Chap. XXII A Description of the Astronomical Machinery serving to explain and illustrate the foregoing part of this Treatise.
Fronting the Title Page.
The Orrery.
434. The Orrery. This Machine shews the Motions of the Sun, Mercury, Venus, Earth, and Moon; and occasionally, the superior Planets, Mars, Jupiter, and Saturn may be put on; Jupiter’s four Satellites are moved round him in their proper times by a small Winch; and Saturn has his five Satellites, and his Ring which keeps its parallelism round the Sun; and by a Lamp put in the Sun’s place, the Ring shews all the Phases described in the 204th Article.
The Sun.
The Ecliptic.
In the Center, No 1. represents the Sun, supported by it’s Axis inclining almost 8 Degrees from the Axis of the Ecliptic; and turning round in 251⁄4 days on its Axis, of which the North Pole inclines toward the 8th Degree of Pisces in the great Ecliptic (No. 11.) whereon the Months and Days are engraven over the Signs and Degrees in which the Sun appears, as seen from the Earth, on the different days of the year.
Mercury.
The nearest Planet (No. 2) to the Sun is Mercury, which goes round him in 87 days 23 hours, or 8723⁄24 diurnal rotations of the Earth; but has no Motion round its Axis in the Machine, because the time of its diurnal Motion in the Heavens is not known to us.
Venus.
The next Planet in order is Venus (No. 3) which performs her annual Course in 224 days 17 hours; and turns round her Axis in 24 days 8 hours, or in 241⁄3 diurnal rotations of the Earth. Her Axis inclines 75 Degrees from the Axis of the Ecliptic, and her North Pole inclines towards the 20th Degree of Aquarius, according to the observations of Bianchini. She shews all the Phenomena described from the 30th to the 44th Article in Chap. I.
The Earth.
Next without the Orbit of Venus is the Earth (No. 4) which turns round its Axis, to any fixed point at a great distance, in 23 hours 56 minutes 4 seconds of mean solar time (221 & seq.) but from the Sun to the Sun again in 24 hours of the same time. No. 6 is a sidereal Dial-Plate under the Earth; and No. 7 a solar Dial-Plate on the cover of the Machine. The Index of the former shews sidereal, and of the latter, solar time; and hence, the former Index gains one entire revolution on the latter every year, as 365 solar or natural days contain 366 sidereal days, or apparent revolutions of the Stars. In the time that the Earth makes 3651⁄4 diurnal rotations on its Axis, it goes once round the Sun in the Plane of the Ecliptic; and always keeps opposite to a moving Index (No. 10) which shews the Sun’s daily change of place, and also the days of the months.
The Earth is half covered with a black cap for dividing the apparently enlightened half next the Sun, from the other half, which when turned away from him is in the dark. The edge of the cap represents the Circle bounding Light and Darkness, and shews at what time the Sun rises and sets to all places throughout the year. The Earth’s Axis inclines 231⁄2 Degrees from the Axis of the Ecliptic, the North Pole inclines toward the beginning of Cancer; and keeps its parallelism throughout its annual Course § 48, 202; so that in Summer the northern parts of the Earth incline towards the Sun, and in the Winter from him: by which means, the different lengths of days and nights, and the cause of the various seasons, are demonstrated to sight.
There is a broad Horizon, to the upper side of which is fixed a Meridian Semi-circle in the North and South Points, graduated on both sides from the Horizon to 90° in the Zenith, or vertical Point. The edge of the Horizon is graduated from the East and West to the South and North Points, and within these Divisions are the Points of the Compass. On the lower side of this thin Horizon Plate stand out four small Wires, to which is fixed a Twilight Circle 18 Degrees from the graduated side of the Horizon all round. This Horizon may be put upon the Earth (when the cap is taken away) and rectified to the Latitude of any place: and then, by a small Wire called the Solar Ray, which may be put on so as to proceed directly from the Sun’s Center towards the Earth’s, but to come no farther than almost to touch the Horizon, the beginning of Twilight, time of Sun-rising, with his Amplitude, Meridian Altitude, time of Setting, Amplitude, and end of Twilight, are shewn for every day of the year, at that place to which the Horizon is rectified.
The Moon.
