. Astronomy for high schools and colleges . and 6 are known, cross the meridian,one north and the other south of the zenith, at zenith distances Z S and Z8\ which call Z and Z, andif we have measured Z and Z\ wecan from such measures find thelatitude ; iov (j) = 6 + Z and 0 =6 — Z, whence 9 = ^[(6 + 6)-\-{Z-Z)\ It will be noted that in this meth-od the latitude depends simplyupon the mean of two declinationswhich can be determined before-hand, and only requires the differ-FiG. 17. ence of zenith distances to be ac- curately measured, while the ab-solute values of these are unknown. In this con
. Astronomy for high schools and colleges . and 6 are known, cross the meridian,one north and the other south of the zenith, at zenith distances Z S and Z8\ which call Z and Z, andif we have measured Z and Z\ wecan from such measures find thelatitude ; iov (j) = 6 + Z and 0 =6 — Z, whence 9 = ^[(6 + 6)-\-{Z-Z)\ It will be noted that in this meth-od the latitude depends simplyupon the mean of two declinationswhich can be determined before-hand, and only requires the differ-FiG. 17. ence of zenith distances to be ac- curately measured, while the ab-solute values of these are unknown. In this consists its by a Single Altitude of a Star.~In the triangleZF8 (Fig. 14) the sides are ZP = 90° — 0; P /S = 90° — c^; Z8 =Z = 90° — a; ZP8 = ?i = the hour-angle. If we can measure atany known sidereal time 6 the altitude a of the star 8^ and if wefurther know the right ascension, a, and the declination, 6^ of thebody (to be derived from the Nautical Almanac or a catalogue ofstars), then we have from the triangle. sin a = sin 0 sin 6 + cos 0 cos 6 cos h (1) a and 6 are known, and h = 6 — a, so that 0 is the only unknown. Put <^ sin D = sin 6 (2) d cos D = cos ^ cos h, (3) whence d and D are known, and (1) becomes d cos (0 — D) = sin a, (4) whence 0 — D and 0 are known. The altitude a is usually measuredwith a sextant. Latitude by a Meridian Altitude.—If the altitude of thebody is observed on the meridian and south of the zenith, the equa-tion above becomes, since h = 0 in this case, or. sin 0 = sin a sin 6 + cos a cos 6, sin 0 = cos (a — (5) .-. 0 = 90° — a -\- 6, which is evidently the simplest method of obtaining 0 from a meas- PABALLAX. 49 ured altitude of a body of known declination. The last method is thatcommonly used at sea, the altitude being measured by the sextant,The student can deduce the formula for a north zenith-distance. § 12. PARALLAX AND SEMIDIAMETER. An observation of the apparent position of a lieavenlvbody can giv
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