Part 38

+-------------------+------------------------------------------------+ | After Christ | Hundreds of Years. | +-------------------+------+------+------+------+------+------+------+ | | 0 | 100 | 200 | 300 | 400 | 500 | 600 | | | 700 | 800 | 900 | 1000 | 1100 | 1200 | 1300 | | Years less | 1400 | 1500 | 1600 | 1700 | 1800 | 1900 | 2000 | | than an | 2100 | 2200 | 2300 | 2400 | 2500 | 2600 | 2700 | | Hundred. | 2800 | 2900 | 3000 | 3100 | 3200 | 3300 | 3400 | | | 3500 | 3600 | 3700 | 3800 | 3900 | 4000 | 4100 | +----+----+----+----+------+------+------+------+------+------+------+ | 0 | 28 | 56 | 84 | D C | E D | F E | G F | A G | B A | C B | +----+----+----+----+------+------+------+------+------+------+------+ | 1 | 29 | 57 | 85 | B | C | D | E | F | G | A | | 2 | 30 | 58 | 86 | A | B | C | D | E | F | G | | 3 | 31 | 59 | 87 | G | A | B | C | D | E | F | | 4 | 32 | 60 | 88 | F E | G F | A G | B A | C B | D C | E D | +----+----+----+----+------+------+------+------+------+------+------+ | 5 | 33 | 61 | 89 | D | E | F | G | A | B | C | | 6 | 34 | 62 | 90 | C | D | E | F | G | A | B | | 7 | 35 | 63 | 91 | B | C | D | E | F | G | A | | 8 | 36 | 64 | 92 | A G | B A | C B | D C | E D | F E | G F | +----+----+----+----+------+------+------+------+------+------+------+ | 9 | 37 | 65 | 93 | F | G | A | B | C | D | E | | 10 | 38 | 66 | 94 | E | F | G | A | B | C | D | | 11 | 39 | 67 | 95 | D | E | F | G | A | B | C | | 12 | 40 | 68 | 96 | C B | D C | E D | F E | G F | A G | B A | +----+----+----+----+------+------+------+------+------+------+------+ | 13 | 41 | 69 | 97 | A | B | C | D | E | F | G | | 14 | 42 | 70 | 98 | G | A | B | C | D | E | F | | 15 | 43 | 71 | 99 | F | G | A | B | C | D | E | | 16 | 44 | 72 | | E D | F E | G F | A G | B A | C B | D C | +----+----+----+----+------+------+------+------+------+------+------+ | 17 | 45 | 73 | | C | D | E | F | G | A | B | | 18 | 46 | 74 | | B | C | D | E | F | G | A | | 19 | 47 | 75 | | A | B | C | D | E | F | G | | 20 | 48 | 76 | | G F | A G | B A | C B | D C | E D | F E | +----+----+----+----+------+------+------+------+------+------+------+ | 21 | 49 | 77 | | E | F | G | A | B | C | D | | 22 | 50 | 78 | | D | E | F | G | A | B | C | | 23 | 51 | 79 | | C | D | E | F | G | A | B | | 24 | 52 | 80 | | B A | C B | D C | E D | F E | G F | A G | +----+----+----+----+------+------+------+------+------+------+------+ | 25 | 53 | 81 | | G | A | B | C | D | E | F | | 26 | 54 | 82 | | F | G | A | B | C | D | E | | 27 | 55 | 83 | | E | F | G | A | B | C | D | +----+----+----+----+------+------+------+------+------+------+------+

TAB. V. _The Dominical Letter, New Style, for 4000 Years after the Christian Æra._

