the Bearing as of any ordinary line. The number of degrees in the reading will be the desired variation of the needle. Fig. 201. (301) By the North Star, when in the Meridian. The North Star, or Pole Star, (called by astronomers Alpha Ursa Minoris, or Polaris), is not situated precisely at the North Pole of the heavens. If it were, the Meridian could be at once determined by sighting to it, or placing the eye at some distance behind a plumbline so that this line should hide the star. But the North Star is about 11 from the Pole. Twice in 24 hours, however, (more precisely 23h. 56m.), it is in the Meridian, being then exactly above or below the Pole, as at A and C in the figure. To know when it is so, is rendered easy by the aid of another star, easily identified, which at these times is almost exactly above or below the North Star, i. e. situated in the same vertical plane. If then we watch for the moment at which a suspended plumb P B ★D C line will cover both these stars, they will then be in the Meridian. The other star is in the well known constellation of the Great Bear, called also the Plough, or the Dipper, or Charles's Wain. Two of its five bright stars (the right-hand ones in Fig. 202) are known as the "Pointers," from their pointing near to the North Star, thus assisting in finding it. The star in the tail or handle, nearest to the four which form a quadrilateral, is the star which comes to the Meridian at the same time with the North Star, twice in 24 hours, as in Fig. 202 or 203. It is known as Alioth, or Epsilon Ursæ Majoris.* To determine the Meridian by this method, suspend a long plumb-line from some elevated point, such as a stick projecting from the highest window of a house suitably situated. The plumbbob may pass into a pail of water to lessen its vibrations. South of this set up the compass, at such a distance from the plumb-line that neither of the stars will be seen above its highest point, i. e. in Latitudes of 40° or 50° not quite as far from the plumb-line as it is long. Or, instead of a compass, place a board on two stakes, so as to form a sort of bench, running East and West, and on it place one of the compass-sights, or anything having a small hole in it to look through. As the time approaches for the North Star to be on the Meridian (as taken from the table given below) place the compass, or the sight, so that, looking through it, the plumb-line shall seem to cover or hide the North Star. As the star moves one way, move the eye and sight the other way, so as to constantly keep the star behind the plumb-line. At last Alioth, too, will be covered by the plumb-line. At that moment the eye and the plumb-line are (approximately) in the Meridian. Fasten down the sight on the board till morning, or with the compass take the bearing at once, and the reading is the variation.† Instead of one plumb-line and a sight, two plumb-lines may be suspended at the end of a horizontal rod, turning on the top of a pole. The line thus obtained points to the East of the true line when the North Star is above Alioth, and vice versa. sa. The North Star is exactly in the Meridian about 17 minutes after it has been in the same vertical plane with Alioth, and may be sighted to after that interval of time, with perfect accuracy. * The North Pole is very nearly at the intersection of the line from Polaris to Alioth, and a perpendicular to this line from the small star seen to the left of it in Fig. 202. † If a Transit or Theodolite be used, the cross-hairs must be illuminated by throwing the light of a lamp into the telescope by its reflection from white paper. 7 45 р. м. Another bright star, which is on the opposite side of the Pole, and is known to astronomers as Gamma Cassiopeiæ, 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 following 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. December, 8 24 Р. М. 7 06 Р. М. * To calculate the time of the North Star passing the Meridian at its upper culmination: 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: 19 minutes. Taking this from 5h. 11m. A. M., we get 4h. 51 m. 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 12o 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 approaches to within half a degree, when it will again recede. The brightest star in the Northern hemisphere, Alpha Lyræ, will be the Pole Star in about 12,000 years, being then within about 5o 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, 027 P.Μ. 019 Α.Μ. 1147 А.М. 11 35 р.М. 11 08 А.М. 1056 р.м. 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 Jan. 1, 1850, is 1° 29′ 25′′; for 1860, 1° 26′ 12′′.7; for 1870, 1° 23° 01"; for 1880, 1° 19′50′′.4; for 1890, 1° 16′ 40′′.7; for 1900, 1° 13′ 32′′.2. |