ferent methods; and (3.) it points out the practical method of obtaining the contents of Hay-ricks, Pits, Timber, and all kinds of Artificers' works; likewise the method of levelling, conveying water from one place to another, and of draining and flooding land. Another, but very different branch of this art is denominated Maritime Surveying, which determines the positions of the remarkable headlands, and other conspicuous objects that present themselves along the coast, or its immediate neighbourhood. It likewise ascertains the situations of the various inlets, rocks, shallows, and soundings, which occur in approaching the shore. The method of performing this, given by Mr. Professor Leslie, is as follows: "To survey a new or inac cessible coast, two boats are moored at a proper interval, which is carefully measured on the surface of the water; and from each boat the bearings of all the prominent points of land are taken by means of an azimuth compass; or the angles subtended by these points and the other boat, are measured by a Hadley's sextant. Having now on paper drawn the base to any scale, straight lines radiating from each end at the observed angles, will, by their intersections, give the positions of the several points from which the coast may be sketched. But a chart is more accurately constructed, by combining a survey made on land, with observations taken on the water. A smooth level piece of ground is chosen, on which a base of considerable length is measured out, and station staves* are fixed at its extremities. If no such place can be found, the mutual distance and position of two points conveniently situate for planting the staves, though divided by a broken surface, are determined from one or more triangles, which connect with a shorter and temporary base assumed near the beach. A boat then explores the offing; and at every rock, shallow, or remarkable sounding, the bearings of the station staves are noticed. These observations furnish so * These staves will be described in the next article, levelling. many triangles, from which the situation of the several points are easily ascertained.—When a correct map of the coast can be procured, the labour of executing a maritime survey is materially shortened. From each notable point of the surface of the water, the bearings of two known objects on the land are taken, or the intermediate angles subtended by three such objects are observed. To facilitate the last construction, an instrument called the Station- Pointer has been invented, consisting of three brass rulers, which open and may be set at the given angles." LEVELLING. LEVELLING is the art of finding a line parallel to the horizon at one or more stations, to determine the height or depth of one place with respect to another, for the purposes of laying out grounds, draining morasses, conducting water, &c. Two or more places are on a true level when they are equally distant from the centre of the earth. Of course one place is higher than another, or out of the level with it, when it is farther from the centre of the earth; and a line equally distant from that centre, in all its points, is called the true level. Hence, since the earth is spherical, that line must be a curve, and make a part of the earth's circumference, or at least one that is parallel, or concentrical to it. The practice of levelling therefore consists: 1. In finding and marking two or more points that shall be in the circumference of a circle, whose centre, and that of the earth, shall coincide; and 2. In comparing the points thus found with other points, to ascertain the difference in their distances from the earth's centre. With respect to the theory of levelling, the following observations may be set down: A plumb line, hanging freely in the air, points directly towards the centre of the earth; and a line drawn at right lines, crossing the direction of the plumb line, and touching the earth's surface, is a true level only in that particular spot; but if this line, which crosses the plumb, be continued for any considerable distance, it will rise above the earth's surface; and the apparent level will be above the true one, because the earth is spherical, and this rising will be as the square of the distance to which the said right line is produced, that is, as much as it is raised above the earth's surface at one mile's distance, it will rise four times as much at the distance of two miles, nine times at the distance of three miles, and so on. This circumstance is, as we have already observed, owing to the globular figure of the earth, and the rise is the difference between the true and apparent levels, the real curve of the earth being the true level, and the tangent to it the apparent level. It appears, that the less distance we take between any two stations, the truer will be the operations in levelling; and as soon as the difference between the true and apparent levels becomes perceptible, it is necessary to make an allowance for it, even if the distance between two stations does not exceed a few chains in length. Levelling may be performed very expeditiously by the assistance of a large theodolite, capable of measuring with precision the vertical angle subtended by a remote object; the distance being known or calculated, and allowance made for the effect of the earth's convexity, and the influence of refraction. But the better method is to employ a spiritlevel, accompanied by a pair of square staves, each of which is composed of two parts that slide out into a rod of ten feet in length, every foot being divided centesimally. A vane slides up and down upon each set of these staves, which, by brass springs, will stand at any given height. These vanes are about ten inches long, and four broad: the breadth is first divided into three equal parts, the two extremes painted white, the middle space divided again into three equal parts, which are less; the middle one of them is also painted white, and the two other parts black; and thus they are suited to all common distances. These vanes have each a brass wire across a small square hole in the centre, which serves to point out the height correctly, by coinciding with the horizontal wire of the telescope of the level. Levelling is distinguished into two kinds, the simple and the compound; the former, which rarely admits of application, assigns the difference of altitude by a single observation; but the latter discovers it by means of a series of observations carried along an irregular surface, the aggregate of the several descents being deducted from that of the ascents. The staves are therefore placed successively along the line of survey, at proper intervals, according to the nature of the ground, and not exceeding three or four hundred yards, the levelling instrument being always planted nearly in the middle between them, and directed backwards to the first staff, and then forwards to the second. The difference between the heights intercepted by the back and the fore observation, must evidently give at each station the quantity of ascent or descent; and the error occasioned by the curvature of the globe may, in very short distances be overlooked, as it will not amount at each station to the hundredth part of a foot. The final result of a series of operations, or the differences of altitude between the extreme stations, is discovered by taking the measures of the back and fore observations collectively, and the excess of the latter above the former, indicates the entire quantity of descent. The following observations will render the whole subject easy and clear to any comprehension. To find the distance between the apparent and true level at the distance of a mile.-In the right-angled triangle ABC, fig. 7, the side A C, the semi-diameter of the earth, is given, suppose 3,982 miles, and the side A B1 mile; to find the hypothenuse C B. Consequently the apparent level at the distance of one mile from the observer's station is higher than the true level by EB-CB-CE=.000125 of a mile 8 inches nearly. The same thing may be done another way. By Eucl. III. 36. 2 EC+EB × EB=AB2; consequently, 2 EC+EB: AB AB: EB. But EB in the first term is so small, in comparison of EC, that it may be neglected, therefore it will be 2 EC:AB:: AB; EB, and EB nearly; that is, the difference between the true and apparent level is equal to the square of the distance between the places, divided by the diameter of the earth; and since the diameter of the earth is a given quantity, it is always proportional to the square of the distance. The diameter of the earth-7964 miles, if AE be equal 1 mile as before, then the difference of levels will be 12 7904 AE 2 2EE 8 inches nearly. If A E=2 miles, then the dif ference of levels will be. = 4 =32 inches, &c. 22 Hence, proportioning the excesses in altitude according to the squares of the distances, the following Table is obtained, shewing the height of the apparent, above the true level, for every 100 yards of distance on the one side, and for each mile on the other. |