Part 9

The globe being kept in the same elevation, and from turning round its axis, move the wooden frame about until the North and South points of the horizon lie exactly in the meridian; then right lines imagined to pass from the center thro’ each Star upon the surface of the globe, will point out the real Star in the heavens, which those on the globe are made to represent. And if you are by the side of some wall whose bearing you know, lay the quadrant of altitude to that bearing in the horizon, and it will cut all those Stars which at that very time are to be seen in the same direction, or close by the side of the said wall. Thus knowing some of the remarkable Stars in any part of the heavens, the neighbouring Stars may be distinguished by observing their situations with respect to those that are already known, and comparing them with the Stars drawn upon the globe.

Thus, if you turn your face towards the North, you will find the North Pole of the globe points to the _Pole-Star_; then you may observe two Stars somewhat less bright than the Pole-Star, almost in a right line with it, and four more which form a sort of _quadrangle_; these seven Stars make the constellation called the _Little Bear_; the Pole Star being in the tip of the tail. In this neighbourhood you will observe seven bright Stars, which are commonly called _Charles’s Wane_; these are the bright Stars in the _Great Bear_, and form much such another figure with those before-mentioned in the _little Bear_: The two foremost of the square lie almost in a right line with the Pole Star, and are called the _Pointers_, so that knowing the Pointers, you may easily find the Pole-Star. Thus the rest of the Stars in this constellation, and all the Stars in the neighbouring constellations may be easily found, by observing how the unknown Stars lie either in _quadrangles_, _triangles_, or strait lines from those that are already known upon the globe.

After the same manner the globe being rectified, you may distinguish those Stars that are to the Southward of you, and be soon acquainted with all the Stars that are visible in our hemisphere.

_SCHOLIUM._

The globe being rectified to the latitude of any place, if you turn it round its axis, all those Stars that do not go below the horizon during a whole revolution of the globe, never set in that place; and those that do not come above the horizon never rise.

PROB. XXXVII. _The latitude of the place being given; to find the Amplitude, Oblique Ascension and Descension, Ascensional Difference, Semi-diurnal Arch, and the time of continuance above the horizon, of any given point in the heavens._

Having rectified the globe for the latitude, and brought the given point to the meridian, set the index to the hour of 12; then turn the globe until the given point be brought to the Eastern side of the horizon, and that degree of the equinoctial which is cut by the horizon at that time, will be the _Oblique Ascension_; and where the given point cuts the horizon, is the _Amplitude Ortive_: If the globe be turned about until the given point be brought to the Western side of the horizon, it will there show the _Amplitude Occasive_; and where the horizon cuts the equinoctial at that time, is the _Oblique Descension_.

The time between the index at either of these two positions, and the hour of 6; or half the difference between the oblique ascension and descension is the _Ascensional Difference_.

If the place be in North latitude and the declination of the given point be (North/South) the ascensional difference reduced into time, and (added to/subtracted from) 6 o’Clock, gives the _Semi-diurnal Arch_; the complement whereof to a semicircle, is the _Semi-nocturnal Arch_. If the place be in South latitude, then the contrary is to be observed with respect to the declination.

The semi-(diurnal/nocturnal) arch being doubled, gives the time of continuance (above/below) the horizon. Or the time of continuance above the horizon, may be found by counting the number of hours contained in the upper part of the horary circle, betwixt the place where the index pointed when the given point was in the Eastern or Western parts of the horizon. If the given point was the Sun’s place, the index pointed the time of his rising and setting, when the said place was in the Eastern and Western parts of the horizon, as in _Prob. 18_. Or the time of Sun-rising may be found by adding or subtracting his ascensional difference, to or from the hour of six, according as the latitude and declination are either contrary or the same way.

Thus, at _London_, on the 31st of _May_, the _Sun’s_

_Amplitude_ is 24 degrees Northerly. _Oblique Ascension_, 20. _Oblique Descension_, 58. _Ascensional Difference_, 19. _Semi-diurnal Arch_, 109. His continuance above the horizon, 14½ hours. Sun rises at three quarters past four. Sun sets a quarter past seven.

