grees between it and the horizon, will be the sun's altitude.

Or, rectify the globe for the latitude of the place in the frigid zone; bring the sun's place in the ecliptic to the brazen meridian, and set the index of the hour circle to twelve; turn the globe on its axis till the index points to the other twelve; and the number of degrees between the sun's place and the horizon, counted on the meridian towards that part of the horizon marked north, will be the sun's altitude,

EXAMPLES.

1. What is the sun's altitude at the North Cape in Lapland, when it is midnight at Alexandria in Egypt, on the 21st of June?

Answer. 5 degrees.

2. When it is midnight to the inhabitants of the island of Sicily on the 22d of May, what is the sun's altitude at the north of Spitzbergen, in latitude 80 degrees north?

3. What is the sun's altitude at the north o. Baffin's Bay, when it is midnight at Buenos Ayres, on the 28th of May ?

PROBLEM XLVII.

The day of the month being given, to find the sun's right ascension, oblique ascension, oblique descension, ascensional difference, and time of rising and setting at any given place.

RULE. Rectify the globe for the given latitude; bring the sun's place in the ecliptic to the brazen meridian, and the degree on the equator cut by the graduated edge of the meridian, reckoning from the point Aries eastward, will be the sun's right ascension. Then, bring the sun's place to the eastern part of the horizon; the degree of the equator cut by the horizon, reckoning from the point Aries as before, will be the sun's oblique ascension; and the difference between the sun's right ascension and oblique ascension, is the ascensional difference.

The oblique descension is found in a similar manner, by bringing the sun's place to the western part of the horizon, and reckoning from the point Aries eastward as before; and the difference between the sun's right ascension and oblique descension, is also the ascensional difference.

If the ascensional difference in degrees be converted into time, (see Prob. XIX.) then, if the sun's declination and the latitude of the place be both of the same name, (that is, both north or both south,) the sun rises before six, or sets after six, an interval of time equal to the ascensional difference; but, if the sun's declination and the latitude be of contrary names, (that is, the one north and the other south) the sun rises after six, or sets after six.

EXAMPLES.

1. Required the sun's right ascension, oblique ascension, oblique descension, ascensional difference, &c. at New-York, on the 21st of June.

Answer. The sun's right ascension is 90 degrees, oblique ascension 68 degrees; therefore, the ascensional difference is 220, which being converted into time, corresponds to 1 hour 28 minutes. Hence, the time of the sun's rising is 4 hours 32 minutes; and the sun sets at 28 minutes past seven. The oblique descension is 68 degrees, the same as the oblique ascension.

2. Required the sun's right ascension, oblique ascension, and oblique descension at St. Louis, on the 22d of December. What is the ascensional difference, and at what time does the sun rise and set?

3. Required the sun's right ascension, oblique

ascension, and oblique descension at Washington City, on the 20th of March. What is the ascensional difference, and at what time does the sun rise and set?

PROBLEM XLVIII.

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

RULE. Rectify the globe to the sun's declination for the given day; bring the given place to the brazen meridian, and set the index of the hour circle to twelve; then, if the given time be before noon, turn the globe westward as many hours as it wants of noon; but, if the given time be past noon, turn the globe eastward as many hours as the time is past noon; keep the globe in this position; then all places along the western part of the horizon have the sun rising; those places along the eastern part have the sun setting; those under that part of the meridian, which is above the horizon, have noon; that particular place which stands under the sun's declination on the meridian has the sun vertical; all places below the western part of the horizon, within eighteen degrees, have morning twilight; those places which are below the eastern part of the horizon, within eighteen degrees of it, have evening twilight; all places under that part of the meridian, which is below the horizon, have midnight; all places above the horizon have day, and those below it have night.

The reason of this rule is very evident from what has been explained in the foregoing problems.

EXAMPLES.

1. When it is forty minutes past four o'clock in the morning at Philadelphia, on the 5th of February, find all the places of the earth where the sun is rising, setting, &c.

Answer. The declination of the sun will be found to be 15° 54' south; therefore, elevate the south pole 15° 54'; then bring Philadelphia to the meridian, and set the index of the hour circle to twelve; turn the globe westward till the index has passed over 7 hours 20 minutes, what the given time wants of noon.

Let the globe be fixed in this position; then, the sun is rising at the northern part of Labrador, or near Hudson's Straits; Upper Canada; States of Ohio, Kentucky, Tennessee, and Alabama; and that part of Mexico, situated between the bays of Campeachy and Honduras. Setting at Russian Lapland, &c.; Tartary; the eastern part of Cabulistan; a part of Hindoostan; the eastern part of the island of Ceylon, &c.

Noon at Falmouth in England; Cadiz; Fez; Ivory Coast, &c.

Vertical at St. Helena.

Morning twilight at the north-western part of Hudson's Bay; Missouri Territory; the internal provinces of Mexico, &c.

Evening twilight at the western coast of New-Holland; Batavia; Sumatra; Malacca; Birman Empire, &c.

Day in all Europe, Africa, and all that part of Asia, comprehended between Ceylon and Little Tibet, &c. towards the east; in all South America; the whole of the West Indies, Florida, Georgia, North and South Carolina, Virginia, District of Columbia, Maryland, Delaware, Pennsylvania, New-Jersey, New-York, &c.

Night in all that part of North America, comprehended between the eastern part of Cuba and Hudson's Straits, &c. towards the west; in all that part of Asia, comprehended between the island of Ceylon and the sea of Obe, towards

the east.

2. When it is fifty-two minutes past four o'clock in the morning at London, on the 1st of March, find all places of the earth where the sun is rising, setting, &c.

3. When it is seven o'clock in the morning at Washington city, on the 17th of February, where is the sun rising, setting, &c.

Questions to exercise the learner in the foregoing

problems.

The questions referring to the rules are in italics, in order that the student may distinguish them from those questions which refer to the examples.

1. On what circles of the terrestrial globe are the latitude and longitude of places counted?

2. Required the latitude and longitude of Bombay, city and island, on the west coast of Hindoostan, and capital of all the British possessions on-that side of the peninsula.

3. How do we find all the places that have the same latitude as any given place?

4. Which places have the same latitude as Berne, the capital of a canton of the same name in Switzerland?

5. How do we find all the places that have the same longitude as any given place?

6. Which places have the same longitude as Hanover, a city of Germany, and capital of the kingdom of the same name?

7. How do we find what place is situated in a particular latitude and longitude?

8. What place in the Austrian dominions is in 48° 12′ north latitude, and 16° 12′ east longitude ?

9. How do we find the difference of latitude between two places, situated either on the same, or on contrary sides of the equator?