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sums will always give the difference of level between the extreme points.
When it is only required to ascertain the difference of level between two distant points, the last process will be sufficient; but when a section of the line is required, the distances between the points at which the staff was placed each time, must be measured by the chain, and regularly registered in the field-book.
Levelling with the Theodolite.
The application of the theodolite to the practice of levelling is an operation of great simplicity. It consists in taking a series of angles of elevation and depression along the line of section: it is only necessary to set up the instrument at every spot on the line to be levelled, where the inclination changes, without regard to minor inequalities of the surface.
The foregoing process is called compound levelling. The following is an example of simple levelling, performed at one operation, and consequently subject to the correction for curvature and refraction to obtain a correct result. Suppose it were required to drain a marsh A, (Fig. 21,) by making a cut to the stream at B, distance suppose twentysix chains: Set up a level at the point D, and direct the
telescope to a staff at the edge of the stream at B. Now the horizontal line C M represents the line of sight which would cut the staff at M, let us suppose the reading to be 20. 40 feet; and the height of the instrument 4 feet, and the depth of the water at A 6 feet; therefore the difference of level between A and B is as follows:
Cut on the staff,
Height of the instrument,
Depth of Marsh,
Curvature and refraction for
Difference of level,
Now it appears the bottom of the pond is higher than the stream by 10.33 feet.
In seeking the best route for a turnpike, road, railway, or canal, so far as the level is concerned, the engineer's labours is much abridged by duly considering the operation of nature, in the formation of mountains and valleys, and water courses. When an engineer is called upon to ascertain the best line of road or canal, a good map of the country will be of the greatest use to him, as it contains the water courses, which usually give direction to the
valleys, and dividing ridges. If upon examining the map of any part of a country, you see the water courses diverging from any particular locality, you may be sure that that locality occupies the highest position.
The most advantageous direction for a line of road or canal, intended to connect two given places, is evidently
that of a straight horizontal line: if one extremity of the line is more elevated than the other, the straight line connecting them will be an inclined plane, having only one rate of inclination; but if a regular slope cannot be obtained in the direct line, it is only necessary to deviate to obtain the best level the country will admit of, avoiding as much as possible useless ascents. A person undertaking such work, should previously devote some time to obtain a knowledge of the country, its localities, structures, and geological character: such knowledge may lead to the choice of different lines of direction, which may appear to the eye equally favorable; in this case it becomes necessary to make such surveys as will direct the engineer to adopt the one which is likely to prove the most advantageous.
After the engineer has determined on the direction of the proposed road, a surveyor is generally employed to make a survey of all the enclosures through which the line. passes. If any part of the base or principal line be inaccessible, by means of a marsh, lake, wood, houses, &c. ; upon this part describe an equilateral triangle by the chain and theodolite; so will you come on the true line back again, and one of the two measured sides will be the required part of the line. You may get over the same difficulty by help of the circumferentor.
Then the principal line is accurately levelled, also the distance from staff to staff, measured with the chain; and the bearings with the compass of each line taken; and when the ground slopes at right angles to the line of road, cross sections must be taken at right angles to it; the cross sections may be taken at the same time you take the longitudinal levels: after having brought up the levels of the mean line, to any point where you wish to take a cross section, place a picket firmly in the ground, at which point place the staff, and without removing the instru
ment, take the level at the point, and also at two points at right angles to the line there; take also the distance between these two last points, then will you have sufficient data to lay down the cross sections where you think the nature of the ground requires it: this plotted, will give it the exact contour of the line as in figure 18.
When the engineer is required to level through the country in a straight line, the best way is to find the bearing of said line, and keep that direction by help of the compass. In like manner when the line takes different positions, find the bearing of each straight portion. If any obstacles oppose themselves in taking the levels along the line of section, level in a zig-zag course until you come on the required line back again, as near as possible to the last point started from. Let the back and foresights be booked in the column of remarks.
These surveys should be very neatly protracted on a large scale, suppose 4 or 5 chains to an inch for the ground plan, and 30 or 40 feet for the vertical scale. Should the line cross a road or a river a cross section should be taken, the greatest heights of the flood, the velocity of the water, and the sectional area of the river should be stated. The engineer cannot be too particular in detailing every such thing, as it is only from minute details of all the circumstances connected with the line, that the parties interested are guided in making a choice.
It is evident, that to obtain the difference of level between any number of places, and from thence to dilineate the contour of the surface, some reference must be made to a point from which to commence the operation. Sometimes the several heights are counted from a point which has reference to the surface of the sea; but in places remote from the sea, some visible mark is assumed at either end of the line, from which the several heights are counted. A line drawn from this point, or from a point below it,
called the datum line, is that upon which the several levels are based, and by means of which the sections is drawn, The direction of this is parallel to the horizon.
The datum is assumed by some engineers to coincide with high-water mark, spring-tides; others assume low-water mark, spring-tides; others assume high-water, ordinary spring-tides. In assuming a datum line, its position might be taken below the lowest point on the line, or you may assume the datum any depth below the first point so it will not cut the surface. If you allow the datum to cut the surface the reduced levels will come out with different signs, which is not so convenient as when they are all of the same name.
Whatever point you assume for the datum, be sure to leave some permanent bench-mark, which will be necessary perhaps for future reference.
On Check Levels.
When a section of a line of country has been completed, it is in most cases necessary to check it by repetition; in doing this it is not required to level over the exact line of ground, but to follow the most convenient route, and at intervals to level to some known point on the line as a bench mark, find the reduced level at this point, and if it agrees with the reduced level before found for the same point, it proves so far to be correct.
Those bench marks are marks or notches cut on gateposts, stumps of trees, &c., or any other immoveable object on or near the line of section, and at intervals, or a mile asunder. These marks are made by the person who takes the first levels: they are so many fixed points on the line, from whence any portion may be levelled over again in case you detect an error; or other lines of level may be conducted to any other place, and the levels compared with those of the mean line. In checking the prin