eye, 20 ft.; bearing by compass S.E. by E. E.; time by chron., 8h 22m 40'4, which had been found fast 1" 41"1 for G.M. noon on March 30th, and on June 1st was 2 252 fast. Find the long., true bearing, and dev., the var. being 12° 15′ W. 3. September 1st, about 3h 30m P.M. at ship, in lat. at noon 51° S., long. D.R. 175° E.; the obs. alt. of the Sun's L.L. was 14° 52′ 20′′; ind. cor., -7' 10"; eye, 15 ft.; bearing by compass N. 50° 30′ W.; time shown by chron., 3h 44m 40', which had been found 13 03 slow for G.M. noon on February 15th, and on August 1st was 10" 30′ slow. Find long. at sights and noon, the run since noon being S.W. by W. W. 53 miles. Also find true bearing, comp. error, and dev., the var. being 16° 10′ E. 4. September 23rd, about 7 A.M. at ship, in lat. at noon 32° S., long. D.R. 55° E.; the obs. alt. of the Sun's L.L. was 10° 36'; ind. cor., 2' 10" ; eye, 19 ft.; bearing by compass East; time shown by chron., 3h 0m 35', which had been found 5" 455 slow for G.M. noon on March 31st, and or June 14th was slow 4" 45"5; run since sights, N. 59° W. 58 miles. Find long. at sights and noon. The var. from chart being 15° 40′ W., find truc bearing, comp. error, and dev. 5. September 1st, about 1 P.M. at ship, in lat. 11° 34' 20" S., long. D.R. 144° E.; the obs. alt. of the Sun's L.L. was 65° 2′; ind. cor., -7′ 17′′; eye, 27 ft.; bearing by compass N. 40° W.; time shown by chron., 2h 32m 48', which had been found slow 1 0m 10' for G.M. noon on April 1st, and on May 1st was 58" 40′ slow. Find the long. and the var. being 5° 45′ E., find comp. error and dev. 6. September 22nd, about 8h 50m A.M., when the chron. showed 0h 20m 32'; the obs. alt. of the Sun's U.L. was 30° 59′ 30′′; ind. cor., 2′ 5′′ off the arc; height of eye, 30 ft.; bearing by compass S.E. E.; var., 11° 30′ W.; lat. at obs., 42° 16' N.; long. by acct., 70° 40′ W.; on June 16th the chron. was slow 1" 14" 30' for G.M. noon, and on August 5th it was 1' 11" 8′ slow. Required long., true azimuth, and dev. .; 7. September 23rd, about 1 45 P.M., lat. at noon, 40° 18' S.; the obs. alt. of the Sun's L.L. was 42° 55' 40"; eye, 7 ft.; long by acct., 148° E. time by chron., 3a 53TM 29′, which had been found fast 16" 20′ for G.M. noon on May 4th, and on August 2nd was 10" 47' fast; run from noon to obs., W.N.W. 21 miles; the sun's comp. bearing was N.W., and the var. 10° 45′ E. Find the long., true bearing, and dev. for the direction of the ship's head. 8. August 5th, about 2h 30TM P.M., in lat. at noon 30° 4′ 45′′ S., long. by acct. 94° E.; the obs. alt. of the Sun's U.L. was 31° 32'; ind. cor., 4' 44"; height of eye, 19 ft.; bearing by compass, N.W. N.; the chron. showed 8 19 41', and had been found to be fast of G.M.T. on May 23rd 7TM 33', and losing daily 21. Find the long. at sights and noon; and if the var. from chart was 14° 20′ W., find true azimuth and dev. for the direction of the ship's head. Run since noon, S. 40° E. 30 miles. 9. September 1st, about 4 P.M., in lat. 2° 10' N., long. D.R. 55° 45′ E.; the chron. showed 10h 57m 5'; the obs. alt. of the Sun's U.L. was 29° 11′ 40′′; ind. cor., 50"; eye, 22 ft.; bearing by compass N. 88° 30' W.; on March 24th the chron. was slow of G.M.T. 56m 34', and on May 4th it was slow 13m 27. Find the long., true azimuth, and dev., the var. being 4° 15′ W. 10. September 1st, about 4" 45" P.M., in lat. at noon 0° 36' N.; long. D.R. 93° W.; the obs. alt. of the Sun's L.L. was 18° 3'; height of eye, 32 ft.; ind. cor., 3' 27"; bearing by compass S. 87° 15′ W.; the chron. showed 10h 57m 27, and had been found correct for M.T.G. on June 30th, and slow 4" 50′ on July 27th; run from noon to obs., S. 35° W. 44 miles. Find the long. at sights and noon; also if the var. is 2° 30′ E., find true azimuth and dev. 11. August 20th, about 8 20 A.M., in lat. at noon 12° 31' S., long. by acct. 168° W., when a chron. showed 7h 19m 19", which had been found 18m 19. slow for G.M. noon on June 8th, and gaining daily '9'; the obs. alt. of the Sun's L.L. was 29° 46′ 10′′; ind. cor., - 2′ 22′′; eye, 45 ft.; run since obs., S. 62° W. 34 miles; Sun's comp. bearing was N. 68° 30' E.; var., 9° 15' E. Find long. at obs. and noon, true azimuth, and dev. 12. September 23rd P.M., in lat. at noon 8° 44' N., long. by acct. 174° W.; the obs. alt. of the Sun's U.L. was 53° 29′ 20′′; ind. cor., 3' 19"; eye, 41 ft.; bearing by compass, W. by S. S.; var., 8° 40′ E.; time by chron., 1h 47m 27', which had been found 1m 58′ slow for G.M. noon on August 18th, and losing daily 1'1; run from noon to obs., N. 28° E. 26 miles. Find long. at sights and noon, true azimuth, and dev. CHAPTER XVIII. SUMNER'S METHOD BY PROJECTION. ART. 88.