* selves for civil engineers, or that they will furnish themselves with suitable instruments for that business, but every surveyor should furnish himself with an instrument with which he can take levels and angles of elevation* or depression, with a sufficient degree of accuracy to answer in cases of locating roads, of ascertaining whether water may be carried in an aqueduct from one place to another, and to ascertain the fall of mill seats; also, to answer in all common cases. A cheap, simply constructed instrument, represented by the following figure, is recommended А B N a Let A B be a strip of a board three inches wide and three feet in length, or longer if necessary, made perfectly straight on the top. The perpendicular piece, which is dovetailed into the top, should be of such a width at the bottom that it may be graduated either way from the centre, ten or fifteen degrees; and of such a length that the radius by which the graduated arch is swept, should be at least a foot. Great care must be taken in the graduation, to have it done correctly, and by fine lines, and to have the centre perpendicuar or at right angles with the top. The plumb line should be a fine smooth silk thread or hair. At z, a hole should be bored of a suitable size to set it on the head of a compass staff. Such an instrument, if correctly made, will answer all the purposes before mentioned. Before directions are given for levelling, the difference between the apparent, and the true level, will be explained. The former is a tangent, or a straight line, drawn and con a * An angle of elevation rises above a horizontal line; a depression falls below it. tinued from any point on the globe, the surface continually departing from it. The latter is the curvature of the earth, or a line parallel with it, like two concentric circles, each part of the true level, whatever may be its length, is equidistant from the centre of the earth. The straight line m n, in the following figure, represents the apparent, and the curved line a z, the true level. Let the above described instrument be set on any part of the ocean, and be levelled by the plummet, the top being even with the surface of the water, and let a line with the top be continued; as the plummet hangs directly towards the centre of the earth, it is evident that this line is a tangent, and at the end of one mile it will be 8 inches, at the end of 10 miles 66 feet 4 inches, and at 20 miles, 266 feet above the surface of the water. In levelling between two points at a considerable distance apart, where the instrument must be often set, as the plummet, like the spokes in a wheel, each time hangs directly towards the centre of the earth, it will keep the top of the instrument on the true level, provided it is set on the centre of each stationary distance. But when the level is taken from the first to the second station, and from the second to the third, and so on in succession to the end, each level will be a tangent; of course, the apparent level will be taken. The surveyor should also be furnished with two observation staves, ten feet, or more, in length, divided into feet and inches. These staves should be committed to the care of two skilful men, who will keep them perpendicular at the stations, and who will be correct in their assistance in taking the observations. Suppose the first stationary distance, on which a level is to be taken, is 20 rods. The staves must be erected at each terminating point, and the surveyor must take his station equidistant from each. A target must be raised on each staff as the surveyor may direct. If the level strikes the back staff 7 feet, and the forward staff 2 feet, above the surface, it is apparent that the rise between the stations is 5 feet; but the substraction need not be made, each observation should be entered in its respective column, under the head of fore heights and back heights, or fore sights and back sights, as the surveyor may choose to term them. When the first observation is completed, the back staff should be carried forward to a convenient place, and the second observation taken as the first. In like manner the rest of the observations must be taken and entered in their respective columns. If the sum of the back sights shall exceed the fore sights, the terminating point is higher than the place of beginning; but if the sum of the fore sights shall exceed the back sights, then the terminating point is lower than the point of beginning, as will appear by the following examples. FIRST EXAMPLE. Fore sights. Back sights. Feet. Inches. Feet. Inches. 8 00 2 00 8 00 1 00 4th 7 00 2 00 5th 7 00 2 00 6th 1 00 7 00 7th 1 00 8 00 8th 1 00 8 00 9th 1 00 8 00 10th 0 00 8 00 46 00 Difference 5 00 The terminating point is 5 feet higher than the point of beginning SECOND EXAMPLE. Fore sights. Back sights. Feet. Inches. Feet. Inches. 8 00 2 00 8 00 00 4th 7 00 2 00 5th 7 00 2 00 6th 1 00 7 00 7th 1 00 8 00 1 00 8 00 9th 1 00 8 00 66 66 8th 66 The terminating point is 3 feet lower than the point of beginning When the sums of the two columns are equal, the extreme points are on the same level. It will not be necessary to enter the stationary distances in the field notes, unless the whole distance between the two extreme points, or a profile of the surface, is wanted. On a distance of 80 rods, the difference between the apparent and true level, is half an inch; at half a mile, two inches. In levelling to ascertain how high a dam across a stream may be raised without flowing the meadows, or impeding the wheel of a mill above, great caution should be observed, for if a dam is raised to a level with a point 80 or 100 rods above, to which it may be supposed that water may flow without damage, it will rise higher at that point than any one would suppose, who has not investigated the subject. The rise of water at the head of a pond, will depend in a great measure on the width of it, and on the size and force of the stream. In locating roads, sometimes it is necessary to ascertain the difference between the elevation of the hills on two routes, both proceeding from one and terminating at the same point. Though the difference, of itself, between the rise and fall on two routes, may not in all cases be a correct rule by which to give preference, yet this evidence, with a comparison between the steepness of the hills on two routes, is sufficient. To perform this service by the slow process of levelling for the conveyance and rise of water, would be attended with an expense which the case would not justify; therefore, a more expeditious method will be pointed out. At convenient distances, take all the angles of elevation and of depression, with the instrument before described, measuring the distance between each station. These angles will be taken more correctly by back sights, as the surveyor can better select proper places for taking them than an inexperienced assistant. The courses or bearings of the several stationary distances, may or may not be taken with a compass. The elevation of the hills may be ascertained as correctly without the courses as with them. If the courses are taken, it will require more time and expense. Having measured all the stationary distances, and taken all the angles of elevation and depression on a route, arrange them, as in the stations; the second, the distances in rods; the third, the degrees of elevation or depression, with the letter E. or D. against them. The column H. D. contains the horizontal distance made on each line. The horizontal distance, with the elevation or depression against it, is the same as the latitude and departure on a course taken by the compass. The column P. H. contains the perpendicular height at the end of each line above the horizontal line. This column, in this case, is formed by adding the elevations, and by substracting the depressions. By this calculation it appears that the sum of the elevations amount to 15.62 rods, or to 257 feet 8 inches, and the depressions amount to 6.11 rods, or to 100 feet 9 inches, which may be thus expressed, 257 feet 8 inches rise, and 100 feet 9 inches fall. It also appears that the hill at the terminating point is 24 links, or 15 feet 10 inches, higher than the top of the first hill. By this method of taking elevations, they are the apparent level, but this will answer the purpose for locating |