A

COMPLETE SYSTEM

OF

ASTRONOM Y.

CHAPTER I.

DEFINITIONS.

Art. 1. ASTRONOMY is that branch of natural philosophy which treats of the heavenly bodies. The determination of their magnitudes, distances and the orbits which they describe, is called plane or pure Astronomy; and the investigation of the causes of their motions is called physical Astronomy. The former is determined from observations on their apparent magnitudes and motions; and the latter from analogy, by applying those principles and laws of motion by which bodies on and near the earth are governed, to the other bodies in the system. The principles of plane Astronomy come first in order to be treated of; and in this, we shall begin with the explanation of such terms as are the fundamental principles of the science.

2. A great circle of a sphere is that whose plane passes through its center; and a small circle is that whose plane does not pass through its center.

3. A diameter of a sphere perpendicular to any great circle, is called the axis of that circle; and the extremities of the diameter are called its Poles.

4. Hence, the pole of a great circle is 90° from every point of it upon the surface of the sphere; but as the axis is perpendicular to the circle when it is perpendicular to any two radii, a point on the surface of a sphere 90° distant from any two points of a great circle will be the pole.

5. All angular distances on the surface of a sphere, to an eye at the center, are measured by the arcs of great circles; for they being arcs to equal radii, will be as the angles.

FIG.

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6. Hence, all triangles formed upon the surface of a sphere, for the solution of spherical problems, must be formed by the arcs of great circles.

7. All great circles must bisect each other; for passing through the center of the sphere their common section must be a diameter, which bisects all circles.

8. Secondaries to a great circle are great circles which pass through its poles. 9. Hence, secondaries must be perpendicular to their great circle; for if" one line be perpendicular to a plane, any plane passing through that line will also be perpendicular to it; therefore as the axis of the great circle is perpendicular to it, and is the common diameter to all the secondaries, they must all be perpendicular to the great circle. Hence also, every secondary, bisecting its great circle (7)*, must bisect every small circle parallel to it; for the plane of the secondary passes through, not only the center of the great circle, but also of the small circles parallel to it.

10. Hence, a great circle passing through the poles of two great circles, must be perpendicular to each; and, vice versâ, a great circle perpendicular to two other great circles must pass through their poles.

11. If an eye be in the plane of a circle it appears a straight line; hence in the representation of the surface of a sphere upon a plane, those circles whose planes pass through the eye are represented by straight lines.

12. The angle formed by the circumferences of two great circles on the surface of a sphere, is equal to the angle formed by the planes of those circles; and is measured by the arc of a great circle intercepted between them, described about the intersection of the circles as a pole.

For let C be the center of the sphere, PQE, PRE two great circles; then as the circumferences of these circles at P are perpendicular to the common intersection PCE, the angle at P between them is equal to the angle between the planes, by Euc. B. XI. Def. 6. Now draw CQ, CR perpendicular to PCE; then the angle QCR is also the angle between the planes, and therefore equal to the angle at P formed by the two circles; and the angle QCR is measured by the arc QR of a great circle, which are has (4) for its pole the point P, because PQ, PR are each 90°.

13. If at the intersection of two great circles as a pole, a great circle be described, and also a small circle parallel to it, the arcs of the great and small circles, intercepted between the two great circles contain the same number of degrees.

For draw AB, AD perpendicular to PCE, then as AB, AD are parallel to CQ, CR, the plane BAD is parallel to the plane QCR, and therefore the small circle BD of which A is the center, is parallel to the great circle QR, and as

* Figures included thus in a Parenthesis refer to the articles.

each angle BAD, QCR, measures the inclination of the planes, they must be equal, and consequently the arcs BD, QR contain the same number of degrees. Hence, the arc of such a small circle measures the angle at the pole between the two great circles. Also QR: BD:: QC: BA:: radius: cos. BQ. Hence QR is the greatest distance between the two circles.

14. The Axis of the earth is that diameter about which it performs its diurnal motion; and the extremities of this diameter are called its poles.

tor.

15. The terrestrial Equator is a great circle of the earth perpendicular to its axis. Hence, the axis and poles of the earth are the axis and poles of its equaThat half of the earth which lies on the side of the equator which we inhabit is called the northern Hemisphere, and the other the southern; and the poles are respectively called the north and south poles.

16. The Latitude of a place on the earth's surface is its angular distance from the equator, measured upon a secondary to it. These secondaries to the equator are called Meridians.

17. The Longitude of a place on the earth's surface is an arc of the equator intercepted between the meridian passing through the place, and another, called the first meridian, passing through that place from which you begin to

measure.

18. If the plane of the terrestrial equator be produced to the sphere of the fixed stars, it marks out a circle called the celestial equator; and if the axis of the earth be produced in like manner, the points in the Heavens to which it is produced are called poles, being the poles of the celestial equator. The star nearest to each pole is called the pole star.

19. Secondaries to the celestial equator are called circles of Declination; of these, 24 which divide the equator into equal parts, each containing 15°, are called Hour circles.

20. Small circles parallel to the celestial equator, are called parallels of De

clination.