These things for the Sun vary every day; but for a Fixed Star the day of the month need not be given, for they are the same all the year round.

In the latitude of 51½ North, _Syrus_’s _Amplitude_ is about 28 degrees Southerly. _Oblique Ascension_, 121. _Oblique Descension_, 75. _Ascensional Difference_, 23. _Semi-diurnal Arch_, 67. Continuance above the horizon, 9 hours.

PROB. XXXVIII. _The Latitude and the Day of the Month being given; to find the Hour when any known Star will be upon the meridian, and also the time of its rising and setting._

Having rectified the globe for the latitude of the Sun’s place, bring the given Star to the meridian, and also to the East or West side of the horizon, and the index will shew accordingly when the Star _culminates_, or the time of the _rising_ or _setting_.

Thus at _London_, on the 21st of _January_, _Syrius_ will be upon the meridian, at a quarter past ten in the evening; rises at 5¼ hours, and sets at three quarters past two in the morning.

By the converse of this problem, knowing the time when any Star is upon the meridian, you may easily find the Sun’s place. Thus, bring the given Star to the meridian, and set the index to the given hour; then turn the globe ’till the index points to 12 at noon, and the meridian will cut the Sun’s place in the ecliptic. Thus when _Syrius_ comes to the meridian at 10½ hours after noon, the Sun’s place will be ≈ ¼ deg.

PROB. XXXIX. _To find at what time of the Year a given Star will be upon the Meridian, at a given Hour of the Night._

Bring the Star to the meridian, and set the index to the given hour, then turn he globe ’till the index points to 12 at noon, and the meridian will cut the ecliptic in the Sun’s place; whence the day of the month may be easily found in the kalendar upon the horizon.

PROB. XL. _The Day of the Month, and the Azimuth of any known Star being given; to find the Hour of the Night._

Having rectified the globe for the latitude and the Sun’s place, if the given Star be due North or South, bring it to the meridian, and the index will show the hour of the night. If the Star be in any other direction, fix the quadrant of altitude in the zenith, and set it to the Star’s azimuth in the horizon; then turn the globe about until the quadrant cuts the center of the Star, and the index will shew the hour of the night.

The bearing of any point in the heavens may be found by the following methods.

Having a meridian line drawn in two windows, that are opposite to one another, you may cross it at right angles with another line representing the East and West; from the point of the intersection describe a circle, and divide each quadrant into 90 degrees; then get a smooth board, of about 2 feet long, and ¾ foot broad (more or less, as you judge convenient) and on the back part of it fix another small board crossways, so that it may serve as a foot to support the biggest board upright, when it is set upon a level, or an horizontal plane. The board being thus prepared, set the lower edge of the smooth, or fore side of it, close to the center of the circle, then turn it about to the meridian, or to any azimuth point required (keeping the edge of it always close to the center) and casting your eye along the flat side of it, you will easily perceive what Stars are upon the meridian, or any other bearing that the board is set to.

PROB. XLI. _Two known Stars having the same Azimuth, or the same Height, being given; to find the Hour of the Night._

Rectify the globe for the latitude, the zenith, and the Sun’s place.

1. When the two Stars are in the same azimuth, turn the globe, and also the quadrant about, until both Stars coincide with the edge thereof; then will the index shew the hour of the night; and where the quadrant cuts the horizon, is the common azimuth of both Stars.

2. If the two Stars are of the same altitude, move the globe so that the same degree on the quadrant will cut both Stars, then the index will shew the hour.

This problem is useful when the quantity of the azimuth of the two Stars in the first case, or of their altitude in the latter case, is not known.

_If two Stars were given, one on the meridian, and the other in the East or West part of the horizon; to find the Latitude._

Bring that Star which was observed on the meridian, to the meridian of the globe, and keep the globe from turning round its axis; then slide the meridian up or down in the notches, ’till the other Star is brought to the East or West part of the horizon, and that elevation of the Pole will be the _Latitude_ sought.

