LEVELLING. The relative heights of a series of points on the ground are obtained by means of their vertical distances from others which, on the supposition of the earth being a sphere, are equally distant from its centre ; and these, which are called level-points, must be found by an instrument constructed for the purpose. [SPIRIT LEVEL; THEODOLITE.] In general, a choice is made of any convenient stations on the line of operation, and the dis tances between them are detezmined by actual admeasurement. The instrument is then set up at or near the middle of the interval be tween every two such points in succession. When the telescope thus placed has been ren dered horizontal by means of the adjusting screws, an assistant at each of the adjoining stations, holding what is called a station stair in a vertical position, moves a vane or index along the staff, upwards or downwards accord ing to the directions of the observer at the telescope, till it appears to coincide with the interisetion of two wires in the telescope. The points thus determined on the staves are level points or points equally distant from the cen tre of the earth ; and the difference between the height of the index on the two staves will give the relative height of the ground at the two stations.
It is frequently the practice to execute a sort of double-levelling ; which consists in placing the instruments successively at each of the stations, a staff being held up vertically at the other, when, the axis of the telescope being at equal heights from the ground at both stations, half the difference between the heights read on the staves will express the difference in the height of the stations.
The profile of the ground is usually expres sed on paper, in portions of any convenient length, for the purpose of enabling the engi neer to determine the depths of his excava tions, or the heights of the masses of earth to be raised, when it is proposed to execute a canal or road. A right line being drawn to represent one parallel to the horizon, and passing through the highest or the lowest point of the natural ground; the heights and depressions of the remarkable points, with respect to such line, are obtained by additions or subtractions from the numbers in the field book, and are, by a proper scale, set out from that line on others drawn perpendicularly to it at intervals equal to the horizontal distances between the same points. The series of points thus obtained, being joined by hand or other wise, give the figure of the required vertical section of the ground.