An essay on the use of celestial and terrestrial globes; exemplified in a greater variety of problems, than are to be found in any other work; exhibiting the general principles of dialing & navigation. / By the late George Adams, mathematical instrument maker to His Majesty, and optician to the Prince of Wales.

THE USE OF THE CELESTIAL GLOBE, IN PRO∣BLEMS RELATIVE TO THE FIXED STARS.

The use of the celestial globe is in no in∣stance more conspicuous, than in the problems concerning the fixed stars. Among many other advantages, it will, if joined with observations on the stars themselves, render the practice and theory of other problems easy and clear to the pupil, and vastly facilitate his progress in astro∣nomical knowledge.

The heavens are as much studded over with stars in the day, as in the night; only they are then rendered invisible to us by the bright∣ness of the solar rays. But when this glorious luminary descends below the horizon, they be∣gin gradually to appear; when the sun is about twelve degrees below the horizon, stars of the first magnitude become visible; when he is

thirteen degrees, those of the second are seen; when fourteen degrees, those of the third mag∣nitude appear; when fifteen degrees, those of the fourth present themselves to view; when he is descended about eighteen degrees, the stars of the fifth and sixth magnitude, and those that are still smaller, become conspicuous, and the azure arch sparkles with all it's glory.

PROBLEM XII.

To find the right ascension and declination of any given star.

Bring the given star to the meridian, and the degree under which it lies is it's decli∣nation; and the point in which the meridian intersects the equinoctial is it's right ascension. Thus the right ascension of Sirius is 99°, it's declination 16° 25′ south; the right ascension of Arcturus is 211° 32′, it's declination 20° 20′ north.

The declination is used to find the latitude of places; the right ascension is used to find the time at which a star or planet comes to the me∣ridian; to find at any given time how long it will be before any celestial body comes to the meridian; to determine in what order those bodies pass the meridian; and to make a cata∣logue of the fixed stars.

PROBLEM XIII.

To find the latitude and longitude of a given star.

Bring the pole of the ecliptic to the meri∣dian, over which fix the quadrant of altitude, and, holding the globe very steady, move the quadrant to lie over the given star, and the de∣gree on the quadrant cut by the star, is it's la∣titude; the degree of the ecliptic cut at the same time by the quadrant, is the longitude of the star.

Thus the latitude of Arcturus is 30° 30′; it's longitude 20° 20′ of Libra: the latitude of Capella is 22° 22′ north; it's longitude 18 8′ of Gemini.

The latitude and longitude of stars is used to fix precisely their place on the globe, to refer planets and comets to the stars, and, lastly, to determine whether they have any mo∣tion, whether any stars vanish, or new ones ap∣pear.

PROBLEM XIV.

The right ascension and declination of a star being given, to find it's place on the globe.

Turn the globe till the meridian cuts the equinoctial in the degree of right ascension▪

Thus, for example, suppose the right ascension of Aldebaran to be 65° 30′, and it's declination to be 16° north, then turn the globe about till the meridian cuts the equinoctial in 65° 30′, and under the 16° of the meridian, on the nor∣thern part, you will observe the star Aldebaran, or the bull's eye.

PROBLEM XV.

To find at what hour any known star passes the me∣ridian, at any given day.

Find the sun's place for that day in the ecliptic, and bring it to the strong brass meri∣dian, set the horary index to XII o'clock, then turn the globe till the star comes to the meri∣dian, and the index will mark the time. Thus on the 15th of August, Lyra comes to the me∣ridian at 45 min. past VIII in the evening. On the 14th of September the brightest of the Pleiades will be on the meridian at IV in the morning.

This problem is useful for directing when to look for any star on the meridian, in order to find the latitude of a place, to adjust a clock, &c.

PROBLEM XVI.

To find on what day a given star will come to the meridian, at any given hour.

Bring the given star to the meridian, and set the index to the proposed hour; then turn the globe till the index points XII at noon, and observe the degree of the ecliptic then at the meridian; this is the sun's place, the day answering to which may be found on the calen∣dar of the broad paper circle.

By knowing whether the hour be in the morning or afternoon, it will be easy to per∣ceive which way to turn the globe, that the proper XII may be pointed to; the globe must be turned towards the west, if the given hour be in the morning, towards the east if it be after∣noon.

Thus Arcturus will be on the meridian at III in the morning on March the 5th, and Cor Leonis at VIII in the evening on April the 21st.

PROBLEM XVII.

To represent the face of the heavens on the globe for a given hour on any day of the year, and learn to distinguish the visible fixed stars.

