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VII. To find at what hour the sun rises and sets any day in the year
at a place, the latitude of which does not exceed 66) degrees ; and also on what point of the compass it rises and sets.
Rectify the globe for the latitude of the place ; bring the sun's place to the meridian, and set the index to 12; then turn the sun's place to the eastern edge of the horizon, and the index will point out the hour of rising; if you bring it to the western edge of the horizon, the index will sbew the hour of setting.
Thus on the 10th day of April, the sun rises at half an hour after five o'clock at Boston, and sets half an hour before seven.
Note. In summer the sun rises and sets a little to the northward of the east and west points; and in winter a little to the southward of them. If, therefore, when the sun's place is brought to the eastern and western edges of the horizon, you look on the horizon directly against the little patch, you will see the point of the compass on which the sun rises and sets that day.
VIII. To find the length of the longest and shortest day at a given
Rectify the globe for that place; if its latitude be north, bring the beginning of Cancer to the meridian; set the index to 12, then bring the same degree of Cancer to the east part of the horizon, and the index will show the time of the sun's rising, which doubled, gives the length of the shortest night.
If the same degree be brought to the western side, the index will show the time of the sun's setting, which doubled will give the length of the longest day.
If we bring the beginning of Capricorn to the meridian, and proceed in all respects as before, we shall have the length of the longest night and shortest day.
Thus in Egypt and Florida the longest day is 14 hours, and the shortest night 10 hours. The shortest day is 10 hours, and the longest night 14 hours.
At Petersburg, the capital of Russia, the longest day is about 191 hours, and the shortest night 41 hours. The shortest day 41 hours, and the longest night 19 hours.
Note. In all places near the equator, the sun rises and sets at 6 o'clock, through the year. Thence to the polar circles, the days increase as the latitude increases ; so that at those circles the longest day is 24 hours, and the longest night the same. From the polar circles, to the poles, the days continue to lengthen into weeks and months; so that at the pole, the sun shines for six months together in summer, and is below the horizon six months in winter. Note also, that when it is summer with the northern inhabitants, it is winter with the southern, and the contrary; and every part of the world partakes of an equal share of light and darkness.
To measure the distance from one place to another.
Only take their distance with a pair of dividers, and apply it to the equinoctial, that will give the number of degrees between them, which, being multiplied by 60, (the number of geographical miles in one degree) gives the exact distance sought: or, extend the quadrant of altitude from one place to another, that will show the number of degrees in like manner, which may be reduced to miles as before.
Thus the distance from London to Madrid is 11} degrees. From Paris to Constantinople 194 degrees. From Bristol in England to Boston 45 degrees, which, multiplied by 69: (the number of English miles in a degree) gives 3127] miles.
Note. No place can be further from another than 180 degrees, that being half the circumference of the globe, and consequently the greatest distance.
PROBLEMS SOLVED ON THE CELESTIAL GLOBE.
The equator, ecliptic, tropics, polar circles, horizon and brazen meridian are exactly alike on both globes. Both also are rectified in the same manner.
N. B. The sun's place for any day of the year stands directly against that day on the horizon of the celestial globe, as it does on that of the terrestrial.
The latitude and longitude of the celestial bodies are reckoned in a very different manner from the latitude and longitude of places on the earth ; for all terrestrial latitudes are reckoned from the equator, and longitudes from the meridian of some remarkable place, as of London by the British, and of Paris by the French. But the astronomers of all nations agree in reckoning the latitudes of the moon, planets, comets and fixed stars, from the ecliptic; and their longitudes, and that of the sun from the equinoctial colure, and from that semicircle of it, which cuts the ecliptic at the beginning of Aries; and thence eastward, quite round to the same semicircle again. Consequently those stars, which lie between the equinoce tial and the northern half of the ecliptic, have north declination, but south latitude ; those which lie between the equinoctial and the southern half of the ecliptic have south declination, but north latitude ; and all those which lie between the tropics and poles have their declination and latitudes of the same denomination.
PROB. I. To find the right ascension and declination of the sun, or
any fixed star, :
Bring the sun's place in the ecliptic to the brazen meridian ; then that degree in the equinoctial which is cut by the meridian is the sun's right ascension ; and that degree of the meridian which is over the sun's place is its declination. Bring any fixed star to the meridian, and its right ascension will be cut by the meridian in the
equinoctial; and the degree of the meridian that stands over it is its declination. So that right ascension and declination on the celestial globe are found in the same manner as longitude and latitude on the terrestrial.
