seen from each of them,
87.
Their proportional bulks as seen from the Sun, 88.
An idea of their distances from the Sun, 89.
Appear bigger and less by turns, and why, 90.
Are kept in their Orbits by the power of gravity, 101, 150-158.
Their motions very irregular as seen from the Earth, 137.
The apparent motions of Mercury and Venus delineated by Pencils in an
Orrery, 138.
Elongations of all the rest as seen from Saturn, 147.
Describe equal areas in equal times, 153.
The excentricities of their Orbits, 155.
In what times they would fall to the Sun by the power of gravity,
157.
Disturb one another’s motions, the consequence thereof, 163.
Appear dimmer when seen through telescopes than by the bare eye, the
reason of this, 170.

_Planetary Globe_ described, 439.

_Polar Circles_, 198.

_Poles_, of the Planets, what, 19.
Of the world, what, 122.
Celestial, seem to keep on the same points of the Heavens all the
year, and why, 196.

_Projectile Force_, 150;
if doubled would require a quadruple power of gravity to retain the
Planets in their Orbits, 153.
Is evidently an impulse from the hand of the ALMIGHTY, 161.

_Precession of the Equinoxes_, 246-251.

_Ptolemean_ System absurd, 96, 140.

R.

_Rays of Light_, if not disturbed, move in straight lines, and hinder
not one another’s motions, 168.
Are refracted in passing through different mediums, 171.

_Reflection of the Atmosphere_ causes the Twilight, 177.

_Refraction of the Atmosphere_ bends the rays of light from straight
lines, and keeps the Sun and Moon longer in sight than they would
otherwise be, 178.
A surprising instance of this, 183.
Must be allowed for in taking the Altitudes of the celestial bodies,
_ib._

_Right Sphere_, 131.

S.

_Satellites_; the times of their revolutions round their primary
Planets, 52, 73, 80.
Their Orbits compared with each other, with the Orbits of the primary
Planets, and with the Sun’s circumference, 271.
What sort of Curves they describe, 272.

_Saturn_, with his Ring and Moon’s, their Phenomena, 78, 79, 82.
The Sun’s light 1000 times as strong to him as the light of the Full
Moon is to us, 85.
The Phenomena of his Ring farther explained, 204.

_Our blessed_ SAVIOUR, the darkness at his crucifixion supernatural,
352.
The prophetic year of his crucifixion found to agree with an
astronomical calculation, 432.

_Seasons_, different, illustrated by an easy experiment, 200;
by a figure, 202.

_Shadow_, what, 312.

_Sidereal Time_, what, 221;
the number of Sidereal Days in a year exceeds the number of Solar
Days by one, and why, 222.
An easy method for regulating Clocks and Watches by it, 223.

_Signs of the Zodiac_, their names and characters, 91, 365.
How they are numbered by Astronomers, 354.

_Sines_, line of, how to make, 369.

SMITH, (Rev. Dr.) his companion between Moon-light and Day-light, 85.
His demonstration that light decreases as the square of the distance
from the luminous body increases, 169.
(_Mr._ GEORGE) his Dissertation on the Progress of a Solar Eclipse,
321-324.

_Solar Astronomer_, the judgment he might be supposed to make
concerning the Planets and Stars, 135, 136.

_Sphere_, parallel, oblique, and right, 131.
It’s Circles, 198.

_Spring and Neap Tides_, 302.

_Stars_, their vast distance from the Earth, 3, 196.
Probably not all at the same distance, 4 Shine by their own light,
and are therefore Suns 7,
probably to other worlds, 8 A demonstration that they do not move
round the Earth, 111.
Have an apparent slow motion round the Poles of the Ecliptic, and
why, 251.
A catalogue of them, 399.
_Cloudy_, 402.
New, 403.
Some of them change their places, 404.

_Starry Heavens_ have the same appearance from any part of the Solar
System, 132.

SUN appears bigger than the Stars, and why, 4 Turns round his Axis, 18.
His proportional breadth as seen from the different Planets, 87.
Describes unequal arcs above and below the Horizon at different
times, and why, 130.
His Center the only place from which the true motions of the Planets
could be seen, 135.
Is for half a year together visible at each Pole in it’s turn, and as
long in visible, 200, 294.
Is nearer the Earth in Winter than in Summer, 205.
Why his motion agrees so seldom with the motion of a well regulated
Clock, 224-245.
Would more than fill the Moon’s Orbit, 271.
Proved to be much bigger than the Earth, and the Earth to be bigger
than the Moon, 315.
To calculate his true place, 360.

_Systems_, the Solar, 17-95;
the Ptolemean, 96;
the Tychonic, 97.

T.

