EXAMPLE.-A ship front lat. 30° 56' N. has sailed 470 miles in a north-westerly direction, until she has made 325 rniles of departure. What course did she steer, and in what latitude has she arrived ? 1. By Construction.—Draw the meridian line AB, (Fig. 8 ) and through B. draw BC at right angles to it, and equal to the departure, 325 ; then from C, with an extent equal to the cisiance, 470, intersect the meridian in A. Join AC, and BC will be the departure, while the angle A B C will be the course, the former measuring 339 m.; and the latter 431.
4. By Gunter's Sca/e.—From 470 to 325 on the line of numbers, will reach from 90 to 43°4, on the scale of sines ; also, from 90 to 46°4, the complement of 43°4, on the scale of sines, will reach from 470 to 339 on the line of numbers.
Hence the course is N. 43° 45' W. or N.W. by N. W. nearly.
3. By Inspection.—Search in the traverse table, until some part of the distance, as of it, (because in the esent example the distance exceeds the limits of the table,) is found in the distance colutnn opposite to -1 of the departure in its column, which will be found to be when the course at the top is 44°, (or in the table we have given, which is only computed to quarter points,) when the course at the top is 3-1; p. The corresponding differ
ence of latitude is 66 5, .k hich, being multiplied by 5, gives, by approximation, 3,33 for the difference of lati tude. When the quantities are considerable, as in the above example, the method by inspection will often dif fer very widely from the truth. It is always possible, indeed, to make suitable corrections fill the want of per fect accordance between the givtil quantities and those found in the tables ; but to do this would be more tedious than the method hy logarithmic calculation, which it is intended to simplify.