Again, when a ship is sailing either in a current of the ocean, or in a tide near a shore, her velocity and the direction of her motion will be affected by those of the current or tide. First, if the ship is impelled by the wind in the same direction as the current is moving, it is evident that the velocity given by the log will be only the difference between the ship's real velocity and that of the current, and conse quently the latter must be added to the velocity given by the log in order to have the true velocity. On the other hand, if the ship is impelled by the wind in a direction contrary to that of the current, the velocity radio latter must be subtracted from that given by the log, in order to obtain the true velocity of the ship. Again, if the direction of the current is oblique to the line of the ship's motion according to the compass, the true path and velocity of the ship will, by tho com position of motions, be the diagonal of a parallelogram formed on lines representing the observed directions and velocities of the ship and current ; consequently, since this rule is the same as that by which is found a path of the ship which shall be equivalent in length and diree• tion to any two successive paths whose lengths and directions are given, it is evident that among the registered courses and velocities of a ship it will be onlysneces.sary to insert the observed direction and velocity of the current, as if the ship had actually moved in that direction, and with that velocity during the time that ftho continued to sail in the current. The like remark may be made respecting the deviation of a ship from the course on which she appears by the com pass to have sailed, in consequence of a ewell of the sea, by which she may be driven in some other direction. This direction must be observed, and the velocity estimated according to the judgment of the seaman.
Now, in order to show how all the corrections may be applied to the observed elements, let it be supposed that at the noon of some day a remarkable object A on the shore was observed by the compass to bear W. by N., and that its estimated distance from the ship was 20 miles. At the same moment let the ship begin to sail on a course which is S.W. by the compass ; and let the velocity by the log be 3 knots, or 3 miles per hone Also let the following table express the several memoranda in the order in which they may be supposed to have been made in the course of one day; that is, according to the practice of seamen, between the noon of one day and the noon of the next.
The bearing of the ship from the point of departure being corrected for the variation of the needle becomes N. 78° 15' E.; the distance is 20 miles.
The first course corrected in like manner becomes S. 21° W.; and the distance run between noon and 10 P.M. is miles.
The third course corrected for lee-wsy and variation becomes S. 60° 34' E.; and the distance run between 10 P.M. and 8 A.m. is 50.5 The fourth course corrected in like manner becomes S. 12° 45' E.; and the distance run between 8 A.M. and noon is 25 miles.
The direction of the swell corrected for the Variation of the needle becomes N. 43° 30' E.; and the distance is 36 miles. Lastly, the direction of the current corrected also for the variation becomes S. 46° 30' E.; and the distance is 24 miles.
These corrected courses and distances are then inserted in order, as in the first and second columns of the following table :- Now, if the navigation is comprehended within about ten degrees on each aide of the equator, such a zone of the earth may be supposed to be projected on the interior surface of a circumscribing cylinder, and then developed on a plane ; in which state the meridians and the parallels of latitude become right lines parallel to themselves respec tively, and the length of a degree of longitude on every parallel equal to that of a degree on the equator or on the meridians. This is called
the plane chart, and the projection of a ship's path on it is called plant sailing.
Let the several directions in which the ship has moved, and the distances passed over in each direction, be represented in the subjoined diagram, the construction of which, agreeably to the nature of the plane chart, is as follows : Draw the lines A 1, A 2, A 3, &c., making with Ap, the meridian of the point of departure, angles equal to the several courses as they occur successively in the preceding table (col. 1), and draw the lines Le, cd, &c., parallel to A 2, A 3, &c., respectively ; the distances AL, Lc, cd, itc., being laid down according to the successive numbers in col. 2 by a scale of equal parts representing geographical miles (or equatorial minutes). At the end of the day the ship is arrived at the point therefore if A and g be joined, and up be drawn perpendicularly to Ap, the angle peg is tho resulting course, Ay the resulting distance, Ap the difference of latitude between A and g, and pg is what is called the departure, which, in plane sailing, is identical with the difference of longitude between the same points A and g.
By drawing lines perpendicular and parallel to Ap, as in the above diagram, there will be formed the several right-angled plane triangles Abu!, ben, &c., in each of which there are given the hypothen use and the angles ; and consequently by the rules of plane trigonometry the several sides Am, bin, nn, bn, &c., may be computed. Now, let these computed values be placed in the third and succeeding columns of the above table in the following order :—those which are parallel to Ap in the column N. or S., according as the lines which represent them lie towards the north or towards the south of that extremity which is first, in order of sailing, on the corresponding hypothenuse ; and those which are perpendicular to Ap in the column E. or NV., according as the lines which represent them lie towards the east or west of that same extremity. Then the sum of the numbers in the column N. being subtracted from the sum of those in S. will be found to leave and this will be the value of Ap in geographical miles (or equa torial minutes) ; consequently 1° 16' 14" will express the extent in latitude to which, on the whole, the ship has sailed southwards during the day. Again the number in W. being subtracted from the sum of those in E. will leave 95'68 (= 1° 35' 41"), and this will be the value of pg, or the extent in longitude which, on the whole, the ship has sailed east ward during the day. Thus the position of A being known, we have that of g. In the right-angled plane triangle Apg, having Ap and pg in miles, as above, we may compute Ag and the angle peg, that is, the resulting distance and course. The former will be found to be .122.35 mike, and the latter S. 51' 27' E. The series of zig-zag lines which a ship may describe is called a traverse ; the preceding table is called a traverse table, and the whole operation of finding the resulting course and distance is called traverse sailing.