The Moon (No. 5) goes round the Earth, from between it and any fixed point at a great distance, in 27 days 7 hours 43 minutes, or through all the Signs and Degrees of her Orbit; which is called her Periodical Revolution; but she goes round from the Sun to the Sun again, or from Change to Change, in 29 days 12 hours 45 minutes, which is her Synodical Revolution; and in that time she exhibits all the Phases already described § 255.
When the above-mentioned Horizon is rectified to the Latitude of any given place, the times of the Moon’s rising and setting, together with her Amplitude, are shewn to that place as well as the Sun’s; and all the various Phenomena of the Harvest Moon § 273 & seq. made obvious to sight.
The Nodes.
The Moon’s Orbit (No. 9.) is inclined to the Ecliptic, (No. 11.) one half being above, and the other below it. The Nodes, or Points at 0 and 0 lie in the Plane of the Ecliptic, as described § 317, 318, and shift backward through all it’s Signs and Degrees in 182⁄3 years. The Degrees of the Moon’s Latitude, to the highest at NL (North Latitude) and lowest at SL (South Latitude) are engraven both ways from her Nodes at 0 and 0; and, as the Moon rises and falls in her Orbit according to its inclination, her Latitude and Distance from her Nodes are shewn for every day; having first rectified her Orbit so as to set the Nodes to their proper places in the Ecliptic: and then, as they come about at different, and almost opposite times of the year § 319, and then point towards the Sun, all the Eclipses may be shewn for hundreds of years (without any new rectification) by turning the Machinery backward for time past, or forward for time to come. At 17 Degrees distance from each Node, on both Sides, is engraved a small Sun; and at 12 Degrees distance, a small Moon; which shew the limits of solar and lunar Eclipses § 317: and when, at any change, the Moon falls between either of these Suns and the Node, the Sun will be eclipsed on the day pointed to by the annual Index (No. 10,) and as the Moon has then North or South Latitude, one may easily judge whether that Eclipse will be visible in the Northern or Southern Hemisphere; especially as the Earth’s Axis inclines towards the Sun or from him at that time. And when, at any Full, the Moon falls between either of the little Moon’s and Node, she will be eclipsed, and the annual Index shews the day of that Eclipse. There is a Circle of 291⁄2 equal parts (No. 8.) on the cover of the Machine, on which an Index shews the days of the Moon’s age.
PLATE IX. Fig. X.
There are two Semi-circles fixed to an elliptical Ring, which being put like a cap upon the Earth, and the forked part F upon the Moon, shews the Tides as the Earth turns round within them, and they are led round it by the Moon. When the different Places come to the Semi-circle AaEbB, they have Tides of Flood; and when they come to the Semicircle CED they have Tides of Ebb § 304, 305; the Index on the hour Circle (No. 7.) shewing the times of these Phenomena.
There is a jointed Wire, of which one end being put into a hole in the upright stem that holds the Earth’s cap, and the Wire laid into a small forked piece which may be occasionally put upon Venus or Mercury, shews the direct and retrograde Motions of these two Planets, with their stationary Times and Places as seen from the Earth.
The whole Machinery is turned by a winch or handle (No. 12,) and is so easily moved that a clock might turn it without any danger of stopping.
To give a Plate of the wheel-work of this Machine, would answer no purpose, because many of the wheels lie so behind others as to hide them from sight in any view whatsoever.
Another Orrery.
PLATE VI. Fig. I.
435. Another Orrery. In this Machine, which is the simplest I ever saw, for shewing the diurnal and annual motions of the Earth, together with the motion of the Moon and her Nodes; A and B are two oblong square Plates held together by four upright pillars; of which three appear at f, g, and g2. Under the Plate A is an endless screw on the Axis of the handle b, which works in a wheel fixed on the same Axis with the double grooved wheel E; and on the top of this Axis is fixed the toothed wheel i, which turns the pinion k, on the top of whose Axis is the pinion k2 which turns another pinion b2, and that other turns a third, on the Axis a2 of which is the Earth U turning round; this last Axis inclining 231⁄2 Degrees. The supporter X2, in which the Axis of the Earth turns, is fixed to the moveable Plate C.
