Parallel wiling may be employed when a ship sails between two places, en the s: the parallel of latitude, in which case, if her head be lit pt accurately and constantly in an e. or w. direction, slot will describe an arc of the parallel between the two places. As in this sailing the departure is the same are of the parallel that the difference of longitude is of the equator, the dep. (which is now the distance) = dif. of long. x e's. lat. The other elements arc found as in plane _Middle latitude sailing is the application of the principle of parallel sailing to the case in which the ship's course is not perpendicular but Alive to the mericlian; it is merely an approximate method, coming very close to a true estimate in low latitudes for any course, and in all latitudes for a course nearly c. and w. (i.e., one in which the distance is large as compared with the difference of latitude), but erring widely under other cir cumstances, though errors may be diminished as much as we please by dividing the dis tance into portions, and calculating the dif. of long. for each. The object of this sailing is to deduce the dif. of long. from the dep.. and vice versa, on the supposition that the whole departure has been made good along the parallel of latitude which is equitlistnnt from each extremity of the course, a method, which. at first sight, would seem to give a correct result, and would do so if the parallels of latitude increased uniformly, which they do not. The dep., when laid off along the parallel of middle latitude, always gives the dif. of long. too small, and hence the limitations above noticed. When the latitudes are of the same name, the middle latitude is half their sum; but when of Contrary names, it is better to find the dif. of long. for the portion on each side of the equator separately, the two middle latitudes being respectively half the latitude of the place sailed from, and half that of the place sailed to. The formulas are the same as for parallel sailing and plane sailing. • ..11ereator'e sailing is a perfect method of obtaining the same result as is found approxi mately by middle latitude sailing, but in the former case the di f. of long. is found from
the departure. while in this method the difference of latitude is employ• d for the same purpose. A table of meridional parts, as it is called, is necessary; this tal le skews the number of Minutes in Mereator's projection (see NAM corresponding to each degree and minute of latitude up to 78°, and is employed as follows. The hoitude sailed from. and that reached, being known or found, the meridional parts for each are obtained. and their difference, if the latitudes are of the same name, or sum if of opposite names. gives the dif. of lat. We have then a right-angled triangle, with the dif. of lat, and dif, of long. forming the two smaller sides, and the vertical tingle representing the course. whence dif. 4 long. = (Ff. of lat. x tan. of course. This sailing is the one most generally I ml ley) d by navieutors, hut is inferior in practice to middle-latitude sailing,. in the •n'Ts noticed under flint head, for though it he a perfect, and the other merely nu approximate method, yet a small e)ror in the course (if large). or in I be dif. of lat.. becomes greatly magnified in the dif of iong.; while in the case of the latter, a considerable error in departure is hardly and a large error in the course (if nearly c. and w.) becomes impel.
/ ceptible in the dif. of long. It is, however, better to work the problem according to both methods, and then estimate the true result as nearly as possible.
Great circle sailing (q.v.), the most perfect of all methods for finding a ship's course, is separately noticed. See also SPHEROGRAPIL The obstacles that interfere with the correctness of the mariner's calculations are chiefly those which affect his data, the course and distance, the more important being the mag netic deviation of the compass produced by the attraction of the ship, errors in tho esti mated leeway or in the set and drift of currents, etc.; all of which require to be taken into account. The necessity for frequently checking the dead-reckoning (q.v.), by means of astronomical observations, is sufficiently apparent.