through the sign cancer; the southern, the tropic of capricorn, because it passes through the sign capricorn.

The imaginary line, which corresponds to the tropic of cancer on the earth, passes Mount Atlas on the western coast of Africa, Syene in Ethiopia, thence over the Red Sea, to Mount Sinai, by Mecca, the city of Mahomet, across Arabia Felix, to the extremity of Persia, the East Indies, China, over the Pacific Ocean to Mexico, and the island of Cuba.

The tropic of capricorn passes through the country of the Hottentots, across Brazil to Paraguay and Peru.

3. The polar circles are two less circles, 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 ob liquity 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 point sof 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. The colures are those two meridians which pass through the solstitial and equinoctial points; that which passes through the equinoctial points is called the equinoctial co lure, and that which passes through the solstitial points is called the solstitial colure.

7. Declination of the sun is its distance north or south of the equator.

8. Altitude of the sun is its distance above the horizon.

9. The analemma is a calendar of the months, placed on some vacant part of the body 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,

OF THE LENGTH OF THE DAYS AND NIGHTS.

Twice a year the days and nights are equal to all places upon the earth; these two days are, when the sun is in the first of aries and libra, or March 21st, and September 23d. These are called the equinoxes,-March 21st the vernal, and Sept. 23d the autumnal equinox. In places under the equator the days and nights are always equal,

In all places between the equator and the north pole the day is longest when the sun is in the first degree of cancer, June 21st, and shortest when in the first degree of capricorn, December 21st; but in those places between the equator and the south pole the contrary happens, the day is shortest when the sun is in the first of cancer, and longest when in the first degree of capricorn. June 21st is called the summer solstice, it being then summer to all places in the northern hemisphere; and December 21st, the winter solstice, it being then winter to the same places.

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 capicorn to the first of cancer; i. e. from December 21st to June 21st:-but the contrary of this happens to all places in the southern hemisphere; the days there increasing whilst the sun moves from cancer to capricorn, or from the 21st of June to the 21st of December.

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 always equal to the length of the longest night at the same place.

The sun's declination is north from March 20th to September 23d, and south the remainder of the year. Its greatest declination, either north or south, is 231°.

The sun's altitude, or height above the horizon, will be increasing to any place, whilst the days are increasing at that place; and its altitude on the same day will be different to places, that have different latitudes: hence the sun's meridian altitude furnishes an easy method of determining the latitude of a place.

These propositions will be made evident by the problems in this section: these are to find the rising and setting of the sun at any place (and consequently the length of the day and night at that place), for any day of the year; also, when the sun is due east or west; its altitude, either at noon or at any other hour; and, from having its altitude, to find the latitude of the place.

Previous to performing these problems, some others are necessary; such as, to find the sun's place, and its decli nation for any day, and to rectify the globe for the sun's place.

All the problems in this section can be performed by either the terrestrial or celestial globe.

PROBLEM XV.

To find the sun's place in the ecliptic.

1. Seek the day of the month in the calendar on the horizon, and against it, in the adjoining circle, will be found the sign and degree in which the sun is for that day.

2. Find the same sign and degree in the ecliptic on the surface of the globe, and this is the sun's place for that day

at noon.

The sun's place, or, as it is otherwise termed, the sun's longitude, may be found for any day of the year in White's Ephemeris, or in the Nau tical Almanack. In White's Ephemeris it is marked in the first column of the right-hand page of every month.

EXAMPLES.

1. What is the sun's place for March 10th?

Answ. 20° 7'.

2. What is the sun's place on the 4th of June?

Answ. II 13° 57'.

What is the sun's place for the following days?

3. January 1st?

4. February 2d?
5. March 3d?
6. April 4th!
7. May 5th?
8. June 6th?

9. July 7th? 10. August 8th?

11. September 9th?

12. October 10th?
13. November 11th?
14. December 12th?
15. March 22d?
16. June 22d?

17. September 23d?
18. December 22d?

PROBLEM XVI.

To find the sun's declination.

Bring the sun's place for the given day to the brass meridian, and the degree over it will be the declination

sought; or bring the day of the month marked on the analemma to the brass meridian, and the degree over it will be the declination as before.

N. B. The sun's declination is given in White's Ephemeris for every day in the year, and also in Table II. at the end of this work.

1. The declination of the sun being its distance north or south from the equator, this problem is exactly the same as that for finding the la titude of a place.

2. The greatest north declination, 23° 28', is when the sun enters cancer, June 21st,-that being the greatest distance of the ecliptic north of the equator. The greatest south declination, 23° 28', is when it enters capricorn, December 21st,-that being the greatest distance of the ecliptic south of the equator.

EXAMPLES.

1. What is the sun's declination for March 10th?

Answ. 3° 54 S.

Answ. 17° 14' S.

2. What is the sun's declination for January 31st?

What is the sun's declination for the following days?

3. April 23d?

5. August 1st ?

4. August 12th? 6. March 5th?

7. July 23d?

8. October 19th?

9. On what days has the sun no declination?

10. When has the sun the greatest declination north? 11. When has the sun the greatest declination south? 12. What is the sun's declination for to-day?

PROBLEM XVII.

To rectify the globe for the sun's place, and day of the

1. Find the sun's declination for the given day, by the last problem.