measure triangles. When this need occurs, each angle of the triangle should be measured directly. If but two angles are measured and their sum is subtracted from 180° to get the third, all errors of measurement of the two angles are thrown into the third angle. When all the angles are measured to a high degree of precision, their sum will ordinarily be more or less than 180°, indicating an impossible triangle. To make the triangle possible, the angles are adjusted so that their sum shall be 180°. The adjustment is effected by dividing the total error equally among the three angles. It might seem that a distribution in some ratio to the size of the angles should be adopted; but the method applied considers that there is no more reason for making an error in measuring a large angle than in measuring a small angle, which is probably true. PRACTICAL ASTRONOMY DEFINITIONS AND TERMS LATITUDE AND LONGITUDE. If a meridian, that is, a circle passing through the axis of the earth, be passed at a given point of the earth's surface, the angular distance of the point from the equator, measured on the meridian, is the latitude of that point. A plane parallel to the equator cuts the earth's surface in a circle called a parallel of latitude. All the points on a parallel of latitude have the same latitude. The longitude of a place is the angle that the plane of the meridian of the place makes with the plane of a reference meridian (usually the meridian of Greenwich). This angle may be measured on the equatorial circle or on the parallel of latitude of the given place. Longitude is counted from the reference meridian toward the west. THE CELESTIAL SPHERE The celestial sphere is an imaginary sphere enclosing all the heavenly bodies. It is of such enormous dimensions that, in comparison with it, the earth may be considered as a mere dot. The earth's axis produced indefinitely is called the axis of the celestial sphere. This axis intersects the celestial sphere in two points, called the north pole and the south pole of heavens. All the great circles of the celestial sphere passing through this axis are called hour circles. The circle in which the plane of the equator intersects the celestial sphere is called the celestial equator. The point on the equator that the sun in its apparent motion over the celestial sphere crosses on March 21, as it passes from the southern to the northern hemisphere, is called the vernal equinox. REFERENCE CIRCLES The accompanying illustration, which represents the celestial hemisphere, shows all the reference circles that are used for determining the position of a heavenly body. O is the position of the earth; OP, one-half of the axis of the celestial sphere, P being the north pole; VQV'L, part of the celestial equator; X, the vernal equinox; and YXC, part of the sun's path. PX is the hour circle passing through X, called the equinoctial colure. S is any star, and PSA is the hour circle passing through it. XA is the right ascension of the star, which is the arc on the equator measured eastwards from the vernal equinox 1 to the hour circle passing through the star. AS is the declination of the star; that is, its angular distance from the equator. The declination is considered positive when the star is north and negative when south of the equator. The complement angle of the declination, SP, is called the polar distance of the star. The zenith of a point on the earth's surface is the point in which the line passing through the center of the earth and the given point intersects the celestial sphere above the given point. The horizon is the plane passing through the given point and perpendicular to this line. In the illustration, Z is the zenith, and NVM is the celestial horizon. The celestial meridian of a given point is a great circle passing through the zenith of the point and the poles. The celestial meridian cuts the horizon in two points N and M, called, respectively, the north point and the south point. A vertical circle is one that passes through the zenith and is perpendicular to the horizon. The prime vertical is the vertical circle at right angles to the meridian; it intersects the horizon in two points V and V', called the west and the east point, respectively. The altitude of a heavenly body is its angular distance from the horizon, measured along the vertical circle passing through the body. The zenith distance is the angular distance of the star from the zenith, measured along the same circle. The zenith distance is the complement of the altitude. In the illustration, DS and SZ are, respectively, the altitude and zenith distance of S. The azimuth of a star is the angle in the plane of the horizon intercepted by the planes of the meridian and the vertical circle passing through the star. It is measured from the north point toward the east or from the south point toward the west. NMD is the azimuth of S, measured from the north toward the east, and MD is the azimuth of S when measured from the south toward the west. The hour angle of a star is the arc intercepted on the equator between the meridian and the foot of the hour circle passing through the star. It is measured from the meridian toward the west. In the illustration, QA is the hour angle of S. TIME The passing of a heavenly body across the meridian of a place is called its culmination, or transit. It is upper or lower culmination, according as it is then occupying the highest or the lowest position with regard to the horizon. The interval of time that elapses between two successive upper or lower transits of a star over the same meridian is called a sidereal day. It begins, for any place, when the vernal equinox crosses the meridian above the pole. This instant is called sidereal noon. Sidereal hours, minutes, and seconds are reckoned from 0 to 24 hr., starting from sidereal noon. Time expressed in sidereal days and fractions (hours, minutes, seconds) is called sidereal time. From this, it follows that sidereal time is the hour angle of the vernal equinox; also, that the right ascension of a star is equal to the sidereal time of its transit, or culmination. For any other position of the star, the sidereal time equals the algebraic sum of the right ascension and the hour angle of the star. The interval between two successive upper transits of the sun is called a true solar day, or an apparent day. Owing to the fact that the motion of the sun is not uniform and that the solar days are not of equal duration, apparent time is not used for the ordinary affairs of life. The mean sun is an imaginary body supposed to start from the vernal equinox at the same time as the true sun, and to move uniformly on the equator, returning to the vernal equinox with the true sun. The time between two successive upper transits of the mean sun is called a mean solar day, and time expressed in mean solar days is called mean solar time, or simply mean time. This is the time shown by ordinary clocks and watches. A mean solar day is the mean of the duration of all the true solar days in a year (a year being the time in which either the true or the mean sun makes a complete circuit of the heavens). As there are 365.2422 true solar days and 366.2422 sidereal days in a year, 1 mean solar day 366.2422 = 1.0027379 sidereal days =24h3m56.55$, sidereal time The equation of time is a certain quantity that must be added algebraically to the apparent solar time to obtain the corresponding mean time. The value of this quantity for each day of the year is given in the American Ephemeris, which is published yearly by the United States Government at Washington, D. C. Civil Time and Astronomical Time.-By civil time is meant the time that is usually reckoned in ordinary life. For astronomical purposes, the day is considered to begin at noon, and hours are counted from 0 to 24. When time is reckoned in this manner it is called astronomical time. The civil day begins at 12 o'clock at night, and the astronomical day begins 12 hr. later. For instance, the date Oct. 17, 7h 14m 38, astronomical time, means 7h 14m 38 after noon of the civil date Oct. 17, and is in civil time, 7h 14m 38 P. M. The astronomical date Feb. 20, 18h 6m 128 means 18h 6m 128 after noon of the civil date Feb. 20, or 6h 6m 12s after midnight of Feb. 20; that is, Feb. 21, 61 6m 128 A. M. Longitude and Time.-The mean sun describes a complete circle in 24 mean solar hours. In 1 hr. it moves over 360° 24 = 15° of arc; in 1 min. of time, over 15' of arc; and in 1 sec. of time, 15" of arc. Relation Between Time and Longitude.-Let A and B be two places on the earth's surface, B being west of A. Let their respective longitudes be ga and go, and let the difference between gb and ga, expressed in measure of time, be dg. Let, also, Ta be the time at A when the time at B is Tь. Then, and Ta= To+dg (1) (2) EXAMPLE 1.-The longitude of Washington, west of Greenwich, is 5h 8m 18; that of San Francisco, 8h 9m 478. What is the time at: (a) Washington when it is 9h 3m at San Francisco? (b) San Francisco when it is 19h 54m 30s at Washington? |