the globe eastward till the index has passed over 34 hours, all the required places will be under the brass meridian, as the eastern coast of Newfoundland, Cayenne, part of Paraguay, &c Or, The difference of me between London, the given place, and the required places, is 3 hours 30 min. 3 h. 30 m. 60 4)210 m. 529 60 4)120 30 m. The difference of longitude between the place and the required places is 52° 30% The hour at the required places being ear ier than that at the given place, they le 52° 30' westward of the given place. Hence, all places situated in 52° 30′ west longitude from London are the places sought, and will be found to be Cayenne, &c. as above. 2. When it is two o'clock in the afternoon at London, at what places is it half past five in the afternoon? Answer. Here the difference of time between Loudon, the given place, and the required places, is 34 hours; but the time at the required places is later than at London The operation will be the same as in example 1, only the globe must be turned 34 hours towards the west, because the required places will be in east longitude, or eastward of the given place. The places sought are the Caspian sea, western part of Nova Zembla, the island of Socotra, eastern part of Madagascar, &c. 3. When it is past four in the afternoon at Paris, where is it noon? 4. When it is past seven in the morning at Ispahan, where is it noon? 5. When it is noon at Madras, where is it past six o'clock in the morning? 6. At sea in latitude 40° north, when it was ten o' clock in the morning by the time-piece, which shows the hour at London, it was exactly 9 o'clock in the morning at the ship, by a correct celestial observation. In what part of the ocean was the ship? 7. When it is noon at London, what inhabitants of the earth have midnight? 8. When it is ten o'clock in the morning at London, where is it ten o'clock in the evening? PROBLEM XX. To find the sun's longitude (commonly called the sun's place in the ecliptic) and his declination. Rule. Look for the given day in the circle of months on the horizon, against which, in the circle of signs, are the sign and degree in which the sun is for that day. Find the same sign and degree in the ecliptic on the surface of the globe; bring the degree of the ecliptic, thus found, to that part of the brass meridian which is numbered from the equator towards the poles, its distance from the equator, reckoned on the brass meridian, is the sun's declination.-This problem may be performed by the celestal globe, using the same rule. OR, BY THE ANALEMMA.* Bring the analemma to that part of the brass meridian which is numbered from the equator towards the poles, and the degree on the brass meridian, exactly above the day of the month, is the sun's declination. Turn the globe till a point of the ecliptic, correspondent to the day of the month, passes under the degree of the sun's declination, that point will be the sun's longitude or place for the given day. If the sun's declination be north, and increasing, the sun's longitude will be somewhere between Aries and Cancer. If the declination be decreasing, the longitude will be between Cancer and Libra. If the sun's declination be south, and increasing, the sun's longitude will be between Libra and Capricorn; if the declination be decreasing, the longitude will be between Capricorn and Aries. The sun's longitude and declination are given in the second page of every month, in the Nautical Almanac, for every day in that month; they are likewise given in White's Ephemeris, for every day in the year. The Analemma is properly an orthographic projection of the sphere on the plane of the meridian; but what is called the Analemma on the globe, is a narrow slip of paper, the length of which is equal to the breadth of the torrid zone It is pasted on some vacant piace on the globe in the torrid zone, and is divided into months, and days of the months, correspondent to the sun's declination for every day in the year It is divided into two parts; the right hand part begins at the winter solstice, or December 21st, and is reckoned upwards towards the summer solstice, or June 21st, where the left hand part begins, which is reckoned downwards in a similar manner, or towards the winter solstice. On Cary's globes the Analemma somewhat resembles the figure 8 It appears to have been drawn in this shape for the convenience of showing the equation of time, by means of a straight line which passes through the middle of it. The equation of time is placed on the horizon of Bardin's globes. Examples. 1. What is the sun's longitude and declination on the 15th of April? Answer. The sun's place is 26° in P, declination 10° N. 2. Required the sun's place and declination for the following days? January 21. May 18. September 9. February 7. June 11. October 16. PROBLEM XXI. To place the globe in the same situation, with respect to the sun, as our earth is at the equinoxes, at the summer solstice, and at the winter solstice, and thereby to show the comparative lengths of the longest and shortest days.