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.

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 e 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. 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.

If

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 or

20 degrees of latitude, the representation will not fall very much short of the globe in exactness; because such maps, if joined together, would form a convex surface nearly as round as the globe itself.

Cardinal Points. The upper part of the map is considered as the north; the bottom is south, being opposite to the north; the east is on the right hand, the face being turned to the north; and the west on the left hand, opposite to the east. From the top to the bottom are drawn meridians, or lines of longitude; and from side to side, parallels of latitude. The meridians and parallels are marked with degrees of latitude or longitude, by means of which, and the scale of miles, which is commonly placed in a corner of the map, the situations, distances, &c. of places may be found as on the artificial globe. Thus to find the distance of two places, suppose Philadelphia and Boston, by the map, we have only to measure the space between them with the compasses, or a piece of thread, and to apply this distance to the scale of miles, which shows that Boston is 286 miles distant in a straight line from Philadelphia. If the places lie directly north or south, east or west, from one another, we have only to observe the degrees on the meridians and parallels, and by reducing these to miles, we obtain the distance without measuring. Rivers are described in maps by black lines, and are wider toward the mouth than toward the head or spring. Mountains are sketched on maps as on a picture. Forests and woods are represented by a kind of shrub; bogs and morasses, by shades; sands and shallows are described by small dots; and roads usually by double lines. Near harbors, the depth of the water is expressed by figures, representing fathoms.

WINDS.

Air is a fine, invisible fluid, surrounding the earth, and extending some miles above its surface; and that collection of it, together with the bodies it contains, circumscribing the earth, is called the atmosphere.

Few natural bodies have been the subject of more experiments than the air; and from these it appears, that it is both heavy and elastic. By its gravity it is capable of supporting all lighter bodies, as, smoke, vapors, odors, &c. And by its elasticity, a small volume of air is capable of expanding itself in such a manner as to fill a very large space, and also of being compressed into a much smaller compass. Cold has the property of compressing air, and heat of expanding it. But as soon as the cause of expansion or compression is removed, it will return to its natural state. Hence, if an alteration be made in any part of the atmosphere, either by heat or cold, the neighboring parts will be put in commotion by the effort which the air always makes to recover its former state. Wind is nothing more than a stream or current of air, capable of very different degrees of velocity, and generally blowing from one point of the horizon to its opposite. The horizon, like all