PROB. XLII. _The Latitude, Day of the Month, and the Altitude of any known Star being given; to find the Hour of the Night._

Rectify the globe for the latitude, zenith, and Sun’s place: Turn the globe, and the quadrant of altitude, backward or forward, ’till the center of that Star meets the quadrant in the degree of altitude given; then the index will point the true hour of the night; and also where the quadrant cuts the horizon, will be the azimuth of the Star at that time.

_If the Latitude, the Sun’s Altitude, and his Declination (instead of his Place in the Ecliptic) are given; to find the Hour of the Day and Azimuth._

Rectify the globe for the latitude and zenith, and having brought the _equinoctial colure_ to the meridian, set the index to 12 at noon; which being done, turn the globe and the quadrant, until the given declination in the equinoctial colure, cuts the altitude on the quadrant; then the index will shew the _Hour_ of the day, and the quadrant cut the _Azimuth_ in the horizon.

_If the Altitude of two Stars on the same Azimuth were given; to find the Latitude of the Place._

Set the quadrant over both Stars at the observed degrees of altitude, and keep it fast upon the globe with your fingers; then slide the meridian up or down in the notches, ’till the quadrant cuts the given azimuth in the horizon; that elevation of the Pole will be the latitude required.

PROB. XLIII. _Having the Latitude of the place, to find the degree of the Ecliptic, which rises or sets with a given Star; and from thence to determine the time of its_ Cosmical _and_ Achronical _rising and setting._

Having rectified the globe for the latitude, bring the given Star to the Eastern side of the horizon, and mark what degree of the ecliptic rises with it: Look for that degree in the wooden horizon, and right against it, in the kalendar, you will find the month and day when the Star _rises Cosmically_. If you bring the Star to the Western side of the horizon, that degree of the ecliptic which rises at that time, will give the day of the month when the said Star _sets Cosmically_. So likewise against the degree which sets with the Star, you will find the day of the month of the _Achronical setting_; and if you bring it to the Eastern part of the horizon, that degree which sets at that time will be the Sun’s place when the Star _rises Achronically_.

Thus, in the latitude of _London_, _Syrius_, or the _Dog-Star_, rises _Cosmically_ the 10th of _August_, and sets _Cosmically_ the 10th of _October_. _Aldebaran_, or the _Bull’s Eye_, rises _Achronically_ on the 22d of _May_, and sets _Achronically_ on the 19th of _December_.

PROB. XLIV. _Having the Latitude of the place, to find the time when a Star rises and sets_ Heliacally.

Having rectified the globe for the latitude, bring the Star to the Eastern side of the horizon, and turn the quadrant round to the Western side, ’till it cuts the ecliptic in 12 degrees of altitude above the horizon, if the Star be of the first magnitude; then that point of the ecliptic which is cut by the quadrant, is 12 degrees high above the Western part of the horizon, when the Star rises; but at the same time the opposite point in the ecliptic is 12 degrees below the Eastern part of the horizon, which is the depression of a Star of the _first magnitude_, when she _rises Heliacally_; or has got so far from the Sun’s beams, that she may be seen in the morning before Sun-rising. Wherefore look for the said point of the ecliptic on the horizon, and right against it will be the day of the month when the Star _rises Heliacally_. To find the _Heliacal setting_, bring the Star to the West side of the horizon, and turn the quadrant about to the Eastern side, ’till the 12th degree of it above the horizon, cuts the ecliptic; then that degree of the ecliptic which is opposite to this point, is the Sun’s place when the Star _sets Heliacally_.

Thus you will find that _Arcturus_ rises Heliacally the 28th of _September_, and sets Heliacally _December_ the 2d.

PROB. XLV. _To find the place of any Planet upon the globe; and so by that means, to find its place in the Heavens: Also to find at what Hour any Planet will rise or set, or be on the meridian at any one Day in the Year._

You must first seek in an Ephemeris (_White_’s Ephemeris will do well enough) for the place of the Planet proposed on that day; then mark that point of the ecliptic, either with chalk, or by sticking on a little black patch; and then for that night you may perform any problem, as before, by a Fixed Star.

Let it be required to find the situation of _Jupiter_ among the Fixed Stars in the heavens, and also what time he rises and sets, and comes to the meridian on the 19th of _May_, 1757, N. S. at _London_.