In the fixed Plate B, beyond H, is fixed the strong wire d, on which hangs the Sun T so as it may turn round the wire. To this Sun is fixed the wire or solar ray Z, which (as the Earth U turns round its Axis) points to all the places that the Sun passes vertically over, every day of the year. The Earth is half covered with a black cap a, as in the former Orrery, for dividing the day from the night; and, as the different places come out from below the edge of the cap, or go in below it, they shew the times of Sun-rising and setting every day of the year. This cap is fixed on the wire b, which has a forked piece C turning round the wire d: and, as the Earth goes round the Sun, it carries the Cap, Wire, and solar Ray round him; so that the solar Ray constantly points towards the Earth’s Center.
On the Axis of the pinion k is the pinion m, which turns a wheel on the cock or supporter n, and on the Axis of this wheel nearest n is a pinion (hid from view) under the Plate C, which pinion turns a wheel that carries the Moon V round the Earth U; the Moon’s Axis rising and falling in the socket W, which is fixed to the triangular piece above Z; and this piece is fixed to the top of the Axis of the last mentioned wheel. The socket W is slit on the outermost side; and in this slit the two pins near Y, fixed in the Moon’s Axis, move up and down; one of them being above the inclined Plane YX, and the other below it. By this mechanism, the Moon V moves round the Earth T in the inclined Orbit q, parallel to the Plane of the Ring YX; of which the Descending Node is at X, and the Ascending Node opposite to it, but hid by the supporter X2.
The small wheel E turns the large wheels D and F, of equal diameters, by cat-gut strings crossing between them: and the Axis of these two wheels are cranked at G and H, above the Plate B. The upright stems of these cranks going through the Plate C, carry it over and over the fixed Plate B, with a motion which carries the Earth U round the Sun T, keeping the Earth’s Axis always parallel to itself; or still inclining towards the left-hand of the Plate; and shewing the vicissitudes of seasons, as described in the tenth chapter. As the Earth goes round the Sun the pinion k goes round the wheel i, for the Axis of k never touches the fixed Plate B; but turns on a wire fixed into the Plate C.
On the top of the crank G is an Index L, which goes round the Circle m2 in the time that the Earth goes round the Sun; and points to the days of the months; which, together with the names of the seasons, are marked in this Circle.
This Index has a small grooved wheel L fixed upon it, round which, and the Plate Z, goes a cat-gut string crossing between them; and by this means the Moon’s inclined Plane YX with its Nodes is turned backward, for shewing the times and returns of Eclipses § 319, 320.
The following parts of this machine must be considered as distinct from those already described.
Towards the right hand, let S be the Earth hung on the wire e, which is fixed into the Plate B; and let O be the Moon fixed on the Axis M, and turning round within the cap P, in which, and in the Plate C the crooked wire Q is fixed. On the Axis M is also fixed the Index K, which goes round a Circle h2, divided into 291⁄2 equal parts, which are the days of the Moon’s age: but to avoid confusion in the scheme, it is only marked with the numeral figures 1 2 3 4, for the Quarters. As the crank H carries this Moon round the Earth S in the Orbit t, she shews all her Phases by means of the cap P for the different days of her age, which are shewn by the Index K; this Index, turning just as the Moon O does, demonstrates her turning round her Axis as she still keeps the same side towards the Earth S § 262.
PL. VIII.
At the other end of the Plate C, a Moon N goes round an Earth R in the Orbit p; but this Moon’s Axis is stuck fast into the Plate C at S2; so that neither Moon nor Axis can turn round; and as this Moon goes round her Earth she shews herself all round to it; which proves, that if the Moon was seen all round from the Earth in a Lunation, she could not turn round her Axis.
N. B. If there were only the two wheels D and F, with a cat-gut string over them, but not crossing between them, the Axis of the Earth U would keep its parallelism round the Sun T, and shew all the seasons; as I sometimes make these Machines: and the Moon O would go round the Earth S, shewing her Phases as above; as likewise would the Moon N round the Earth R; but then, neither could the diurnal motion of the Earth U on its Axis be shewn, nor the motion of the Moon V round that Earth.
The Calculator.
436. In the year 1746 I contrived a very simple Machine, and described it’s performance in a small treatise upon the Phenomena of the Harvest Moon, published in the year 1747. I improved it soon after, by adding another wheel, and called it the Calculator. It may be easily made by any Gentleman who has a mechanical Genius.
Fig. I.
