are called the poles of the ecliptic; which points are 231° from the celestial poles.

This No. should be illustrated and explained to young pupils ; familiar examples will readily occur to the instructer.

63. Hence the latitude of a heavenly body is its distance from the ecliptic, on a secondary to the ecliptic passing through it; and, like latitude on the earth, can never exceed 90°. The longitude of a heavenly body is the distance of a secondary to the ecliptic passing through it, from some uniform prime secondary. But the longitude of heavenly bodies, unlike longitude on the earth, is reckoned only eastward ; consequently it may extend to 360°. It is usually stated in signs, degrees, minutes, &c.; and the prime secondary, from which it is reckoned, cuts the ecliptic in the beginning of the sign Aries, a point where the celestial equator crosses the ecliptic. Thus, if a secondary, passing through a heavenly body, cuts the ecliptic, say 18° in the sign Capricorn, the longitude of that body is 9 signs, 18°.

If a celestial globe be at hand, the pupil may be exercised in finding the latitude and longitude of some of the principal stars, &c." See Appendix, Sect. VIII. Prob. XIX.

64. But it is often important to know the distance of a heavenly body from the celestial equator, as well as from the ecliptic. This distance is its declination, and is reckoned on a meridian as latitude is on the earth. Its distance from the beginning of Aries, reckoned on the equator, is its right ascension ; which, like celestial longitude, is reckoned through the whole circle, or 360°.

The learner should have a distinct idea of the difference between celestial latitude and declination, that one is reckoned from the ecliptic and the other from the equator. Also of longitude and right ascension, that one is reckoned on the ecliptic and the other on the equator; and both from the same point, viz. the beginning ef Aries,

65. Let us return to the consideration of terrestrial

latitude and longitude. As the latitude of a place is its distance from the equator measured on its meridian, and all meridians are great circles and consequently equally large, it is obvious that a degree, or 3ő part, of one is equal to the same part of another. Hence degrees of latitude are all of the same absolute length, containing 60 geographical, or 69 statute miles of 320 rods. Thus, if two places on the same meridian, whether near the equator br distant from it, differ in latitude 2°, their absolute distance from each other is 60 X 2 = 120 geographical miles, or 691 X 2 = 139 statute miles.

By The statements in this No. are not strictly true, because the earth is not a perfect globe, as will be shown hereafter. But the earth is so nearly a perfect sphere, that it is always so represented on maps and globes.

66. With regard to longitude, the case is different. The equator is a great circle like a meridian; and a degree, or já part of it, is equal to the same part of meridian; and consequently a degree of longitude on the equator is equal to a degree of latitude. But the parallels of latitude are not great circles, but are continually becoming less as they are farther from the equator and nearer the poles. Consequently a degree, or são part, of one parallel is not equal to the same part of another parallel, nor to the same part of the equator. For example, the places x and v are 20° apart (Pl. III. fig. 1.); but obviously they are not so many miles apart as they would be, if situated on the same meridians at the equator; and further apart, than if situated on the same meridians nearer the poles. Hence it is obvious, that as latitude increases, the length of a degree of longitude decreases ; and when the latitude is 90°, longitude vanishes.

At the close of this Chapter is a Table, showing the length of a degree of longitude for every degree of latitude.

а

67. What has been said will enable us readily to find a place on a globe, map, or chart, when its latitude and longitude are stated. But the question forces itself upon us, how were the latitude and longitude first ascertained ? I look on the map of the world, and find Boston placed in latitude about 42° north, and in longitude little more than 70° west. But how did he, who first gave Boston this place, know that such was its real latitude and longitude? He could not go to the equator and measure its latitude; he could not go to London and measure its longitude. Or how can the latitude and longitude of a vessel be found, when driven about in the ocean and constantly changing its situation ? The compass will show the mariner in what direction his vessel is going, but it will not show him the port he has left, nor that which he wishes to reach.

