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When the course which a ship has steered by the compass, and the variation of the compass are given, to find the true course.

If the variation is west allow it to the left, but if east allow it to the right of the compass course, and you will have the true course corresponding to that given by the compass.


If a ship steered NNW by a compass which has 14 points westerly variation, required her true course?

Answer, 14 points allowed to the left of NNW gives NWN for the true course.


In the following examples the true courses are required.

Answer. Compass Course. Variation, Points. True Course. 1. SSE E

24 W

SE bE 2. EN

3 E


33 E


Sb W W 5. SSW

SIW 6. N

5 E

NEbE . Ebs

21 E

SEE 8. S 60 E

18 W

S 78 E 9. N 24 W

36 E

N 12 E 10, S 16 W

40 E

S 56 W

4 W


The angle included between the direction of the fore and aft line of a ship, and that in which she moves through the water, is called the leeway.

When the wind is on the right hand side of a ship, she is said to be on the starboard tack; and when on the left hand side, she is said to be on the larboard tack; and when she sails as near the wind as she will lie, she is said to be close hauled. Few large vessels will lie within less than six points to the wind, though small ones will sometimes lie within about five points, or even less ; but, under such circumstances, the real course of a ship is seldom precisely in the direction of her head; for a considerable portion of the force of the wind is then exerted in driving her to leeward, and hence her course through the water is in general found to be leeward of that on which she is steered by the compass. Therefore to determine the point towards which a ship is actually moving, the leeway must be allowed from the wind, or towards the right of her apparent course, when she is on the larboard tack; but towards the left when she is on the starboard tack.

It is evident that the track which a ship leaves on the water, or the wake, as the track is called, will lie directly opposite to the point towards which she is moving, whatever way her head may lie. If therefore the figure of a compass were drawn in any convenient situation, so that its meridian were parallel to the fore and aft line of the ship, the angle included between the meridian of this compass and that point of it which was directed towards the wake, would be the leeway; and in some such manner as this it is desirable that the leeway should be determined when practicable.

The quantity of leeway which a ship will make varies however under different circumstances. If all other circumstances be the same, a light ship will make more leeway than a loaden one. It is seldom that two ships on the same course make precisely the same leeway; and it not unfrequently happens that the same ship makes a different leeway on each tack. It is the duty of the officer of the watch to exercise his best skill in determining, or estimating, how much this deviation from the apparent course amounts to; and in the dark the chief reliance must be placed on the judgment of the experienced mariner.

In estimating the leeway, there are certain rules by which mariners are often guided; and though they can only be considered as affording a general approximation to the truth, and often a very distant approximation, they are here given : but no opportunity should be neglected to determine this important element by observation.

General rules for estimating the leeway when a ship is close hauled.

1. When the water is smooth, all sails set, and the wind moderate, allow no leeway.

If there be a strong breeze, the leeway may amount to 1 point.

2. When top gallant sails are handed, the leeway may be from 1 point to 1 points.

3. Under close reefed top sails, the allowance may be from 2 to 3 points.

4. With top sails handed, from 3 to 4 points. 5. Under courses, from 4 to 6 points, according to circumstances, 6. Under reefed courses, possibly 6 points. 7. Under storm stay sails, possibly 7 points. 8. Under bare poles, from 7 to 8 points.

It has not been attempted in the above rules, and indeed it is impossible, to state precisely what the allowance for leeway ought to be under all or any circumstances. This in any given case must be left to the judgment of the mariner, whose knowledge must extend to a number of minutia bearing upon the question, before he will affirm that, after exercising his best skill, he has satisfied himself that his estimate is right.

But supposing the leeway to be known, the course steered must be corrected for it; and the following examples are given as exercises in correcting the courses both for leeway, and variation, the true course being required.

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In plane sailing the earth is considered as a plane, the meridians as parallel straight lines, and the parallels of latitude as lines cutting to consider any part of the earth's surface as a plane, yet when the operations to be performed are confined within the distance of a few miles, no material error will arise from considering them as performed on a plane surface. And, as we have already seen, in all questions where the nautical distance, difference of latitude, departure, and course, are the objects of consideration, the results will be the same whether the lines are considered as curves drawn on the surface of the globe, or as equal straight lines drawn on a plane.

In all maps and charts and coustructions, when it is not otherwise stated, it is customary to consider the top of the page as pointing towards the north, the lower part as the south, the right side as the east, and the left as the west. The meridians therefore, in any construction, will be represented by vertical lines, and the parallels of latitude by horizontal ones.

Hence in constructing a figure for the solution of any case in plane sailing, the difference of latitude will be represented by a vertical line, the departure by a horizontal one, and the distance by the hypothenusal line, which forms with the difference of latitude and departure a right angle triangle; and the course will be the angle included between the difference of latitude and distance.

With this understanding, the solution of any case that can arise from varying the data in plane sailing will present no difficulty.

EXAMPLES. If a ship sail from Cape St. Vincent SWS 148 miles, required her latitude in, and the departure which she has made ?


Draw the vertical line A B, to represent the meridian ; from the line of rhumbs take the angle BAC = 34 points, the given course ; and from a scale of equal parts take AC= = 148 miles, the given distance; from C on A B draw the perpendicular CB, then A B will be the difference of latitude, and B C the required departure; and measured on the scale from which A C was taken, AB will be found 114:4 and B C 93.9.



E Dilat.




With 2 A 3 points in Table 2. and AC 148 miles in the dist column, A B is found 114:4 in the lat column, and B C 93.9 in the dep column.

BY GUNTER'S SCALE. Extend from 8 to 34 points, the course, on the line S R, and that extent will reach from 148, the dist, towards the left on the line of numbers, to the departure 93.9. Again extend on the line S R from 8 to 4 points (the complement of 34 points) and that extent will reach from 148 towards the left on the line of numbers to 114:4, the difference of latitude.


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2. If a ship sail from the Cape of Good Hope southwestward, till she arrive in lat 36° 34' S, and it be found that upon the whole she has made 75 miles of departure, required the course and distance which she has made ?

Lat Cape of Good Hope 34° 29' S
Lat in...

36 34 S
Diff lat

2 5 S = 125 miles.


Draw A B and BC (see the last figure) perpendicular to each other, make A B = 125, and BC = 75, from a scale of equal parts, and join AC; then the 2 A, the course, will be found=31°, and AC, the distance, = 146 miles.


In Table 3. with A B 125, in the lat column, and B C 75, in the dep column, 2 A is found at the top of the table = 31° nearly, and AC in the dist column 146.


Extend from the diff lat 125, to the dep 75, on the line of numbers, that extent will reach on the line of tangents from 45°, or radius, to about 31°, the course. Again extend from radius 90° on the

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