The great flat Ring supported by twelve pillars, and on which the twelve Signs with their respective Degrees are laid down, is the Ecliptic; nearly in the center of it is the Sun S supported by the strong crooked Wire I; and from the Sun proceeds a Wire W, called the Solar Ray, pointing towards the center of the Earth E, which is furnished with a moveable Horizon H, together with a brazen Meridian, and Quadrant of Altitude. R is a small Ecliptic, whose Plane co-incides with that of the great one, and has the like Signs and Degrees marked upon it; and is supported by two Wires D and D, which enter into the Plate PP, but may be taken off at pleasure. As the Earth goes round the Sun, the Signs of this small Circle keep parallel to themselves, and to those of the great Ecliptic. When it is taken off, and the solar Ray W drawn farther out, so as almost to touch the Horizon H, or the Quadrant of Altitude, the Horizon being rectified to any given Latitude, and the Earth turned round its Axis by hand, the point of the Wire W shews the Sun’s Declination in passing over the graduated brass Meridian, and his height at any given time upon the Quadrant of Altitude, together with his Azimuth, or point of Bearing upon the Horizon at that time; and likewise his Amplitude, and time of Rising and Setting by the hour Index, for any day of the year that the annual Index U points to in the Circle of Months below the Sun. M is a solar Index or Pointer supported by the Wire L which is fixed into the knob K: the use of this Index is to shew the Sun’s place in the Ecliptic every day in the year; for it goes over the Signs and Degrees as the Index U goes over the months and days; or rather as they pass under the Index U, in moving the cover plate with the Earth and its Furniture round the Sun; for the Index U is fixed tight on the immoveable Axis in the Center of the Machine. K is a knob or handle for moving the Earth round the Sun, and the Moon round the Earth.
As the Earth is carried round the Sun, its Axis constantly keeps the same oblique direction, or parallel to itself § 48, 202, shewing thereby the different lengths of days and nights at different times of the year, with all the various seasons. And, in one annual revolution of the Earth, the Moon M goes 121⁄3 times round it from Change to Change, having an occasional provision for shewing her different Phases. The lower end of the Moon’s Axis bears by a small friction wheel upon the inclined Plane T, which causes the Moon to rise above and sink below the Ecliptic R in every Lunation; crossing it in her Nodes, which shift backward through all the Signs and Degrees of the said Ecliptic, by the retrograde Motion of the inclined Plane T, in 18 years and 225 days. On this Plane the Degrees and Parts of the Moon’s North and South Latitude are laid down from both the Nodes, one of which, viz. the Descending Node appears at 0, by DN above B; the other Node being hid from Sight on this Plane by the plate PP; and from both Nodes, at proper distances, as in the other Orrery, the limits of Eclipses are marked, and all the solar and lunar Eclipses are shewn in the same manner, for any given year, within the limits of 6000, either before or after the Christian Æra. On the plate that covers the wheel-work, under the Sun S, and round the knob K are Astronomical Tables, by which the Machine may be rectified to the beginning of any given year within these limits, in three or four minutes of time; and when once set right, may be turned backward for 300 years past, or forward for as many to come, without requiring any new rectification. There is a method for its adding up the 29th of February every fourth year, and allowing only 28 days to that month for every other three: but all this being performed by a particular manner of cutting the teeth of the wheels, and dividing the month circle, too long and intricate to be described here, I shall only shew how these motions may be performed near enough for common use, by wheels with grooves and cat-gut strings round them, only here I must put the Operator in mind that the grooves are to be made sharp (not round) bottomed to keep the strings from slipping.
The Moon’s Axis moves up and down in the socket N fixed into the bar O (which carries her round the Earth) as she rises above or sinks below the Ecliptic; and immediately below the inclined Plane T is a flat circular plate (between Y and T) on which the different Excentricities of the Moon’s Orbit are laid down; and likewise her mean Anomaly and elliptic Equation by which her true Place may be very nearly found at any time. Below this Apogee-plate, which shews the Anomaly, &c. is a Circle Y divided into 291⁄2 equal parts which are the days of the Moon’s age: and the forked end A of the Index AB (Fig II) may be put into the Apogee-part of this plate; there being just such another Index to put into the inclined Plane T at the Ascending Node; and then the curved points B of these Indexes shew the direct motion of the Apogee, and retrograde motion of the Nodes through the Ecliptic R, with their Places in it at any given time. As the Moon M goes round the Earth E, she shews her Place every day in the Ecliptic R, and the lower end of her Axis shews her Latitude and distance from her Node on the inclined Plane T, also her distance from her Apogee and Perigee, together with her mean Anomaly, the then Excentricity of her Orbit, and her elliptic Equation, all on the Apogee Plate, and the day of her age in the Circle Y of 291⁄2 equal parts; for every day of the year pointed out by the annual Index U in the Circle of months.