68. The horizon is the circle where the visible sky and land or water meet. For example, when the sun rises, he comes above the horizon; when he sets, he sinks below the horizon. When the plane of the horizon is supposed to just touch the earth's surface, the horizon is called sensible ; but when the plane is súpposed to pass through the earth's centre, the horizon is called rational. Thus, (Pl. I. fig. 3.) if E be the earth, the line ab represents the plane of the sensible horizon, and cd that of the rational. But the distance of the heavenly bodies is so great, that the difference between the sensible and rational horizon is not perceptible ; and when they rise above or sink below the rational, they at the same time appear to rise above or sink below the sensible. We shall therefore for the present consider them as one; but uniformly, when the word horizon occurs in this treatise, the rational is meant, if the sensible be not stated. When a distinct idea of the horizon is obtained, it will be obvious, that the zenith, or point directly over head is always exactly 90° from

e

g

every part of the horizon. The nadir is the point in the heavens exactly opposite to the zenith..

The Zenith and Nadir are sometimes called the poles of the horizon; they being to the horizon, what the celestial poles are to the equator.

}; 69. The zenith of any place is just as many degrees from the celestial equator, as that place is from the earth's equator. Let SENQ be the earth, (Pl. II. fig. 4.) SN its axis, and EQ the equator. Let be 90° of a circle in the starry heavens, equal to EON, 90° of a meridian on earth. To a person at E on the earth's equator, the point e, in the celestial equator, will be in the zenith. If the person move from E through o to N (90°), every successive point in eg (90°), will come into the zenith; so that when he comes to N, * will be in the zenith. And in like manner,

if he move through any part, as Eo, (40%), the zenith will be at g, 40° from the celestial equator. Hence it is obvious, that if the distance of the zenith of any place from the celestial equator can be found, it will show the latitude of that place.

70. It is to be noticed, that as a person changes his latitude, the plane of the horizon changes its position. For example, to a person at E, on the equator, the line DSN* will represent the plane of the horizon ; and both the terrestrial and celestial poles will be in the horizon. But if he move from the equator towards either pole, say N, and come to o, then the plane of the horizon is represented by the line HO. Here the pole star * will not be in the horizon, but above it; and just as far above it as the zenith g is from the celestial equator e. For the horizon is always just 90° every way from the zenith. Hence it is just as far from g to d, as from e to *;

consequently just as far from * to d, as from g to e. Therefore, in order to find the distance of the zenith of any place from the celestial equator, (which is just the same as the latitude of that place, it is only necessary to measure the height of the celestial pole above the horizon. This can be readily done by an instrument called a quadrant.

In order to show how the altitude, or height of a heavenly body above the horizon, can be ascertained, let A a e (Pl. III. fig. 2.) be a quadrant, that is a quarter of a circle ; its circular edge being divided into 90°, and each degree, when practicable, divided into minutes, &c. Let o, o, be small sight-holes, and Av, a plumb-line, hanging loose from the point A. Let *1 be in the horizon, and *2 in the zenith. It is obvious, that, when the quadrant is so held, that the *1 in the horizon is seen through the sights 0, 0, the plumb-line will hang by the edge A e. But if the quadrant be turned gradually towards B, the plumb-line will successively intersect the divisions of the quadrant, 10. 20, 30, &c.; and when the zenith *2, is seen through the sights 0, 0, the plumb-line will coincide with the edge A a. Thus, while the eye directed through 0, 0, successively passes over 90° of the heavens, the plumb-line passes over 90° of the quadrant. And just so of any part. For example, if the *3, 400 above the horizon, be seen through o, o, the plumb-line intersects the 40th degree, on the divided or graduated edge of the quadrant.

The place of the north celestial pole is very nearly marked by the pole star; and the situation of the south is so well described, that little difficulty is experienced in ascertaining it.

71. But this method of ascertaining latitude can be practised only by night, when the stars are visible. This is sufficient on land; but at sea it is often necessary to find the latitude by day. This can be readily done by taking the height of the sun at noon, called its meridian altitude. For if the sun be in the celestial equator e, and a person at o notices with a quadrant its distance from H, the horizon, by subtracting this distance from g e H, (90°), the distance g e, or the latitude of o, is ascertained. But if the sun be not in the celestial equator, but have either north or south declination, this declination must be first found by a nautical almanac or a common globe, and added to or subtracted from the sun's meridian altitude. For it is the height of the equator and not of the sun, which must be