Having the Hour given at any place, to find where it is Noon.

BY THE GLOBE. Bring the given place to the meridian, and set the index to the given hour.

Turn the globe till the index point to 12 at noon, and the places then under the meridian are those required. BY CALCULATION.-Reduce the number of hours between the given time and noon into degrees, and it will be the difference of longitude between the places.

When the given hour is in the morning, the place where it is noon will lie so many degrees to the eastward: hence the difference of longitude must be added to the longitude of the given place, if it be E.; but substracted from it, if it be W.

When the hour is in the evening, the places where it is noon will lie to the westward of the given place: hence the difference of longitude must be added, if the longitude of the given place be W.; but subtracted if it be E.;-and the sum, or difference, will be the longitude of the places required.

1. If, in subtracting, the difference of longitude be greater than the longitude of the given place, subtract the latter from the former-and the remainder of a contrary name will be the longitude required.

2. If, in adding, the sum exceeds 180°, subtract it from 360°, and the remainder will be the required longitude, but of a contrary name.

3. By this problem, it may also be found where it is any other given hour; only, instead of turning the globe till the index point to 12, turn it till it point to the given hour.

EXAMPLES.

1. Where is it noon, when it is 5 p.m. at Paris? Calculation.-5 hours=75o the difference of longitude. As the given hour is evening, the places where it is noon will lie to the west. The longitude of Paris is 2o 20′ E.: from this, according to the rule, 75o ought to be subtracted; but as that cannot be done, subtract 2° 20′ from 75°, (as directed in note 1,) and the remainder, 72° 40′, will be the longitude of the places required, and will be W., being of a contrary name. It will therefore be noon at Labrador, New England, Pennsylvania, St. Domingo, Terra Firma, Peru, &c.

2. Where is it noon, when it is 9 a.m. at Newcastle? Answ. Nisney Novogorod, in Russia; Armenia and Georgia; Bagdad; the middle parts of Arabia; Mocha; the Strait of Babelmandeb; the north-east part of Africa; and the western coast of Madagascar.

3. When it is 7 a.m. at Kingston, in Jamaica, where is it noon? Answ. At London, and all other places which are situated under the meridian of London.

4. At 40 m. past 2 p.m. at Ispahan, where is it noon? 5. Where is it noon, when it is 1 a.m. at New Zealand? 6. Where is it noon, when it is midnight at London? 7. When it is 7 a.m. at Jerusalem, where is it noon? 8. When it is midnight at Mexico, where is it 9 a.m.? 9. Where is it noon, when it is 4 a.m. at Botany Bay? 10. Where is it midnight, when it is past 10 a.m. at Bencoolen, in Sumatra?

11. When it is 43 p.m. at Paris, where is it noon? 12. At past 7 a.m. at Shiraz, where is it noon?

13. Being noon at London, where is it past 8 a.m.? 14. When it is 2 o'clock in the afternoon at London, at what place is it past 5 in the afternoon? 15. Being noon at Bombay, where is it past 6 a.m.? 16. When it is midnight at Brusa, where is it 3 p.m.? 17. When it is past 6 in the morning at Quebec, where is it 11 in the forenoon?

QUESTIONS FOR EXAMINATION IN SECTION III.

What are the horary circles? How does the earth turn on its axis? What is it that produces noon at any place? Do the meridians that lie to the east, or those that lie to the west, come sooner opposite to the sun?

How long is the earth in turning on its axis? At what rate does it turn per hour? How is that found? How many degrees of longitude make an hour's difference of time? To places that lie in 30o E. L. are the hours of the day more or less advanced than they are at London ? Having the hour given at any place, how is it found what hour it is at any other place? Having the hour given at any place, how is it found where it is noon?

6. How much are the clocks at Barbadoes behind ours?
7. Where is it noon, when it is 3 a.m. at Newcastle?
8. Where is it noon, when it is 7 p.m. at Pekin?

9 When it is midnight at Mexico, where is it noon? 10. When is it 11 p.m. at Jamaica, where is it noon? 11. When it is 3 a.m. at Paris, where is it noon?

12. My watch was well regulated at London, and when I arrived at Madras, which was after a five months' voyage, it was 4 hours 50 min. slower than the clocks there. Had it gained or lost during the voyage, and how much?

13. When it is 7 p.m. at Edinburgh, what is the hour at Washington? 14. When it is 5 p.m. at Philadelphia, where is it midnight?

15. Are the clocks at Calcutta faster or slower than the clocks at London, and how much?

SECTION IV.

DEFINITIONS.

1. The ecliptic is the circle described by the earth in its annual motion round the sun; or it is that circle in which the sun appears to move.

The ecliptic is proper only to the celestial globe; but, on account of its great use in performing many geographical problems, it is always drawn on the terrestrial: it crosses the equator obliquely, and extends 23o 28' to the north of it on one side, and 23° 28′ to the south of it on the other side. The angle which it makes with the equator is called the obliquity of the ecliptic.

It is called the ecliptic, because eclipses happen when the moon is in or near this circle: it is divided into 12 equal parts, called signs, each containing 30 degrees; they are thus marked and named;

The winter and spring signs are termed ascending, and the summer and autumnal descending.

2. The tropics are parallel to the equator, and distant from it 23° 28': that which lies on the north side is called the tropic of cancer; and that which lies on the south side is called the tropic of capricorn.

The obliquity of the ecliptic determines the distance of the tropics from the equator; as they are drawn parallel to the equator, through those two points of the ecliptic which are at the greatest distance from it. The northern tropic is called the tropic of cancer, because it passes through the sign cancer; the southern, the tropic of capricorn, because it passes through the sign capricorn.

3. The polar circles are two circles, which are parallel to the equator, and as far distant from the poles as the tropics are from the equator: that which lies towards the north pole is called the arctic circle, and that which is towards the south pole is called the antarctic circle.

The distance of the polar circles from the poles depends upon the obliquity of the ecliptic: their distance from the poles being 23° 28′, their distance from the equator is 66° 32'.

4. The equinoctial points are those points in which the equator and ecliptic cross each other; they are the first points of aries and libra.

5. The solstitial points are those two points of the ecliptic that are at the greatest distance from the equator, and at which the ecliptic touches the tropics: they are the first points of cancer and capricorn.

6. Declination of the sun is its distance north or south

of the equator.

7. Altitude of the sun is its distance above the horizon. 8. The analemma is a calendar of the months, placed on some vacant part of the globe, extending from tropic to tropic; the months and days are so divided as to correspond to the sun's declination for every day in the year.

The days increase continually to all places in the northern hemisphere, whilst the sun is moving through the ascending signs, or from the first of capricorn to the first of cancer; i. e. from Dec. 21st to June 21st: but the contrary happens to all places in the southern hemisphere; the days there increasing whilst the sun moves from cancer to capricorn, or from June 21st to Dec. 21st.

As, at the equator, the days and nights are always equal, so, of all other places, those that are the nearer to the equator have the less inequality in their days and nights; and the greater the latitude of the place, the greater is the length of its longest day. The length of the longest day at any place is equal to the length of its longest night.