PROBLEM XXVII. The month, day, and hour of the day 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. Find the sun's declination (by Problem XX.) and mark it on the brass meridian; elevate the north or south pole, according as the sun's declination is north or south, so many degrees above the horizon as are equal to the sun's declination; bring the given place 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 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 edge of the horizon have the sun rising; those places along the eastern edge have the sun setting; those under the brass meridian, above the horizon, have noon; that particular place which stands under the sun's declination on the brass meridian has the sun vertical; all places below the western edge of the horizon, within eighteen degrees, have morning twilight; those places which are below the eastern edge of the horizon, within eighteen degrees, have evening twilight; all places under the brass meridian, below the horizon, have midnight; all the places above the horizon have day, and those below it have night, or twilight. Examples. 1. When it is fifty-two minutes past four o'clock in the morning at London, on the fifth of March, find all places of the earth where the sun is rising, setting, &c. Answer. The sun's declination will be found to be 64° south; therefore, elevate the south pole 64o above the horizon. The given time being seven hours eight minutes before noon (=12 h.-4 h. 52 m.) the globe must be turned towards the west till the index has passed over seven hours eight minutes.* Let the globe be fixed in this position; then. The sun is rising at the western part of the White Sea, Petersburg, the Morea in Turkey, &c. Setting at the eastern coast of Kamtschatka, Jesus island, Palmerston island, &c. between the Friendly and Society islands. Noon at the lake Baikal in Irkoutsk, Cochin China, Cambodia, Sunda islands, &c. Vertical at Batavia. Morning twilight at Sweden, part of Germany, the southern part of Italy, Sicily, the western coast of Africa along the Æthiopian Ocean, &c. Evening twilight at the north west extremity of North America, the Sandwich islands, Society islands, &c Midnight at Labrador, New-York, western part of St. Domingo, Chili, and the western coast of South America. Day at the eastern part of Russia in Europe, Turkey, Egypt, the Cape of Good Hope, and all the eastern part of Africa, almost the whole of Asia, &c. Night at the whole of North and South America, the western part of Africa, The British isles, France, Spain, Portugal. &c. 2. When it is four o'clock in the afternoon at London, on the 25th of April, where is the sun rising, setting, &c. &c.? Answer. The sun's declination being 15o north, the north pole must be elevated 13° above the horizon;t and as the given time is four o'clock in the afternoon, the globe must be turned four hours towards the east; then the sun will be rising at O'why'hee, &c setting at the Cape of Good Hope, &c. it will be noon at Buenos Ayres, &c.; the sun will be vertical at Barbadoes; and following the directions in the problem, all the other places are readily found. 3. When it is ten o'clock in the morning at London, on the longest day, to what countries is the sun rising, setting, &c. &c.? 4. When it is ten o'clock in the afternoon at Botany Bay, on the 15th of October, where is the sun rising, setting, &c. &c.? 5. When it is seven o'clock in the morning at Washington, on the 17th of February, where is the sun rising, setting, &c. &c. ? * The hour circles, in general, are not divided into parts less than a quarter of an hour, but the odd minutes are easily reckoned. In this example having turned the globe westward till the index has passed over seven hours; then, because four minutes of time make one degree, reckon two degrees on the equator eastward, and turn the globe till they pass under the brass meridian. + If the hour circle of the globe be placed above the brass meridian, it must be unscrewed and removed from the pole; the hours may then be counted on the equator.-See the note to definition 18, page 5. 