number of degrees to the declination, will be constantly illuminated, while a similar portion around the other pole will be always in darkness. At the tropics, therefore, the portions of the earth which have a day or night of twenty-four hours, will extend to 23° 28'. The circles which bound these portions of the earth are termed polar circles, and also the arctic, and antarctic circles, that to the north being the arctic.

The Seasons.] The change in the declination of the sun not only occasions a variation in the length of the days and nights, but is also the cause of the difference in the heat at different times of the year. The quantity of solar rays which fall upon any part of the surface of the earth will be greater the less their degree of obliquity be: for as the obliquity is increased, the same number of rays must be spread over a wider surface, and a change in the declination must evidently alter the angle at which the rays impinge upon any part of the earth. The difference too in the time which the sun continues above the horizon, must also occasion a variation in the temperature: for the longer the sun shines upon any place a larger portion of heat will be accumulated.

From

The equinoxes and solstices divide the year into four seasons. the vernal equinox to the summer solstice is with us the astronomical spring. From the summer solstice to the autumnal equinox is our summer. The time betwixt the autumnal equinox and the winter solstice is our autumn; and from the winter solstice to the vernal equinox is our winter. In the southern hemisphere the seasons are reversed: it being spring with them when autumn with us, and their summer corresponding to our winter. The orbit of the earth being an ellipse, in one of the foci of which the sun is situated, and the earth during our summer being in that part of her orbit which is farthest from the sun, the latter body will, from the nature of the physical laws which regulate the movements of the planets, employ a longer time in passing through that season than our winter. This occasions the summer in the northern hemisphere to be about eight days longer than that which the inhabitants of the southern hemisphere enjoy.

Zones or Climates.] The ancients divided the earth into different zones, which they termed climates, by means of the length of the longest day increasing as we recede from the equator. This mode of dividing the earth is not now much in use, but in perusing the works of ancient authors upon history and geography, it is proper that we should be acquainted with it. A climate, according to the ancients, is a portion of the earth's surface bounded by two parallels so far distant from each other that the longest day at the one differs half-an-hour from the longest day at the other. Almost all the places known to the ancients were comprehended in seven such climates, the southern boundary of the first climate being that parallel in which the longest day is twelve hours and three quarters. The climates were denominated from some remarkable place situated about the middle of them. Their names, beginning with the most southern, were Meroe, Syene, Alexandria, Rhodes, Rome, the Borysthenes, and the Riphean Mountains. The ancients expressed the position of places, simply by saying they were in such a particular climate. When the moderns divide the earth into climates, they begin at the equator, and reckon by the difference of half-an-hour, in the length of the longest day till we reach the polar circles; after that they are counted by the increase of a month, in the time during which there is constant day. The climates between the equator and polar

circles are termed hour climates, and those beyond these circles month climates.

The tropics and polar circles divide the earth into five zones: that part of the earth which lies between the tropics, receiving constantly the solar rays in a direction very little oblique, is called the torrid zone. The parts which lie between the tropics and polar circles, receiving the sun's rays more obliquely, are called temperate zones; and the regions within the polar circles, being deprived of the sun's rays during a great part of the year, and during the other part receiving these rays very obliquely are termed the frigid zones. Some geographers make the zones to be six in number, by dividing the torrid zone into two parts by the equator. Ascii, Amphiscii, Heteroscii, and Periscii.] The inhabitants of the different regions of the earth are sometimes distinguished by the ancient geographers, according to the direction of their shadows. When the sun at mid-day is vertical to any place, the inhabitants of that place were said to be ascii, that is, without shadow. All the inhabitants between the tropics must be ascii twice a year. The inhabitants of the torrid zone too, having the sun sometimes to the north, and sometimes to the south, will project shadows directed by turns towards either pole, and they were therefore said to be amphiscii, that is having both kinds of shadows. Those who inhabit the temperate zones were called heteroscii, because their shadows fall in opposite directions. Within the polar circles the inhabitants must, for a while, project shadows in all directions, and they are therefore said to be periscii.

Periæci, and Antiæci.] The seasons which the inhabitants of opposite places on the earth enjoy at the same time, as well as the hours of the day at these places, being contrasted, give rise to certain distinctions with which it is also necessary to be acquainted. Those who live under opposite meridians, at equal distances from the equator, and upon the same side of it, are termed periæci. They have the same seasons, but reckon at the same instant opposite hours: it being midnight with the one when mid-day with the other. Those who live under the same meridian on opposite sides of the equator, and at equal distances from it, are called antiæci. They have the seasons at opposite times, but reckon at the same instant the same hours. The people who live at equal distances from the equator, and under opposite meridians, are termed antechthones, or antipodes. They have both the seasons and the hours of the day at opposite times.