Looking for the 19th of _May_, 1757, in _White_’s Ephemeris, I find that _Jupiter_’s place at that time is in about 12 degrees of ♏; latitude about 1¼ degree North. Then looking for that point upon the Celestial globe, I find that ♃ is then nearly in conjunction with the bright Star in the Southern Balance, and about 1 degree North of it.

To find when he rises and sets, and comes to the meridian: Having put a little black patch on the place of _Jupiter_, elevate the globe according to the latitude, and having brought the Sun’s place to the meridian, set the hour index to 12 at noon; then turn the mark which was made for _Jupiter_, to the Eastern part of the horizon, I find ♃ will rise somewhat more than half an hour after three in the afternoon; and turning the globe about, I find it comes to the meridian a little before eleven at night; and sets almost a quarter past six next morning.

This example being understood, it will be easy to find when either of the other two superior Planets, _viz. Mars_ and _Saturn_, rise, set, and come to the meridian.

I shall conclude this subject about the Globes with the following problems.

PROB. XLVI. _To find all that space upon the Earth, where an Eclipse of one of the Satellites of_ Jupiter _will be visible._

Having found that place upon the Earth, in which the Sun is vertical at the time of the eclipse, by _Prob. 13_, elevate the globe according to the latitude of the said place; then bring the place to the meridian, and set the hour index to 12 at noon. If _Jupiter_ be in consequence of the Sun, draw a line with black lead, or the like, along the Eastern side of the horizon, which line, will pass over all those places where the Sun is setting at that time; then count the difference betwixt the right ascension of the Sun, and that of _Jupiter_, and turn the globe Westward, ’till the hour index points to this difference; then keep the globe from turning round its axis, and elevate the meridian, according to the declination of _Jupiter_. The globe being in this position, draw a line along the Eastern side of the horizon; then the space between this line, and the line before drawn, will comprehend all those places of the Earth where _Jupiter_ will be visible, from the setting of the Sun, to the setting of _Jupiter_.

But if _Jupiter_ be in antecedence of the Sun (_i. e._ rises before him) having brought the place where the Sun is vertical, to the zenith, and put the hour index to 12 at noon, draw a line on the Western side of the horizon; then elevate the globe according to the declination of _Jupiter_, and turn it about Eastward, until the index points to so many hours distant from noon, as is the difference of right ascension of the Sun and _Jupiter_. The globe being in this position, draw a line along the Western side of the horizon; then the space contained between this line, and the other last drawn, will comprehend all those places upon the Earth where the Eclipse is visible, between the rising of the Sun, and that of _Jupiter_.

_The_ DESCRIPTION _of the Great_ ORRERY, _lately made by Mr._ THOMAS WRIGHT, Mathematical Instrument-Maker to his late MAJESTY, and now by BENJAMIN COLE, _his Successor_.

The ORRERY is an Astronomical Machine, made to represent the motions of the Planets. These machines are made of various sizes, some having more Planets than others; but I shall here confine myself to the description of that above-mentioned.

In the Introduction we gave a short account of the _Order_, _Periods_, _Distances_, and _Magnitudes_ of the _Primary Planets_; and of the _Distances_ and _Periodical Resolutions_ of the _Secondary Planets_ round their respective Primaries. We shall here explain their _Stations_, _Regradations_, _Eclipses_, _Phases_, _&c._ but first let us take a general view of the _Orrery_.

[Sidenote: The Description of the _Orrery_.]

[Sidenote: Vide _Frontispiece_.]

The frame which contains the wheel-work, _&c._ that regulates the whole _Machine_, is made of fine ebony, and is near four feet in diameter; the outside thereof is adorned with twelve pilasters, curiously wrought and gilt: Between these pilasters the twelve Signs of the _Zodiac_ are neatly painted, with gilded frames. Above the frame is a broad ring, supported with twelve pillars: This ring represents the _Plane_ of the _Ecliptic_, upon which there are two scales of degrees, and between those the names and characters of the twelve Signs. Near the outside is a scale of months and days, exactly corresponding to the Sun’s place at noon, each day throughout the year.