* 1. FOR THE EQUINOXES. Place the two poles of the globe in the horizon; for at this time the sun has no declination, being in the equinoctial in the heavens, which is an imaginary line standing vertically over the equator on the earth. Now, if we suppose the sun to be fixed, at a considerable distance from the globe, vertically over that point of the brass meridian which is marked O, it is evident that the wooden horizon will be the boundary of light and darkness on the globe, and that the upper hemisphere will be enlightened from pole to pole. Meridians, or lines of longitude, being generally drawn on the globe through every 15 degrees of the equator, the sun will apparently pass from one meridian to another in an hour. If you bring the point Aries on the equator to the eastern part of the horizon, the point Libra will be in the western part thereof; and the sun will appear to be setting to the inhabitants of * In this problem, as in all others where the pole is elevated to the sun's declination, he sun is supposed to be fixed, and the earth to move on its axis from west to east. ihe author of this work has a little brass ball made to represent the sun; this ball is fixed upon a strong wire, and when used, slides out of a socket like an acromatic telescope. The socket is made to screw to the brass meridian (of any giobe) over the sun's declination, and the little brass ball, representing the sun, stands over the declination, at a consid erable distance from the globe. : London and to all places under the same meridian: let the globe be now turned gently on its axis towards the east, the sun will appear to move towards the west, and, as the different places successively enter the dark hemisphere, the sun will appear to be setting in the west. Continue the motion of the globe eastward, till London comes to the western edge of the horizon; the moment it emerges above the horizon, the sun will appear to be rising in the east. If the motion of the globe on its axis be continued eastward, the sun will appear to rise higher and higher, and to move towards the west; when London comes to the brass meridian, the sun will appear at its greatest height; and after London has passed the brass meridian, he will continue his apparent motion westward, and gradually diminish in altitude till London comes to the eastern part of the horizon, when he will again be setting. During this revolution of the earth on its axis, every place on its surface has been twelve hours in the dark hemisphere, and twelve hours in the enlightened hemisphere: consequently the days and nights are equal all over the world; for all the parallels of latitude are divided into two equal parts by the horizon, and in every degree of latitude there are six meridians between the eastern part of the horizon and the brass meridian; each of these meridians answers to one hour; hence, half the length of the day is six hours, and the whole length twelve hours. If any place be brought to the brass meridian, the number of degrees between that place and the horizon (reckoned the nearest way) will be the sun's meridian altitude. Thus, if London be brought to the meridian, the sun will then appear exactly south, and its altitude will be 38 degrees; the sun's meridian altitude at Philadelphia will be 50 degrees; his meridian altitude at Quito 90 degrees; and here, as in every place on the equator, as the globe turns on its axis, the sun will be vertical. At the Cape of Good Hope the sun will appear due north at noon, and his altitude will be 55 degrees. 1 2. FOR THE SUMMER SOLSTICE.-The summer solstice, to the inhabitants of north latitude, happens on the 21st of June, when the sun enters Cancer, at which time his declination is 23° 28′ north. Elevate the north pole 23 degrees above the northern point of the horizon, bring the sign of Cancer in the ecliptic to the brass meridian, and over that degree of the brass meridian under which this sign stands, let the sun be supposed to be fixed at a considerable distance from the globe. While the globe remains in this position, it will be seen that the equator is exactly divided into two equal parts, the equinoctial point Aries being in the western. part of the horizon, and the opposite point Libra in the eastern part, and between the horizon and the brass meridian (counting on the equator) there are six meridians, each fifteen degrees, or an hour apart: consequently, the day at the equator is twelve hours long. From the equator northward, as far as the Arctic circle, the diurnal arches will exceed the nocturnal arches ; that is, more than one half of any of the parallels of latitude will be above the horizon, and of course less than one half will be below; so that the days are longer than the nights. All the parallels of latitude within the Arctic circle will be wholly above the horizon, consequently, those inhabitants will have no night. From the equator southward, as far as the Antarctic circle, the nocturnal arches will exceed the diurnal arches; that is, more than one half of any one of the parallels of latitude will be below the horizon; and, consequently, less than one half will be above. All the parallels of latitude within the Antarctic circle will be wholly below the horizon, and the inhabitants, if any, will have twilight or dark night. From a little attention to the parallels of latitude, while the globe remains in this position, it will easily be seen that the arches of those parallels which are above the horizon, north of the equator, are exactly of the same length as those below the horizon, south of the equator; consequently, when the inhabitants of north latitude have the longest day, those in south latitude have the longest night. It will likewise appear, that the arches of those parallels which are above the horizon, south of the equator, are exactly of the same length as those below the horizon, north of the equator; therefore, when the inhabitants who are situated south of the equator have the shortest day, those who live north of the equator have the shortest night. |