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This method I omit for two reasons; first, because it is to be deduced from the writers on navigation : and, secondly, because the distances thus measured are liable to the errours of currents, which generally attend shoals or sands near the shore.
The second method, where there are no distances to be measured on the water, tho' still there is one inconvenience, common also to the former, because the bearings or observations are to be taken on that unstable element (an errour scarce mentioned by practical artists) I shall briefly hint at; and so rather choose a third, which is liable to neither of these imperfections.
Let a boat be manned out with a single flag, a log and line, lead and line, and to observe the bearings of any land mark, a compass with sights.
Take two or more objects or places, as A, B, C, on the shore, from whence the boat may be seen on the several parts of this shoal, and determine their relative position by bearing and distances, either before or after the other necessary observations are made.
One of the boat's crew is to sound till he finds himself on the edge of the sand by the depth of water, and then to come to an anchor; which he is to signify to two persons on the shore, at B and C, by his signal. And then from those known land-market and C, the observers are to take the bearings of the boat, and to register their observations; which when done, they are to signify to the crew by waving a flag, or by some other signal.
And in the mean time, to prevent mistakes, let the grew take the bearings of each of these land-marks : then weigh anchor, which suppose at D.
Then, by sounding proceed to E, and make like observations. And so at E, F, G, &c. till you have surrounded your sand.
And if in this process, you are about to lose the sight of one of your land-marks, suppose C, let your assistant at C, or B, who at that time will also be about to lose sight of the boat, by signals (before agreed on) remove to some other object before-hand agreed on, suppose to H, or K; and then to proceed as before.
Lastly, if the sand runs so far out to sea, that the object cannot be seen from the boat, nor the boat by the observer on shore ; there may be rockets fired by the boat's crew, and also by the observers on shore in the night, whereby those bearings may be taken almost at as great a distance as the light can be seen. For supposing they rise but a quarter of a mile above the apparent horizon, its stay will be about 9 seconds, and its distance for this quarter of a mile will be vi. sible about 44 miles.
But rockets rise much higher, and then the distances are much greater at which they are visible.
Or two boats may lie at anchor instead of the land
Now, since the land marks B and C are fixed, their position may be laid down in the draught, as in com. mon surveying, by plotting the distance between B and C. And then, by plotting the line BD, and the line DC, according to their position, their common intersection, will give the point D. And in like manner E, F, G, &c, may be plotted; and so the shoals completed : and this from the bearings taken at B and C,
If this be a standing lake, environed by bogs, or other impediments, the observations at D, E, F, &c. by taking their opposites, may suffice to plot the same from the land-marks, A, B, C, &c. as well as those taken on the land ; or indeed, by the course and distance, as in navigation, if the water be smooth and without a current.
In sea shoals it is convenient to note at each ob. servation the depth of the water found by the lead, and the drift and setting of the current by the log and compass, while the boat is at anchor, which may be done with ease and expedition enough. For while the boat rides at an anchor, her stern points out the setting of the current, and the log and glass will measure its drift.
And these ought to be noted on the draught, which may be thus :
The currents may be shewn, by drawing a dart pointing out its setting, and its drift by the Roman capital letters, the depth of water by the small figures, and rocks by little crosses, &c.
Levelling is the art of ascertaining the perpendicalar ascent or descent of one place (or more) above or below the horizontal level of another, for various in. tentions; and of marking out courses for the conveyance of water, &c.
The true level is a curve conforming to the surface of the earth; as ABG.
The apparent level is a tangent to that curve ; as ADE.
The correction, or allowance for the earth's curvature, is the difference between the apparent level and the true, as BD. The quantity of this correction may be known by having; in the right-angled triangle CAD, the two legs, AC=the semidiameter of the earth (=1267500 perches) and AD=the distance of the object, to find the hypothenuse CD, from which taking (CB=CA) the remainder will be the correction