The following is the established rule for laying down a traverse course on pa. per. Having drawn the meridian and pa rallel of latitude (or east and west line) in a circle representing the horizon of the place, mark in the circumference the place of the wind, that is, the point from which it blows; draw your rhumb passing through the place bound to, and lay there on the distance of that place from the centre ; on each side of the wind lay off in the circumference those points, or de grees, that chew how near the wind the vessel can lie, and draw their rhumba. Now the first course will be one of these rhumba, according to the tack the ship first sails upon ; when she goes on the other tack, it will be at such an angle as may correspond with her ability to lay near the wind; but, in general, for square rigged vessels the angle should be twelve points, (i. e. six for the distance on each tack, as shewn in fig. 12.) But where the wind is not directly adverse, it would be improper to make the tacks towards both rhsmbs of equal duration or length. Therefore that tack should be longest which lays nearest the intended course ; the other (i.e. "the board") should be short, so that the vessel should not go too far from the intention, but adhere as much as may be practicable to the rhumb of her course, as 'hewn in fig. 13, in which the arrow shews the wind's locality at three points east of the destination B.
To resolve a traverse, is to reduce and bring several courses into one ; the course are known by the compass, the distance by the log: while the dead-rec koning they produce is corrected by daily observation of the sun and other planets, whenever opportunity offers.
In constructing figures relating to a ship's course, let the top of the paper al. ways represent the north : your meridian is described perpendicular thereto, and your chart may either be in squares, for degrees, or five or ten degrees, or it may be divided according to the projected tables now in common use (see Losex.
Tuna) and which is by far the best, as it shews the real distances and bearings, ac cording to the actual positions of places, as proved by observation. In that table the letters D. L. imply the degree of la titude, measured from the equator, either northwards or southwards; in the columns of miles corresponding thereto, you will see how many miles, of sixty to a degree, called geographical miles, are contained in each degree of longitude tinder such latitudes. Thus, if I would know how many miles are contained in a degree in latitude 18 ; I find there are 57.06. There fore it must be evident, that, as the lati tude recedes from the equator, the small er the degrees of longitude become : hence, if a vessel could sail round the north pole in latitude 80°, where there are only 10° 42' miles in a degree of lati tude, and were to run 123 miles in the twenty-four hours, she would sail ten times round the pole, and indeed round the world, in that time, and see the sun rise and set no less than twelve times ! From this we arc satisfied, that the old practice of laying down a chart, or map, in square degrees, was erroneous in the extreme ; and that what is called " Mer cator's projection," which gives every de gree its just and exact value in breadth, at both its northern and southern extre mities, is the only correct and rational mode of description.
We shall now give the reader a few ex amples under the head of plane sailing, which supposes the earth to be a perfect level, or plane. This is but the application of plane trigonometry to the solution of the several variations ; where the hypo thenuse, or longest side, is always the rhumb on which the ship's course lies. The perpendicular is the difference of la titude counted on the meridian, and the base the departure (which is either Bast ing or westing) counting from the meri dian. The angle opposite the base is that which the ship makes with the meridian : the angle at the perpendicular is the com plement of the course ; which, taken to gether, always make 90 degrees, or eight points. When the course is given in de grees, they must be set off from a line of chords of 60, corresponding with the ra dius of the circle, or quadrant, drawn ei ther easterly or westerly, as the ship's course may be from the meridian. Where the course is given in points, it may be set down with its corresponding logarithm in points in the calculation, as found in the first page of logarithms in general. In all cases, wherever the complement course is used, the degrees or points put down correspond with the course itself; yet the logarithm belonging to the comple ment of that course Is taken.
Example 1. " Course and distance sailed being given, to find the difference of latitude, and the departure from the meridian." Suppose a ship from the Li zard, in the latitude of 49° 57' north, sails S. W. by W. 496 miles ; required the la titude conic to, and her departure from the meridian. Draw the meridian, or difference of latitude ; with the chord of 60° in your compasses, and one foot in C, fig. 14, describe an arch : take 56° 15', or five points, in your compasses, and lay off that distance upon the arch, from BC to wards CA : through the point where it cuts draw the distance CA, upon which set off 496: from A let fall the perpendi cular AB, the departure, and it is done. For AB, being measured on the same scale that AC was, will give the departure 412.4, and BC 275.6 for the difference of latitude.