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show the sun's place in the ecliptic, called the sun's longitude, for any given day.

4. The zenith is that point in the heavens directly over our heads, and is at an equal distance from all points of the horizon.

5. The nadir is that point in the heavens opposite the zenith, and is directly under our feet.

The zenith and nadir are the poles of the horizon, being each 90° distant from it.

The quadrant of altitude is a thin slip of brass or other material, divided into 90°, and is used to measure the distance of places, altitudes of the sun or stars, &c.

6. Antoci are those who live under the same meridian but on different sides of the equator, and at equal distances from it; or they are those that have the same longitude but opposite latitudes.

The appearances to the antoci are these:

They have the same hours, but contrary seasons at the same time: thus when it is noon to the one it is noon to the other, and when it is summer with the one it is winter with the other.

The days of the one are equal to the nights of the other; and the nights of the one to the days of the other.

The stars that never set to the one never rise to the other; and contrariwise.

Those who live at the equator have no antœci.

7. Perioci are those who live under opposite meridians but on the same side of the equator, and at equal distances from it; or they are those who have the same latitude but opposite longitudes.

The appearances to the periœci are these:

The hours of the day, though nominally the same, are really contrary; for when it is noon with the one it is midnight with the other; and when it is two in the morning with the one, it is two in the afternoon with the other, &c.

They have the same seasons of the year at the same time.

The length of the day or night at any place is always the same as it is to the pericci of that place.

The sun and stars rise to both places on the same point of the horizon, and are the same number of hours above or below it.

The same stars that never rise or set to the one place never rise or set to the other.

Those who live at the poles have no periœci.

8. The Antipodes are those who live diametrically opposite to each other; or they are those who have both opposite latitudes and opposite longitudes.

A line, supposed to be drawn from any place through the centre of the earth, and continued to the opposite side, will point out the antipodes of that place. The north and south poles are antipodes to each other.

The appearances to the antipodes are these:

The hours of the day are contrary, it being noon to one when it is midnight to the other.

They have contrary seasons at the same time.

The days of the one are equal to the nights of the other; hence the shortest day to the one is the longest day to the other.

The sun and stars rise to the one when they set to the other, all the year round, for they have the same horizon; but the zenith to the one is the nadir to the other.

Those stars that are always above the horizon of the one place are always under the horizon of the other.

PROBLEM VII.

To find the Antoci of any given place.'

BY THE GLOBE.-Bring the given place to the meridian; and having found its latitude, count as many degrees from the equator towards the contrary pole,-and the point thus arrived at will be the antoci required.

BY MAPS.-Having found the latitude and longitude of the place, find another place of the same longitude whose latitude is equal to the former, but of a contrary name.

EXAMPLES.

Required the antoci of the following places :
1. Malta. Answ. Cape of Good Hope, nearly.
2. Potosi, in South America. Answ. Hispaniola.
3. Quebec. Answ. Patagonia, in South America.

4. Van Dieman's Land.

5. Madagascar (south point).

6. Cape Horn.

7. Juan Fernandez.

8. Kerguelen's Land.

9. Is. of Bermudas.

10. Falkland Isles.
11. Boston, U. S.
12. Azof.

13. Sandwich Is.

14. A ship in the Indian Ocean was in longitude 80° E., and in latitude 13o S.: required the antoci to that place. Required the antoci to the following longitudes and

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To find the Perioci of any given place.

BY THE GLOBE.-Bring the given place to the brass meridian, and set the index to 12.

Turn the globe till the index point to the other 12, that place below the meridian, whose latitude is equal to that of the given place, is the periceci required.

BY MAPS.-Subtract the longitude of the given place from 180°, and the remainder will be the longitude of the pericci, of a contrary name.

Find, by Prob. I., a place whose longitude is equal to this, and whose latitude is the same with that given.

EXAMPLES.

1. What place has its inhabitants the perioci of Newcastle-upon-Tyne? Answ. The Aleutian, or Fox Islands. 2. What place has its inhabitants the perioci of Quito? Answ. Podang, in the island of Sumatra.

3. Who are the perioci of California, in N. America ?

Required the perioci of the following places.

4. St. John's, Newfound

land.

8. Mindanao.
9. St. Petersburgh.

10. Sandwich Islands.

5. Philadelphia.

6. Gulf of Siam.

7. Cook's Strait.

11. Society Islands.

12. Martinique.

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PROBLEM IX.

To find the Antipodes of any place.

Find the antoci of the given place, and the pericci of this will be the antipodes of the first place; or, bring the given place to any part of the horizon, and the place at the opposite point of the horizon will be the antipodes.

EXAMPLES.

1. What place is that the inhabitants of which are the antipodes to Pekin? Answ. Near the mouth of the river Sauces, or Colerado, in Patagonia.

2. Where are the antipodes of London? Answ. A little S. of New Zealand, in long. 180°, and 51° 31'S. lat. What are the antipodes of the following places?

3. Cape Horn.

4. Otaheite.

5. New Caledonia.

6. Buenos Ayres.

7. Falkland Islands.

8. Madrid.

9. Juan Fernandez.

10. Friendly Isles.

11. Philippine Isles.

12. Sierra Leone.

13. Pelew Islands, in the Eastern Archipelago.

14. A ship, in the Pacific Ocean, found its lat. 51° S. and long. 180°,-required the antipodes.

15. Suppose a line drawn from the island of Jamaica through the centre of the earth, in what part would this line meet the surface of the earth on the opposite side? 16. Required the antipodes to the Bermudas.

Required the antipodes of the following longitudes and

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To elevate the Globe for the Latitude of any place.

Elevate the pole, which is of the same name with the latitude, as many degrees as are equal to it, and bring the given place to the brass meridian.

When the globe is rectified for the latitude of any place, that place is in the zenith, and the wooden horizon represents the rational horizon of the place.

EXAMPLES.

1. Elevate the globe for Lisbon.

Ans. The latitude of Lisbon is 39o N.; hence the north pole must be raised 39o above the horizon, and Lisbon brought to the brass meridian.

2. Elevate the globe for the Cape of Good Hope.

Ans. The Cape of Good Hope has 35° S. L.; hence the south pole must be raised 35o above the horizon, and the Cape of Good Hope brought to the meridian.

PROBLEM XI.

To find the Distance between two Places.

Case I.-When the distance is less than 90o.

1. Lay the quadrant of altitude over both the places, so that the division marked 0 may be on one of the

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