a TRAVERSE,-in other words, a compound course, consisting of several different courses and distances; and TRAVERSE SAILING is the method of working (or calculating) these compound courses, so as to bring them into the true course, and distance made good. We must know the meaning of difference of latitude and departure. DIFFERENCE OF LATITUDE admits of two or three meanings; for example— (1) If we know a place to be in Lat 10° N. and another in 25° N., their difference of latitude is 15°. Again, if a place is in Lat. 4° S. and another in 5° N., their difference of latitude is 9°, owing to their situation on different sides of the equator; the sum of the latitudes is taken in this case, on the same principle that if, from a given line, you walked 4 miles in one direction and your friend 5 miles in an exactly opposite one, you would then be (4 + 5) 9 miles apart. (2) But difference of latitude, in sailing, generally refers to change of latitude, arising out of the ship's course and distance run; she may be making northing, or southing. The term is abbreviated into Diff. Lat., or D. Lat. DEPARTURE is the east or west distance (in nautical miles) that a ship makes when her course trends easterly or westerly. It is written Dep. COURSE, as you know, is direction, and a ship under sail changes her position on a given course according to the DISTANCE RUN; she will thus make :— (1) Diff. Lat., and no Dep., when her course is on a meridian (as along the line N 8 of Fig. 2, p. 11); and it will be N. diff. lat. if the course is North, but S. diff. lat. with the course South. (2) Dep., and no Diff. Lat., when her course is on a parallel (as along the straight line a b of Fig. 2, p. 11); and it will be E. dep. if the course is East, but W. dep. with the course West. (3) Diff. Lat. and Dep. when her course is athwart parallels and meridians (as along the line joining the two dots below E Q in Fig. 3, p. 11); and the Diff. Lat. will be N. or S., and the Dep. E. or W., according to the direction of the course in one or other of the quarters of the compass; thus, course S.E. will give S. diff. lat., and E. dep. Relation of Course and Distance to Diff. Lat. and Dep. (refer to Fig. 1, p. 9). -We will call the line в E the meridian, and the line AD the parallel of a place c. (1) A ship bound from o to H sails 8. by E. (i.e. S. 1 point E., or one point from the meridian), making the distance c H, in which the perpendicular from A D to H is equal to the Diff. Lat., and exceeds the perpendicular from в E to н, which is the Dep. (2) A ship bound from a to G, sails W. by N. (i.e. N. 7 points W., or seven points from the meridian), making the distance c a, in which the perpendicular from B E to G is equal to the Dep., and exceeds the perpendicular from A D to G, which is the Diff. Lat. (3) A ship bound from c to r sails N.E. (i.e. N. 4 points E., or four points from the meridian), making the distance c F, in which the perpendicular from F to A D is equal to the Diff. Lat., and the perpendicular from F to BE is the Dep.; and if you measure them with the dividers you will find them equal to one another. These examples show, and this you should bear in mind, that- How TO USE the TRAVERSE TABLES. The Traverse Tables are useful for a variety of calculations in Navigation, and especially for working up the Dead Reckoning. Turn to them. We will use those from NORIE'S "Epitome of Navigation Table I. gives "Difference of Latitude and Departure" for Points of the Compass, Table II. for Degrees: when the Course is less than 4 points or 45° you read from the top of the page, when more than 4 points from the bottom: the "Dist." column remains Dist. whichever way you read; but the "Lat." and "Dep." columns are reversed in the two instances; thus Course 1 points and Dist. 50 give Lat. 47·1 and Dep. 16.8, but Course 35° and Dist. 87 give Lat. 71-3 and Dep. 49 9, but and these are miles of Lat. and Dep. corresponding to the miles of Dist. at certain angles. By the reverse process, if the Diff. Lat. and Dep. are given, or have been found, we can obtain the corresponding Course and Dist. ;-but better and closer from Tab. II. than from Tab. I. Say, Diff. Lat. 49-4 and Dep. 404; and since Diff. Lat. is the greater we read from the top of page: turn over the pages of the Tables until you find the nearest to them; in the present case we find Diff. Lat. 49.7 and Dep. 40. 3 (the nearest to the given quantities) by the side of Dist. 64 and under Course 39°; had we taken Dep. 49.4 and Diff. Lat. 40·4 we should have read from bottom of page, and while we got the same Dist. 64, we should have Course 51°. We can now work a Traverse, which I will explain as we go along. Rule to resolve a Traverse-Make a Form (as on p. 30), and divide it into six columns; in the first of these set down the courses, and opposite to them, in the second column, their corresponding distances: the third column is to be marked N., and the fourth S., under the heading of Diff. Lat.; the fifth column is to be marked E., and the sixth W., under the heading of Departure. Find the difference of latitude and departure corresponding to each course and distance, by Inspection from Trav. Tab., as already shown; set these down opposite the distance in their proper columns, observing that the Diff. Lat. must be placed in the N. column, if the course be Northerly, but in the S. column, if the course be southerly; and that the Departure must be placed in the E. column, if the course be easterly, but in the W. column, if it be Westerly. When the course is due North, South, East, or West, set down the distance in that column answering to it. Add up the columns of northing, southing, easting, and westing, and set down the sum of each at the bottom; then the difference between the sums of the north and south columns will be the difference of latitude made good, of the same name as the greater; and the difference between the sums of the east and west columns will be the departure made good, of the same name as the greater. With this Diff. Lat. and Dep. made good, find (by Inspection from Table II.) Course and Distance made good, giving the course its proper name reckoned from N. or S. according to the Diff. Lat., and towards E. or W. according to the Dep. Ex.