_Table_, of the Periods, Revolutions, Magnitudes, Distances, _&c._ of
the Planets, facing § 99.
Of the Air’s rarity, compression, and expansion at different heights,
174.
Of refractions, 182.
For converting time into motion, and the reverse, 220.
For shewing how much of the celestial Equator passes over the
Meridian in any part of a mean Solar Day; and how much the Stars
accelerate upon the mean Solar time for a month, 221.
Of the first part of the Equation of time, 229;
of the second part, 241.
Of the precession of the Equinox, 247.
Of the length of Sidereal, Julian, and Tropical Years, 251.
Of the Sun’s place and Anomaly, following 251.
Of the Equation of natural Days, following 251
Of the Conjunctions of the hour and minute hands of a Watch, 264.
Of the Curves described by the Satellites, 272.
Of the difference of time in the Moon’s rising and setting on the
parallel of
_London_ every day during her course round the Ecliptic, 277.
Of Eclipses, 327.
For calculating New and Full Moons and Eclipses, following 390.
Of the Constellations and number of the Stars, 399.
Of the _Jewish_, _Egyptian_, _Arabic_, and _Grecian_ months, 415.
For inserting the Golden Numbers right in the Calendar, 423.
Of the times of all the New Moons for 76 years, 424.
Of remarkable Æras or Events, 433.
Of the Golden Number, Number of Direction, Dominical Letter and Days
of the Months, following 433.

THALES’s Eclipse, 323.

THUCYDIDES’s Eclipse 324.

_Tides_, their Cause and Phenomena, 295-311.

_Tide-Dial_ described, 441.

_Trajectorium Lunare_ described, 440.

_Tropics_, 198.

_Twilight_, none in the Moon, 254.

_Tychonic System_ absurd, 97.

U.

_Universe_, the Work of Almighty Power, 5, 161.

_Up_ and _down_, only relative terms, 122.

_Upper_ or _under side of the Earth_ no such thing, 123.

V.

_Velocity of Light_ compared with the velocity of the Earth in it’s
annual Orbit, 197.

_Venus_, her bulk, distance, period, length of days and nights, 26.
Shines not by her own light, _ib._
Is our morning and evening Star, 28.
Her Axis, how situated, 29.
Her surprising Phenomena, 29-43.
The inclination of her Orbit, 45.
When she will be seen on the Sun, _ib._
How it may probably be soon known if she has a Satellite, 46.
Appears in all the Shapes of the Moon, 23, 141.
An experiment to shew her phases and apparent motion, 141.

_Vision_, how caused, 167.

W.

_Weather_, not hottest when the Sun is nearest to us, and why, 205.

_Weight_, the cause of it, 122.

_World_ not eternal, 164.

Y.

_Year_, 407,
Great, 251,
Tropical, 408,
Sidereal, 400,
Lunar, 410,
Civil, 411,
Bissextile, _ib._
_Roman_, 413,
_Jewish_, _Egyptian_, _Arabic_, and _Grecian_, 415,
how long it would be if the Sun moved round the Earth, 111.

Z.

_Zodiac_, what, 397.
How divided by the antients, 398.

_Zones_, what, 199.

DIRECTIONS to the BOOKBINDER.

The ORRERY PLATE is to front the Title Page.

PLATE I fronting Page 5
II 39
III 49
IV 73
V 81
VI 97
VII 125
VIII 147
IX 147
X 157
XI 179
XII 203
XIII 279

Footnotes

Footnote 1:

Dr. YOUNG’s Night Thoughts.

Footnote 2:

If a thread be tied loosely round two pins stuck in a table, and
moderately stretched by the point of a black lead pencil carried round
by an even motion and light pressure of the hand, an oval or ellipsis
will be described; the two points where the pins are fixed being
called the _foci_ or focuses thereof. The Orbits of all the Planets
are elliptical, and the Sun is placed in or near to one of the _foci_
of each of them: and _that_ in which he is placed, is called the
_lower focus_.

Footnote 3:

Astronomers are not far from the truth, when they reckon the Sun’s
center the lower focus of all the Planetary Orbits. Though strictly
speaking, if we consider the focus of Mercury’s Orbit to be in the
Sun’s center, the focus of Venus’s Orbit will be in the common center
of gravity of the Sun and Mercury; the focus of the Earth’s Orbit in
the common center of gravity of the Sun, Mercury, and Venus; the focus
of the Orbit of Mars in the common center of gravity of the Sun,
Mercury, Venus, and the Earth; and so of the rest. Yet, the focuses of
the Orbits of all the Planets, except Saturn, will not be sensibly
removed from the center of the Sun; nor will the focus of Saturn’s
Orbit recede sensibly from the common center of gravity of the Sun and
Jupiter.

Footnote 4:

As represented in Plate III. Fig. I. and described in § 138.

Footnote 5:

When he is between the Earth and the Sun in the nearer part of his
Orbit.

Footnote 6:

The time between the Sun’s rising and setting.

Footnote 7:

One entire revolution, or 24 hours.

Footnote 8:

These are lesser circles parallel to the Equator, and as many degrees
from it, towards the Poles, as the Axis of the Planet is inclined to
the Axis of it’s Orbit. When the Sun is advanced so far north or south
of the Equator as to be directly over either Tropic, he goes no
farther; but returns towards the other.

Footnote 9:

These are lesser circles round the Poles, and as far from them as the
Tropics are from the Equator. The Poles are the very north and south
points of the Planet.

Footnote 10:

A Degree is a 360th part of any Circle. See § 21.

