314. Reduction of Azimuth Observations.-The time of observation of a star is first to be corrected for the difference in longitude, assuming that standard time has been used, and for the error of the watch. It is then reduced from mean to sidereal time. From the sidereal time of observation is to be subtracted the right ascension of Polaris, if that star is used, which is given in the Nautical Almanac, the result being the hour-angle or the sidereal time which has elapsed since it passed the meridian of the place of observation, given in hours, minutes, and seconds. This result is to be converted into degrees, minutes, and seconds. Then The angle between the star and the mark is to be corrected for level as follows: level corr. = 4 (w+w') − (e + e')] tan h. (141) where d value of a division of the level; ww readings of west end of level-bubble; w+w' = = ee' readings of east end of level-bubble; h = the angular elevation of pole-star. AZIMUTH AT ELONGATION. EXAMPLE OF REDUCTION. (Station: West base; December 27, 1888. Observer, S. S. G.) 721 315. Azimuth at Elongation. When observations for azimuth are to be made at elongation, it is necessary to know the mean time of elongation. This is computed by obtaining the hour-angle at elongation from the following equation: The hour-angle plus the right ascension of the star gives the sidereal time of its western elongation, which, reduced to mean time, gives the local mean time in question. The azimuth of a pole-star at elongation is determined by the use of the equation EXAMPLE OF COMPUTATION OF THE AZIMUTH AT ELONGATION, AND THE LOCAL MEAN TIMES OF BOTH ELONGATIONS OF POLARIS. (Latitude == 40°. Meridian of Washington. November 28, 1891.) Sidereal time western elongation, Ts= 7 15 20.4 ... = 16 29 14.4 Sidereal interval before noon, ..... = 9 13 54.0 I 30.7 9 12 23.3 Nov. 28. Mean interval before noon........ as 16 29 14.4 Sidereal interval after noon, I.....,... = 2 54 35.6 - O 28.6 Local mean time eastern elongation..... = 2 54 07.0 P.M., Nov. 28. = For longitudes west of Washington decrease times of elongation o*.66 for each degree. CHAPTER XXXIV. LATITUDE. 316. Methods of Determining Latitude.-1. The most precise method known for determination of a terrestrial latitude is by measuring small differences of zenith distances of two stars with zenith telescope. (Art. 319.) 2. The simplest method is by measuring the meridian zenith distance or altitude of a known star, though the result is relatively approximate only. It is only essential to follow a star near meridian until its altitude is greatest. The formula is sign of depending on whether the star is north or south of the zenith. 3. If the time be known, latitude may be determined by a single measured altitude of the sun or a star. (Art. 318.) This method gives fairly approximate results when time is known by a chronometer or watch to within two or three seconds, and is very useful in exploratory work. 4. Time being known, latitude may be simply and quite accurately determined by measuring circummeridian altitudes of Polaris; this consists in applying the third method to Polaris. Then = hp cos t + sin 1". sin' t . tan h, (145) in which p = polar distance of Polaris or complement of in seconds, which is about 5400". Tables for finding and psin " are given in the American Ephemeris. The best time of observation is when the star is at one of the culminations. This method is especially adapted to the instruments available to the topographer, namely, a good theodolite or engineer's transit and a good timepiece. 5. Approximate latitude may be determined from an observation on the sun at noon. (Art. 317.) This is a very useful method for the explorer or land surveyor. 317. Approximate Solar Latitude. The following is a method of obtaining the approximate latitude from an observation on the sun at noon: Measure two altitudes, one of the upper and the other of the lower limb of the sun, commencing before noon and watching until the sun has reached its highest altitude. In order to eliminate errors of collimation, these two observations should be made on each limb with the telescope direct and inverted. refraction; Let r h = altitude of sun's center; $ = latitude; d= sun's declination at time of observation. The declination is taken from the Nautical Almanac for the date of observation, and increased or diminished by the hourly difference multiplied by the longitude from the locus of the almanac, expressed in hours. Then $ = 90° - (h — r — d). == (146) |