Latitude and Longitude.] We shall next explain the methods of determining the relative position of the different parts of the earth's surface.

The position of an object being, of course, entirely a matter of relation, the first thing to be done in finding the place of any body, is to fix upon some known points or lines in reference to which the position may be determined. The simplest way of determining the position of points

Y

A

Fig. 4.

situated upon a plane, is by ascertaining their distance from two lines drawn on the same plane, and intersecting each other at right angles. Thus, let S be a given point, and A X, A Y, two lines drawn on the plane on which S is situated, and intersecting each other at right angles in A. Draw SQ -x parallel to A X, and S P parallel to A Y. It is evident, that if the magnitude of SP

and SQ be ascertained, the position of S is known. Points situated upon the surface of a sphere, may, in a similar manner, be referred to two great circles of the sphere drawn at right angles to each other. For, suppose in the above figure, the lines of reference A X and A Y to be great circles of a sphere, then SP and SQ will be arcs of parallel small circles, and the situation of S will be known if the length of those curve lines be ascertained. Even without determining the absolute magnitude of SP and SQ, the relative position of S will be found by merely ascertaining the number of degrees contained in them, or in the similar arcs AP and AQ. It is in this latter way that the relative position of the different parts of the earth's surface is determined. Two great circles of the celestial sphere are made choice of, and the position of any place is found by ascertaining the distance of its zenith from these circles. The arcs upon the earth corresponding to the celestial arcs, not being exactly circular, cannot be proportional to them, as we shall afterwards see.

With regard to the circles of reference made choice of, all geographers have agreed in adopting the equator, or that great circle which is perpendicular to the earth's axis, as one of the two. The motion of the earth, however, does not point out any of the meridians as more particularly fit to be made choice of than another: and one of them, therefore, must be adopted upon arbitrary principles. The ancients made choice for their first meridian of that one which passes through the Fortunate or Canary Isles, because these islands were at the most western limit of the then known earth. Various others have been successively adopted; but in almost all countries, that meridian which passes through the principal observatory of the kingdom is now employed. Thus the English count from the meridian of the observatory of Greenwich, and the French from that of the observatory of Paris. The reason of this is, that tables of astronomical observations are of essential use in finding the longitude, as we shall soon see; and the position of the heavenly bodies at any given time, is most conveniently referred to the meridian of the place where the observations are made.

The distance of a place from the equator is termed latitude, and its distance from the first meridian longitude. The terms latitude and longitude had their origin from the earth, as known to the ancients, being of much greater extent in the direction of the equator, than in that of the meridian. The latitude and longitude must be expressed in such manner that it may be known on which side of the equator and first meridian the place is situated. This is easily accomplished. The latitude is called north or south, according as the place lies to the north or south of the equator. It is counted from the equator towards the poles, and can never exceed 90 degrees. The longitude is expressed in two different ways. Beginning at the first meridian and proceeding eastward, it may be reckoned, in the same direction, completely round the globe, and may in that way extend to 360 degrees. The other method is to divide it into east and west longitude, in which case it can never exceed 180 degrees. The mode of converting the longitude expressed in one of those ways into an expression of similar import in the other, is sufficiently obvious, and scarcely requires to be noticed. We shall merely give a few examples. Long. 143° 10′ 55′′ East long. 143° 10′ 55′′. Long. 236° 25′ 35′′ West long. 123° 34′ 25′′, and West long. 14° 44′ 10" Long. 345° 15' 50".

Method of Reducing the Longi

Different first meridians being

tude to any Given Meridian. employed in different countries, it is often necessary to reduce the longitude estimated in reference to one meridian to that of another. This may be easily done if we know the difference of longitude between the two meridians, and the direction in which it lies, whether east or west: for we have only to add or subtract the difference. To illustrate this, we shall, as in the former case, merely give one or two examples. The meridian of Paris is 2° 20′ 15′′ east from the meridian of Greenwich. A place, therefore, in 59° 7′ long. from Paris, will be 61° 27′ 15" from Greenwich. If, in 359° 15', it will be in 1° 35' 15" of Greenwich longitude.

