Horizon cut by the Quadrant, is the Sun's Azimuth, reckoned from the South.

Examples. Give the Sun's Altitude and Azimuth at London on the 21st of May at 9 in the morning.-on the 21st of June at the same hour.-on the 21st of December at the same hour.-Give the Sun's Altitude and Azimuth at Smyrna on the 5th of April at 7 in the morning-at 3 in the afternoon. at Edinburgh on the 4th of October at 8 in the morning.

PROBLEM XXIV.-The Latitude, Sun's place, and his Altitude, being given, to find the hour of the day and the Sun's Azimuth.

Rectify the globe. Bring the Sun's place to the given height upon the Quadrant of Altitude, on the Eastern side of the Wooden Horizon if the time be in the forenoon, or on the Western side if the time be in the afternoon. The Index will now show the hour of the day; and the number of degrees in the Horizon intercepted between the Quadrant of Altitude and the South point will be the Sun's Azimuth at that time.

Examples. Give the hour of the day and the Sun's Azimuth at London, on the 9th of March, when his altitude is 52°.-At Jerusalem on the 8th of May, when his altitude is 68°.-At Canton on the 20th of August when his Altitude is 390.-At the Cape of Good Hope on the 1st of November when his Altitude is 27°.

PROBLEM XXV. The Latitude of a place, not exceeding 66°, and the day of the month, being given, to find the Sun's Amplitude.

Rectify the globe. Bring the Sun's place to the Eastern side of the Horizon; and the point of the compass on the Wooden Horizon, which stands right against the Sun's place is his amplitude at rising. Now turn the globe Westward, until the Sun's place comes to the Western side of the Horizon, and it will cut the point of his Amplitude at setting.-The Amplitude may be likewise counted in degrees: viz. at sun-rise from the East point of the Horizon to that point where the Sun's place cuts it; and at sun-set, from the West point of the Horizon to that point where the Sun's place cuts it again.

Examples. What is the Sun's Amplitude at rising and setting on the 1st of November in Lat. 60° North ?-in Lat. 45° North ?-in Lat. 30° South ?-in Lat. 48° South ?-What is his Amplitude at rising and setting in Lat. 51° North, on the 20th of June?-on the 21st of December ?-on the 25th of March?

PROBLEM XXVI. The day and hour of a Lunar Eclipse being given, to find all those places of the Earth where it will be visible.

Find the place to which the Sun is vertical at the given hour by Problem XI. Elevate the pole according to the Latitude of that place, and bring the place to the brazen Meridian. Now, as the Sun will be visible to all those parts of the globe which are above the Horizon, the Moon will be visible to all those parts which are below the Horizon at the time of her greatest obscuration.

Examples. To what places was the Eclipse of the Moon visible, which took place at 6 in the morning on the 10th of July?—at 4 in the afternoon on the 1st of November ?-at 10 at night on the 1st of March ?-at 2 in the morning on the 12th of August?

THE CELESTIAL GLOBE.

DEFINITIONS. 1. The Celestial Globe is an artificial delineation of the heavens. In the use of it we are to suppose that its motion represents the apparent diurnal motion of the heavens from East to West; and that we

are in its centre, because the stars would then appear, as they naturally do, in the concave surface of the heavens.

2. The Equator, Ecliptic, Tropics, Polar Circles, Brazen Meridian, and Wooden Horizon, are exactly alike on both globes; the method of rectifying the two globes is exactly the same: and all the foregoing problems concern ing the Sun are solved the same way by both Globes.

3. The Equinoctial Colure is that great circle which passes through the Equinoctial points at the beginning of Aries and Libra, and through the Poles of the world. The Solstitial Colure is that great circle which passes through the beginning of Cancer and Capricorn, as well as through the Poles of the World, and the Poles of the Ecliptic.

4. The Latitudes of the Moon, Stars, Planets, and Comets, are reckoned North and South from the Ecliptic, and not from the Equator. Hence it follows that, as the greatest Latitudes on the Earth are at the North and South poles of the earth, so, the greatest latitudes of the heavens are at the North and South poles of the Ecliptic.

5. The Longitudes of the heavenly bodies are reckoned from the Equinoctial Colure at the first point of Aries, Eastward quite round the globe.

6. Those Stars which lie between the Equinoctial and the Northern half of the Ecliptic have North Declination and South Latitude; those which lie between the Equinoctial and the Southern half of the Ecliptic have South Declination and North Latitude; and all those which lie between the Tropics and the Poles have their Declinations and Latitudes of the same denomination.

7. The point of the Equinoctial, reckoned from the beginning of Aries, that comes to the meridian with a Heavenly Body, is called its Right Ascension; and may be rendered either in time or degrees.

8. The distance of a Heavenly Body, in degrees, from the Equinoctial, towards the North or South Pole, is its Declination, which is North or South accordingly.

