4 satellites tables have been computed and published, calculated in this country for the meridian of Greenwich, so that by comparing the period of an eclipse or any other phenomenon of these bodies, as observed at any distant place, with the time in the tables when the same appearances are observable at Greenwich, the difference between the two meridians of the difference of longitude will be readily ascertained. Unfortunately however for the mariner the operations requisite for observing the eclipses of Jupiter's satellites are, from the constant motion of a ship at sea, next to impracticable, nor has any method of surmounting the difficulty yet been discovered. The attention of astronomers and navigators has therefore been of late drawn to the best mode of measuring the angular apparent distance between the sun and the moon, or between the moon and some remarkable star near her path: and for this purpose the Nautical Almanacks contain every calculation requisite for assisting in the solution of this very nice problem. The instruments required for this operation are a good watch, which can be depended on for keeping time within the error of a minute for six hours together, and a quadrant of Hadley's construction, or rather a sextant, the limbe being one-sixth part of a circle containing 60°, but on account of the double reflection comprehending in fact 120°, fitted up with a small telescope the more accurately to ascertain the instant of the moon's contact with any given star. The precise moment of this contact being ascertained, and the altitudes of both bodies being at the same time carefully measured by assistants, the materials are obtained for deter mining the longitude of the place of observation; for com paring the difference in time between the contact of the two bodies as observed at the ship and as stated in the Nautical Almanack for the meridian of Greenwich, and converting that difference into degrees and minutes of the equator, the longitude of the ship will be ascertained. As As the state of the atmosphere will not at all times allow the proper operations to be performed, for determining the latitude and longitude by celestial observation; and as it is the indispensable duty of the navigator to avail himself of every method of ascertaining his position during his voyage, various modes of calculating a ship's place have been adopted, such as Plane sailing, Traverse sailing, Parallel sailing, Middle latitude sailing, Mercator's sailing, Oblique sailing, Windward sailing, Current sailing; all of which are useful according to the circumstance of the voyage. PLANE SAILING. In this method of navigation, the earth is supposed to be not a globe but one vast extended plane, in which the meridians instead of centring at the poles lie parallel to each other and every where equidistant, and where consequently the degrees of longitude are, at all distances from the equator, of equal extent on the surface of the earth. This supposition, it is true, is entirely contrary to fact: but in short courses and in latitudes adjoining to or not far removed from the equator, the errors occasioned by such a supposition are not of great importance. In Plane sailing the things given or required are the Course or point of the compass on which the ship sails, the Distance run on that course in a given time, the Difference in latitude between the ship's place at the beginning and at the end of the course, and the Departure or distance between the meridian of the place sailed from and that of the place come to the difference of latitude is also called the Soutbing, and Northing, and the departure is called the Easting, and Westing. CASE 1st Given the course and distance, to find the difference of latitude and the departure. If a vessel sail from Cape St. Vincent in Portugal, situated situated in N. lat. 37° 3', 156 nautical or geographical miles, in a direction 3 points to the westward of south, that is south west by south, what is her latitude at the end of the course, and how much has she departed from the meridian of the cape? Let an indefinite line be drawn on paper N and S, to represent the meridian passing through Cape St. Vincent: choose any point in the northern part of this line for the position of the cape or of the ship considered as at it, and describing round that point a circle (or so much only as may be requisite), set off upon this arch from the southern part of the meridian, and on the left hand or western side, the number of degrees and minutes corresponding to the angle of the course SW by S or 3 points, which at 11° 15 will be equal to 33° 45', and through this intersection drawing another indefinite line from the point representing the cape, it will be the direction of the ship's course, on which measuring off the distance sailed 156 miles, the ship's. place at the end of the run will be obtained. If from this last point a line be let fall perpendicularly on the meridian of the cape, it will cut it in a point showing the latitude of the ship's place come to, and the perpendicular itself will show how much she has departed westerly from that meridian. By this process will be formed a rightangled triangle of which the angle of the course, (and consequently its complement to 90), with the hypothenuse or distance run being given, we can by the rule given in case 4th of rightangled trigonometry, (vol. i. p. 415) discover the remaining sides: thus, As radius For the Departure. 90° 00′ = 10.00000 156 = 9.74474 2.19312 Το To the sine of the angle of the course 33 45 This difference of latitude being divided by 60 gives 2 degrees 9.7 or nearly 10 minutes; and the ship having sailed from a N. latitude southerly, consequently nearer to the equator, that quantity subtracted from the lat. of the cape 37° 3′, leaves 34° 53′ N. for the latitudes come to at the end of her course, and she has departed 86.7 or 87 miles to the westward of the meridian of the point where she set out. CASE 2d. Given the course and the difference of latitude, to find the distance and departure. A ship from a port in N. lat. 22° 36′ sailed on a course NNELE, until by observation she came to be in lat. 26° 14′, required the distance run, and the departure easterly from the meridian of the port. The course NNE E or two points and a half to the eastward of N. forms an angle of 28° 7': the difference of lat. between the first and last stations of the ship 22° 36' and 26° 14' is 3° 38′ equal to 218 nautical miles: we have therefore in a rightangled triangle the angles and one of the sides, and by Case 3d of rightangled trigonometry, (vol. i. p. 414), the other side and the hypothenuse may be found, thus. As the sine of the complement of the course 61° 52 = 9.94543 Το CASE 3d.-Given the distance run and the diff. of lat. to find the course sailed and the departure. A ship from James-town in St. Helena in S. lat. 15° 55' sails 238 miles between N and W until she comes into lat. 1951, required the point of the compass on which she sails and her departure from the meridian of St. Helena. By the application of the rules given in case 2d of rightangled Trigon. (vol. i. p. 415) if the distance be made radius the diff. of lat. will be the sine of the complement of the course or 50° 37', consequently the course itself 39° 22' which divided by 11° 15', the quantity contained in 1 point of the compass will quote 3 points; and as the ship sailed between N and W this quantity reckoned on the compass to the westward of N will point out NW N for the course held during the run in question. By means of the distance and diff. of lat. the departure will be found 151 miles westerly from the meridian of James-town. These three cases include all the possible varieties of plane sailing, for other cases in which the departure is supposed to be given can never occur, since that departure can never be discovered but from the previous knowledge of the course, distance, and difference of latitude, or at least of some two of these particulars. |