LEVELLING is the art of determining the heights or depressions of points on the ground with respect to a spherical or spheroidal surface coinciding nearly with that of the earth, or, when the extent of ground is inconsiderable, with respect to a horizontal plane passing through some given point on the ground.
In extensive operations of this nature, which are connected with the researches of physical astronomy, an attention to that figure of the earth which approaches the nearest to the truth is of importance ; but when the object is merely to determine the profile of the ground, fOr a canal, or a line of road, it is sufficient to consider the surface to which the points are referred as that of a sphere.
The relativ‘heights of a series of points on the ground are obtained by means of their vertical distances from others which, on the supposi tion of the earth being a sphere, are equally distant from its centre ; and these, which are called level-points, must be found by an instru ment constructed for the purpose. Now, a plane being supposed to touch the earth at any given point, all the points in the circumference of a circle described ou that plane, about that point of contract as a centre, will be level-points : consequently, if a telescope be so adjusted that, when turned round upon the vertical axis of the instrument to which it is applied, its line of collimation (that which passes through the centres of all the lenses) may remain parallel to the horizon, any number of such level-points will be determined, if, being at equal dis tances from the said axis, they are in the direction of the line of collimation produced. The instrument alluded to is called a spirit level [SPIRIT LEVEL ; THEODOLITE] ; and by certain adjusting screws the line of collimation, or optical axis of the telescope, is capable of being brought into the position above mentioned, which is indi cated by a bubble of air remaining, during a complete revolution of the telescope, in the middle of the tube containing the water or spirit. • The instrument is employed for the purpose of ascertaining the relative heights of points on the ground in either of the following ways, the first of which is the most simple, and is frequently adopted.
Choice is made of any convenient stations, A, D, &c., on the line of operation, and the distances between them are determined either by actual admeasurement, or by computations founded on the data afforded by a previous survey of the ground. The instrument is then set up at, or near, the middle of the interval between every two such points in succession. When the telescope thus placed, as at a, has been rendered horizontal by means of the adjusting screws, an assistant at each of the stations A and B, holding what is called a station staff in a vertical position, moves a vane or index along the staff, upwards or downwards, according to the directions of the observer at the telescope, till it appears to coincide with the intersection of two wires in the telescope, that intersection having, by the adjustment of the instrument, been made to coincide with the optical axis, or line of collimation.
The points thus determined on the staves are represented by m and n; and, from what has been said, these are level-points, or points equally distant from the centre of the earth. Therefore, the heights A m and B n being read on tho graduated staves, the difference between them will give the relative heights of the ground at A and B ; that point, of course, being the highest at which the distance of the vano from the ground is the least. A similar process is repeated with respect to the points n and c, the instrument being placed at 1, midway between them ; sump the operation is to be continued to the end of the line ow which the profile is required. It is customary to insert the heights s a. eq. ac., in a column beaded Fure-siphts, in a sort of field book, and the heights Ara, imp, itc, in a collateral column headed Buck. :whir. The difference between the sums of the numbers in these two columns will be equal to the height of one extremity of the line above the other.