Example 4.-March 3rd, 1890; a.m. at ship; latitude by account 9° 45' S.; longitude 85° E.; the following observations of a Centauri were taken for latitude by double altitudes:- height of eye 20 feet; ship's course and distance in the interval between the observations, North, 17 miles: find the latitude when the second. observation was taken. In the isosceles triangle A P B, Fig. 5; given and the sides P A and P B, to find the side A B. dicular on A B, bisecting the P and the side A B; spherical triangle A P C, right angled at C, given find A C. P, the sidereal interval From P let fall a perpenthen in the right-angled In the same triangle given P A and A C to find D. In the spherical triangle Z P A, Fig. 5; given P A, Z A, and A, to find P Z, the co-latitude. EXAMPLES FOR PRACTICE IN FINDING A SHIP'S POSITION FROM TWO OBSERVATIONS N.B. To correct the altitude for run the azimuth is required; this can be taken from Norie's A and B Tables. Example 1. December 3rd, 1890, at ship, the following observations of the sun were taken : Approx. ship time. height of eye 17 feet. At the time of taking the first observation the ship by dead reckoning was in latitude 36° S.; longitude 10° W. The true course in the interval S. 27° E., distance 32 miles. The chronometer was supposed to be correct for Greenwich mean time. Required the latitude at the time of taking the second observation. Ans. Lat. 36° 13′ 55′′ S. Example 2.-November 3rd, 1890, at ship, the following observations of the sun were taken : height of eye 26 feet. When the first observation was taken the ship was in latitude by account 19° N.; longitude by account 65° E. The true course in the interval was S. 24° W., distance 32 miles. The chronometer was supposed to be 15m. 40s. slow for Greenwich mean time. Required the latitude when the second observation was taken. Ans. Lat. 18° 47′ 57′′ N. Example 3.-January 10th, 1890, at ship, the following observations of the sun were taken : Index error of the sextant 2' to be added, height of the eye 26 feet. When the first observation was taken the latitude by account was 47° N.; longitude by account 52° 30′ W. The true course in the interval was S.W., distance 31 miles. The chronometer was supposed to be correct for mean time at Greenwich. Required the latitude of the ship when the second observation was taken. Ans. Lat. 46° 48' N. Example 4.-June 14th, 1890, at ship, the following observations of the sun were taken : height of eye 19 feet. At the time of taking the first observation the ship was by dead reckoning in latitude 3° N.; longitude 40° 30′ W. The true course in the interval was S. 66° W., distance 20 miles. The chronometer was supposed to be correct for Greenwich mean time. Required the latitude at the time of taking the second observation. Ans. Lat. 3° 2' 54" N. Example 5.-January 26th, 1890, at about 10h. 57m. p.m. ship time, and again at about 4h. 5m. a.m. January 27th the following observations of Regulus (a Leonis) were taken : was in latitude by account 49° 50' N.; longitude by account 11° W. The true course in the interval E. 8° N., distance 36 miles. The chronometer was supposed to be correct for mean time at Greenwich. Required the latitude of the ship when the second observation was taken. Ans. Lat. 49° 50′ N. Example 6.-January 10th, 1890, at about 8h. 5m. p.m. ship time, and again January 11th at about oh. 20m. a.m. ship time, the following observations of Sirius (a Canis Majoris) were taken : height of eye 19 feet. When the first observation was taken the position of the ship was supposed to be latitude 50° N., longitude 30° W. The true course in the interval was west, distance 38 miles. The chronometer was supposed to be 2m. 10s. fast for mean time at Greenwich. Required the latitude when the second observation was taken. Ans. Lat. 50° 10′ N. Example 7.-August 12th, 1890, at about 11h. 44m. p.m. ship time in lat. by dead reckoning 51° 30′ N., long. by dead reckoning 6° W., when the chronometer (corrected) indicated oh. 4m. 50s. the following simultaneous observations were taken :-Capella (a Auriga) observed altitude was 19° 36′ 30′′ east of the meridian and Benetnasch (ʼn Ursa Majoris) observed altitude was 26° 55′ 40′′ west of the meridian, height of the eye 24 feet. Required the ship's position. Ans. Lat. 50° 58′ N.; Long. 6° 12′ W. Example 8.-March 2nd, 1890, at about 7h. 22m. p.m. ship time in latitude by account 46° 43′ N., longitude by account 52° 30′ W., the following observations were taken when the chronometer indicated 10h. 42m. 20s. Procyon (a Canis Minoris) observed altitude 44° 17′ 30′′ east of meridian and Aldebaran (a Tauri) observed altitude 53° 46′ 20′′ west of meridian, height of the eye 24 feet. The chronometer was supposed to be 6m. 36s. slow on mean time at Greenwich. Required the latitude and longitude by observation. Ans. Lat. 47° o' N.; Long. 52° 4′ W. Elements from the Nautical Almanac, see page 585. |