-At any given moment the Sun is vertical over some place on the Earth's surface, and if a circle be drawn with this point as the centre, the Sun would have the same altitude from all points on the circumference of this circle. Advantage is taken of this fact to find the Ship's Position by Projection on a chart. Two points on the circumference of the circle can be found from the Sun's altitude, and two assumed latitudes; the projection on the chart of the arc of the circle of equal altitudes passing through these two positions would pass through the actual position of the ship. After an interval of time another altitude is observed, and with the same assumed latitudes, two other points on a new circle of position are found, and projected on the chart in the same way. The intersection of the two projected lines gives the ship's position. In practice, the longitudes computed are marked on Mercator's Chart on the parallels of assumed latitudes, and connected by straight lines called Lines of Position. The point of intersection of these lines gives the latitude and longitude of the ship. The Sun's true bearing is at right angles to the line of position at each observation - towards the east if A.M., and towards the west if P.M. If the ship changes place during the interval, the first line of position has to be moved (parallel to itself) according to the course and distance sailed. Thus in figure, NESW is plane of observer's horizon, NZS the celestial meridian, X the position of object at first observation, and Y its position at second observation; Z the zenith, ZX and ZY the zenith distances of object. With X as centre and XZ as radius, describe a circle. This will be a circle of position for first observation, because the zenith of all places having the object at X would be situated on its circumference. Similarly, with Y as centre and YZ as radius, draw a second circle of N position cutting the first in the points Z and C. Hence either Z or C is the position of the observer. With suitably selected observations, these points are so wide apart that the true one may be chosen by comparison with the latitude by account. The lines ZXA, ZYB are portions of vertical circles, showing the bearings of the objects, and are seen to cut the circumferences of the circles of position at right angles, hence the bearing of the object is always at right angles to the line of position, which is a tangent to the circle of position at Z. W X E A S FIG. 139. B ART. 89. Rules for working Sumner problem(1) Find G.M.T.'s. (2) Find correct declination for each time, and polar distances, correct observed altitudes. (3) With the first altitude and polar distance, using the two assumed latitudes, work as in chronometer problem for two-hour angles, and hence two longitudes. These when projected on the chart and joined would give the first line of position. With the second altitude and polar distance, using the two assumed latitudes, find as before two longitudes. These positions are projected on the chart and joined for the second line of position. The direction of a line of position is taken from the chart, like a course, and may be named in either of the two ways the line trends. The true bearings are at right angles to the lines of position, and are obtained by subtracting the direction of each line from 90°; and marked towards the east for E.H.A.'s; and towards the west for W.H.A.'s. The run is laid off from any point of the first line, and where a parallel line to the first line, through the end of the run, cuts the second line is the position of the ship. Example. August 5th, about 9h 15m A.M., in long. by account 55° 15′ W.; when a chron. correct for M.T.G. showed 1 2m 21, the obs. alt of the Sun's L.L. was 44° 14' 20"; ind. cor., - 2' 7"; eye, 30 ft.; and again P.M. at ship on the same day, when the chron. showed 7 5 23', the obs. alt. of the Sun's L.L. was 39° 21′ 25′′; run in the interval, S. W. 63 miles. Find the line of position and Sun's true bearing at the first obs., and position of the ship at the second obs. by Sumner's method, by projection, assuming lats. 47° and 47° 45' N. |