PROBLEM XXVII. To find the Right Ascension and Declination of the Sun or any Fixed Star.

Bring the Sun's place in the Ecliptic to the Brazen Meridian. Then that degree in the Equinoctial which is cut by the Meridian, is the Sun's Right Ascension; and that degree of the Meridian which is over the Sun's place is his Declination. Bring any Fixed Star to the Meridian, and its Right As cension will be cut by the Meridian in the Equinoctial; and the degree of the Meridian that stands over it is its Declination.

Examples. Give the Right Ascension and Declination of the Sun on the 1st of May.-on the 21st of December.-on the 20th of June.-on the 29th of September.-Give the Right Ascension and Declination of the Pole Star.-of Arcturus.-of a Lyræ.-of B Leonis.-of ß Hydra.-of Sirius. -of Fomalhaut.-of & Ceti.-of γ Eridani.-of Procyon.

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PROBLEM XXVIII. To find the Latitude and Longitude of any Star. Place the centre of the Quadrant of Altitude on the Pole of the Ecliptic (either North or South, as the case may be), and its graduated edge on the Star. Then, the number of degrees on the Quadrant between the Ecliptic and the Star, is its Latitude, North or South as the case may be; and the degree of the Ecliptic cut by the Quadrant is the Star's Longitude, reckoned according to the Sign in which the Quadrant then is.

Examples. Give the Latitude and Longitude of Cor Caroli.-of Cor Hydra of Arcturus. of Rigel. of Capella,-of ß Ceti.—of a Lyræ.of a Cygni.-of 6 Serpentis.-of y Leonis.-of Regulus.-of Procyon.of B Leporis. of Canopus.

PROBLEM XXIX. To represent the face of the Heavens, as seen from any given place of the Earth, at any hour of the night.

Rectify the globe for the Latitude, Zenith, and Sun's place: set the globe due North and South; and turn it about until the Index points to the given hour. Then, the upper hemisphere of the globe will represent the visible half of the heavens at that time; and as every star on the globe points towards the same star in the Heavens, the several constellations may be easily known and pointed to. All those stars which are in the Eastern side of the Horizon are then rising, and all in the Western are setting. All those stars which are under the upper part of the Brazen Meridian, between the South point of the Horizon and the North Pole, are at their greatest altitude, if the Latitude be North: but if the Latitude be South, those stars which lie under the upper part of the Meridian, between the North point of the Horizon and the South Pole, are at their greatest altitude.

Examples. Let the face of the heavens be represented as seen from London at 2 o'clock in the morning, on the 28th of December.-on the 29th of March. on the 2nd of July.-on the 10th of September.-As seen from Buenos Ayres on the 1st of August at 12 at night.-As seen from Canton on the 10th of May at 3 in the morning.-As seen from The Cape of Good Hope on the 1st of November at one in the morning.

PROBLEM XXX. The Latitude of the place, and day of the month, being given, to find the time when any Heavenly body will rise, culminate, or set; as also how many hours it is above the horizon.

Having rectified the globe, turn it about until the given Star comes to the Eastern edge of the Horizon, and the Index will show the time of the Star's rising; then turn the globe Westward till the Star comes to the Brazen Meridian, when the Index will show the time of the Star's culminating at the given place; lastly, turn the globe until the Star comes to the Western side of the Horizon, and the Index will show the time of the Star's setting*. The time elapsed from the hour of its rising to that of its setting, is the time that the Star is above the Horizon.

Examples. Give the hour of the rising, setting, and culminating, of Procyon on the 10th of August.—of Aldebaran on the 1st of May.-of a Lyre on the 7th of January. of Rigel on the 20th of November.-of Sirius on the 2nd of October.-of Fomalhaut on the 6th of June.—of Capella on the 9th of February.-of y Eridani on the 1st of June.

PROBLEM XXXI. To find at what time of the year a given Star will be upon the Meridian, at a given hour of the night.

1

Bring the given Star to the upper semicircle of the Brazen Meridian, and set the Index to the given hour. Then, turn the globe until the Index points to XII. at noon, and the upper semicircle of the Meridian will then cut the Sun's place answering to the day of the year required.

Examples. When will Rigel be upon the Meridian of London at 5 in the morning? at 9 in the evening?-at 11 at night ?-When will Arcturus be on the Meridian of London at 2 in the morning?-at 6 in the evening?at 10 at night? When will Sirius be upon the meridian of the Cape of Good Hope at 4 in the morning?—at 1 in the morning?—at 5 in the afternoon ?— When will a Crucis be upon the Meridian of Port Jackson at midnight?

"In Northern Latitudes those stars which are less distant from the North Pole than the quantity of its elevation above the North point of the Horizon, never set; those which are less distant from the South Pole than the number of degrees by which it is depressed below the Horizon, never rise: and vice versa in Southern Latitudes,