To divide off 120 acres, adjoining and parallel to AD. As S. 4 D:x:: Rad.: Db = 18.15 As S. A:x:: Rad.: Aa = 18.43 If it were required to cut off from a given farm any number of acres by a line, having a given bearing, the problem might be solved from the precepts already given; for by drawing a line from any convenient angle in the direction required, find its length, by the feregoing problem, and then the content it incloses which done, the last problem will give the position of the line required. ; EXAMPLE. Let it it be required to cut off 100 acres from the N. end of the foregoing survey, by a line running north-west and south-east. From C, draw CE, North East; then since DC is S. 37° 45′ E. the angle DCE must be 7° 15' and the angle D is 64° 15', therefore angle E is 108° 00'. As S. E.: DC:: S. D: CE hence the triangle DCE area to be cut off difference 39.94 = a 105.85 chs. 1000. SECT. VIII, CONTAINING THE SURVEYING OF HARBOURS, &c. Of surveying Harbours, Shoals, Sands, &c. ) THERE are three methods whereby this may be performed; for the observations may be made either on the water or on the land. Those made on the water are of two kinds, one by the log-line and compass (as in plane sailing) measuring the course and distance round the sand; and then to be plotted as a large wood, or any inclosure taken by the circumferentor. 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-marks, B 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 Rag, or by some other signal. And in the mean time to prevent mistakes, let the crew 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 visible 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 landmarks, and then you may work as before. |