Above the ecliptic stands some of the principal circles of the sphere, according to their respective situations in the heavens, _viz._ N° 10, are the two _Colures_, divided into degrees, and half degrees; N° 11, is one half of the Equinoctial Circle, making an angle with the ecliptic of 23½ degrees. The _Tropic of Cancer_, and the _Arctic Circle_, are each fixed parallel, and at their proper distance from the equinoctial. On the Northern half of the ecliptic is a brass semicircle, moveable upon two points fixed in ♈ and ♎: This semicircle serves as a moveable horizon, to be put to any degree of latitude upon the North part of the meridian. The whole machine is also so contrived, as to be set to any latitude, without in the least affecting any of the inside motions: For this purpose there are two strong hinges (N° 13,) fixed to the bottom frame, upon which the instrument moves, and a strong brass arch, having holes at every degree, thro’ which a strong pin is to be put, according to the elevation. This arch and the two hinges, support the whole machine, when it is lifted up according to any latitude; and the arch at other times lies conveniently under the bottom frame.

When the machine is set to any latitude (which is easily done by two men, each taking hold of two handles, conveniently fixed for that purpose) set the moveable horizon to the same degree upon the meridian, and you may form an idea of the respective altitude, or depressions of the Planets, above or below the horizon, according to their respective positions, with regard to the meridian.

Within the ecliptic, and nearly in the same place thereof, stands the Sun, and all the Planets, both Primary and Secondary. The Sun (Nº 1.) stands in the middle of the whole system, upon a wire, making an angle with the plane of the ecliptic, of about 82 degrees; which is the inclination of the Sun’s axis, to the axis of the ecliptic. Next to the Sun is a Small ball (Nº 2.) representing _Mercury_: Next to _Mercury_ is _Venus_ (Nº 3.) represented by a larger ball (and both these stand upon wires,) so that the balls themselves may be more visibly perceived by the eye. The Earth is represented (Nº 4.) by an ivory ball, having some of the principal meridians and parallels, and a little sketch of a map described upon it. The wire which supports the Earth, makes an angle with the plane of the ecliptic 66½ degrees, which is the inclination of the Earth’s axis to that of the ecliptic. Near the bottom of the Earth’s axis is a Dial Plate (Nº 9.) having an index pointing to the hours of the day, as the Earth turns round its axis.

Round the Earth is a ring, supported by two small pillars, which ring represents the Orbit of the Moon, and the division upon it answers to the Moon’s latitude; the motion of this ring represents the motion of the Moon’s Orbit, according to that of the Nodes. Within this ring is the Moon (Nº 5.) having a black cap or case, which by its motion, represents the _Phases_ of the Moon according to her age. Without the Orbits of the Earth and Moon is _Mars_ (Nº 6.) The next in order to _Mars_ is _Jupiter_, and his four Moons (Nº 7); each of these moons is supported by a crooked wire fixed in a socket, which turns about the pillar that supports _Jupiter_. These satellites may be turned by the hand to any position; and yet when the machine is put in motion, they will all move in their proper times. The outermost of all is _Saturn_, and his five Moons (Nº 8.) These moons are supported and contrived after the same manner with those of _Jupiter_. The whole machine is put into motion by turning a small winch (like the key of a clock, Nº 14.) and all the inside work is so truly wrought, that it requires but very small strength to put the whole motion.

Above the handle there is a cylindrical pin, which may be drawn a little out, or pushed in, at pleasure: when it is pushed in, all the Planets, both primary and Secondary, will move according to their respective periods, by turning the handle: When it is drawn out, the motions of the Satellites of _Jupiter_ and _Saturn_ will be stopped, while all the rest move without interruption. This is a very good contrivance to preserve the instrument from being clogged by the swift motions of the wheels belonging to the Satellites of _Jupiter_ and _Saturn_, when the motions of the rest of the Planets are only considered.

There is also a brass lamp having two convex glasses, to be put in the room of the Sun; and also a smaller Earth and Moon, made somewhat in proportion to their distance from each other, which may be put on at pleasure.