cal: it crosses the horizon at the eastern and western

points.

Any azimuth circle may be represented by the graduated edge of the brass quadrant of altitude, when the centre upon which it turns is screwed to that point of the strong brass meridian which answers to the latitude of the place, and the place is brought into the zenith.

If the said graduated edge should lie over the sun's centre or place, at any given time, it will represent the sun's azimuth at that time.

If the graduated edge be fixed at any point, so as to represent any particular azimuth, and the sun's place be brought there, the horary index will shew at what time of that day the sun will be in that particular azimuth.

Here it may be observed, that the amplitude and azimuth are much the same.

The amplitude shewing the bearing of any object when it rises or sets, from the east and west points of the horizon.

The azimuth the bearing of any object when it is above the horizon, either from the north or south points thereof. These descriptions and illustrations being understood we may proceed to

PROBLEM XXII. To find at what time the sun is due east, the day and the latitude being given.

Rectify the globe; then if the latitude and declination are of one kind, bring the quadrant of alti

tude to the eastern point of the horizon, and the sun's place to the edge of the quadrant, and the index will shew the hour.

If the latitude and declination are of different kinds, bring the quadrant to the western point of the horizon, and the point in the ecliptic opposite to the sun's place to the edge of the quadrant, and then the index will shew the hour.

You will easily comprehend the reason of the foregoing distinction, because when the sun is in the equinoctial, it rises due east; but when it is in that part of the ecliptic which is towards the elevated pole, it rises before it is in the eastern vertical circle, and is therefore at that time above the horizon: whereas, when it is in the other part of the ecliptic, it the passes eastern prime vertical before it rises, that is, below the horizon; whence it is evident, that the opposite point of the ecliptic must then be in the west, and above the horizon. The sun is due east at London at 7 h. 6 min. on the 18th of May. The second of Aug. at Cape Horn, the sun is due east at 5 h. 10 min,

PROBLEM XXIII. To find the rising, setting, and culminating of a star, its continuance above the horizon, and its oblique ascension and descension, and also its eastern and western amplitude, for any given day and place.

1. Rectify the globe to the latitude and zenith, bring the sun's place for the day to the meridian, and set the hour index to XII. 2. Bring the star

to the eastern side of the horizon, and its eastern amplitude, oblique ascension, and time of rising, will be found as taught of the sun. 3. Carry the star to the western side of the horizon; and in the same manner its western amplitude, oblique descension, and time of setting, will be found. 4. The time of rising, subtracted from that of setting, leaves the continuance of the star above the horizon. 5. This remainder, subtracted from 24 hours, gives the time of its continuance below the horizon. 6. The hour to which the index points, when the star comes to the meridian, is the time of its culminating or being on the meridian.

Let the given day be March 14, the place London, the star Sirius; by working the problem you will find 2 h. 24 min. afternoon.

It rises at

Culminates at

Its oblique ascension and descension are 120° 47', and 77° 15'; its amplitude 27° southward.

PROBLEM XXIV. The latitude, the altitude of the sun by day, or of a star by night, being given, to find the hour of the day, and the sun or star's azimuth.

Rectify the globe for the latitude, the zenith, and the sun's place, turn the globe and the quadrant of altitude, so that the sun's place, or the given star, may cut the given degree of altitude, the index will shew the hour, and the quadrant will be the azimuth in the horizon.

Thus, on the 21st of August, at London, when the sun's altitude is 36° in the forenoon, the hour is IX, and the azimuth 58° from the south.

At Boston, December 8th, when Rigel had 15° of altitude, the hour was VIII, the azimuth S. E. by E. 7°.

PROBLEM XXV.

The latitude and hour of the day being given, to find the altitude and azimuth of the sun, or of a star.

Rectify the globe for the latitude, the zenith, and the sun's place, then the number of degrees contained betwixt the sun's place and the vertex is the sun's meridional zenith distance; the complement of which to 90 deg. is the sun's meridian altitude. If you turn the globe about until the index points to any other given hour, then bringing the quadrant of altitude to cut the sun's place, you will have the sun's altitude at that hour; and where the quadrant cuts the horizon, is the sun's azimuth at the same time. Thus, May the first, at London, the sun's meridian altitude will be 53 degrees; and at 10 o'clock in the morning, the sun's altitude will be 46 degrees, and his azimuth about 44 degrees from the south part of the meridian. On the 2d of Decentber, at Rome, at five in the morning, the altitude of Capella is 41. deg. 58 min. its azimuth 60 deg. 50 min. from N. to W.

PROBLEM XXVI.

The latitude of the place, and the day of the month being given, to find the depression of the sun below the horizon, and the azimuth, at any hour of the night.

Having rectified the globe for the latitude, the zenith, and the sun's place, take a point in the ecliptic exactly opposite to the sun's place, and find the sun's altitude and azimuth, as by the last problem, and these will be the depression and the altitude required.

Thus, if the time given be the first of November, at 10 o'clock at night, the depression and azimuth will be the same as was found in the last problem.

PROBLEM XXVII. The latitude, the sun's place, and his azimuth being given, to find his altitude, and the hour.

Rectify the globe for the latitude, the zenith, and the sun's place; then put the quadrant of altitude to the sun's azimuth in the horizon, and turn the globe till the sun's place meets the edge of the quadrant; then the said edge will shew the altitude, and the index point to the hour.

Thus, May 21st, at London, when the sun is due east, his altitude will be about 24 deg. and the hour about VII in the morning; and when his azimuth is 60 deg. south-westerly, the altitude will be about 44 deg. and the hour 113 in the afternoon.

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