Footnote 11:

The Limit of any inhabitant’s view, where the Sky seems to touch the
Planet all round him.

Footnote 12:

This is not strictly true, as will appear when we come to treat of the
Recession of the Equinoctial Points in the Heavens § 246; which
recession is equal to the deviation of the Earth’s Axis from it’s
parallelism: but this is rather too small to be sensible in an age,
except to those who make very nice observations.

Footnote 13:

_Memoirs d’Acad. ann. 1720._

Footnote 14:

The Moon’s Orbit crosses the Ecliptic in two opposite points called
the Moon’s Nodes; so that one half of her Orbit is above the Ecliptic,
and the other half below it. The Angle of it’s Obliquity is 5-1/3
degrees.

Footnote 15:

CASSINI _Elements d’Astronomie_, _Liv._ ix. _Chap._ 3.

Footnote 16:

Optics, Art. 95.

Footnote 17:

Mr. WHISTON, in his Astronomical Principles of Religion.

Footnote 18:

As will be demonstrated in the ninth Chapter.

Footnote 19:

Optics, B. I. § 1178.

Footnote 20:

Astronomy, B. II. §. 838.

Footnote 21:

Philosophy, Vol. I. p. 401.

Footnote 22:

Account of Sir Isaac Newton’s _Philosophical Discoveries_, B. III. c.
2. § 3.

Footnote 23:

_Elements d’Astronomie_, § 381.

Footnote 24:

The face of the Sun, Moon, or any Planet, as it appears to the eye, is
called it’s Disc.

Footnote 25:

The utmost limit of a person’s view, where the Sky seems to touch the
Earth all around, is called his Horizon; which shifts as the person
changes his place.

Footnote 26:

The Plane of a Circle, or a thin circular Plate, being turned edgewise
to the eye appears to be a straight line.

Footnote 27:

A Degree is the 360th part of a Circle.

Footnote 28:

Here we do not mean such a conjunction, as that the nearer Planet
should hide all the rest from the observer’s sight; (for that would be
impossible unless the intersections of all their Orbits were
coincident, which they are not, _See_ § 21.) but when they were all in
a line crossing the standard Orbit at right Angles.

Footnote 29:

The ORRERY fronting the Title-page.

Footnote 30:

To make the projectile force balance the gravitating power so exactly
as that the body may move in a Circle, the projectile velocity of the
body must be such as it would have acquired by gravity alone in
falling through half the radius.

Footnote 31:

Astronomical Principles of Religion, p. 66.

Footnote 32:

Δὸς ποῦ στῶ, καὶ τὸν κόσμον κινήσω, _i. e._ Give me a place to stand
on, and I shall move the Earth.

Footnote 33:

If the Sun was not agitated about the common center of gravity of the
whole System, and the Planets did not act mutually upon one another,
their Orbits would be elliptical, and the areas described by them
would be exactly proportionate to the times of description § 153. But
observations prove that these areas are not in such exact proportion,
and are most varied when the greatest number of Planets are in any
particular quarter of the Heavens. When any two Planets are in
conjunction, their mutual attractions, which tend to bring them nearer
to one another, draws the inferior one a little farther from the Sun,
and the superior one a little nearer to him; by which means, the
figure of their Orbits is somewhat altered; but this alteration is too
small to be discovered in several ages.

Footnote 34:

Religious Philosopher, Vol. III. page 65.

Footnote 35:

This will be demonstrated in the eleventh Chapter.

Footnote 36:

A fine net-work membrane in the bottom of the eye.

Footnote 37:

Book I. Art. 57.

Footnote 38:

A medium, in this sense, is any transparent body, or that through
which the rays of light can pass; as water, glass, diamond, air; and
even a vacuum is sometimes called a Medium.

Footnote 39:

NEWTON’s _System of the World_, _p._ 120.

Footnote 40:

This is evident from pumps, since none can draw water higher than 33
foot.

Footnote 41:

Namely 10000 times the distance of Saturn from the Sun; p. 94.

Footnote 42:

See his Astronomy, p. 232.

Footnote 43:

As far as one can see round him on the Earth.

Footnote 44:

[Sidenote: Fig. V.]

An Angle is the inclination of two right lines, as _IH_ and _KH_,
meeting in a point at _H_; and in describing an Angle by three
letters, the middle letter always denotes the angular point: thus, the
above lines _IH_ and _KH_ meeting each other at _H_, make the Angle
_IHK_. And the point _H_ is supposed to be the center of a Circle, the
circumference of which contains 360 equal parts called degrees. A
fourth part of a Circle, called a Quadrant, as _GE_, contains 90
degrees; and every Angle is measured by the number of degrees in the
arc it cuts off; as the angle _EHP_ is 45 degrees, the Angle _EHF_ 33,
&c: and so the Angle _EHF_ is the same with the angle _CHN_, and also
with the Angle _AHM_, because they all cut off the same arc or portion
of the Quadrant _EG_; and so likewise the Angle _EHF_ is greater than
the Angle _CHD_ or _AHL_, because it cuts off a greater arc.