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In the annexed figure, let B D, B E, and B F be the position of the leading and other indexes when the revolving central mirror is parallel to
E the fixed one KL. Let A C and MN
H be two positions of the revolving mirror, when it is equally inclined to K L. K Then the arcs D G, D G', EH, E H', FI, FI', passed over by BD, BE, and
HD BF, will be all equal; and if, when
CM the mirror has the position MN, the 1 face of the instrument be reversed, MN and K L will then have the same relative position to each other that A C and K L have; and, consequently, if an object is seen by reflection from A C and KL it will also, when the instrument is reversed, be seen by reflection from M N and K L by an eye placed in the same situation; hence the degrees, &c. on the arcs G G', H H', II', are each the measure of double the distance of the object and its reflected image ; it is evident therefore that in observing with the instrument in this manner its index error does not affect the measure of the required angle.
DEFINITIONS AND PRINCIPLES.
ASTRONOMY is the science which treats of the heavenly bodies, their distances, appearances, and the laws by which their motions are governed; and Nautical Astronomy is that application of the principles of the science by which, from the angular positions of celestial objects, with respect to each other and to the horizon, the mariner is enabled to determine his situation at sea.
The sun, which to us is the fountain of light and heat, is an immense spherical body, of about 880,000 miles in diameter, and it is the centre round which eleven other bodies, called planets, are known to revolve at different distances, and in different periods. The planes in which the planets revolve all pass through the centre of the sun, and they are in general inclined to each other in very
small angles. They are called primary planets; and several of them are attended by smaller ones, called satellites, which revolve round them, in the same manner as they revolve round the sun.
The sun and the planets are called the solar system. The orbits of the planets are not strictly circular, but elliptical or oval ; and the sun is situated nearer one extremity of the longer axis than the other,
in a point in that axis called the focus ; so that the planets at one period of their revolutions are nearer to the sun than at another ; and when they are nearest to him, their velocities are greatest ; the fundamental law of planetary motion being, that a line drawn from a planet to the sun describes equal areas round him in equal times.
Besides this periodical revolution round the sun, each of the planets has a uniform rotatory motion round an imaginary line, called the aris, passing through the centre ; and during the whole of any planet's revolution, its axis of rotation preserves the same parallel position. In consequence of this rotation, the different parts of the surfaces of the planets are presented to the sun in succession; but it has not been observed that the axis round which any planet rotates is perpendicular to the plane in which it revolves round the sun ; therefore at one period of the revolution one extremity of the axis and the adjacent parts of the surface will be inclined towards the sun, and the other at the opposite period. There is a class of bodies called comets, which also revolve round
appear to be governed in their motions by the same laws that regulate the motions of the planets. Their orbits are greatly elongated, and they come towards the sun from all quarters of the heavens, differing in this respect from the planets, which revolve pretty nearly in the same plane.
The planets become visible or shine only by reflecting the light of the sun, and they can therefore be seen only when some part of their surface on which the sun shines is turned towards the observer.
The earth on which we live is one of the planets; it revolves round the sun in a year, and performs its rotation on its axis, from west to east, once in a day. The moon is a satellite attending the earth, round which it revolves, from west to east, in about 27 days 8 hours, at a mean distance of about 240,000 miles.
The planets, in the order of their distances from the sun, are Mercury, Venus, the Earth, Mars, Vesta, Juno, Ceres, Pallas, Jupiter, Saturn, and Herschel.-Mercury, and Venus, which are nearer the sun than the earth, are called inferior planets ; and those which are more distant are called superior planets. Jupiter, Saturn, and Herschel, are by far the largest ; and Vesta, Juno, Ceres, and Pallas, which are all nearly at the same distance from the sun, are so small that they are generally termed Asteroids. Jupiter has four satellites, Saturn seven, and Herschel six; and Saturn is besides surrounded by a thin, broad, and beautiful ring, perfectly detached from his body.
The mean distance of the earth from the sun is 95,000,000 miles, and the mean distances of all the planets are nearly proportional to the following numbers. Mercury, Venus, Earth, Mars, Asteroids, Jupiter, Saturn, Herschel.
Hence, from the mean distance of the earth, that of any of the other planets may be obtained by proportion.
When an inferior planet is between the earth and the sun, its dark side being turned towards the earth, it cannot of course be seen by us, unless as a spot apparently passing over the surface of the sun ; but it can be so seen only when it passes the sun in one of those points at which its orbit crosses the plane of the orbit of the earth. These points are called the nodes of the planet's orbit.
The moon in like manner is invisible when she is in the vicinity of the sun, or at new moon, and she appears like a full circle when she is in the opposite quarter of the heavens ; and the various' appearances which she exhibits in other situations are merely those which arise from a greater or less portion of her enlightened hemisphere being seen from the earth; but the convex edge of the visible part is always turned towards the sun.
When the moon passes directly between the earth and the sun she intercepts his light, and forms a solar eclipse; and when at full, the earth is between the moon and the sun, it intercepts the light of the sun, and produces a lunar eclipse; the moon in that case passing through the earth's shadow, as the moon's shadow in a solar eclipse passes over the earth.
