! EXAMPLES. 1. What is the sun's meridian altitude at NewYork on the 21st of June ? Answer. 72° 45' 20". This is the greatest altitude at New-York. 2. What is the sun's meridian altitude at Quito on the 20th of March? 3. What is the sun's meridian altitude at NewYork on the 22d of December ? 4. What is the difference between the greatest and least meridian altitude of the sun at Washington city ? 5. What is the sun's meridian altitude at Petersburg in Russia, on the 22d of December? PROBLEM XLII. Given the sun's meridian, altitude, and the day of the month, to find the latitude of the place of observation. RULE. Bring the sun's place in the ecliptic to the brazen meridian; then count as many degrees frpm the sun's place on the meridian, as is equal to the given altitude, reckoning towards the south point of the horizon, if the sun was south when the altitude was taken, or towards the north, if the sun was to the north of the observer, and mark the degree where the reckoning ends; elevate or depress the pole till this mark coincides with the horizon, and the number of degrees the elevated pole is above the horizon, will be the latitude required. Or, by calculation. Subtract the sun's altitude from 90 degrees, and the remainder is the zenith distance. If the sun be south when his altitude is taken, call the zenith distance north; but, if north, call it south; find the sun's declination in the Nautical Almanac, or in a table of the sun's declination; and observe whether it be north or south; then, if the zenith distance and declination have the same name, their sum is the latitude; but if they have contrary names, their difference is the latitude, and it is always of the same name with the greater of the two quantities. EXAMPLES. 1. On the 1st of August 1825, I observed the sun's meridian altitude to be 20° 25′ 19′′, and it was south of me at that time; required the latitude of the place. Answer. 87 degrees 38 minutes 22 seconds. 20° 25′ 19′′ S. sun's altitude at noon. *69° 34′ 41" N. the zenith distance. 18 3 41 N. sun's declination 1st of August, 1825. $7° 38′ 22" N. the latitude sought. 2. On the 21st of June, 1825, the sun's meridian altitude was observed to be 66° 20 north of the observer; what was the latitude of the place of observation? 3. On the 21st of June, 1825, I observed the sun's meridian altitude to be 72° 45′ 20′′, and it was south of me at that time; required the latitude of the place. 4. On the 14th of July, 1825, the sun's meridian altitude was observed to be 50° 30′ 29" north of the observer; what was the latitude of the piace of observation? PROBLEM XLIII. To find the sun's azimuth and his altitude at any given place, the day and hour being given. RULE. Rectify the globe for the latitude of the giver place, and for the sun's place on the given day; (by Prob. XXVII.) then, if the given time be before noon, turn the globe eastward as many hours as it wants of noon; but if the given place 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 altitude. This problem may be also resolved by the analemma; but as the method is nearly similar to that above given, it can be readily supplied by the intelligent student. It may not be improper to observe that, 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, the sun will appear twice in the forenoon, and twice in the afternoon, on the same point of the compass; and consequently, its azimuth will be the same at two different hours. EXAMPLES. 1. What is the sun's altitude, and his azimuth from the north, on the 10th of May, at New-York, at 9 o'clock in the morning? Answer. The altitude is 45° 30', and the azimuth 1070 30' from the north. 2. 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? Answer. The sun's azimuth is 690 from the north, at both those hours; the altitude at half-past six, is 120 nearly; and the altitude at half-past ten, is 670 nearly. These altitudes are found by the globe, and therefore are not so accurate as if they had been found by calculation. 3. What is the sun's azimuth and altitude at New-York on the 20th of May at seven o'clock in the morning? 4. What is the sun's azimuth and altitude at Barbadoes, on the 20th of May, at six o'clock in the morning; and at what other hour in the forenoon has the sun the same azimuth?. PROBLEM XLIV. To find the Sun's amplitude at any given place, on a given day. RULE. Rectify the globe for the latitude of the given place; bring the sun's place in the ecliptic to the east part of the horizon, and the degree cut on the horizon, reckoning from the east, will be the sun's amplitude at rising; bring the sun's place to the western part of the horizon, by turning the globe on its axis, and the degree cut on the horizon, reckoning from the west point of it, will be the sun's amplitude at setting. This problem may be also resolved by the analemma. For a table of the sun's amplitude, corresponding to every degree of the sun's declination, and also to every degree of latitude from the equator to the polar circles, the student is referred to Bowditch's New American Practical Navigator. EXAMPLES. 1. What is the sun's amplitude at Philadelphia on the 21st of June ? Answer. 31° 19' to the north of the east, nearly; and, 310 19 to the north of the west. 2. On what point of the compass does the sun rise and set at New-Orleans on the 20th of April? 3. On what point of the compass does the sun rise and set at Boston on the 4th of July ? 4. What is the sun's amplitude at Charleston, in South Carolina, on the 22d of December? PROBLEM XLV. Given the sun's amplitude and the day of the month, to find the latitude of the place of observation. RULE. Bring the sun's place in the ecliptic to the eastern or western part of the horizon, according as the eastern or western amplitude is given; then elevate or depress the pole till the sun's place coincides with the given amplitude on the horizon, and the elevation of the pole will show the latitude. EXAMPLES. 1. The sun's amplitude was observed to be 390 48' from the east towards the north, on the 21st of June; required the latitude of the place of observation. Answer 510 32' north. 2. The sun's amplitude was observed to be 150 30' from the east towards the north, at the same time his declination was 15° 30'; required the latitude. 3. When the sun's declination was 2o north, his rising amplitude was 4o north of the east; required the latitude. PROBLEM XLVI When it is midnight at any place in the torrid or temperate 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 horizon. RULE. Rectify the globe to the sun's declination for the given day, (by Prob. XXV.;) bring the place in the frigid zone to that part of the brazen meridian which is numbered from the north pole towards the equator, and the number of de |