Rectify the globe to the given latitude of the place and day of the month, setting it due

north and south by the needle; then turn the globe on it's axis till the index points to the given hour of the night; then all the upper hemisphere of the globe will represent the vi∣sible face of the heavens for that time, by which it will be easily seen what constellations and stars of note are then above our horizon, and what position they have with respect to the points of the compass. In this case, supposing the eye was placed in the center of the globe, and holes were pierced through the centers of the stars on it's surface, the eye would perceive through those holes the various corresponding stars in the firmament; and hence it would be easy to know the various constellations at sight, and to be able to call all the stars by their names.

Observe some star that you know, as one of the pointers in the Great Bear, or Sirius; find the same on the globe, and take notice of the position of the contiguous stars in the same or an adjoining constellation; direct your sight to the heavens, and you will see those stars in the same situation. Thus you may proceed from one constellation to another, till you are acquainted with most of the principal stars.

For example: the situation of the stars at London on the 9th of February, at 2 min. past IX in the evening, is as follows.

Sirius, or the Dog-star, is on the meridian,

it's altitude 22°: Procyon, or the little Dog-star, 16′ towards the east, it's altitude 43½: about 24° above this last, and something more towards the east, are the twins, Castor and Pollux: S. 65° E. and 35° in height, is the bright star Regulus, or Cor Leonis: exactly in the east and 22° high, is the star Deneb Alased in the Lion's tail: 30° from the east towards the north Arcturus is about 3° above the horizon: directly over Arc∣turus, and 31° above the horizon, is Cor Caroli: in the north-east are the stars in the extremity of the Great Bear's tail, Aleath the first star in the tail, and Dubhe the northernmost pointer in the same constellation; the altitude of the first of these is 30½, that of the second 41°, and that of the third 56°.

Reckoning westward, we see the beauti∣ful constellation Orion; the middle star of the three in his belt, is S. 20° W. it's altitude 35°: nine degrees below the belt, and a little more to the west, is Rigel the bright star in his heel: above his belt in a strait line drawn from Rigel between the middle and most northward in his belt, and 9° above it, is the bright star in his shoulder: S. 49° W. and 45½ above the horizon, is Aldebaran the southern eye of the Bull: a little to the west of Aldebaran, are the Hyades: the same altitude, and about S. 70° W, are the Pleiades: in the W. by S. point is Capella in Auriga, it's altitude 73°: in the north-west, and

about 42° high, is the constellation Cassiopeia: and almost in the north, near the horizon, is the constellation Cygnus.* 1.1

PROBLEM XVIII.

To trace the circles of the sphere in the starry fir∣mament.

I shall solve this problem for the time of the autumnal equinox; because that intersec∣tion of the equator and ecliptic will be directly under the depressed part of the meridian about midnight; and then the opposite intersection will be elevated above the horizon; and also because our first meridian upon the terrestrial globe passing through London, and the first point of Aries, when both globes are rectified to the latitude of London, and to the sun's place, and the first point of Aries is brought under the graduated side of each of their meri∣dians, we shall have the corresponding face of the heavens and the earth represented, as they are with respect to each other at that time, and the principal circles of each sphere will corres∣pond with each other.

The horizon is then distinguished, if we begin from the north, and count westward, by the following constellations; the hounds and waist of Bootes, the northern crown, the head

of Hercules, the shoulders of Serpentarius, and Sobieski's shield; it passes a little below the feet of Antinous, and through those of Capri∣corn, through the Sculptor's frame, Eridanus, the star Rigel in Orion's foot, the head of Mo∣noceros, the Crab, the head of the Little Lion, and lower part of the Great Bear.

The meridian is then represented by the equinoctial colure, which passes through the star marked δ in the tail of the Little Bear, under the north pole, the pole star, one of the stars in the back of Cassiopeia's chair marked β, the head of Andromeda, the bright star in the wing of Pegasus marked γ, and the extremity of the tail of the Whale.

That part of the equator which is then above the horizon, is distinguished on the western side by the northern part of Sobieski's shield, the shoulder of Antinous, the head and vessel of Aquarius, the belly of the western fish in Pisces; it passes through the head of the Whale, and a bright star marked δ in the corner of his mouth, and thence through the star marked δ in the belt of Orion, at that time near the eastern side of the horizon.

That half of the ecliptic which is then a∣bove the horizon, if we begin from the western side, presents to our view Capricornus, Aqua∣rius, Pisces, Aries, Taurus, Gemini, and a part of the constellation Cancer.

The solstitia colure, from the western side, passes through Cerberus, and the hand of Her∣cules, thence by the western side of the constel∣lation Lyra, and through the Dragon's head and body, through the pole point under the polar star, to the east of Auriga, through the star marked η in the foot of Castor, and through the hand and elbow of Orion.

