4. Two ports lie under the same meridian, one in latitude 52° 30' N. and the other in latitude 47° 10' N. A ship from the southernmost sails due east, at the rate of 9 miles an hour, and two days after meets a sloop which had sailed from the northernmost port; required the sloop's direct course and distance run. Course S. 53° 28' E., or S.E. E.; distance run 537.6 miles. 5. If a ship from lat. 48° 27' S. sail S.W. by W. 7 miles an hour, in what time will she arrive at the parallel of 50° S? In 23.914 hours. 6. If after a ship has sailed from lat. 40° 21′ N. to lat. 46° 18′ N., she be found 216 miles to the eastward of the port left; required her course and distance sailed. Course N. 31° 11' E., distance 417.3 miles. TRAVERSE SAILING 98. Is where a ship, in going from one place to another, sails on different courses; the determination of the single course and distance from the one place to the other is called working or compounding the traverse. The method of proceeding is to rule seven columns (see next page), the first to contain the courses, the second the number of points and quarter points. in these courses which may be found from the table of Rhumbs (Tab,. XXVIII.), the third the distances sailed on these courses, the fourth and fifth the differences of latitude in two columns entitled N. and S., in the former of which the dif. of lat. for the N. courses is entered, and in the latter of which the dif. of lat. for the S. courses; the sixth and seventh contain the departures, the former those of the E. courses, the latter those of the W. courses, sometimes called eastings and westings. When these several particulars are all inserted, the columns are added up, and the difference of the sums of the N. and S. columns will be the whole difference of the latitude which the ship has made, and the difference of the sums of the E. and W. columns will be her whole departure. The columns appropriated to the difference of latitude and departures are usually filled up from a table (Table I.), already computed to every quarter point of the compass, and to all distances from one mile up to 300; so that by entering this table with any given course and distance, the proper difference of latitude and departure is found by inspection. The course is found at the top or bottom of the page, and the distance in the first column, the dif. of lat. in the second column, and the departure in the third, if the course be found at top; but if at the bottom, the lat. and dep. columns are interchanged, as may be seen by the entitling in the bottom of the columns. If the distance sailed be more than 300 miles, it will exceed the limit of the table; but the difference of latitude and departure may still be determined from it by this simple operation: divide the given distance by any number that will give a quotient not exceeding 300; enter the table with this quotient, and multiply the corresponding diff. of lat. and dep. by the assumed divisor, and there will result the diff. of lat. and dep. due to the proposed distance. If there be a remainder add the diff. of lat. and dep. corresponding to this. Or take any two numbers whose sum is equal to the given distance; the sum of their differences of lat. and dep. will be the lat and dep. of the given distance. These rules depend upon the principle that for the same course the differences of latitude and departure are proportional to the distance run, which will be evident if we recollect that dist., diff. of lat. and dep. form a right angled triangle, and that two right angled triangles are similar when an acute angle of one is equal to an acute angle of the other. 1. A ship sails from lat. 24° 32' N., and runs the following courses and distances, viz. 1st, S.W. by W., distance 45 miles; 2d, E. S. E., distance 50 miles; 3d, S. W., distance 30 miles; 4th, S. E. by E., distance 60 miles; 5th, S.W. by S. W., distance 63 miles required her present latitude, with the direct course and distance from the place left, to the place arrived at. It appears from the results of this table that the difference of latitude made by the ship during the traverse is 149.2 S. =2° 29' S. It appears also that the departures east are equal to the departures west, so that the ship has returned to the meridian she sailed from, consequently the direct course from the place left to that come to is due south, and the distance is equal to the difference of latitude, which is 149.2 miles. N There is another mode of finding the direct course and distance, much practised by seamen, viz., by construction. For this purpose the mariner's scale is employed, which is a two foot flat rule exhibiting several scales on each side, by help of which and a pair of compasses the usual problems in sailing may be all solved. One of these scales, which is called a scale of rhumbs, is a scale of chords, to every point and quarter point of the compass; and another is a more enlarged scale of chords to every degree. Both these scales are constructed for a circle with the same common radius, so that the chords on the scale of rhumbs belong to that circle whose radius equals the chord of 60° on the scale of chords; and the method of laying down a traverse from these scales, and a scale of equal parts, and of thence measuring the equivalent single course, and distance made good, will be at once understood from the example. Construction of the traverse for the last example is as follows: With the chord of 60°, taken from the line of chords on the mariner's scale, describe the horizon circle, and draw the north and south line N. S. From the line of rhumbs take the chords of the several courses, and as these are all southerly they must be laid off from the south point S, those which are westerly to the left, and those which are easterly to the right, their extremities being marked 1, 2, 3, &c., in the order of the courses. This done, lay off from any scale of equal parts, and in the direction of A1, the distance AB sailed on the first course; then in the direction parallel to A2, the distance BC sailed on the second course; in the direction parallel to A3, the distance CD on the third course; in the direction parallel to B D F C E A4, the distance DE on the fourth course; and, lastly, in the direction parallel to A5, the distance EF on the fifth course; then F will represent the place of the ship at the end of the traverse; FA, being applied to the scale of equal parts, will show the distance made good, and the chord of the arc included between this distance, and the meridian, being applied to the line of rhumbs, will show the direct course. In the present case the intercepted arc will be 0, showing that F is on the meridian of A. 2. A ship from Cape Clear, in lat 51° 25′ N., sails 1st, S.S.E. E., 16 miles; 2d, E.S.E., 23 miles; 3d, S.W. by W. W., 36 miles; 4th, W. N., 12 miles; 5th, S.E. by E. E., 41 miles: required the distance made good, the direct course, and the latitude reached? Then by means of the whole dif. of lat. and dep., which are the two perpendicular sides of a right angled triangle, one of the acute angles and hypothenuse, or the direct course and distance, may be computed as follows: therefore, as the difference of latitude is south, and the departure east, the direct course is S. 18° 12' E., and the distance made good 62.74 miles. To construct this traverse, describe, as before, the horizon circle, with a radius equal to the chord of 60°, and taking from the line of rhumbs the chord of the first course, 24 points, apply it from S to 1, to the right of SN, as this course is south-easterly; apply, in like manner, the chord of the second course, six points from S to 2, also to the right of the meri dian line; apply the chord of the third course, 5 points from S to 3, to the left of the meridian, the chord of the fourth course, 74 from N. to 4, to the left of N S, this course D S F of equal parts, we shall find it reach from 0 to 623; and applying the distance Sa to the line of chords, we shall find it reach from 0 to 18°, or by the scale of rhumbs it will be found to measure one point and a half. |