EXAMPLES. Ex. 1. A ship from lat. 55° 1' N., long. 1° 25′ W., sails S.S.E. E., 246 miles: required the lat. in and long. in. Entering Traverse Table II, with course S. 2 points E., and distance 246, we obtain diff. lat. 2170, and dep. 116·0. The course 2 points, and half mer. diff. lat. 181.5 (in diff. lat. column), the nearest found in the Table is 1817, the corresponding departure is 971, which multiplied by 2 (having divided mer. diff. lat. by 2), gives diff. long. 1942 miles. Ex. 2. A ship from lat. 42° 36′ S., long. 178° 43′ E., sails S.E. E., 299 miles: find lat. in and long. in. Course 4 points, and dist. 299, give diff. lat. 178'1, dep. 240'2. Course 4 points, and half mer. diff. lat. 124 (in diff. lat. column), give in dep. column 167.1, which doubled is 334′2, the diff. long. 6,0)33,4°2 Long. left 178° 43′ E. D. long. 5 34 E. 184 17 E. 360 0 Ex. 3. From lat. 50° 48' N., and long. 1° 10' W., sailed S. 41° E., 275 miles: required the lat. in and long. in. In the Traverse Table at the distance 275, and course 41°, the corresponding true diff. lat. is 207'5, or 3° 27'5, which being subtracted from 50° 48′ N., the lat. in is 47° 20'5 N.; taking out the mer. parts for 50° 48′, and 47° 20′5, the mer. diff. lat. is found to be 317, to half which as a true diff. lat., and the course 41°, the dep. is 1378, twice which is 2756, that is, the diff. long. is 4° 36′ E. hence the long. in is 3° 26′ E. Ex. 4. From lat, 50° 30' N., and long. 37° 55′ W., sailed S.W. S., until arrived at lat. 52° 15' N. EXAMPLES FOR PRACTICE. Ex. I. A ship from lat. 51° 29' S., long. 28° 35' W., sails N.N.E. E., 78 miles; N. by E., 112 miles; N.N.W., 61 miles; and N.W. W., 82 miles: required the latitude and longitude arrived at. Ex. 2. A ship from latitude o' 5′ N., and long. 0° 17′ W., sails S. W. by S., 7 miles; S. by E., 22 miles; S.S.W. W., 8 miles; and N.E. by E., 20 miles: required the compass course and distance to Cape Palmas, by Mercator's Sailing. Variation of compass 19° W.; lat. of Cape Palmas 4° 22′ N., long, 7° 44′ W. Ex. 3. A ship from the Cape of Good Hope, lat. 34° 29' S., long. 18° 23′ E., sails as follows (true courses) :-S.W. by W., 47 miles; S.W. S., 80 miles; W. S., 87 miles; S.W. by S., 140 miles; S.S.W. W, 118 miles; S.E., 124 miles; W. by N., 130 miles; W.S.W., 140 miles: required the latitude and longitude arrived at, and course and distance from thence (by Mercator's Sailing) to Cape Horn in lat. 55° 58' S., long. 67° 21′ W. Ex. 4. A ship from Cape Finisterre in lat. 42° 53′ N., long. 9° 15′ W., sails the following (true) courses:-W. by S., 64 miles; W. by N. N., 84 miles; W. ¦ S., 50 miles; S.W. S, 73 miles; N.W. by W., 85 miles; W. S., 65 miles; W. by N. N., 78 miles: required the latitude and longitude arrived at, and the course and distance thence to New York in lat. 40° 42′ N., long. 73° 59′ W. REMARKS ON MIDDLE LATITUDE AND MERCATOR'S SAILINGS. "The difference of longitude found by middle latitude is true at the equator, and very nearly true for short distances in all latitudes, especially when the course is E. or W. In high latitudes, when the distance is great and the course oblique, the error becomes considerable; but the result may be made as accurate as we please by sub-dividing the distance run into small portions, and finding the difference of longitude for each portion separately. The difference of longitude deduced by middle latitude sailing is too small: an estimate of the error for places on the same side of the equator may be formed by the help of a few cases. Suppose the course 4 points or 45°, and the difference of latitude 10 or 600'; then if this difference of latitude is made good in any latitude below 30°, the error of the difference of longitude will not exceed 2′; if made good between the parallels of 40° and 50°, the error will be about 3'; and between 60° and 70° about 19', or § of a degree. For smaller distances the errors will be much less, and for greater distances much greater, as they vary in much more rapid proportion than the distances. It has been observed before that when the course is large, the difference of longitude should be found by middle latitude in preference to Mercator's Sailing; because, although the latter is mathematically correct in principle, yet a small error in the course may, when the course is large, produce a considerable error in the difference of longitude. The reason of this is easily shown. In middle latitude sailing we convert the departure into difference of longitude. The process increases the departure in a proportion which is less than 2 to 1 in all latitudes below 60'; and exceeds 3 to 1 in all latitudes beyond 70°. The error of the departure, increased in the same proportion, becomes thus the error of difference of longitude. Now when the course is nearly E. or W., the departure is nearly the same as the distance, and an error of some degrees in the course does not affect the departure sensibly; hence in this case the error of the difference of longitude depends on that of the distance alone. But in Mercator's Sailing, on the other hand, we convert the meridional difference of latitude into difference of longitude, and the process, when the course is large, converts a given meridional difference of latitude into a difference of longitude much greater than itself; and thus increases the error of the meridional difference of latitude in the same proportion. Thus, for example, at the course 80', the difference of longitude exceeds the meridional difference of latitude in the proportion of 6 to 1; at the course 85° this proportion is 11 to 1. Now when the course is large, a slight change in it sensibly affects the difference of latitude and also the meridional difference of latitude, which is deduced directly from it. In high latitudes the meridional parts vary rapidly, and the error of the difference of longitude is increased accordingly; hence the precept more especially demands attention in high latitudes."