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BY INSPECTION.

The co. mid. latitude being about 3610, first look for 36° as a course, and for the departure 109 in one of the dep. columns, against the nearest to which is 186 in a dist. column; then look for the departure 109 in the page with 37° at the top, opposite which stands 181 in a dist. column; the sum of this and 186 is 367, the half of which is 183. 5, the difference of longitude by Middle Lat. Sailing: or, the course being 4210, look in the pages with 420 and 43° at the top for the mer. diff. of latitude 201 in a lat. column, against the nearest to which will be 181.3 and 187.5 in the corresponding dep. columns; the sum of these is 368. 8, half of which is 184. 4, the diff of longitude by Mercator's Sailing.

The above method is that generally practised at sea in estimating the difference of longitude made good in a day's run, being considered sufficiently exact for the distance sailed by a ship in that time; but when the distances are considerable, especially in high latitudes, it is more accurate to estimate the difference of longitude made upon each course and distance, according to the following rules.

I. By Middle Latitude. To the Traverse Table annex a Longitude Table, divided into six columns; the first is to contain the latitude left, and the several latitudes the ship is in at the end of each course and distance, estimated by the latitudes left, and differences of latitude in the Traverse Table; the second, the sums of each following pair of latitudes; the third, half the sums of middle latitudes; the fourth, the complements of the middle latitude; and the fifth and sixth columns are to contain the differences of longitude. Having found the co. mid. latitudes, with these and their corresponding departures in the Traverse Table, find the differences of longitude, and place them in the east or west columns, according to the name of the departure; then the difference of the sums of these columns will be the difference of longitude made good, of the same name with the greater.

II. By Mercator. To the Traverse Table annex a Longitude Table, consisting of five columns; the first is to contain the latitude left, and the latitudes of the ship at the end of each course and distance; the second, the meridional parts corresponding to each latitude; the third, the meridional differences of latitude; and the fourth and fifth, the differences of longitude.

Having found the meridional differences of latitude, with these and the courses in the Traverse Table, find the corresponding differences of longitude, which place in the east or west columns, according as the course is easterly or westerly; then the difference between the sums of these columns will be the difference of longitude made good upon the whole Traverse, of the same name with the greater.

NOTE. When the course is north or south, there is no difference of longitude; and when it is east or west, the difference of longitude must

The differences of longitude may be found by any of the methods given in the Sailings; but in the following Example we have used Inspection only.

EXAMPLE.

A ship from Hangcliff, in latitude 60° 9′ N., and sailed as follows, viz. Ñ. E. b. N. 69 miles; N. N. E. 48 78 miles; N. E. 108 miles; and S. E. b. E. 50 miles and longitude in.

BY MIDDLE LATITUDE.

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The longitude of the ship, according to the first method, is 4° 17 E. by Middle Latitude, and the same by Mercator's Sailing, differing from the above 12 and 13 miles; but as we have already observed, it is seldom necessary to use the latter methods at sea.

OBLIQUE SAILING.

OBLIQUE SAILING is the application of oblique-angled plane triangles to various cases at sea; as in coasting along shores, approaching or leaving the land, surveying coasts or harbours, &c.

In this kind of sailing, to set an object, means to observe what rhumb, or point of the compass, is directed to it; and the bearing of an object is the rhumb on which it is seen; also the bearing of one place from another, is reckoned by the name of the rhumb passing through those two places: hence the bearing of two places from each other are upon opposite points of the compass; thus, if one place bear E. N. E. from another, the latter will bear W. S. W. from the former, being in the same line, but in opposite directions.

A great variety of Examples might be given in this Sailing; but as they would rather tend to exercise the learner in Trigonometry than answer any direct purpose, we shall select those only that appear to be useful in practice.

EXAMPLE I.

Sailing down the Channel, I observed the Eddystone bear N. W. b. N.; and after sailing W. S. W. 18 miles, I found it bore from me N. b. E.: required the distance of the ship from the Eddystone at both stations.

BY CONSTRUCTION.

Describe the circle N. W. S. E., to represent the compass, and draw the diameters W. E. and N. S. at right angles to each other; draw the N. W.b.N., W.S. W., and N. b. E. rhumb lines, and on the W. S. W. line lay off 18 from A to B, taken from any scale of equal parts; through в draw в c parallel to the N. b. E. line, meeting the N. W. b. N. line A c in c; then will a represent the place of the ship at her first station, B her place at the second station, and c the place of the Eddystone; A c will be the ship's distance from the Eddystone at the first station, measuring 21 miles, and B C the distance at the second sta

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BY CALCULATION.

In the triangle A B C are given the side A B 18 miles, the angle C A B equal to 7 points, the measure of the arch contained between the N.W.b.N. and the W. S. W. lines; the angle A B C equal to 5 points, the interval between the N. b. E. and the E. N. E. line (being the opposite to the W. S. W. rhumb); and the angle B C A equal to 4 points, the interval between the S. b. W. and the S. E. b. S. lines; to find the sides AC and BC.

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Hence the distance of the Eddystone from the ship's first station is 21. 17 miles, and from the second station 24. 97, or 25 miles nearly.

EXAMPLE II.

Coasting along shore, I observed two Capes: the first bore N. b. E., and at the same time the second bore N. E. E.; now, by the Chart, these Capes bear from each other N. W. W., and S. E. E. (by compass), distant 21 miles: required my distance from both places at that time.

BY CONSTRUCTION.

Having drawn the compass N.W. S. E., the centre of which is to represent the ship's place, draw the Ñ.b. E. and N. E. E. rhumb lines AB and AC, being the bearings of the Capes from the ship; draw likewise the N. W. W and 5. E. E. line, the bearing of the Capes from each other, on which from A to D lay off 21 miles, the distance between the Capes; through D draw DC parallel to the w N. b. E. line, and through c draw CB parallel to the N. W. W. and S. È. E. line; then в will represent the place of the first Cape, c the second Cape, Aв the distance of the first Cape from the ship,

B

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measuring 31 miles, and a c the distance of the second Cape, measuring 27 miles.

BY CALCULATION.

In the triangle ABC are given the angle BAC 33 points, the arch between the N. b. E. and N. E. E. lines; the angle ABC 5 points, the interval between the S. b. W. and S. E. E. lines; and the angle ACB 7 points, the interval between the N. W. į W. and S. W. W. lines; and the side B C 21 miles; to find the sides A B and A C.

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Hence the distance of the ship from the first Cape is 30. 67 miles, and from the second Cape 26. 82, or 27 miles nearly.

EXAMPLE III.

Being close in with Dungeness, I ran 27 miles on a direct course to the westward, and then found Beachy Head bear N. N.W.; now the bearing of Beachy Head from Dungeness (by compass) is W. N., and the distance 29 miles: required the course steered, and the distance of the ship from Beachy Head.

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distance run, 27 miles in the compasses, set one foot in A, and with the other describe an arch cutting в c in c, and draw the line AC: then will c represent the ship's place, BC the distance of the ship from Beachy Head, measuring 197 miles, and the angle s AC the course steered from the south, measuring 53°39'.

BY CALCULATION.

In the triangle ABC are given the side A B, equal to 29 miles; the side A c 27 miles; and the angle A B C 5 points, the interval between

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