If the earth were exactly spherical, the degrees of latitude upon its surface, being parts of a great circle, would be all equal to each other. The degrees of longitude, however, would continually diminish as we recede from the equator, and at the pole they would converge to a point. The magnitude of a degree of longitude in any latitude would be easily found, for the radius of the parallel on which it is measured would be equal to the cosine of the latitude, and the circumferences of circles are to one another as their radii. A degree of longitude, therefore, would be equal to a degree on the equator, multiplied by the cosine of the latitude, if the radius of the sphere be reckoned unity. The earth being almost exactly spherical, the degrees of latitude upon its surface will be very nearly equal, and those of longitude will diminish in much the same manner as in an exact sphere. Tables of the degrees of longitude, therefore, on the earth may be found with sufficient accuracy from the above formula. We shall afterwards have an opportunity, when considering the magnitude and figure of the earth, of inquiring how much the degrees of latitude increase as we approach the poles.

Having discussed these preliminary matters, we shall now explain the different methods for ascertaining the latitude and longitude that have hitherto been discovered. In doing so, however, we shall content ourselves with pointing out the general principles upon which those methods depend, leaving the subject to be more fully discussed by those who treat of navigation and astronomy. We begin with the latitude. Method of finding the Latitude.] The ascertaining both of the latitude and longitude we have seen is equivalent to the measurement of celestial arcs. The arcs, which it is necessary to determine in order to find the latitude of any place, is that intercepted by the equator and the zenith. This arc cannot be directly measured, the position of the equator not being marked out in the heavens. It may be found,

however, from the following considerations:-The change which takes place on the altitude of the stars when an observer removes from one part of the earth to S another, north or south, is equal to the variation in the latitude; thus, let AHh be a meridian, A A' two positions of an h observer, and Hh, H'h' the corresponding horizons. Draw AC and A'C perpendicular to Hh and H'h' respectively. These lines h' will not really meet at the centre of the earth, though so drawn in the figure, but this will not affect the reasoning. When

the observer has arrived at A', the star S will appear more elevated than at A by the arc hh'. But that arc is equal to the arc A A'. For the arcs A h and A'h' are equal, each of them being a quadrant. Take away the common arc A'h, and there remains A A' equal to h h'. The difference in the latitude of any two places, therefore, may be ascertained by finding the difference in the meridian altitudes of any star at these places. But farther, since, to a person on the terrestrial equator, the poles must be situated in the horizon, and the celestial equator directly over his head, the elevation of the pole above the horizon must be equal to the latitude, and the meridian height of any point of the equator above the horizon must be equal to its complement. Again, the inclination of the planes in which the stars move must be equal to the complement of the latitude. For, in the above figure, suppose AC to be the equator To an observer at A', the inclination of the planes of the equator and horizon is measured by the arc A H', the lines AC and H'C being drawn in these planes, and at right angles to their common intersection. But that are being the height of the equator, is equal to the complement of the latitude, and since all the planes in which the stars move are parallel to each other, the truth of our proposition is manifest. The latitude of any place, therefore, may be discovered by finding at that place, the elevation of the pole,—the height of the equator,-the altitude of any star whose distance from the pole, or from the equator is known,— or the inclination of the planes in which the stars move with the horizon. We shall now show how these different problems may be determined.

The stars which never set furnish us with the means of ascertaining the height of the pole. These stars describe circles around it, and must pass the meridian twice a day. By ascertaining the altitude of any one of them when it passes the meridian above and below, the elevation of the pole will be ascertained, for it must evidently be equal to the arithmetical mean between the two altitudes. The height of the equator may be ascertained in the following manner:-Find all those stars which are 90 degrees distant from the pole. Those stars will be in the equator, and by finding the altitude of any one of them when it passes the meridian, the equatorial height will be determined. Tables of the declination of the stars, or their distance from the equator have been formed, which enable us to determine the latitude from the ascertained altitude of any star, for the complement of the latitude will be equal to the sum or difference of the meridian height and declination, according as the star is situated to the south or the north of the equator. The declination of the sun, is, from the causes formerly explained, constantly varying, and allowance must be made for this, in deducing the latitude from the height of the sun. The laws of the variations in the sun's declination being known, tables of the daily changes in that declination have been formed, which enable us to find the latitude from the meridian altitude of the sun at the given place, on a particular day being known, as accurately as if the declination of that luminary continued always invariable. This last method is a very common mode of determining the problem.

The inclination of the planes in which the stars move with the plane of the horizon, may be found by ascertaining the distance of any star from the southern point of the horizon when it rises, which is termed the azimuth of the star, and by also finding its meridian altitude. This we shall now show. The investigation requires only a slight acquaint

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