The northern polar circle, from that part of the meridian under the elevated pole, ad∣vancing towards the west, passes through the shoulder of the Great Bear, thence a little to the north of the star marked α in the Dragon's tail, the great knot of the dragon, the middle of the body of Cepheus, the northern part of Cassiopeia, and base of her throne, through Cameloparda∣lus, and the head of the Great Bear.

The tropic of Cancer, from the western edge of the horizon, passes under the arm of Hercules, under the Vulture, through the Goose and Fox, which is under the beak and wing of the SWAN, under the star called Sheat, marked β in Pegasus, under the head of Andromeda, and through the star marked Φ in the fish of the con∣stellation Pisces, above the bright star in the head of the Ram marked α, through the Pleiades, between the horns of the Bull, and through a group of stars at the foot of Castor, thence above a star marked δ, between Castor and Pol∣lux, and so through a part of the constellation

Cancer, where it disappears by passing under the eastern part of the horizon.

The tropic of Capricorn, from the western side of the horizon, passes through the belly, and under the tail of Capricorn, thence under Aqua∣rius, through a star in Eridanus marked c, thence under the belly of the Whale, through the base of the Chemical Furnace, whence it goes under the Hare at the feet of Orion, being there depres∣sed under the horizon.

The southern polar circle is invisible to the inhabitants of London, by being under our ho∣rizon.

Arctic and antarctic circles, or circles of perpetual apparition and occultation.

The largest parallel of latitude on the terres∣trial globe, as well as the largest circle of decli∣nation on the celestial, that appears entire above the horizon of any place in north latitude, was called by the ancients the arctic circle, or circle of perpetual apparition.

Between the arctic circle and the north pole in the celestial sphere, are contained all those stars which never set at that place, and seem to us, by the rotative motion of the earth, to be perpetually carried round above our horizon, in circles parallel to the equator.

The largest parallel of latitude on the ter∣restrial,

and the largest parallel of declination on the celestial globe, which is entirely hid be∣low the horizon of any place, was by the an∣cients called the antarctic circle, or circle of perpetual occultation.

This circle includes all the stars which never rise in that place to an inhabitant of the northern hemisphere, but are perpetually below the horizon.

All arctic circles touch their horizons in the north point, and all antarctic circles touch their horizons in the south point; which point, in the terrestrial and celestial spheres, is the in∣tersection of the meridian and horizon.

If the elevation of the pole be 45 degrees, the most elevated part either of the arctic or antarctic circle will be in the zenith of the place.

If the pole's elevation be less than 45 de∣grees, the zenith point of those places will fall without it's arctic or antarctic circle; if greater, it will fall within.

Therefore, the nearer any place is to the equator, the less will it's arctic and antarctic circles be; and on the contrary, the farther any place is from the equator, the greater they are. So that,

At the poles, the equator may be con∣sidered as both an arctic and antarctic circle,

because it's plane is coincident with that of the horizon.

But at the equator (that is, in a right sphere) there is neither arctic nor antarctic circle.

They who live under the northern polar circle, have the tropic of Cancer for their arc∣tic, and that of Capricorn for their antarctic circle.

And they who live on either tropic, have one of the polar circles for their arctic, and the other for their antarctic circle.

Hence, whether these circles fall within or without the tropics, their distance from the ze∣nith of any place is ever equal to the difference between the pole's elevation, and that of the equator, above the horizon of that place.

From what has been said, it is plain there may be as many arctic and antarctic circles, as there are individual points upon any one meri∣dian, between the north and south poles of the earth.

Many authors have mistaken these mutable circles, and have given their names to the im∣mutable polar circles, which last are arctic and antarctic circles, in one particular case only, as has been shewn.

PROBLEM XIX.

To find the circle, or parallel of perpetual appa∣rition, or occulation of the fixed star, in a given latitude.

By rectifying the globe to the latitude of the place, and turning it round on it's axis, it will be immediately evident, that the circle of perpe∣tual apparition is that parallel of declination which is equal to the complement of the given latitude northward; and for the perpetual occul∣tation, it is the same parallel southward; that is to say, in other words, all those stars, whose declinations exceed the co-latitude, will al∣ways be visible, or above the horizon; and all those in the opposite hemisphere, whose declina∣tion exceeds the co-latitude, never rise above the horizon.

For instance; in the latitude of London 51 deg. 30 min. whose co-latitude is 38 deg. 30 min. gives the parallels desired; for all those stars which are within the circle, towards the north pole, never descend below our horizon; and all those stars which are within the same circle, about the south pole, can never be seen in the latitude of London, as they never ascend above it's horizon.

Notes

• * 1.1

  Bransby's Use of the Globes.