Having rectified the Machine by the Tables for the beginning of any year, move the Earth and Moon forward by the knob K, until the annual Index comes to any given day of the month; then stop, and not only all the above Phenomena may be shewn for that day, but also, by turning the Earth round its Axis, the Declination, Azimuth, Amplitude, Altitude of the Moon at any hour, and the times of her Rising and Setting, are shewn by the Horizon, Quadrant of Altitude, and hour Index. And in moving the Earth round the Sun, the days of all the New and Full Moons and Eclipses in any given year are shewn. The Phenomena of the Harvest Moon, and those of the Tides, by such a cap as that in Plate 9 Fig. 10. put upon the Earth and Moon, together with the solution of many problems not here related, are made conspicuous.
PL. VIII.
The easiest, though not the best way, that I can instruct any mechanical person to make the wheel-work of such a machine, is as follows; which is the way that I made it, before I thought of numbers exact enough to make it worth the trouble of cutting teeth in the wheels.
Fig. III.
Fig. 3d of Plate 8 is a section of this Machine; in which ABCD is a frame of wood held together by four pillars at the corners, whereof two appear at AC and BD. In the lower Plate CD of this Frame are three small friction-wheels, at equal distances from each other; two of them appearing at e and e. As the frame is moved round, these wheels run upon the fixed bottom Plate EE which supports the whole work.
In the Center of this last mentioned Plate is fixed the upright Axis f FFG, and on the same Axis is fixed the wheel HHH in which are four grooves I, X, k, L of different Diameters. In these grooves are cat-gut strings going also round the separate wheels M, N, O and P.
The wheel M is fixed on a solid Spindle or Axis, the lower pivot of which turns at R in the under Plate of the moveable frame ABCD; and on the upper end of this Axis is fixed the Plate o o (which is PP, under the Earth, in Fig. I.) and to this Plate is fixed, at an Angle of 231⁄2 Degrees inclination, the Dial-plate below the Earth T; on the Axis of which, the Index q is turned round by the Earth. This Axis, together with the Wheel M, and Plate o o, keep their parallelism in going round the Sun S.
On the Axis of the wheel M is a moveable socket on which the small wheel N is fixed, and on the upper end of this socket is put on tight (but so as it may be occasionally turned by hand) the bar ZZ (viz. the bar O in Fig. I.) which carries the Moon m round the Earth T, by the Socket n, fixed into the bar. As the Moon goes round the Earth her Axis rises and falls in the Socket n; because, on the lower end of her Axis, which is turned inward, there is a small friction Wheel s running on the inclined Plane X (which is T in Fig. I.) and so causes the Moon alternately to rise above and sink below the little Ecliptic VV (R in Fig. I.) in every Lunation.
On the Socket or hollow Axis of the Wheel N, there is another Socket on which the Wheel O is fixed; and the Moon’s inclined Plane X is put tightly on the upper end of this Socket, not on a square, but on a round, that it may be occasionally set by hand without wrenching the Wheel or Axle.
Lastly, on the hollow Axis of the Wheel O is another Socket on which is fixed the Wheel P, and on the upper end of this Socket is put on tightly the Apogee-plate Y, (that immediately below T in Fig. I.) all these Axles turn in the upper Plate of the moveable frame at Q which Plate is covered with the thin Plate cc (screwed to it) whereon are the fore-mentioned Tables and month Circle in Fig. I.
The middle part of the thick fixed Wheel HHH is much broader than the rest of it, and comes out between the Wheels M and O almost to the Wheel N. To adjust the diameters of the grooves of this fixed wheel to the grooves of the separate Wheels M, N, O and P, so as they may perform their motions in the proper times, the following method must be observed.
