The quadrant of altitude is a thin slip of brass, one edge of which is graduated into ninety degrees and their quarters, equal to those of the meridian. To one end of this is fixed a brass nut and screw, by which it is put on and fastened to the meridian; if it be fixed in the zenith, or pole of the horizon, then the graduated edge represents a vertical circle passing through any point of the horizon, to which it is directed.

Beside these, there are several circles, described on the surfaces of both globes; as the equator, ecliptic, circles of longitude and right ascension, the tropics, polar circles, parallels of latitude and declination, on the celestial globe; and on the terrestrial, the equator, ecliptic, tropics, polar circles, parallels of latitude, hour circles or meridians, to every 15 degrees; and on some globes, the spiral rhumbs flowing from several centres, called flies.

In using the globes keep the graduated side of the meridian towards you, unless the problem require a different position. With respect to the terrestrial, we are to suppose ourselves situated at a point on its surface; with respect to the celestial, at its centre. The motion of the former represents the real diurnal motion of the earth; that of the latter, the apparent diurnal motion of the heavens.

The following PROBLEMS, as being most useful and entertaining, are selected from a great variety of others, which are easily solved with a terrestrial globe, fitted up with the aforesaid appurte

nances.

The latitude of a place being given, to rectify the globe for that place.

Let it be required to rectify the globe for the latitude of Boston, 42 degrees 23 minutes north.

Elevate the north pole, till the horizon cut the brazen meridian in 42 23, and the globe is then rectified for the latitude of Boston. Bring Boston to the meridian, and you will find it in the zenith, or directly on the top of the globe. And so of any other place.

II. To find the latitude and longitude of a place on the globe.

Bring the given place under that half of the graduated brazen meridian, where the degrees begin at the equator, and under the graduated side of it; then the degree of the meridian over it shows the latitude; and the degree of the equator, under the meridian, shows the longitude.

Thus Boston will be found to lie in about 42 23 north latitude, and 71 west longitude from Greenwich.

III. To find the sun's place in the ecliptic,

Look the day of the month on the horizon, and opposite to it, you will find the sign and degree the sun is in that day. Thus on

the 25th of March, the sun's place is 4 degrees in Aries. Then look for that sign and degree in the ecliptic line marked on the globe, and you will find the sun's place; there fix on a small black patch, so is it prepared for the solution of the following problems. Note. The earth's place is always in the sign and degree opposite to the sun; thus, when the sun is 4 degrees in Aries, the earth is 4 degrees in Libra; and so of any other.

IV. To find the sun's declination, that is, its distance from the equinoctial line, either northward or southward.

Bring its place to the meridian; observe what degree of the meridian lies over it, and that is the declination. If the sun lie on the north side of the line, the declination is north, but if on the south side the declination is south.

Thus on the 20th of April the sun has 11 degrees of north declination, but on the 26th of October, it has 12 of south declination.

Note. The greatest declination can never be more, either north or south, than the distance of a tropic from the equator.

V. To find where the sun is vertical on any day.

Bring the sun's place to the meridian, observe its declination, or hold a pen or wire over it; then turn the globe round, and all those countries which pass under the wire, will have the sun vertical, or nearly so, that day at noon. Thus on the 16th day of April, the inhabitants of the north part of Terra Firma, Porto-Bello, Philippine Isles, southern parts of India, Abyssinia, Ethiopia, and Guinea, have the sun over their heads that day at 12 o'clock.

Note. This appearance can only happen to those who live in the torrid zone.

VI. To find at any hour of the day, what o'clock it is at any place.

Bring the place where you are, to the brass meridian; set the index to the hour, turn the globe till the place you are looking for come under the meridian, and the index will point out the time required.

Thus when it is 10 o'clock in the morning, at Boston, it is 24 minutes past 12 at Olinda in Brazil, and 8 at Mexico in NewSpain; the former being at 35 degrees west longitude, and the latter at 100 degrees west longitude.

Note. By this problem you may likewise see at one view, in distant countries, where the inhabitants are rising, where breakfasting, dining, drinking tea, where going to assemblies, and where to bed.

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 661 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 shew 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 place.

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 19 hours, and the shortest night 4 hours. hours, and the longest night 19 hours.

longest day is about The shortest day 41

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.

IX. 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 19 degrees. From Bristol in England to Boston 45 degrees, which, multiplied by 691 (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.

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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 equinoctial 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 sign in which the quadrant then is.

METHODS OF FINDING THE LATITUDES AND LONGITUDES OF PLACES FROM CELESTIAL OBSERVATIONS.

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