D's increase of dec. per hour = 16′,52 S.

Corr. of gr. alt. = corr. of lat. = 52′′ = 1' nearly.

Lat. 29° 12′ + 1′ = 29° 13′ N.

2. An observer sailing south 12 miles per hour, found, by observation, the greatest central altitude of the moon bearing south, to be 25° 15'; what was the latitude, if the moon's declination was 1° 12′ N., and her increase of declination per hour 18'.5?

Ans, 66° 1' N,

Obliquity.

Equinoxes.

CHAPTER V.

THE ECLIPTIC.

Signs.

53. The careful observation of the sun's motion shows this body to move nearly in the circumference of a great circle. This great circle is called the ecliptic. [B. p. 48.]

54. The angle which the ecliptic makes with the equator is called the obliquity of the ecliptic.

55. The points, where the ecliptic intersects the equator, are called the equinoctial points; or the equinoxes. The point through which the sun ascends from the southern to the northern side of the equator, is called the vernal equinox ; and the other equinox is called the autumnal equinox.

The points 90° distant from the ecliptic are called the solstitial points, or the solstices. [B. p. 49.]

56. The circumference of the ecliptic is divided into twelve equal parts, called signs, beginning with the vernal equinox, and proceeding with the sun from west to east.

The names of these signs are Aries (Y), Taurus (8), Gemini (II), Cancer (), Leo (N), Virgo (m), Libra (—),

Colures.

Tropics.

Latitude of a star.

Scorpio (m), Sagittarius ( ↑), Capricornus (V), Aquarius (m), Pisces (x). The vernal equinox is therefore the first point, or beginning of Aries, and the autumnal equinox is the first point of Libra; the first six signs are north of the equator, and the last six south of the equator. The northern solstice is the first point of Cancer, and the southern solstice the first point of Capricorn. [B. p. 49.]

57. Secondary circles drawn perpendicular to the ecliptic are called circles of latitude.

The circle of latitude drawn through the equinoxes is called the equinoctial colure.

The circle of latitude drawn through the solstices is called the solstitial colure. [B. p. 49.]

Corollary. The solstitial colure is also a secondary to the equator, so that it passes through the poles of both the equator and the ecliptic.

58. Small circles, drawn parallel to the equator through the solstitial points, are called tropics.

The northern tropic is called the tropic of Cancer; the southern tropic the tropic of Capricorn.

Small circles, drawn at the same distance from the poles which the tropics are from the equator, are called polar circles.

The northern polar circle is called the arctic circle, the southern the antartic.

59. The latitude of a star is its distance from the ecliptic measured upon the circle of latitude, which

Longitude of a star.

Nonagesimal point.

passes through the star. If the observer is supposed to be at the earth, the latitude is called geocentric latitude; but if he is at the sun, it is heliocentric latitude. [B. p. 49.]

60. The longitude of a star is the arc of the ecliptic contained between the circle of latitude drawn through the star and the vernal equinox. [B. p. 50.]

Corollary. The longitude and right ascension of the first point of Cancer are each equal to 6", and those of the first point of Capricorn are each equal to 18".

61. The nonagesimal point of the ecliptic is the highest point at any time.

Corollary. The distance of the nonagesimal from the zenith is therefore equal to the distance of the zenith from the ecliptic, that is, to the celestial latitude of the zenith; and the longitude of the nonagesimal is the celestial longitude of the zenith.

62. Problem. To find the latitude and longitude of a star, when its right ascension and declination are known.

Solution. Let P (fig. 35) be the north pole of the equator, Z the north pole of the ecliptic, and B the star. Then EQ W will be the equator, NESW the ecliptic, and NP ZS the solstitial colure, so that the point S is the southern solstice, and N the northern solstice. Now if the arc PB be produced to cut the equator at M, and ZB to cut the ecliptic at L; the angle ZPB is measured by the arc

To find a star's latitude and longitude.

QM, that is, by the difference of the right ascensions of Q and M, or by the difference of the ✶'s right ascension and 18h; that is,

in which the first values of ZPB and PZB correspond to the star's being east of the solstitial colure; the second and third values to the star's being west of the colure. We also have

obliquity of ecliptic E, (457)

in which the declination and latitude are positive when north, and negative when south, and E has the same sign with R. A.

12h.

The present problem does not, then, differ from that of 28, and if we put

APC - 90°,

in which the upper sign is used, when R. A.

12h is posi

tive, and otherwise the lower sign, we have by (298, 299, and 300),

tang. PC = cotan. A = cos. (R. A. + 6") cotan. Dec. - sin. R. A. cotan. Dec. (458)

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