Part 40

439. The _Planetary Globe_. In this Machine, _T_ is a terrestrial Globe fixed on its Axis standing upright on the Pedestal _CDE_, on which is an Hour Circle, having its Index fixed on the Axis, which turns somewhat tightly in the Pedestal, so that the Globe may not be liable to shake; to prevent which, the Pedestal is about two Inches thick, and the Axis goes quite through it, bearing on a shoulder. The Globe is hung in a graduated brasen Meridian, much in the usual way; and the thin Plate _N_, _NE_, _E_, is a moveable Horizon, graduated round the outer edge, for shewing the Bearings and Amplitudes of the Sun, Moon, and Planets. The brasen Meridian is grooved round the outer edge; and in this Groove is a slender Semi-circle of brass, the ends of which are fixed to the Horizon in its North and South Points: this Semi-circle slides in the Groove as the Horizon is moved in rectifying it for different Latitudes. To the middle of the Semi-circle is fixed a Pin which always keeps in the Zenith of the Horizon, and on this Pin the Quadrant of Altitude _q_ turns; the lower end of which, in all Positions, touches the Horizon as it is moved round the same. This Quadrant is divided into 90 Degrees from the Horizon to the zenithal Pin on which it is turned, at 90. The great flat Circle or Plate _AB_ is the Ecliptic, on the outer edge of which, the Signs and Degrees are laid down; and every fifth Degree is drawn through the rest of the surface of this Plate towards its Center. On this Plate are seven Grooves, to which seven little Balls are adjusted by sliding Wires, so that they are easily moved in the Grooves, without danger of starting out of them. The Ball next the terrestrial Globe is the Moon, the next without it is Mercury, the next Venus, the next the Sun, then Mars, then Jupiter, and lastly Saturn; and in order to know them, they are separately stampt with the following Characters; ☽, ☿, ♀, ☉, ♂, ♃, ♄. This Plate or Ecliptic is supported by four strong Wires, having their lower ends fixed into the Pedestal, at _C_, _D_, and _E_, the fourth being hid by the Globe. The Ecliptic is inclined 23-1/2 Degrees to the Pedestal, and is therefore properly inclined to the Axis of the Globe which stands upright on the Pedestal.

[Sidenote: To rectify it.]

_To rectify this Machine._ Set all the planetary Balls to their geocentric places in the Ecliptic for any given time by an Ephemeris: then, set the North Point of the Horizon to the Latitude of your place on the brasen Meridian, and the Quadrant of Altitude to the South Point of the Horizon; which done, turn the Globe with its Furniture till the Quadrant of Altitude comes right against the Sun, _viz._ to his place in the Ecliptic; and keeping it there, set the Hour Index to the XII next the letter _C_; and the Machine will be rectified, not only for the following Problems, but for several others, which the Artist may easily find out.

PROBLEM I.

_To find the Amplitudes, Meridian Altitudes, and times of Rising, Culminating, and Setting, of the Sun, Moon, and Planets._

[Sidenote: It’s use.]

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_.

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.