EXAMPLES.

1. Find the difference of longitude between Alexandria, the ancient capital of Egypt, and Rome, a large and famous city of Italy, formerly the seat of the Roman Empire, and the capital of the

world.

The longitude of Alexandria is found to be 300 5 east, and the longitude of Rome 12° 28′ east; hence their difference, 17° 37', is the difference of longitude required.

2. Find the difference of longitude between Smyrna, a city of Asia Minor, and Panama, a city and sea-port on the isthmus of Darien.

The longitude of Smyrna is readily found to be 270 20 east, and the longitude of Panama 790 19 west: hence their sum, 106° 39', is the difference of longitude required.

3. Required the difference of longitude between Jerusalem, capital of the ancient Judea, and Fez, a large city of Morocco, in Africa, and once the capital of all the Western Mahometan States.

4. Find the difference of longitude between Batavia, a city in the island of Java, and the mouth of Columbia, or Oregon river, on the north-west coast of America.

5. What is the difference in longitude between St. Jago, in the Atlantic Ocean, and the Straits of Babelmandel on the coast of Arabia ?

6. What between Cape Breton in the gulf of St. Lawrence, and Cape Cambodia, the southern extremity of Cambodia, in the gulf of Siam?

7. What between Cape Farewell, the southern extremity of Greenland, and Cape Farewell, on the coast of New-Zealand in the Pacific Ocean?

8. Required the difference of longitude between the following places: Portsmouth, the capital of New-Hampshire, and the city of Jeddo in the empire of Japan; Portland, the capital of Maine, and Port Jackson, in New-Holland; St. Fee de Bogata, a city in the Republic of Colombia, and Kesho, the capital of the empire of Tonkin; Natchez, the capital of the State of Mississippi, and Lassa, the capital of Tibet; Cape Comorin in Hindostan, and Gondar, the capital of Abyssinia.

PROBLEM VII.

To find the distance between any two places on the globe. Definition. The shortest distance between any two places on the earth, considered as a sphere, is an arc of a great circle contained between the two places.

The length of a degree of any great circle on the surface of the earth, is 69 American miles, supposing it to be a sphere of 7920 miles in diameter, and 24880 miles in circumference: because, 360°: 24880 miles::10: 690 miles.

It is proper to observe that, in geography and navigation, a degree on the surface of the earth contains 60 geographical miles; hence, a geographical mile is greater than an American, in the proportion of 60: 69, or of 1: 1.15185.

It may be also remarked that an American mile is the same as an English mile, each containing 5280 American or English feet.

RULE. Lay the graduated edge of the quadrant of altitude over the two places, so that the division marked 0 may be on one of them, the degrees on the quadrant, contained between the two places, will give their distance; and if their dis-tance in degrees be multiplied by 60, the product will be the distance in geographical miles; or multiply the degrees by 69, and the product will be the distance in American miles. Or, take the distance between the two places with a pair of compasses, and that distance applied to the equator will give the number of degrees between them:

which may be reduced to geographical and American miles, as before.

If the distance between the two places should exceed the length of the quadrant, stretch a piece of thread over the two places and mark their distance; the extent of the thread between these marks, applied to the equator, from the first meridian, will show the distance between the two places in degrees, which may be reduced, if necessary, to Geographical and American miles, as above.

EXAMPLES.

1. What is the nearest distance between Albany

and St. Louis ?

Answer. The distance in degrees is 13.

13 distance in degrees.

60

780 geographical miles.

13 distance in degrees.

69

117

78

14

898 American miles.

Hence, the nearest distance is equal to 780 geographical, or to 898 American miles.

2. What is the nearest distance between London and Port Jackson, a bay and English settlement, on the eastern coast of New-Holland, and 9 miles north of Botany Bay?

Here the distance between the two places exceeds the quadrant of altitude; therefore, by measuring the nearest distance with a thread, and applying that distance to the equator, it will be found to be 154 degrees nearly.

154 distance in degrees.

60

9240 geographical miles.

154 distance in degrees.

69

1386

924

1

17

10643 American miles

Answer. The distance in degrees is 154; the distance in geographical miles is 9240, and the distance in American miles is 10643

3. What is the nearest distance between NewHaven, and Puebla, a considerable city in Mexico, situated on a plain elevated more than 1000 feet above the level of the sea?

4. What is the extent of America from Cape Horn, the most southern extremity of Terra del Fuego, to the Icy Cape, on the north-west coast of America, in the Frozen Sea ?

5. What is the extent of the United States in Geographical and American miles, from Cape Florida to the mouth of Columbia river; and also the extent from the mouth of the Sabine river in Louisiana, to the northern extremity of Maine in about 47 degrees north latitude ?

6. What is the nearest distance in American miles from the north to the south pole ?

7. What is the extent of Africa in American miles, from Cape Verd to Cape Guardafui, the most eastern point of Africa, at the entrance into the Red Sea ?

8. What is the extent of Africa in American miles, from the Cape of Good Hope to the Straits of Gibraltar ?

9. What is the extent of Europe in American miles, from Cape Matapan in the Morea, to the North Cape in Lapland ?

10. Suppose the tract of a ship to Canton be (the shortest distances) from New-York to Bermudas, thence to Ascension island in the Atlantic Ocean, between Africa and Brazil, thence to St. Helena, thence to the Cape of Good Hope, thence to the Straits of Sunda, between Java and Suma

tra, thence to Canton: How many American miles from New-York to Canton on these different courses?.

Simple as the preceding problem may appear in theory, on a superficial view, yet, when applied to practice, the difficulties which occur are almost insuperable. In sailing across the trackless ocean, or travelling through extensive and unknown countries, our only guide is the compass; and except two places be situated directly north and south of each other, or upon the equator, though we may travel or sail from one place to the other, by the compass, yet we cannot take the shortest route, as measured by the quadrant of altitude.

PROBLEM VIII.

A place being given on the globe, to find all places which are situated at the same distance from it as any other given place.

RULE. Bring the first given place to the brass meridian, and screw the quadrant of altitudė over it; next move the quadrant till its graduated edge falls upon the other place, and mark the degree over it; then move the quadrant entirely round, keeping the globe in its first situation, and all places which pass under the same degree which was observed to stand over the second place, will be those sought.

Or, place one foot of a pair of compasses in one of the given places, and extend the other foot to the second given place; a circle described from the first given place, with this extent, will pass through all the places sought. If the length between the two given places should exceed the length of the quadrant, or the extent of a pair of compasses, stretch a piece of thread over the two places, with which describe a circle as before.

EXAMPLES,

1. Find all those places that are at the same, or nearly the same distance from Paris, as the Mael