Paper III. 1. Oct. 2nd 1854: at 8h 26m 545 P.M. mean time at ship: lat. 36° 10'S.: long. by ac. 18°E.: the observed distance of Antares (a Scorpii) from the C's near limb being 74° 46': index error +5” required the true longitude. : 2. Oct. 7th, 1854, A.M. at ship: approximate lat. 31°: long. 45° 45'W.. observed meridian altitude ( 51° 10'40": observer S. of the moon: index error +1' 9": eye 26 feet : required the latitude. 3. October 5th, 1854: long. 160° 30°W.: at 7h 10m 40s A.M. mean time at ship: the observed altitude of Polaris off the meridian being 46° 50' 20": eye 18 feet : required the latitude. . 4. Oct. 29th, 1854: the following observations were made for latitude by double altitudes, app. time at ship. obs. alt. O 29d 1h 13m 88 58° 37'25” bearing N.W.N. 29 3 38 20 35 16 20 eye 12 feet : course and distance in the interval S.E., S. 13 miles : lat. by ac. 40° 28'S. : long. 1° 5'E. : required the true latitude when the second observation was taken. 4a. Verify the above by Sumner's method. 5. Oct. 4th, 1854: lat. 34° 19'S. : long. 115° 6'E.: equal altitudes of the sun's lower limb being observed, when the corresponding times by chronometer were 3d 19h Om 50% and 3d 23h 50m 50: required the error of the chronometer for apparent and mean time at the place of observation, and also on mean time at Greenwich. 6. Oct. 10th, 1854: the observed altitude of the sun's lower limb in the artificial horizon being 65° 10' 40": index error +2' 4": required the true altitude of the sun's centre. : 7. A ship by dead reckoning makes E. 158 miles, but by observation, N.48°E. 130 miles : required the set and drift of the current. : Paper IV. 1. Nov. 29th, 1854: at 6h 42m 24' P.M. mean time at ship: lat. 24° 58'N.: long. by ac. 134°W.: the observed distance of Jupiter's centre from O's near limb being 79° 44' 20": index error -16": required the true longitude. 2. Nov. 27th, 1854: approximate lat. 34°: long. 48° 15°W.: observed meridian altitude ( 45° 10' 40": observer N. of moon : eye 17 feet: required the true latitude. 3. Nov. 15th 1854: long. 30° 15'W.: at gh 10m mean time at ship: the observed altitude of Polaris off the meridian being 56° 20' 30': index error -1' 2": eye 19 feet: required the latitude. m 4. Sept. 4th, 1854: the following observations were made for latitude by double altitudes, app. time at ship. obs. alt. O 22 56 50 bearing N.72°E. 3 23 8 25 59 5 5 eye 21 feet: course and distance in the interval N. 72°E. 19 miles : lat. by account 20° 51'S : long. 84° 5°W.: required the true latitude when the second observation was made. 4a. Verify the above by Sumner's method. 5. Dec. 9th 1854: lat. 48° 52'N.: long. 144° 46'E.: equal altitudes of the sun's lower limb being observed when the corresponding times by chronometer were gd 20h 12m 42 and 8d 22h 30m 46s : required the error of the chronometer for apparent and mean time at the place of observation, and also on mean time at Greenwich. 6. Nov. 17th, 1854: the observed meridian altitude of the sun's lower limb in an artificial horizon being 79° 46' 30': index error —l' 16" : required the true altitude of the sun's centre. 7. A ship by dead reckoning had made N.W.76 miles, but by observation it is found she has made S. 81°W. 61 miles : required the set and drift of the current. 2 GREAT CIRCLE SAILING. 1. If, on a Mercator's Chart, any two places (not on the equator, nor on the same meridian) be selected, we see that the shortest distance between them is a straight line, and providing no land intervene and the winds and currents are favourable for the purpose, the navigator has no occasion to change the course on which he starts, in order to sail from the one to the other. 2. On a terrestrial globe, apply a piece of thread (stretching it evenly) to the same two places, and it will then be seen, that the shortest distance between them is not on a straight line, but on a portion of a circle, and in order to to arrive at either place from the other, by such a route, the course to be sailed must be constantly varying. (a.) When both places are on the equator, or on the same meridian, the track on the great circle and that on the rhumb line are the same, and the course will be N.,S., E., or W., according to the relative position of the ports. 3. Now the Earth is an oblate spheroid, or sphere of revolution, and the small difference between the equatorial and polar diameters does not preclude our regarding it as a perfect sphere in numerous computations. 4 If a sphere be cut in any direction by a plane, the section must be a circle. (a.) If the plane pass through the centre of the sphere, we have a Great Circle, and the sphere is divided into two equal parts: the equator and meridians are examples. (b.) If the plane does not pass through the centre of the sphere, the section is a Small Circle, dividing the sphere unequally: take the parallels of latitude as examples. a 5. Two great circles always intersect in two points at the distance of a semicircle from each other. (a.) The equator, which is a great circle, bisects every other great circle on the earth's surface, and there must necessarily be two points in every such circle, equi-distant from the equator, and at the same time furthest removed from it: each of these points is called “ Vertex;" and the “ Latitude of Vertex,” which is the highest latitude attained in sailing on a Great Circle, is the nearest approach to the elevated pole. The meridian cutting the great circle at right angles, and dividing it into quadrants, is called the “Meridian of Vertex;" and the “Longitude from Vertex" is the arc of the equator intercepted between the meridian of any place and the meridian of Vertex. 6. The arc of a great circle joining two points, is the shortest distance between them on the surface of a sphere. (a.) The same great circle cannot be drawn through more than two points, selected at random on the sur face of a sphere. 7. A spherical triangle is the portion of space on the surface of a sphere, included between three arcs of intersecting great circles. All the computations for Great Circle Sailing are performed by Spherical Trigonometry. 8. The configuration of the earth is truly represented on Mercator's chart only at the equator, every where else it is distorted : the great circle track between any two places, drawn on such a chart, instead of appearing (as it really is,) the shortest, would be represented as a curved line. It is impossible, under any circumstances, to sail a ship on the true , great circle track, but a very close approximation may be made to it in some latitudes; and moreover a knowledge of Great Circle Sailing is very useful in all latitudes, for when adverse winds are encountered, it teaches on which tack to lay the ship, in order to arrive most speedily at her destination. These few observations will suffice, since it is not required to enter into calculations, and it is necessary to be provided with Towson's 6 Tables to facilitate the Practice of Great Circle sailing," at the end of which will be found explanations as to their use, as well as of the linear index which accompanies them. GREAT CIRCLE TRACKS AND DISTANCES, AND AZIMUTHS WITHOUT CALCULATION. Mr. Russel has supplied Diagrams of Great Circle Sailing (published by Mrs. Taylor, of the Nautical Academy, in the Minories), by which the science becomes little more than a mechanical operation, and which relieves it of all the difficulty of abstruse calculation, On Mr. Russel's sheet there is with a Spherical Diagram, a Mercator's Chart,—to facilitate the finding of the Great Circle, and the distance between any two given places. The principle on which the Diagram is constructed may be easily understood; for, as every Great Circle cuts the Equator in two points diametrically opposite, it follows that a series of Great Circles drawn through a given point in the Equator, in every possible direction, will all meet at another point in it, 180° distant from the former. Any person accustomed to navigate his ship by Great Circle Sailing will readily understand the nature and advantage of Mr. Russels plan; and we recommend it to the attention of commanders of vessels, who are bound on distant voyages. Vide Shipping Gazette, March 19, 1853. |