place in the ecliptic, and bring it to that part of the brass meridian which is numbered from the equator towards the poles; count the number of degrees contained on the brass meridian between the sun's place and the horizon, and they will show the altitude.*

To find the sun's altitude at any hour, see Problem XLIV.

OR, BY THE ANALEMMA.

Elevate the pole so many degrees above the horizon as are equal to the latitude of the place; find the day of the month on the analemma, and bring it to that part of the brass meridian which is numbered from the equator towards the poles; count the number of degrees contained on the brass meridian between the given day of the month and the horizon, and they will show the altitude. To find the sun's altitude at any hour, see Problem XLIV.

Examples. 1. What is the sun's meridian altitude at London on the 21st of June?

Answer. 62 degrees.

2. What is the sun's meridian altitude at London on the 21st of March?

3. What is the sun's least meridian altitude at London ?

4. What is the sun's greatest meridian altitude at Cape Horn?

5. What is the sun's meridian altitude at Madras on the 20th of June?

6. What is the sun's meridian altitude at Bencoolen on the 15th of January?

EXAMPLES TO THE NOTE.

1. What is the sun's altitude at Madrid on the 24th of August, at 11 o'clock in the morning?†

* See Problem XXII.

+ This example is taken from a prospectus. announcing the publication of New Globes, to be executed by Mr. Dudley Adams, and called the Newtonian Globes, wherein the author has treated the common globes with uncommon severity; he has however been rather unfortunate in the choice of his examples. which are designed to show " the absurdities and ridiculous inconsistencies of the common globes." He says, By working this problem on the common globes, we find with the greatest astonishment, that Madrid, where it is understood to be eleven

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Answer. The sun's declination is 114 degrees north, by elevating the north pole 114 degrees above the horizon, and turning the globe so that Madrid may be one hour westward of the meridian, the sun's altitude will be found to be 574 degrees.

2. What is the sun's altitude at London at 3 o'clock in the afternoon on the 25th of April?

3. What is the sun's altitude at Rome on the 16th of January at 10 o'clock in the morning?

4. Required the sun's altitude at Buenos Ayres on the 21st of December at 2 o'clock in the afternoon.

PROBLEM XLII.

When it is midnight at any place in the temperate or torrid zones, to find the sun's altitude at any place (on the same meridian) in the north frigid zone, where the sun does not descend below the horison.

Rule. Find the sun's declination for the given day, and elevate the pole to that declination; bring the place (in the frigid zone) to that part of the brass meridian which is numbered from the north pole towards the equator, and the number of degrees between it and the horizon will be the sun's altitude.

OR,

Elevate the north pole so many degrees above the horizon as are equal to the latitude of the place in the frigid zone; bring the sun's place in the ecliptic to the brass 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 brass 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?

o'clock in the morning, is at that time in the dark, under the horizon; and consequently, we hardly conceive how the inhabitants can see the sun take its altitude, and calculate the time to be eleven o'clock.”—Ęx uno disce Omnes.

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° north?

3. What is the sun's altitude at the north east of Nova Zembla, when it is midnight at Tobolsk, on the 15th of July?

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

PROBLEM XLIII.

To find the sun's amplitude at any place.

Elevate the pole so many degrees above the horizon as are equal to the latitude of the given place; find the sun's place in the ecliptic, and bring it to the eastern semi-circle of the horizon; the number of degrees from the sun's place to the east point of the horizon will be the rising amplitude: bring the sun's place to the western semi-circle of the horizon, and the number of degrees from the sun's place to the west point of the horizon will be the setting amplitude.

OR, BY THE ANALEMMA.

Elevate the pole so many degrees above the horizon as are equal to the latitude of the place; bring the day of the month on the analemma to the eastern semi-circle of the horizon; the number of degrees from the day of the month to the east point of the horizon will be the rising amplitude: bring the day of the month to the western semi-circle of the horizon, and the number of degrees from the day of the month to the west point of the horizon will be the setting amplitude.

Examples. 1. What is the sun's amplitude at London on the 21st of June?

Answer. 39° 48′ to the north of the east, and 39° 48′ to the north of the west.

2. On what point of the compass does the sun rise and set at London on the 17th of May ?

3. On what point of the compass does the sun rise and set at the Cape of Good Hope on the 21st of December?

4. On what point of the compass does the sun rise and set on the 21st of March?

5. On what point of the compass does the sun rise and set at Washington on the 21st of October?

6. On what point of the compass does the sun rise and set at Petersburg on the 18th of December?

PROBLEM XLIV.

To find the sun's azimuth and his altitude at any place, the day and hour being given.

Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridian, over that latitude; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour circle to twelve; then, if the given time be before noon, turn the globe eastward* as many hours as it wants of noon; but if the given time be past noon, turn the globe westward as many hours as it is past noon; bring the graduated edge of the quadrant of altitude to coincide with the sun's place, then the number of degrees on the horizon, reckoned from the north or south point thereof to the graduated edge of the quadrant, will show the azimuth; and the number of degrees on the quadrant, counting from the horizon to the sun's place will be the sun's altitude.

OR, BY THE ANALEMMA.

Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridian, over that latitude; bring the middle of the analemma to the brass meridian, and set the index of the hour circle to twelve; then, if the given time be before noon, turn the globe

* Whenever the pole is elevated for the latitude of the place, the proper motion of the globe is from east to west, and the sun is on the east side of the brass meridian in the morning, and on the west side in the afternoon; but, when the pole is elevated for the sun's declination, the motion is from west to east, aud the place is on the west side of the meridian in the morning, and on the east side in the afternoon.

eastward on its axis as many hours as it wants of noon; but, if the given time be past noon, turn the globe westward as many hours as it is past noon; bring the graduated edge of the quadrant of altitude to coincide with the day of the month on the analemma, then the number of degrees on the horizon, reckoned from the north or south point thereof to the graduated edge of the quadrant, will show the azimuth; and the number of degrees on the quadrant, counting from the horizon to the day of the month, will be the sun's altitude.

Examples. 1. What is the sun's altitude, and his azimuth from the north, at London, on the 1st of May, at ten o'clock in the morning?

Answer. The altitude is 47°, and the azimuth from the north 135°, or from the south 44°.

2. What is the sun's altitude and azimuth at Petersburg, on the 13th of August, at half past five o'clock in the morning?

3. What is the sun's azimuth and altitude at Antigua, on the 21st of June, at half past six in the morning, and at half past ten ?*

4. At Barbadoes on the 20th of May, when the sun's declination is 20 degrees north, required the time of the sun's appearing on the same azimuth, twice in the forenoon and twice in the afternoon?

5. On the 13th of August at half past eight o'clock in the morning, at sea in latitude 57° N. the observed azimuth of the sun was S. 40° 14′ E. what was the the sun's altitude, his true azimuth, and the variation of the compass?

6. On the 14th of January, in latitude 33° 52′ S. at half past three o'clock in the afternoon, the sun's magnetic azimuth was observed to be N. 63° 51′ W.; what was the true azimuth, the variation of the compass, and the sun's altitude?

* At all places in the torrid zone, whenever the declination of the sun exceeds the latitude of the place, and both are of the same name, the sun will appear twice in the forenoon and twice in the afternoon, on the same point of the compass, and will cause the shadow of an azimuth dial to go back several degrees. In this example, the sun's, azimuth at the hours given above, will be 69° from the north towards the east; and at half past eight o'clock, the sun will appear to have the same azimuth for some time.