The Groove of the Wheel M, which keeps the parallelism of the Earth’s Axis, must be precisely of the same Diameter as the lower Groove I of the fixed Wheel HHH; but, when this Groove is so well adjusted as to shew, that in ever so many annual revolutions of the Earth, its Axis keeps its parallelism, as may be observed by the solar Ray W (Fig. I.) always coming precisely to the same Degree of the small Ecliptic R at the end of every annual revolution, when the Index M points to the like Degree in the great Ecliptic; then, with the edge of a thin File give the Groove of the Wheel M a small rub all round; and by that means, lessening the Diameter of the Groove, perhaps about the 20th part of a hair’s breadth, it will cause the Earth to shew the precession of the Equinoxes; which, in many annual revolutions will begin to be sensible as the Earth’s Axis slowly deviates from its parallelism § 246, towards the antecedent Signs of the Ecliptic.
The Diameter of the Groove of the Wheel N, which carries the Moon round the Earth, must be to the Diameter of the Groove X as a Lunation is to a year; that is, as 291⁄2 to 3651⁄4.
The Diameter of the Groove of the Wheel O, which turns the inclined Plane X with the Moon’s Nodes backward, must be to the Diameter of the Groove k as 20 to 18225⁄365. And,
Lastly, the Diameter of the Groove of the Wheel P, which carries the Moon’s Apogee forward, must be to the Diameter of the Groove L as 70 to 62.
PLATE IV.
But, after all this nice adjustment of the Grooves to the proportional times of their respective Wheels turning round, and which seems to promise very well in Theory, there will still be found a necessity of a farther adjustment by hand; because proper allowance must be made for the Diameters of the cat-gut strings: and the Grooves must be so adjusted by hand, as, that in the time the Earth is moved once round the Sun, the Moon must perform 12 synodical revolutions round the Earth, and be almost 11 days old in her 13th revolution. The inclined Plane with its Nodes must go once round backward through all the Signs and Degrees of the small Ecliptic in 18 annual revolutions of the Earth and 225 days over. And the Apogee-plate must go once round forward, so as its Index may go over all the Signs and Degrees of the small Ecliptic in eight years (or so many annual revolutions of the Earth) and 312 days over.
N. B. The string which goes round the Grooves X and N for the Moon’s Motion must cross between these Wheels; but all the rest of the strings go in their respective Grooves IM, kO, and LP without crossing.
The Cometarium.
437. The Cometarium. This curious Machine shews the Motion of a Comet or excentric Body moving round the Sun, describing equal Areas in equal times § 152, and may be so contrived as to shew such a Motion for any Degree of Excentricity. It was invented by the late Dr. Desaguliers.
Fig. IV.
The dark elliptical Groove round the letters abcdefghiklm is the Orbit of the Comet Y: this Comet is carried round in the Groove according to the order of letters, by the Wire W, fixed in the Sun S, and slides on the Wire as it approaches nearer to or recedes farther from the Sun, being nearest of all in the Perihelion a, and farthest in the Aphelion g. The Areas aSb, bSc, cSd &c. or contents of these several Triangles are all equal; and in every turn of the Winch N the Comet Y is carried over one of these Areas; consequently in as much time as it moves, from f to g, or from g to h, it moves from m to a, or from a to b; and so of the rest, being quickest of all at a, and slowest at g. Thus, the Comet’s velocity in its Orbit continually decreases from the Perihelion a to the Aphelion g; and increases in the same proportion from g to a.
PLATE IV.
The elliptic Orbit is divided into 12 equal Parts or Signs with their respective Degrees, and so is the Circle n o p q r s t n which represents a great Circle in the Heavens, and to which all the fixed Stars in the Comet’s way are referred. Whilst the Comet moves from f to g in its Orbit it appears to move only about 5 Degrees in this Circle, as is shewn by the small knob on the end of the Wire W; but in as short time as the Comet moves from m to a, or from a to b, and it appears to describe the large space tn or no in the Heavens, either of which spaces contains 120 Degrees or four Signs. Were the Excentricity of its Orbit greater, the greater still would be the difference of its Motion, and vice versâ.