-A ship from Start Point, in Lat. 50° 13′ N., sail W.S.W. 51 miles, W. by N. 35 miles, S. by E. 45 miles, S.W. by W. 55 miles, and S.S.E. 41 miles required her course and distance made good. : *Turn to NORIE'S Trav. Tab. I.; seek 6 points; in Dist. column find 31, and alongside of it you will see Dep. 47.1 and Lat. 195, read from bottom of page, because course (6 points) is at bottom; enter these in S. and W. columns of our Traverse Form because Course is S. and W. †Turn to Trav. Tab. I.; seek 1 point; in Dist. column find 45, and alongside of it you will see Lat. 44.1 and Dep. 088, read from top of page because course (1 point) is at top; enter these in S. and E. columns of our Traverse Form because Course is S. and E.; the O in the Dep. is to be omitted since it is supplied in Trav. Tab. only to preserve the uni formity of the column of figures. You will understand the rest, if you have carefully read p. 29. We have taken the sum of the four columns N., S., E., and W.; and then found the difference between the N. and S. columns; and also the difference between the E. and W. columns. As the result of all our courses in 6 different directions, our total Difference of Latitude made good is 125.3 miles of Southing, and our total Departure is 102.6 miles of Westing. With these we proceed to find the Course made good, and Distance run, that is, the direction and distance in which we really are from the Start Point. To find this Course and Dist. is a mere matter of looking and seeking through Trav. Tab. II. till we come to the page where Diff. Lat. 125.3 and Dep. 102.6 are side by side; one thing we know, that is, we must read the columns from the top because Lat. exceeds Dep. We turn over the pages, taking 125 as our guide; at last we come to the page where 125.9 and 101.9 are side by side; and looking carefully at the pages on each side, we see that we cannot improve on this, so we take it; and then the Course read from the top is 39°, and the Dist. (by the side of 125.9 and 101.9) is 162. Consequently Diff. Lat. 125.3 and Dep. 102 6 give us Course made good S. 39° W., and Distance run 162 miles, the meaning of which is, that after having sailed on 6 different courses and run (51 +35 +45 + 55 + 41) 227 miles in the whole, we bear S. 39o W., or S.W. S. distant 162 miles from Start Point. It is probable that you would like to see this projected into a diagram, and understand it better after you have done so. Here it is. The construction is as follows:-With the chord of 60° describe the circle NEW, to represent the compass; draw the diameters N 8 and E w at right angles, in which N s represents the meridian, and Ew the parallel the ship sailed from :* take each course from the line of rhumbs, and lay them off from the meridian in their respective quarters, and number them in order 1, 2, 3, 4, 5; thus, from S. to 1 lay off 6 points for the first course W.S.W.; from N. to 2 lay off 7 points for the second course W. by N.; from S to 3 lay off 1 point for the third course S. by E.; from S. to 4 lay off 5 points for the fourth course S.W. by W.; from S. to 5 lay off 2 points for the fifth course S.S.E; and from the centre of the circle draw rhumb† lines to each of these points, which may be produced to any length that is necessary. Upon the first rhumb c 1, lay off (from scale of equal parts) the first distance 51 miles, from c to A; then will a represent the ship's place at the end of the first course; from a draw ▲ в parallel to the second course c 2, and make it equal to the second distance * Instead of following the method here described, you could, after you had drawn a circle with the two diameters to correspond in size to the horn protractor (Fig. 4, Plate I.), lay off the courses by its aid; the distances would have to be taken from the scale of equal parts. 1 † A rhumb line is a track on the earth's surface that cuts all the meridians at the same angle; it is also the straight line from the ship's position to the circumference of the horizon, and thus course and distance. You will require a parallel rule for this. 35 miles; from в draw в c parallel to c 3, and equal to 45 miles; from a draw o D parallel to o 4, and equal to 55 miles; and from D draw D E parallel to o 5, and equal to 41 miles. From E draw the line E F parallel to the east and west line w E, meeting N s produced to F, and join c E. Then, having started from c (Start Point) and sailed along the zig-zag line C A B C D E, by your arrival at E (which is the ship's place), c F will be the Diff. Lat. made good, measuring 125.3 miles; E F the Departure 102.6 miles; c E the Distance 162 miles from Start Point; and the angle E C F the direct course (39° or 3 points) from the Start. LATITUDE LEFT AND LATITUDE IN. LAT. LEFT is the latitude from which the ship has departed. DIFF. LAT. is the change of latitude in any interval. LAT. IN is the latitude at which the ship arrives, and is determined either by observation, or by means of the Diff. Lat. as shown in the Traverse, p. 30. I will explain the method of obtaining the Lat. in, from the Lat. left and Diff. Lat., using the following examples : Understanding that latitude is reckoned from the equator towards the pole― (1) If you are in north latitude, and sail north, Lat. left must be increased by Diff. Lat. made good. (2) If you are in north latitude, and sail south, Lat. left must be decreased by Diff. Lat. (3) If you are in north latitude, and sail south, and the Diff. Lat. exceeds the Lat. left, take the less from the greater, and the remainder will be the Lat. in, south. (4) If you are in south latitude, and sail south, Lat, left must be increased by the Diff. Lat. (5) If you are in south latitude, and sail north, Lat. left must be decreased by Diff. Lat. (6) If you are in south latitude, and sail north, and the Diff. Lat. exceeds the Lat. left, take the less from the greater, and the remainder will be the Lat. in, north. The Rule stated briefly resolves itself into this:-For Lat. in, if Lat. left and Diff. Lat. are of the same name, take their sum; if they are of different names take their difference, and in this case the Lat. in will be of the same name as the greater. The Lat, in, when it has been obtained by Dead Reckoning (compass and log), is indifferently called the Latitude by Account, or Latitude by Dead Reckoning, and written in short Lat. by Acc., or Lat. by D. R. 1 |