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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 tit that time above the horizon: whereas, when it is in the other part of the ecliptic, it passes the 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, arid 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
It rises at - 2 h. 24 min afternoon.
Culminates at - -657
Sets at - - - 11 50
Is above the horizon 9 6
Its oblique ascension and descension are 120° 47', and 77° 15'; its amplitude 27° southward.
Problem xxW. The latitude, the altitude of the sun by day, or of a star by night, being given, tojind 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. f.
Problem^ xxv. The latitude and hour of the day being given, to find the altitude and azimuth of the mui, 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 IO 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 December, 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 21 st, 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 6o deg. south-westerly, the altitude will be about 44 ^ deg. and the hour 11'- in the afternoon.
Thus the latitude and the day being known, and having, beside?, either the latitude, the azimuth, or the hour, the other two may be easily found.
Problem xxvm. The latitude of the place, and the azimuth of the mm or of a star being given, to find' the hour of the. day or night.
Rectify the globe for the latitude and sun's place, and bring the quadrant of altitude to the given azimuth in the horizon; turn the globe till the sun or star comes to the quadrant, and the index will shew the time. Nov. 5, at Gibraltar, given the sun's azimuth 50 degrees from the south towards the east, the time you will find to be half-past VIII in the morning. Given the azimuth of Vega at London, 57 degrees from the north towards the east, February the 8th, the time you will find twenty minutes past II in the morning.
But as it may possibly happen that we may see' a star, and would be glad to know what star it is, or whether it may not be a new star, or a comet; how that may be discovered, will be seen under the following
Problem xxix. The latitude of the place, the sun's place, the hour of the night, and the altitude and azimuth of any star being given, tojind the star.
Rectify the globe for the latitude of the place, and the sun's place; fix the quadrant of altitude in the