-Raper's Practice of Navigation, pp. 103, 104. THIS is the process of finding the ship's place at noon-that is, its latitude and longitude, having given the latitude and longitude at the noon preceding, or a departure taken since, the compass courses and distances run in the interval, the leeway (if any), variation and deviation (if any), direction and rate of current (if any), &c., &c. 1o. RULE L.* Correct each course for leeway and variation (see Rule XXXVI to XXXVIII, pages 77 to 84), which arrange in the tabular form as in the example following. Add together the hourly distances sailed on each course, and insert the same in the Table, opposite the true course. (a) When a departure has been taken, consider the opposite to the bearing as a course, which correct for variation, and insert in the Table as an actual course, with the distance of the object as a distance. The departure course is generally put down in the Table as the first course. As the ship leaves the land, the bearing (by compass) of some prominent object or known headland is taken, and its distance is generally estimated by the eye; this process is called "taking a departure." The latitude and longitude of the landmark are known; and thence, by supposing the ship to have sailed on a course the opposite to the bearing of the object, through the distance that object is off, we thus obtain, on commencing a voyage, a determinate starting point, from whence to reckon the subsequent courses and distances. Thus, suppose for example a ship leaving the Tyne observes Tynemouth Light dipping, and setting it finds its bearing to be W. by N., distant (by estimation) 20 miles. Now in sailing from Tynemouth lights to the present position of the ship, she would have to sail in the opposite direction to the bearing of the lights, viz., E. by S., 20 miles. At the end of the day, the Day's Work gives us the change of the ship's place as referred to the landmark, and not the supposed position. For methods of determining the distance, sce Raper's Practice of Navigation, on Taking Departures, ch. IV, pp. 114—122. (b) The set of a current is to be corrected for variation, and inserted in the Table as a course; the drift being taken as a distance. The current course is generally inserted in the Table as the last course. 2°. Take out of the Traverse Tables (Table I or II, Raper or Norie) the difference of latitude and departure to each course and distance (see page 98), and proceed to find the difference of latitude and departure made good as directed in Rule XLII, page 98, Traverse Sailing. Nearly the entire process of computing the Day's Work has already been given, and if the learner has thoroughly mastered the rules laid down in the preceding pages, he will find no difficulty in working the Day's Work without reference to them. 3°. Find the course and distance made good (see Rule XLIII, page 100). 4°. Find the latitude in by applying the difference of latitude to the latitude from (see Rule XXXII, page 72). If a departure has been taken, the difference of latitude is to be applied to latitude of the point of land; if otherwise, to yesterday's latitude. 5°. To find the difference of longitude by Middle Latitude Sailing. (c) Find the middle latitude as directed, Rule XXXIII, page 73. (d) Next at the page of Traverse Table on which the degrees (at top or bottom) correspond to middle latitude, find the departure in a difference of latitude column, then the corresponding distance is the difference of longitude. When the latitude left and latitude in are of contrary names, no sensible error can arise from taking the departure itself as the difference of longitude. 6°. If the ship has made a due E. or due W. course good, the difference of longitude is found by Parallel Sailing, thus: (e) With the latitude as a course and the departure in a difference of latitude column, then the corresponding distance is the difference of longitude (see Rule XLVI, page 106). 7°. To find the difference of longitude by Mercator's Sailing. (f) Find meridional difference of latitude (see Rule XXXI, page 71). (g) Then with course and meridional difference of latitude (in a latitude column), find the corresponding departure, which is the difference of longitude. When the course is less than 5 points or 56°, the difference of longitude may be found by either or both Middle Latitude or Mercator's method, but if the course exceeds 5 points, the method of Middle Latitude should be used in preference to Mercator's (see Remarks in page 114). 8°. With the longitude left and difference of longitude find the longitude in (see Rule XXXV, page 75). When a departure has been taken the longitude left is that of the point of land; otherwise that of yesterday. Remark. It will effect a considerable saving of time and trouble, more especially when the variation is given in degrees, to correct the compass courses for leeway only; then with these courses and the distance run on each, to proceed to find difference of latitude and departure, and thence the course (magnetic) and distance made good. Allow the variation upon this magnetic course, and so get the true course, with which, and distance made good, find the true difference of latitude and departure; but, in the Papers set at the Examination, such method of proceeding is not allowed, as it is required to correct each course for variation and lecway. 2MON O∞ IN SO ONM+IN+ NSN 734 35 3 35 LEE WAY. REMARKS, &C. A point of land in lat. 42° 12' S., long. 42° 58′ W., bearing by compass E. by N. N., distance 21 miles. Variation 1 West. 65 2 10 II 12 A current set by compass W.S.W., 26 miles from the time the departure was taken to the end of the day. Correct the courses for variation and leeway, and find the course and distance from the given point, and the latitude and longitude in by inspection. (1.) To correct the courses (see Rule XXXVIII, pages 81 and 84). |