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places; then the degree cut by the other place will show the distance in degrees.

2. Multiply these degrees by 69}, and the product will be the distance in English miles. It will in general be sufficiently accurate to multiply by 70.

Case II.When the distance is greater than 90°. 1. Find the antipodes of one of the places, and by Case I. measure the distance between it and the other.

2. Subtract this distance from 180, and the remainder will be the whole distance required.

EXAMPLES.

Required the distance between London and 1. Copenhagen. Ans. 9°, = 625 miles. 2. Stockholm. Ans. 13', = 903 miles. 3. Petersburg

11. Constantinople. 4. Amsterdam.

12. Grand Cairo. 5. Paris.

13. Jerusalem. 6. Berlin.

14. Madras. 7. Vienna.

15. Botany Bay. 8. Berne.

16. Otaheite. 9. Lisbon.

17. Manilla. 10. Rome.

18. Navarino. 19. What is the length of Europe, from Lisbon, in the west, to the Uralian mountains, in the east?

20. How far is Constantinople from Pekin?

21. What is the breadth of N. America from the Promontory of Alashka to Cape Charles ?

22. What is the breadth of S. America from Cape Blanco, in Peru, to Cape St. Roque, in Brazil ?

23. What is the breadth of Africa from Cape Verd, in the west, to Cape Guardafui, in the east?

24. What is the distance between Cape Verd, in Africa, and Cape St. Roque, in America ?

25. What is the distance between Panama, in America, and Manilla, one of the Philippine islands?

26. Between Bornbay and Nootka Sound ?

27. What is the distance between Newcastle and Malta, by way of Gibraltar ?

28. The following is the track pursued by Captain Cook, in his first voyage,-required its length. From Portsmouth to Cape Verd Isles.

Cape Verd Isles to Cape Horn.
Cape Horn to Otaheite.
Otaheite to New Zealand, Cape South.
Cape South to Port Hicks, in New Holland.
Port Hicks, in New Holland, to Endeavour Straits.
Endeavour Straits to Batavia, in Java.
Batavia, in Java, to the Cape of Good Hope.
Cape of Good Hope to Ascension Island.
Ascension Island to the Azores.

Azores to England. 29. How many miles will be gone over in the following route :- from Newcastle to Carlisle, Lancaster, Liverpool, Shrewsbury, Birmingham, Gloucester, Bristol, Oxford, and London?

QUESTIONS FOR EXAMINATION IN SECTION II. What are the anteci, and what is observed of their hours of the day and seasons of the year? What are the periæci, and what is observed of their hours of the day and seasons of the year? What are the antipodes, and what is observed of their hours of the day and seasons of the year?

How is the horizon distinguished ? What is the sensible horizon ? What is the rational horizon? What is the wooden horizon? Doe it represent the rational or sensible horizon? What circles are marked upon the wooden horizon, and what is their use ?

What is the zenith of any place, and what is the nadir ? What is the quadrant of altitude, into how many degrees is it divided, and what is its principal use ?

How are the anteci, the perieci, and the antipodes of any place found upon the globe, and how upon maps ? Where must those people live that have no anteci? What point upon the globe has no pericci? Where are the antipodes to the north pole?

How is the globe elevated for the latitude of any place? .
How is the distance of two places found, when that distance is less

than 90°? How is the distance of two places found, when it is more than 90° ? Why must degrees be multiplied by 69; to bring them to English miles ?

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QUESTIONS FOR EXERCISE IN SECTION II. Required the antoci answering to the following : Longitude.

Latitude. 330 16' E.

34 30s. 72 18 w.

46 s. 1700 w.

14 ON. 13 43 E.

38 10 s. Required the periæci answering to the following: 200 Ow.

56° ON. 6. 83 2 w.

17 0 N. 100 8 w.

1142 . Give the antipodes corresponding to the following: 8. 171° 30'E.

52 06. 9. 160 0 E.

63 20 s. 10. 176 6 w.

39 51 s. 11. Required the shortest distance between Africa and America.

12. Required the number of miles that an East India ship sails in her voyage from London to Madras.

13. How many miles must a ship sail in going from St. John's, in Newfoundland, to Nootka Sound, -and what is the difference between this distance and the direct distance between the two places ?

14. How many miles does a ship sail in her voyage from London to Botany Bay, supposing her to go in as straight a course as possible?

15. What is the distance between the north and south Poles ?

Measure the distances between the following places on a map. 16. Ushant Island and Strasburg. 20. Havre de Grace and 17. Calais and Montpelier.

Nice. 18. Bourdeaux and Narbonne. 21. St. Maloe and Marseilles. 19. Caen and Geneva.

22. Toulouse and Paris.

SECTION III.

DEFINITION. The horary, or hour circles, are small circles on the globe, placed at the north and south poles, having the hours of the day marked upon them, with an index to each.

THE TIME OF DIFFERENT PLACES COMPARED. The earth, turning on its axis from west to east, causes a different part of its surface to be successively presented to the sun. When the meridian of a place is directly opposite the sun, it is noon to all places on that meridian.

The meridians that lie to the east will come opposite to the sun before those that lie to the west; and hence the people there will have noon so much sooner,-the other hours of the day will be proportionably advanced.

The earth taking 24 hours to turn round on its axis, the rate at which it turns per hour may be found by dividing 360 (the number of degrees in the circumference of the globe) by 24: the quotient, 15, is the number of degrees the earth turns in an hour. Thus, a place that lies 15" to the east will have noon one hour sooner; if it lie 30° or 45°, it will have noon two or three hours sooner ; and so on in the same proportion.

Places that lie 15°, 30", or 45° to the W. will have noon one, two, or three hours later; and so on in proportion.

PROBLEM XII. The Hour being given at any Place, to find what Hour it is

in any other Part of the World. 1. Bring the place, at which the time is given, to the meridian, and set the index to the given hour.

2. Turn the globe till the other place come to the meridian, and the index will show the time required.

By CALCULATION.–Find the difference of longitude between the two places, and reduce it to time.

Add this difference of time to the given hour, if the place at which the time is required lie to the east; but subtract it, if it lie to the west.

1. If, in adding, the sum is greater than 12, take 12 away, and change the name from morning to afternoon hours, or vice versa.

2. If, in subtracting, the difference of time be greater than the given hour, add 12 to the given hour, and change the name.

3. By this problem the longitude of places is determined; for if by 7 a.m.

astronomical observation, or any other means, it can be known what hour it is at London, and at the place whose longitude is to be determined, this difference of time, reduced to degrees, will give the longitude of that place; and which will be east or west according as the time is sooner or later.

EXAMPLES.

1. What hour is it at Boston, in America, when it is 3 p.m. at London ? Answ. 18 min. past 10 a.m.

This example performed without the globe. The longitude of Boston is 70° 30', which, in this example, is the difference of longitude=4 hrs. 42 m. diff. of time.

Boston lying to the west, this must be subtracted; but the difference here being greater than the hour given, add 12 to the given hour, as directed in note 2, and change the name from p.m. to a.m.

Thus, 3 hrs. O min. p.m. given hour.

12 O added.

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2. What is the hour at Pekin, when it is 9 a.m. at Lisbon ?

Answ. 22 min. past 5 p.m. The difference of longitude is 125° 33'=8 hrs. 22 min.; and as Pekin is east of Lisbon, this must be added.

9 hrs. O min. a.m. given hour.
8 22 difference of time.

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Having the hour given at one place, required the hour at the other place given in the following examples : Place where time is given. Given time. Place where time is required.

3. Newcastle, 11 a.m. Port Royal.
4. -

Madras.

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