Another bright star, which is on the opposite side of the Pole, and is known to astronomers as Gamma Cassiopeia, also comes on the Meridian nearly at the same time as the North Star, and will thus assist in determining its direction. (302) The time at which the North Star passes the Meridian above the Pole, for every 10th day in the year, is given in the fol lowing Table, in common clock time." The upper transit is the most convenient, since at the other transit Alioth is too high to be conveniently observed. Times of North Star passing the Meridian. July, 06 P. M. 0 28 A. M.11 45 P. M.11 November, 10 22 P. M. 9 43 P. M. 9 04 P. M. *To calculate the time of the North Star passing the Meridian at its upper cui mination: Find in the "American Almanac," (Boston), or the "Astronomical Ephemeris," (Washington), or the "Nautical Almanac," (London), or by interpolation from the data at the end of this note, the right ascension of the star, and from it (increased by twenty-four hours if necessary to render the subtraction possible) subtract the Right ascension of the Sun at mean noon, or the sidereal time at mean noon, for the given day, as found in the "Ephemeris of the Sun,” in the same Almanacs. From the remainder subtract the acceleration of sidereal on mean time corresponding to this remainder, (3m. 56s. for 24 hours), and the new remainder is the required mean solar time of the upper passage of the star across the Meridian, in "Astronomical" reckoning, the astronomical day beginning at noon of the common civil day of the same date. The right ascension of the North Star for Jan. 1, 1850, is 1h. 05m. 01.4s.; for 1860, 1h. 08m. 02.8s.; for 1870, 1h. 11m. 16.9s.; for 1880, 1h. 14m. 45.1s.; for 1890, 1h. 18m. 29.2s.; for 1900, 1h. 22m. 31s. To find the time of the star's passage of the Meridian for other days than those given in the Table, take from it the time for the day most nearly preceding that desired, and subtract from this time 4 minutes for each day from the date of the day in the Table to that of the desired day; or, more accurately, interpolate, by saying: As the number of days between those given in the Table is to the number of days from the next preceding day in the Table to the desired day, so is the difference between the times given in the Table for the days next preceding and following the desired day to the time to be subtracted from that of the next preceding day. The first term of the preceding proportion is always ten, except at the end of months having more or less than 30 days. For example, let the time of the North Star's passing the Meridian on July 26th be required. From July 21st to August 1st being 11 days, we have this proportion: 11 days: 5 days :: 43 minutes: 1911 19 minutes. Taking this from 5h. 11m. A. M., we get 4h. 514m. A. M. for the time of passage required. The North Star passes the Meridian later every year. In 1860, it will pass the Meridian about two minutes later than in 1854; in 1870, five minutes, in 1880, eight minutes, in 1890, twelve minutes, and in 1900, sixteen minutes, later than in 1854: the year for which the preceding table has been calculated. The times at which the North Star passes the Meridian below the Pole, in its lower Transit, can be found by adding 11h. 58m. to the time of the upper Transit, or by subtracting that interval from it.* (303) By the North Star at its extreme elongation. When the North Star is at its greatest apparent angular distance East or West of the Pole, as at B or D in Fig. 201, it is said to be at its extreme Eastern, or extreme Western, Elongation. If it be observed at either of these times, the direction of the Meridian can be easily * The North Star, which is now about 1° 28′ from the Pole, was 12° distant from it when its place was first recorded. Its distance is now diminishing at the rate of about a third of a minute in a year, and will continue to do so till it ap proaches to within half a degree, when it will again recede. The brightest star in the Northern hemisphere, Alpha Lyra, will be the Fole Star in about 12,000 years, heing then within about 50 of the Pole, though now more than 51° distant from it obtained from the observation. The great advantage of this method over the preceding is that then the star's motion apparently ceases for a short time. (304) The following Table gives the TIMES OF EXTREME ELONGATIONS OF THE NORTH STAR." * MONTH. 