6. When it is midnight at the Cape of Good Hope, on the 27th of July, where is the sun rising, setting, &c. &c. ? PROBLEM XXVIII. To find the time of the sun's rising and setting, and the length of the day and night at any place. Rule. Find the sun's declination (by Problem XX.) and elevate the north or south pole, according as the declination is north or south, so many degrees above the horizon as are equal to the sun's declination; bring the given place to the brass meridian, and set the index of the hour circle to twelve; turn the globe eastward till the given place comes to the eastern semi-circle of the horizon, and the number of hours passed over by the index will be the time of the sun's setting: deduct these hours from twelve, and you have the time of the sun's rising; because the sun rises as many hours before twelve as it sets after twelve. Double the time of the sun's setting gives the length of the day, and double the time of rising gives the length of the night. By the same rule, the length of the longest day, at all places not in the frigid zones, may be readily found for the longest day at all places in north latitude is on the 21st of June, or when the sun enters Cancer: and the longest day at all places in south latitude is on the 21st of December, or when the sun enters the sign Capricorn. OR, Find the latitude of the given place, and elevate the north or south pole, according as the latitude is north or south, so many degrees above the horizon as are equal to the latitude; find the sun's place in the ecliptic (by Problem XX.) bring it to the brass meridian, and set the index of the hour circle to twelve; turn the globe westward till the sun's place comes to the western semicircle of the horizon, and the number of hours passed over by the index will be the time of the sun's setting; and these hours taken from twelve will give the time of rising then, as before, double the time of setting gives the length of the day, and double the time of rising gives the length of the night. OR, BY THE ANALEMMA. Find the latitude of the given place, and elevate the north or south pole, according as the latitude is north or south, the same number of degrees above the horizon ; bring the middle of the analemma to the brass meridian, and set the index of the hour circle to twelve; turn the globe westward till the day of the month on the analemma comes to the western semi-circle of the horizon, and the number of hours passed over by the index, will be the time of the sun's setting, &c. as above. Examples. 1. What time does the sun rise and set at London on the 1st of June, and what is the length of the day and night? Answer. The sun sets at 8 min. past 8, and rises 52 min past 3. the length of the day is 16 hours 16 minutes, and the length of the night 7 hours 44 minutes. The learner will readily perceive that, if the time at which the sun rises be given, the time at which it sets, together with the length of the day and night, may be found without a globe; if the length of the day be given, the length of the night, aud the time the sun rises and sets, may be found; if the length of the night be given, the length of the day and the time the sun rises and sets are easily known 2. At what time does the sun rise and set at the following places, on the respective days mentioned, and what is the length of the day and night? London, 17th of May Cape of Good Hope, 7 Dec. 3. Find the time the sun rises and sets at every place on the surface of the globe, on the 21st of March, and likewise on the 23d of September. 4. Required the length of the longest day and shortest night at the following places: London Petersburg Aberdeen Dublin Paris Vienna Berlin Pekin Buenos Ayres Cape of Good Hope Glasgow Botany Bay Copenhagen. Required the length of the shortest day and longest night at the following places : 6. How much longer is the 21st of June at Petersburg than at Alexandria ? 7. How much longer is the 21st of December at Alexandria than at Petersburg? 8. At what time does the sun rise and set at Spitzbergen on the 5th of April? PROBLEM XXIX. The length of the day at any place being given, to find the sun's declination, and the day of the month. Rule. Bring the given place to the brass meridian, and set the index to twelve; turn the globe eastward till the index has passed over as many hours as are equal to half the length of the day; keep the globe from revolving on its axis, and elevate or depress one of the poles, till the given place exactly coincides with the eastern semi-circle of the horizon; the distance of the elevated pole from the horizon will be the sun's declination: mark the sun's declination, thus found, on the brass meridian : turn the globe on its axis, and observe what two points of the ecliptic pass under this mark; seek those points in the circle of signs on the horizon, and exactly against them, in the circle of months, stand the days of the months required. OR, Bring the meridian passing through Libra* to coincide with the brass meridian, elevate the pole to the latitude of the place, and set the index of the hour circle to twelve; turn the globe eastward till the index has passed over as many hours as are equal to half the length of the day, and mark where the meridian, passing through Any meridian will answer the purpose, and the globe may be turned either eastward or westward; but it is the most convenient to turn ït eastward, hecause the brass meridian is graduated on the east side. |