EXAMPLES.

1. In what degree of north latitude, and at what place, does the sun continue above the horizon for 77 days?

Answer. Half the number of days is 381, and if reckoned backward from the 21st of June, will answer to the 14th of May; or, if counted forward, it will answer to the 30th of July; on either of which days the sun's declination is 18 degrees N., consequently the places are in 71 degrees north latitude, viz. the North Cape in Lapland, the south of Nova Zembla, Icy Cape, &c.

2. In what degree of north latitude is the longest day 134 days, or 3216 hours in length?

3. In what degree of north latitude does the sun continue above the horizon for 2160 hours?

4. In what degree of north latitude does the sun continue above the horizon for 1152 hours?

PROBLEM XVI.

To find the Anteci of any given place.

DEFINITION. The Antoci are those inhabitants of the earth who live in the same degree of longitude, and in equal degrees of latitude, but the one has north and the other south latitude. They have noon at the same time, but contrary seasons of the year, and the length of the day to the one is equal to the length of the night to the other.

Find the lati

RULE FOR PERFORMING THE PROBLEM. tude of the given place in a map of the world, then on the same meridian, and in the same latitude, in the opposite hemisphere, you will find the Antœci.

EXAMPLES.

1. Required the Antoci of the island of Bermudas? Answer. A part of Paraguay, a little N. W. of Buenos Ayres.

2. Required the Antœci to the Cape of Good Hope? 3. Required the Antoci of the Falkland Islands.

To find the Perioci of any given place.

DEFINITION. The Perioci are those who live in the same latitude, but in opposite longitudes; when it is noon with the one, it is midnight with the other they have the same length of days and the same seasons of the year.

RULE FOR PERFORMING THE PROBLEM. Find the latitude of the given place in a map of the world, and mark its longitude on the equator. Count 180 degrees on the equator either eastward or westward, and under the same degree of latitude with the given place you will find the Periœci.

་་

EXAMPLES.

1. Required the Pericci to London ?

Answer. Fox islands, between America and Asia. 2. Required the Pericci to Pekin?

3. Required the Pericci to Porto Bello ?

4. Required the Perioci to Nubia?

PROBLEM XVIII.

To find the Antipodes of any given place. DEFINITION. The inhabitants of the earth who live diametrically opposite to each other, or walk feet to feet, are called Antipodes. Their latitudes, longitudes, seasons of the year, days and nights, are all contrary to each other.

RULE FOR PERFORMING THE PROBLEM. Find the latitude of the given place in a map of the world, and mark its longitude on the equator. Count 180 degrees on the equator either eastward or westward, and under the same degree of latitude with the given place, but in the opposite hemisphere, you will find the Antipodes.

EXAMPLES.

gol Required the Antipodes to the island of Bermudas?

Answer. The south-west part of New Holland. M.

2. What inhabitants of the earth are Antipodes to Buenos Ayres?

I

3. Captain Cook, in one of his voyages, was in 50 degrees south latitude, and 180 degrees of longitude; in what part of Europe was his Antipodes ?

4. Required the Antipodes of Madrid?

PROBLEM XIX.

The day and hour at any place being given, to find all places of the earth where the sun is rising, where it is setting, where it is noon, where it is midnight, those inhabitants who have morning twilight and those who have evening twilight.

RULE. Find the place where the sun is vertical at the given time (by PROB. IX.). All places 90 degrees to the westward of the meridian of this place will have the sun rising, those 90 degrees to the eastward will have the sun setting, all places on the same meridian within 90 degrees of the given place will have noon, those on the opposite meridian will have midnight. All places beyond 90 degrees westward of the meridian of the place where the sun is vertical, and within 108 degrees of the same meridian, will have the morning twilight; those situated eastward in a similar manner will have evening twilight.

1. When it is 52 minutes past 4 o'clock in the morning at London, on the 5th of March, find all places of the earth where the sun is rising, &c.?

Answer. Vertical at Batavia.

Rising. At the western part of the White Sea, Petersburg, the Morea in Turkey, &c.

Setting. At the eastern coast of Kamtschatka, Palmerston island, between the Friendly and Society islands,

&c.

Noon. At the lake Baikal in Irkoutsk, Cochin China, Cambodia, Sunda islands, &c.

Midnight. At Labrador, New York, western part of

St. Domingo, Chili, and the western part of South America.

Morning Twilight. At Sweden, part of Germany, the southern part of Italy, Sicily, the western coast of Africa along the Ethiopic Ocean, &c.

Evening Twilight. At the north-west extremity of North America, the Sandwich Islands, the Society Islands, &c.

2. When it is 4 o'clock in the afternoon at London, on the 25th of April, where is the sun rising, setting, &c.?

3. When it is 10 o'clock in the morning at London, ⚫ on the longest day, to what countries is the sun rising, setting, &c.?

4. When it is midnight at the Cape of Good Hope on the 27th of July, where is the sun rising, setting, &c.?

PROBLEM XX.

The day and hour being given when a lunar eclipse will happen, to find where it will be visible.

RULE. Find the place where the sun is vertical at the given time (by PROBLEM IX.), then find the antipodes of that place (by PROB. XVIII.), and to all places within 90 degrees of this last place, the eclipse will be visible.

EXAMPLES.

1. On the 26th of January, 1804,, at 58 minutes past 7 o'clock in the afternoon at London, there was an eclipse of the moon; where was it visible?

Answer. To the whole of Europe, Africa, and the continent of Asia.

2. On the 30th of June, 1806, at 10 o'clock in the evening at London, the moon was eclipsed; where was the eclipse visible?

3. On the 10th May, 1808, at 8 o'clock in the morning at London, the moon was eclipsed; where was the eclipse visible?

4. On the 2d of September, 1811, at 11 o'clock in the evening at London, the moon was eclipsed; where was the eclipse visible?

359

THE

GEOMETRICAL CONSTRUCTION OF MAPS.ˆ

Introductory Problems.

PROBLEM I.

To erect a perpendicular on the end of a given line AB. (PLATE I. Fig. I.)

RULE. From the centre B, at any distance BF, describe the arc FG: set off BF from F to G, and from G with the same distance describe an arc at P. Through F and G draw the line FGP to cut the arc in P. Then draw BP, which will be perpendicular to AB.

PROBLEM II.

From a given point P, to let fall a perpendicular upon a given line AB. (PLATE I. Fig. II.).

RULE. From the centre P describe an arc to cut AB in two points E and F; with the same, or any other, opening of the compasses, describe two arcs to intersect each other in I. Then through P and I draw PC, which will be the perpendicular required.

PROBLEM III.

To bisect a given right line AB; or, to draw two lines at right angles to each other. (PLATE I. Fig. III.)

RULE. Place one foot of the compasses on the point A; then with any extent, greater than half AB, describe an arc; with the same extent, and B as a centre, describe another arc intersecting the former in C and D. Through C and D draw CID, then the given line AB is bisected in I, and CD is drawn at right angles to AB as required.