1ST DAY. 11TH DAY. 21ST DAY. EASTERN. WESTERN. EASTERN. WESTERN. EASTERN. WESTERN. Jan'y, 0 27 P.M. 019 A.M. 11 47 A.M. 11 35 P.M. 11 08 A.M. 10 56 P.M. The Eastern Elongations from October to March, and the Western Elongations from April to September, occurring in the day time, they will generally not be visible except with the aid of a powerful telescope. * To calculate the times of the greatest elongation of the North Star: Find in one of the Almanacs before referred to, or from the data below, its Polar distance at the given time. Add the logarithm of its tangent to the logarithm of the tangent of the Latitude of the place, and the sum will be the logarithm of the cosine of the Hour angle before or after the culmination. Reduce the space to time; correct for sidereal acceleration (3m. 56s. for 24 hours) and subtract the result from the time of the star's passing the meridian on that day, to get the time of the Eastern elongation, or add it to get the Western. The Polar distance of the North Star, for Tan. 1, 1850, is 1° 29′ 25′′; for 1860, 1o 26′ 12′′.7; for 1870, 1o 23° 01"; for 1880, 1° 19 50".4; for 1890, 1° 16′ 40′′.7; for 1900, 1° 13′ 32′′.2. The preceding Table was calculated for Latitude 40°. The Time at which the Elongations occur vary slightly for other Latitudes. In Latitude 50°, the Eastern Elongations occur about 2 minutes later and the Western Elongations about 2 minutes earlier than the times in the Table. In Latitude 26°, precisely the reverse takes place. The Times of Elongation are continually, though slowly, becoming later. The preceding Table was calculated for July 1st, 1854. In 1860, the times will be nearly 2 minutes later; and in 1900, the Eastern Elongations will be about 15 minutes, and the Western Elongations 17 minutes later than in 1854. (305) Observations. Knowing from the preceding Table the hour and minute of the extreme Elongation on any day, a little before that time suspend a plumb-line, precisely as in Art. (301), and place yourself south of it as there directed. As the North Star moves one way, move your eye the other, so that the plumbline shall continually seem to cover the star. At last the star will appear to stop moving for a time, and then begin to move backwards. Fix the sight on the board (or the compass, &c.) in the position in which it was when the star ceased moving; for the star was then at its extreme apparent Elongation, East or West, as the case may be. (306) Azimuths. The angle which the line from the eye to the plumb-line, makes with the True Meridian (i. e. the angle between the meridian plane and the vertical plane passing through the eye and the star) is called the Azimuth of the Star. It is given in the following Table for different Latitudes, and for a number of years to come, For the intermediate Latitudes, it can be obtained by a simple proportion, similar to that explained in detail in Art. (302).* *To calculate this Azimuth: From the logarithm of the sine of the Polar dis tance of the star, subtract the logarithm of the cosine of the Latitude of the place; the remainder will be the logarithm of the sine of the angle required. The Po lar distance can be obtained as directed in the last note. AZIMUTHS OF THE NORTH STAR. Latitudes. 1854 1855 1856 1857 1858 1859 1860 1870 500 20 16 20 161/20 16' 20 1512° 15′ 2° 14120 141 20 091 49° 2° 14′ 20 13120 131/2012/20 121/20 12 20 11/20 061 480 2011 2011 20 101 20 101 20 093/20 091/2009 2004 470 2009 2008 2008 2007 2007 2006 20061 20 01 46° 2° 06′2° 0612° 05′2° 0512° 05′ 2° 04120 041/10 591 450 20 0412° 04' 20 03120 031/20 02/20 021/20 02 10 573 20 013/20 011/20 01' 20 00120 00′ 44° 2° 0212° 02′ 43°' 2° 00′2° 00′ 420 1058110 58' 2 1° 55; 1° 5911° 59′ 1° 583/10 5811° 58′ 1° 531 10 57110 5711° 56/10561/10 56' 1° 51% 41° 1° 56′10 5611° 55'10 5511° 55′ 1° 5411° 54′1° 50′ 40° 1° 55′ 1° 5411° 54′ 1° 53'10 5311° 53' 10 521/10 481 390 10 53 10 528 10 5211° 52′ 10 51 10 511051 1° 463 38° 1° 51′1° 511′1° 51′ 10 5011° 50′ 1° 49′10 491/10 451 370 10 50110 498 10 4911° 49' 1° 48'10 4811° 48′ 1° 44′ 36° 1° 483/10 4811° 48′ 10 471° 4711° 47′ 10 46110 423 35° 1° 47′1° 47′ 1° 4631° 4611° 46′ 1° 45'10 45110 411 34° 1° 4611° 45′ 10 4511° 45′ 1° 44′1° 44'1° 44′ 10 401 33° 1° 45′ 1° 44′1° 4411° 4331° 4311° 43′ 32° 1° 44′ 1° 43′ 1° 43′ 1° 423′1° 421′ 1° 42′ 310 10 428/10 421'1° 42' 300 10 411 411'1° 41′ 2 3 1° 41'1° 41' 10 403 1° 423′1° 39′ 1° 41'1° 38′ 10 40110 37 1° 3911° 36' P (307) Setting out a Meridian. When two points in the direction of the North Star at its extreme elongation have been Fig. 204. obtained, as in Art. (305), the True Meridian can be found thus. Let A and B be the two points. Multiply the natural tangent of the Azimuth given in the Table, by the distance AB. The product will be the length of a line which is to be set off from B, perpendicular to AB, to some point C. A and C will then be points in the True Meridian. This operation may be postponed till morning. C If the directions of both the extreme Eastern and extreme Western elongations be set out, the line lying midway between them will be the True Meridian. |