II. To find the latitude and longitude of a star.
If the given star be on the north side of the ecliptic, place the 90th degree of the quadrant of altitude on the north pole of the ecliptic, where the twelve semicircles meet, which divide the ecliptic into the twelve signs; but if the star be on the south side of the ecliptic, place the 90th degree of the quadrant on the south pole of the ecliptic: keeping the 90th degree of the quadrant on the proper pole, turn the quadrant about, until its graduated edge cut the star; then the number of degrees on the quadrant, between the ecliptic and the star, is its latitude ; and the degrees of the ecliptic cut by the quadrant is the star's longitude, reckoned according to the sigo in which the quadrant then is.
METHODS OF FINDING THE LATITUDES AND LONGITUDES OF PLACES FROM
What is meant by latitude and longitude has already been sufficiently explained; it remains that we show the methods of finding both by celestial observations.
Of finding the latitude. There are two methods of finding the latitude of any place. The first is by observing the height of the pole above the horizon; the second by discovering the distance of the zenith of the place from the equator. The elevation of the pole is always equal to the latitude; and is thus found. As there is no star, towards which either pole points directly, fix upon some star near the pole. Take its greatest and least height when it is on the meridian. The half of these two sums (proper allowance being made for the refraction of the atmosphere) will be the latitude. The other method is this. The distance of the zenith of any place, from the celestial equator, measured in degrees on the meridian, is equal to the latitude. Fix upon some star lying in or near the equator. Observe its zenith distance when it is in the meridian. If it is directly in the equator this will be the latitude. If it is nearer than the equator add its declination to its zenith distance; if farther, deduct its declination from its zenith distance; the sum or difference will be the latitude.
Of finding the longitude. There are three approved methods of discovering the longitude ; 1st, By the moon's distance from the sun or a fixed star; 2d, By a time-keeper; 3d, By an eclipse of the moon, or of one of Jupiter's satellites. The last only will be described in this place. By the earth's rotation on its axis in 24 hours, the sun appears to describe, in the same space of time, an apparent circle of 360 degrees in the heavens. The apparent motion of the sun is therefore 15 degrees in an hour. If two places
therefore differ 15 degrees in longitude, the sun will pass the meridian of the eastern place 1 hour sooner than the western. The commencement of a lunar eclipse is seen, at the same moment of time, from all places where the eclipse is visible. If then an eclipse of the moon is seen to commence, at one place, at 12 o'clock at night, and at another place, at 1 o'clock; the places differ 15 degrees in longitude, and the last lies eastward of the first. The nautical almanac, published in London, and calculated for the meridian of Greenwich, contains the exact time when the eclipses of the moon commence at that place. When the time of the commencement of an eclipse at any place has been observed, a comparison of it with the time in the almanac will determine the difference of time between the place and Greenwich. If the hour is later than the hour in the almanac, the place is situated to the east of Greenwich ; if earlier, to the west. As 1 hour in time is 15 degrees in motion, so is one minute, 15 minutes, and one second, 15 seconds. This would be the easiest and most accurate method of ascertaining the longitude, if we could determine the precise moment of time when a lunar eclipse commences. But this cannot, in general, be determined nearer than 1 minute, and often not nearer then 2 or 3 minutes. A variance of 1 minute would make the difference of 15 minutes or miles in longitude ; of 2 minutes, 30 minutes; and of 3 minutes, 45 minutes.
This objection does not lie against the method of ascertaining the longitude by the eclipses of Jupiter's satellites. The telescope enables us to determine the precise moment when they are immersed in the shadow of their primary. The hour at the place, therefore, being ascertained, and compared with the hour in the almanac, we are enabled to determine, as before, the exact difference of longitude.
On the equator a degree of longitude is equal to 60 geographical miles ; and of course a minute on the equator is equal to 1 geographical mile. But as all the meridians cut the equator at right angles and approach nearer and nearer till they cross each other at the poles, it is obvious that the degrees of longitude decrease as you go from the equator to the pole.
A TABLE Showing the number of geographical miles contained in a degree
of longitude in each parallel of latitude from the equator.
A map is the representation of some part of the earth's surface, delineated on a plane, according to the laws of projection; for as the earth is of a globular form no part of its spherical surface can be accurately exhibited on a plane.
Maps differ from the globe in the same manner as a picture does from a statue. The globe truly represents the earth; but a map not more than a plane surface represents one that is spherical. But although the earth can never be exhibited exactly by one map, yet by means of several of them, each containing about 10 er