+-------------------+---------------------------+ | After Christ. | Hundreds of Years. | +-------------------+------+------+------+------+ | | 100 | 200 | 300 | 400 | | | 500 | 600 | 700 | 800 | | | 900 | 1000 | 1100 | 1200 | | | 1300 | 1400 | 1500 | 1600 | | | 1700 | 1800 | 1900 | 2000 | | Years less than | 2100 | 2200 | 2300 | 2400 | | an Hundred. | 2500 | 2600 | 2700 | 2800 | | | 2900 | 3000 | 3100 | 3200 | | | 3300 | 3400 | 3500 | 3600 | | | 3700 | 3800 | 3900 | 4000 | | +------+------+------+------+ | | C | E | G | B A | +----+----+----+----+------+------+------+------+ | 1 | 29 | 57 | 85 | B | D | F | G | | 2 | 30 | 58 | 86 | A | C | E | F | | 3 | 31 | 59 | 87 | G | B | D | E | | 4 | 32 | 60 | 88 | F E | A G | C B | D C | +----+----+----+----+------+------+------+------+ | 5 | 33 | 61 | 89 | D | F | A | B | | 6 | 34 | 62 | 90 | C | E | G | A | | 7 | 35 | 63 | 91 | B | D | F | G | | 8 | 36 | 64 | 92 | A G | C B | C D | F E | +----+----+----+----+------+------+------+------+ | 9 | 37 | 65 | 93 | F | A | C | D | | 10 | 38 | 66 | 94 | E | G | B | C | | 11 | 39 | 67 | 95 | D | F | A | B | | 12 | 40 | 68 | 96 | C B | E D | G F | A G | +----+----+----+----+------+------+------+------+ | 13 | 41 | 69 | 97 | A | C | E | F | | 14 | 42 | 70 | 98 | G | B | D | E | | 15 | 43 | 71 | 99 | F | A | C | D | | 16 | 44 | 72 | | E D | G F | B A | C B | +----+----+----+----+------+------+------+------+ | 17 | 45 | 73 | | C | E | G | A | | 18 | 46 | 74 | | B | D | F | G | | 19 | 47 | 75 | | A | C | E | F | | 20 | 48 | 76 | | G F | B A | D C | E D | +----+----+----+----+------+------+------+------+ | 21 | 49 | 77 | | E | G | B | C | | 22 | 50 | 78 | | D | F | A | B | | 23 | 51 | 79 | | C | E | G | A | | 24 | 52 | 80 | | B A | D C | F E | G F | +----+----+----+----+------+------+------+------+ | 25 | 53 | 81 | | G | B | D | E | | 26 | 54 | 82 | | F | A | C | D | | 27 | 55 | 83 | | E | G | B | C | | 28 | 56 | 84 | | D C | F E | A G | B A | +----+----+----+----+------+------+------+------+

TAB. VI. _Shewing the Days of the Months for both Styles by the Dominical Letters._

+-------------+----+----+----+----+----+----+----+ | Week Day. | A | B | C | D | E | F | G | +-------------+----+----+----+----+----+----+----+ | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | | | 8 | 9 | 10 | 11 | 12 | 13 | 14 | | January 31 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | | October 31 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | | | 29 | 30 | 31 |----|----|----|----| +-------------+----|----|----| 1 | 2 | 3 | 4 | | | 5 | 6 | 7 | 8 | 9 | 10 | 11 | | Feb. 28-29 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | | March 31 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | | Nov. 30 | 26 | 27 | 28 | 29 | 30 | 31 |----| +-------------+----+----+----+----+----+----+ 1 | | | 2 | 3 | 4 | 5 | 6 | 7 | 8 | | | 9 | 10 | 11 | 12 | 13 | 14 | 15 | | April 30 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | | July 31 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | | | 30 | 31 |----|----|----|----|----| +-------------+----|----| 1 | 2 | 3 | 4 | 5 | | | 6 | 7 | 8 | 9 | 10 | 11 | 12 | | | 13 | 14 | 15 | 16 | 17 | 18 | 19 | | August 31 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | | | 27 | 28 | 29 | 30 | 31 |----|----| +-------------+----|----|----|----|----| 1 | 2 | | | 3 | 4 | 5 | 6 | 7 | 8 | 9 | | | 10 | 11 | 12 | 13 | 14 | 15 | 16 | | Septemb. 30 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | | Decemb. 31 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | | | 31 |----|----|----|----|----|----| +-------------+----| 1 | 2 | 3 | 4 | 5 | 6 | | | 7 | 8 | 9 | 10 | 11 | 12 | 13 | | | 14 | 15 | 16 | 17 | 18 | 19 | 20 | | May 31 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | | | 28 | 29 | 30 | 31 |----|----|----| +-------------+----|----|----|----| 1 | 2 | 3 | | | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | | 11 | 12 | 13 | 14 | 15 | 16 | 17 | | June 30 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | | | 25 | 26 | 27 | 28 | 29 | 30 | | +-------------+----+----+----+----+----+----+----+

CHAP. XXII.

_A Description of the Astronomical Machinery serving to explain and illustrate the foregoing part of this Treatise._

[Sidenote: 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.

[Sidenote: 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 25-1/4 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.

[Sidenote: Mercury.]

The nearest Planet (No. 2) to the Sun is _Mercury_, which goes round him in 87 days 23 hours, or 87-23/24 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.

[Sidenote: 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 24-1/3 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.

[Sidenote: 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 365-1/4 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 23-1/2 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.

[Sidenote: 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.

[Sidenote: 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 18-2/3 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 29-1/2 equal parts (No. 8.) on the cover of the Machine, on which an Index shews the days of the Moon’s age.

[Sidenote: 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.

[Sidenote: 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 _g_2. 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 _k_2 which turns another pinion _b_2, and that other turns a third, on the Axis _a_2 of which is the Earth _U_ turning round; this last Axis inclining 23-1/2 Degrees. The supporter _X_2, 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 _X_2.

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 _m_2 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 _h_2, divided into 29-1/2 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.

[Sidenote: 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 _S_2; 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.

[Sidenote: 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.

[Sidenote: Fig. I.]