21. The sensible horizon is that circle in the heavens whose plane touches the earth at the spectator. The rational horizon is a great circle in the heavens, passing through the earth's center, parallel to the sensible horizon.

22. Almacanter is a small circle parallel to the horizon.

23. If the radius of the earth to the place where the spectator stands, be produced both ways to the heavens, that point vertical to him is called the Zenith, and the opposite point the Nadir. Hence, the zenith and nadir are (3) the poles of the rational horizon; for the radius produced being perpendicular to the sensible, must also be perpendicular to the rational horizon.

24. Secondaries to the horizon are called vertical circles, because they are (9) perpendicular to the horizon; on these circles therefore the altitude of an heavenly body is measured.

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25. A Secondary common to the celestial equator and the horizon of any place, and which therefore (10) passes through the poles of each, is the celestial meridian of that place. Hence, the plane of the celestial meridian of any place coincides with the plane of the terrestrial meridian of the same place. 26. That direction which passes through the north pole is called north, and the opposite direction is called south. Hence, the meridian must cut the horizon in the north and south points.

27. Hence, the meridian of any place divides the heavens into two hemispheres lying to the east and west; that lying to the east is called the eastern hemisphere, and the other lying to the west is called the western hemisphere.

28. The vertical circle which cuts the meridian of any place at right angles, is called the prime vertical; and the points where it cuts the horizon are called the east and west points. Hence, the east and west points are 90° distant from the north and south. These four are called the cardinal points.

29. The Azimuth of an heavenly body is its distance on the horizon, when referred to it by a secondary, from the north or south points. The Amplitude is its distance from the east or west points.

30. The Ecliptic is that great circle in the heavens which the sun appears to describe in the course of a year.

31. The ecliptic and equator being great circles must (7) bisect each other, and their angle of inclination is called the obliquity of the ecliptic; also the points where they intersect are called the equinoctial points. The times when the sun comes to these points are called the Equinoxes.

32. The ecliptic is divided into 12 equal parts, called Signs; Aries v, Taurus 8, Gemini п, Cancer, Leo a, Virgo m, Libra, Scorpio m, Sagittarius, Capricornus, Aquarius, Pisces x. The order of these is according to the motion of the sun. The first point of aries coincides with one of the equinoctial points, and the first point of libra with the other. The first six signs are called northern, lying on the north side of the equator; and the last six are called southern, lying on the south side. The signs, #, x, v, are called ascending, the sun approaching our (or the north) pole whilst it passes through them; and, &, m, ~, m, are called descending, the sun receding from our pole as it moves through them.

33. The motion of the heavenly bodies which is according to the order of the signs, is called direct, or in consequentia; and the motion in the contrary direction is called retrograde, or in antecedentia. The real motion of all the planets is according to the order of the signs, but their apparent motion is sometimes in an opposite direction.

34. The Zodiac is a space extending on each side of the ecliptic, within which the motion of all the planets is contained.

35. The right ascension of a body is an arc of the equator intercepted be

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tween the first point of aries and a declination circle passing through the body, measured according to the order of the signs.

36. The oblique ascension is an arc of the equator intercepted between the first point of aries and that point of the equator which rises with any‍body, measured according to the order of the signs.

37. The ascensional difference is the difference between the right and oblique

ascension.

38. The Declination of a body is its angular distance from the equator, measured upon a secondary to it drawn through the body.

39. The Longitude of a star is an arc of the ecliptic intercepted between the first point of aries and a secondary to the ecliptic passing through the body, measured according to the order of the signs. If the body be in our system, and seen from the sun, it is called the heliocentric longitude; but if seen from the earth, it is called the geocentric longitude; the body in each case being referred perpendicularly to the ecliptic in a plane passing through the eye.

40. The Latitude of a star is its angular distance from the ecliptic, measured upon a secondary to it drawn through the body. If the body be in our system, its angular distance from the ecliptic seen from the earth is called the geocentric latitude; but if seen from the sun it is called the heliocentric latitude.

41. Hence, if Q be the equator, C the ecliptic, the first point of aries, s a star, and the great circles sr, sn be drawn perpendicular to C and Q; then vn is its right ascension, sn its declination, sr its latitude and vr its longitude. The circle sr is called a circle of latitude.

42. The Tropics are two parallels of declination touching the ecliptic. One, touching it at the beginning of cancer, is called the tropic of cancer; and the other touching it at the beginning of capricorn, is called the tropic of capricorn. The two points where the tropics touch the ecliptic are called the solstitial points.

43. Colures are two secondaries to the celestial equator, one passing through the equinoctial points, called the equinoctial colure; and the other passing through the solstitial points, called the solstitial colure. The times when the sun comes to the solstitial points are called the Solstices.

44. The Arctic and Antarctic circles are two parallels of declination, the former about the north and the latter about the south pole, the distance of which from the two poles is equal to the distance of the tropics from the equator. These are also called polar circles.

45. The two tropics and two polar circles, when referred to the earth, divide it into five parts, called Zones; the two parts within the polar circles are called the frigid zones; the two parts between the polar circles and tropics are called the temperate zones; and the part between the tropics is called the torrid zone. Small circles in the heavens are referred to the earth, or the contrary, by lines

FIG.

2.