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Let a boat be manned out with a signal 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 bis signal. And then from those known land-narks, B and C, the observers are to take the bearings of the boat, and to register their observations; wbich, 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 crew take the bearings of each of these landmarks: 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 the process, you are about to lose the sight of one of your land-marks, suppose Co let your assistant at C, or B, who at that time will also be about to lose the sight of the boat, by signals (before agreed on) remove to some other object beforehand agreed on, suppose to H, or K; and then to proceed as before.

Lastly, if the sand runs so far out at sea, that the object cannot be seen by 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 the 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 visible about 44 miles.

But rockets rise much higher, and then the distances are much greater, whereby they are visible.

Or two boats may lay at anchor instead of the land-marks, and then you may work as before.

Now, since the land-marks B and C are fixed, their position may be laid down in the draught, as in common 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. Andin 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 froin 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 loge 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 shown, by drawing a dartpointing out its setting, and its drift by the Roman capital letters, the depth of the water by the small figures, and rocks by little crosses, &c.

SECTION IX.

OF LEVELLING.

PL. 13. fig. 2. LEVELLING is the art of ascertaining the perpendicular ascent or descent of one place (or more) above or below the horizontal level of another, for various intentions, and of marking out courses for 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 eurve: 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 rightangled 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 BD; but it may be obtained more practically thus ;

Square the distance in
four-pole chains, and divide by 800,
or in perches, and divide by 12800,
or in miles, and multiply by

for the correction in inches.

8,

EXAMPLE.

Required the correction for 20 four-pole chains =80 perches= mile.

800) 20x20=400(:5 12800)80 x 80=6400(.5

1.25, and .25X.25x8=.5 that is, .5, or ; inch, the correction required.

But, to save the trouble of calculation, we insert the following table of corrections.

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A Table of Corrections.
The distances in four-pole chains.

Distan. Correc. Distan. Correc.

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The first thing necessary in levelling, is the adjusting of the level, which may be performed several ways; The following is very easy and practical.

Choose some ground which is not above 4 or 5 feet out of the level, for the distance of 8 or 10 chains in length, and suppose it be AB (fig. 3.) and

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