The inferior planets, when viewed through a telescope, present all the varying appearances of the moon; but as the superior ones are never between the earth and the sun, the apparent form of their visible discs undergoes a comparatively inconsiderable change.
From the rotation of the planets, the axes round which they revolve are shortened, and the diameters perpendicular to them, or their equatorial diameters, are lengthened; that is, they are flattened at the poles. This is particularly observable in the larger planets, and which have besides a quick rotation. Jupiter's equatorial diameter is to his polar one nearly as 14 to 13, Saturn's as 12 to 11, and the earth's as 230 to 229. The earth is therefore much less flattened by its rotation, or it is more nearly spherical than either Jupiter or Saturn; and the cause is obvious, for Jupiter and Saturn are both immensely larger than the earth, and they revolve also in less than half the time.
Besides the bodies which form the solar system, whose positions, both real and apparent, are continually varying, there are numberless other stars, which shine by their own light, and whose relative situations appear not to be subject to any such change. They are called fired stars, and their distance is so great that the whole extent of the solar system is absolutely as nothing when compared with it. Therefore, from whatever part of the earth's orbit the fixed stars are viewed, their apparent situations in space are the same.
The vicissitudes of day and night are produced by the diurnal rotation of the earth on its axis ; and the inequality of the days and the alternations of the seasons, by the inclination of its axis to the plane of its orbit.
It is not however the real, but the apparent motions of the heavenly bodies that are the objects of consideration in Nautical Astronomy; and all the apparent motions would be the same if the earth were conceived to be stationary, the sun to revolve annually among the fixed stars in the plane of the earth's orbit, the planets at the same time performing their apparent evolutions round him on the immeasurably distant concavity of the celestial sphere, and that sphere, with the sun, stars, and planets, to revolve daily round the earth, from east to west.
The plane of the earth's orbit, or the circle in which the sun appears to move among the stars, is called the ecliptic, and circles perpendicular to it are called circles of celestial latitude.
The axis of the earth produced to the heavens points out the celestial poles, or the points round which the apparent diurnal revolution of the celestial sphere is performed ; the terrestrial equator produced to the heavens is called the celestial equator; the meridians produced in like manner are called celestial meridians; and the parallels of latitude similarly produced are called parallels of declination.
The ecliptic intersects the equator in two points, called equinoctial points ; that at which the sun crosses from the south to the north side of the plane of the equator is called the first point of Aries; Aries being the first of twelve equal parts, called signs, into which astronomers divide the ecliptic.
From the attraction of the sun on the protuberant parts of the earth about the equator, the equinoctial points move westward along the ecliptic about 50% in a year; this motion is called the precession of the equinoxes.
The signs of the ecliptic, in order, with their distinguishing marks, are as follows, viz. : Signs. Aries, Taurus, Gemini, Cancer,
Leo, Virgo, MARKS. Υ
2 me SIGNs. Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. MARKS.
y The inclination of the equator to the ecliptic is called the obliquity of the ecliptic.
The latitude of a celestial body is an arc of a circle of latitude intercepted between the object and the ecliptic, and it is called north or south, according as the object is on the north or south side of the
ecliptic intercepted between the circle of latitude passing over the object and the first point of Aries, estimated in the order of the signs.
The declination of a celestial object is its distance from the equator measured on the meridian passing over the object, and it is called north or south according as the object is on the north or south side of the equator; and the right ascension of a celestial object is the arc of the equator intercepted between that meridian and the first point of Aries, estimated like the longitude, in the order of the signs. The right ascension of any meridian is the same as that of a celestial object conceived to be on the meridian.
The sensible horizon is a plane conceived to touch the earth at the point at which an observer is situated ; and the rational horizon is a plane parallel to the sensible one passing through the centre of the
The pole of the horizon vertically over an observer is called the zenith, and the opposite point the nadir. The zenith is at the same angular distance from the celestial equator that the observer himself is from the terrestrial one.
Great circles perpendicular to the horizon, and which of course meet in the zenith, are called vertical circles, azimuth circles, or circles of altitude. The angle which the vertical circle passing over any object makes with the meridian passing through the zenith, or the arc of the horizon which these circles intercept, is called the azimuth of the object.
The vertical circle, which is at right angles to the meridian, is called the prime vertical, and it meets the horizon in the east and west points; the meridian meeting it in the north and south points.
The amplitude of an object, is the angle included between the prime vertical, and the vertical circle on which the object rises or sets; or the angular distance of the object at rising or setting from the east or west points of the horizon.
Small circles parallel to and above the horizon are called parallels of altitude, and the small circle 180 degrees below the horizon, is called the twilight circle, because the twilight begins in the morning and ends in the evening when the sun is on that circle.
The polar distance of an object is its distance from the pole nearest the zenith of the observer, and it is consequently equal to the sum or difference of a quadrant and the declination, according as the latitude and declination are of a contrary or the same denomination.
A sidereal day is the interval between two successive transits of a ficed slar; and a solar or an apparent day is the interval between two successive transits of the sun over any meridian. The sidereal day commences when the first point of Aries is on the meridian, and the