ABCDEFGHIKLMA is a circular Orbit for shewing the equable Motion of a Body round the Sun S, describing equal Areas ASB, BSC, &c. in equal times with those of the Body Y in its elliptical Orbit above mentioned; but with this difference, that the circular Motion describes the equal Arcs AB, BC, &c. in the same equal times that the elliptical Motion describes the unequal Arcs ab, bc, &c.
Now, suppose the two Bodies Y and I to start from the Points a and A at the same moment of time, and each having gone round its respective Orbit, to arrive at these Points again at the same instant, the Body Y will be forwarder in its Orbit than the Body I all the way from a to g, and from A to G; but I will be forwarder than Y through all the other half of the Orbit; and the difference is equal to the Equation of the Body Y in its Orbit. At the Points a, A, and g, G, that is, in the Perihelion and Aphelion, they will be equal; and then the Equation vanishes. This shews why the Equation of a Body moving in an elliptic Orbit, is added to the mean or supposed circular Motion from the Perihelion to the Aphelion, and subtracted from the Aphelion to the Perihelion, in Bodies moving round the Sun, or from the Perigee to the Apogee, and from the Apogee to the Perigee in the Moon’s Motion round the Earth, according to the Precepts in the 355th Article; only we are to consider, that when Motion is turned into Time, it reverses the titles in the Table of The Moon’s elliptic Equation.
Fig. V.
This curious Motion is performed in the following manner. ABC is a wooden bar (in the box containing the wheel-work) above which are the wheels D and E; and below it the elliptic Plates FF and GG; each Plate being fixed on an Axis in one of its Focuses, at E and K; and the Wheel E is fixed on the same Axis with the Plate FF. These Plates have Grooves round their edges precisely of equal Diameters to one another, and in these Grooves is the cat-gut string gg, gg crossing between the Plates at h. On H, the Axis of the handle or winch N in Fig. 4th, is an endless screw in Fig. 5, working in the Wheels D and E, whose numbers of teeth being equal, and should be equal to the number of lines aS, bS, cS, &c. in Fig. 4, they turn round their Axes in equal times to one another, and to the Motion of the elliptic Plates. For, the Wheels D and E having equal numbers of teeth, the Plate FF being fixed on the same Axis with the Wheel E, and the Plate FF turning the equally big Plate GG by a cat-gut string round them both, they must all go round their Axes in as many turns of the handle N as either of the Wheels has teeth.
’Tis easy to see, that the end h of the elliptical Plate FF being farther from its Axis E than the opposite end i is, must describe a Circle so much the larger in proportion; and therefore move through so much more space in the same time; and for that reason the end h moves so much faster than the end i, although it goes no sooner round the Center E. But then, the quick-moving end h of the Plate FF leads about the short end hK of the Plate GG with the same velocity; and the slow moving end i of the Plate FF coming half round as to B, must then lead the long end k of the Plate GG as slowly about: So that the elliptical Plate FF and it’s Axis E move uniformly and equally quick in every part of its revolution; but the elliptical Plate GG, together with its Axis K must move very unequally in different parts of its revolution; the difference being always inversely as the distance of any point of the Circumference of GG from its Axis at K: or in other words, to instance in two points, if the distance Kk be four, five, or six times as great as the distance Kh, the Point h will move in that position four, five, or six times as fast as the Point k does, when the Plate GG has gone half round: and so on for any other Excentricity or difference of the Distances Kk and Kh. The tooth i on the Plate FF falls in between the two teeth at k on the Plate GG, by which means the revolution of the latter is so adjusted to that of the former, that they can never vary from one another.
On the top of the Axis of the equally moving Wheel D, in Fig. 5th, is the Sun S in Fig. 4th; which Sun, by the Wire Z fixed to it, carries the Ball I round the Circle ABCD, &c. with an equable Motion according to the order of the letters: and on the top of the Axis K of the unequally moving Ellipsis GG, in Fig. 5th, is the Sun S in Fig. 4th, carrying the Ball Y unequably round in the elliptical Groove a b c d, &c. N.B. This elliptical Groove must be precisely equal and similar to the verge of the Plate GG, which is also equal to that of FF.
In this manner, Machines may be made to shew the true Motion of the Moon about the Earth, or of any Planet about the Sun; by making the elliptical Plates of the same Excentricities, in proportion to the Radius, as the Orbits of the Planets are whose Motions they represent: and so, their different Equations in different parts of their Orbits may be made plain to sight; and clearer Ideas of these Motions and Equations acquired in half an hour, than could be gained from reading half a day about such Motions and Equations.
