PROBLEM XI.

To find the Antæci of any given place.

RULE. Bring the given place to the brass meridian, and observe its latitude; then in the opposite hemisphere, under the same degree of latitude, you will find the antœci.

EXAMPLES.

1. Required the antæci of Cape Fear, the south point of Smith's island in the mouth of Cape Fear river, North Carolina.

Answer. Juan Fernandez, an island in the Pacific Ocean, west of Chili, celebrated for having been the solitary residence of Alexander Selkirk for several years, from whose adventures upon it De Foe wrote the popular novel of Robinson Crusoe.

2. Required the antœci of Cusco, anciently the capital of the Peruvian empire, and the seat of the Incas.

3. Required the antæci of Thebes, ancient city and capital of Egypt, famous as "the city of an hundred gates," the theme and admiration of ancient poets and historians, and the wonder of travellers.

4. Required the antæci of Azoph, a town in Asiatic Russia, on the east extremity of the sea of Azoph, at the mouth of the river Don.

PROBLEM XII.

To find the Periæci of any given place.

RULE. Bring the given place to the brass meridian, and set the index of the hour circle to 12. turn the globe half round, or till the index points to the other 12, then under the latitude of the given place you will find the periœci.

1. Required the periœci of Mayze, the east cape of Cuba, and the west point of the windward passage.

Answer. Kesho, or Cachoa, the capital of Tonkin, an empire in India, east of the Ganges.

2. Required the pericæci of Milledgeville, the seat of government of the State of Georgia.

3. Required the periæci of Albany, the seat of government of the State of New-York.

4. Required the periœci of Bastia, a sea-port and city, formerly the capital of the island of Corsica.

5. Required the periœci of Naples, a large city in the south-west of Italy, and capital of the kingdom of Naples.

PROBLEM XIII.

To find the Antipodes of any given place.

RULE. Bring the given place to the brass meridian, and set the index of the hour circle to 12, turn the globe half round, or till the index points to the other 12; then under the same degree of latitude with the given place, but in the opposite hemisphere, you will find the antipodes.

Or, find the antæci of the given place, and the periæci of this will be the antipodes or point of the globe, diametrically opposite to the first place.

EXAMPLES.

1. Required the antipodes of Trinidad, an island near the coast of South America, the largest, most fertile, and most beautiful of all the windward islands, and was compared by Columbus, its discoverer, to a terrestrial paradise.

Answer. Sandalwood, an island in the East Indian Sea, south of Flores and west of Timor.

When it is summer to the inhabitants of Trinidad it is winter to those of Sandalwood, and when it is day to the one, it is night to the other.

2. Required the antipodes of Anguilla, the most northern island of the Caribbees.

3. Required the antipodes of Owhyee, an island in the North Pacific Ocean, the most easterly and by much the largest of the Sandwich Islands : it was on this island that the celebrated Captain Cook was killed by the natives, on Sunday the 14th of February, 1779.

4. Required the antipodes of the following places: Madrid; Malta, in the Mediterranean; Bermudas ; Cape Horn; Havanna; Halifax, the capital of Nova-Scotia; and Avignon, a city in France, on the river Rhone.

5. What place on the earth is diametrically opposite to Cape Charlotte, the southern extremity of New-Georgia, a desolate island in the South Atlantic Ocean?

After the student has resolved the examples in the last three problems, it may not be improper to exercise him in finding the antœci, periœci, and antipodes of any given place, by the following method.

PROBLEM XVI.

To find the Antæci, Periæci, and Antipodes of any given

place.

RULE. Place the two poles of the globe in the horizon, and bring the given place to the eastern part of the horizon; then, if the given place be in north latitude, observe how many degrees it is to the northward of the east point of the horizon; the same number of degrees to the southward of the east point will show the Antœci; an equal number of degrees, counted from the west point of the horizon towards the north, will show the Periœci; and the same number of degrees, reckoned towards the south from the west, will point out the Antipodes.

If the place be in south latitude, the same rule will serve, by reading south for north, and the contrary.

EXAMPLES.

1. Required the Anteci, Pericæci, and Antipodes of St. Ambrose, an island in the Atlantic Ocean, west of Chili.

Answer. The Antæci is the southern part of Florida, a Territory belonging to the United States; the Periæci is in the Indian Ocean, a little west of Tryal Rocks on Flinder's tract in 1813; and the Antipodes is a little east of Ava, a town in Asia, and ancient capital of the Birman empire.

2. Required the Antœci, Periæci, and Antipodes of the following places: Falkland Islands, west of Patagonia; Albany, the seat of government of the State of New-York; and Cadiz, a fortified city and sea-port in Spain.

PROBLEM XV.

To find the angle of position between any two given places.

RULE. Elevate the north or south pole, according as the latitude is north or south, so many degrees above the horizon as are equal to the latitude of one of the given places; bring that place to the brass meridian, and screw the quadrant of altitude upon the degree over it; next move the quadrant till its graduated edge falls upon the other place; then the number of degrees on the wooden horizon, between the graduated edge of the quadrant and the meridian, reckoning towards the elevated pole, is the angle of position between the two places.

EXAMPLES.

1. What is the angle of position between NewYork and Syracuse, a sea-port in the island of Sicily, formerly a superb city, and flourishing republic: Archimedes, the famous geometrician, was a native of this city.

Answer. 60 degrees from the north towards the east, the quadrant of altitude will pass over or near the following places: Nantucket, an island belonging to Massachusetts; Cape Sable, the south-west point of Nova-Scotia; the northern part of the Banks of Newfoundland; Bayonne, a seaport in France, about 3 miles from the Bay of Biscay; Barcelona, a city in Spain; Cagliari in Sardinia; and Thebes in Upper Egypt. Hence all these places have the same angle of position from New-York.

2. What is the angle of position between Lyons, a large and celebrated city of France, situated at the conflux of the Rhone and Saone; and Teflis, a city of Asia on the sublime banks of the Kur, and capital of Georgia, formerly a province of Persia, but now belonging to the Russian empire.