The improved Celestial Globe.
PLATE III. Fig. III.
438. The Improved Celestial Globe. On the North Pole of the Axis, above the Hour Circle, is fixed an Arch MKH of 231⁄2 Degrees; and at the end H is fixed an upright pin HG, which stands directly over the North Pole of the Ecliptic, and perpendicular to that part of the surface of the Globe. On this pin are two moveable Collets at D and H, to which are fixed the quadrantal Wires N and O, having two little Balls on their ends for the Sun and Moon, as in the Figure. The Collet D is fixed to the circular Plate F whereon the 291⁄2 days of the Moon’s age are engraven, beginning just under the Sun’s Wire N; and as this Wire is moved round the Globe, the Plate F turns round with it. These Wires are easily turned if the Screw G be slackened; and when they are set to their proper places, the Screw serves to fix them there so, as in turning the Ball of the Globe, the Wires with the Sun and Moon go round with it; and these two little Balls rise and set at the same times, and on the same points of the Horizon, for the day to which they are rectified, as the Sun and Moon do in the Heavens.
Because the Moon keeps not her course in the Ecliptic (as the Sun appears to do) but has a Declination of 51⁄3 Degrees on each side from it in every Lunation § 317, her Ball may be screwed as many Degrees to either side of the Ecliptic as her Latitude or Declination from the Ecliptic amounts to at any given time; and for this purpose S is a small piece of pasteboard, of which the curved edge S is to be set upon the Globe at right Angles to the Ecliptic, and the dark line over S to stand upright upon it. From this line, on the convex edge, are drawn the 51⁄3 Degrees of the Moon’s Latitude on both sides of the Ecliptic; and when this piece is set upright on the Globe, it’s graduated edge reaches to the Moon on the Wire O, by which means she is easily adjusted to her Latitude found by an Ephemeris.
The Horizon is supported by two semicircular Arches, because Pillars would stop the progress of the Balls when they go below the Horizon in an oblique sphere.
To rectify it.
To rectify the Globe. Elevate the Pole to the Latitude of the Place; then bring the Sun’s place in the Ecliptic for the given day to the brasen Meridian, and set the Hour Index to XII at noon, that is, to the upper XII on the Hour Circle; keeping the Globe in that situation, slacken the Screw G, and set the Sun directly over his place on the Meridian; which done, set the Moon’s Wire under the number that expresses her age for that day on the Plate F, and she will then stand over her place in the Ecliptic, and shew what Constellation she is in. Lastly, fasten the Screw G, and laying the curved edge of the pasteboard S over the Ecliptic below the Moon, adjust the Moon to her Latitude over the graduated edge of the pasteboard; and the Globe will be rectified.
It’s use.
Having thus rectified the Globe, turn it round, and observe on what points of the Horizon the Sun and Moon Balls rise and set, for these agree with the points of the Compass on which the Sun and Moon rise and set in the Heavens on the given day; and the Hour Index shews the times of their rising and setting; and likewise the time of the Moon’s passing over the Meridian.
This simple Apparatus shews all the varieties that can happen in the rising and setting of the Sun and Moon; and makes the forementioned Phenomena of the Harvest Moon (Chap. xvi.) plain to the Eye. It is also very useful in reading Lectures on the Globes, because a large company can see this Sun and Moon going round, rising above and setting below the Horizon at different times, according to the seasons of the year; and making their appulses to different fixed Stars. But, in the usual way, where there is only the places of the Sun and Moon in the Ecliptic to keep the Eye upon, they are easily lost sight of, unless covered with Patches.
The Planetary Globe.
PL. VIII. Fig. IV.
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; ☽, ☿, ♀, sun, ♂, ♃, ♄. 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 231⁄2 Degrees to the Pedestal, and is therefore properly inclined to the Axis of the Globe which stands upright on the Pedestal.
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.
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.
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 3651⁄4 days is to 291⁄2; 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 291⁄2 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 291⁄2 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.
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 291⁄2 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.
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 291⁄2 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.
Plate XIII.
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 291⁄2 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 291⁄2 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.
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 291⁄2 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 291⁄2 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.
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 231⁄2 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.
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.
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.
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