PART II.

PLANE AND TACHYMETRIC SURVEYING.

CHAPTER VII.

PLANE-TABLES AND ALIDADES.

52. Plane and Topographic Surveying.-Plane surveying consists of the representation of any portion of the surface of the earth in horizontal plan as it would appear viewed from vertical positions over every point on the surface. The resulting map may be considered as consisting of an infinite number of points, the positions and relations of only so many of which are established as may be necessary to define the features which it is desired to represent, and this constitutes the instrumental work of the survey. The prime element of position in the construction of such a map is a point in space. Such a position is indefinite, however, and to introduce the definite elements of direction and distance it is necessary to add at least one other point. The addition of a third point introduces trigonometric functions by which any three elements of a triangle, except the three angles alone, serve to determine all others. These trigonometric functions may be solved or determined mathematically in figures from linear measures or angles, and graphically by means of the planetable.

The element of direction or azimuth is the deflection from

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a true north and south line, or it may be a compass bearing, which is a deflection from the magnetic north and south line, or it may be the amount of deflection from any assumed line. The amount of such deflection of one line from another is measured by the angle formed at their intersection. The element of distance is measured by any unit conventionally established, the most definite of which in present use are the yard and meter (Art. 293).

The representation of any portion of the earth's surface by a topographic map requires that, in addition to the projection upon a horizontal plane of a sufficient number of points to reproduce in plan the surface of the land, there shall also be indicated in some way the relief of the surface or its changes of height above, within, or below a fixed level surface. Such representation is made by determining instrumentally the elevation of such a number of points that the survey may be completed by drawing in the details between them. new method of topographic surveying is by the determination of the least number of such points, and therefore calls for the greatest display of artistic and topographic skill, perception, and judgment on the part of the topographer.

The

53. Plane-table Surveying. The plane-table (Art. 56) is peculiarly well adapted to the mapping of topography, not only because it permits of quickly and graphically obtaining all the instrumental data which is requisite, but also because it has the added advantages,

First, of having the map made in the field while the terrane is in view of the topographer;

Second, the topographer can see at all times whether he has obtained all data necessary for the representation of the country; and

Third, any insufficiency of instrumental or interpolated data can at once be supplied before leaving the field.

In surveying with the plane-table the errors in measurement of horizontal angles can be so far eliminated in practice

that they may be neglected. In practice the horizontal projections of existing angles are recorded graphically and are therefore free from errors of record, adjustment, or platting. In using the plane-table a number of points may have had their positions previously determined and platted on the map sheet. After the plane-table has been oriented and clamped each of these should be sighted from the first position occupied, and all other points in view should appear in vertical planes passing through the station and corresponding points on the sheet. Such points as do not meet this geometric test should be rejected until corrected or relocated graphically.

In locating from a given station positions which are to be used in controlling the details of the sketching, a series of radial lines (Fig. 46) should be drawn from the station in all

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3

FIG. 46.-DRAWING RADIAL SIGHT LINES.

directions to salient points. This operation should be repeated at other stations, and the intersection (Fig. 47) of any two on the same object gives its elementary location, a third line through the same point placing beyond doubt the accuracy of its location. Accordingly, in this mode of surveying, constant opportunities occur for checking locations without calculation. The causes of failure to check may be immediately

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tested, and the scale being ever present, it controls the amount of detail which it is necessary to gather.

Another advantage of the plane-table as a surveying instrument lies in the fact that, any two points being taken on the sheet as a base, a map may be constructed therefrom independent of scale, yet perfect in its proportion, by the method of intersection alone. If the base chosen be a very long one, as the two points of a trigonometric survey, and

FIG. 47.-INTERSECTING ON RADIAL LINES.

the details of the plane-table survey be included within the limits of the base, then the survey is a contracting one with a diminishing chance of error, and each pair of intersections which has been tested geometrically becomes in turn a base for further triangulation. Ultimately the length and azimuth of some line in this survey may be determined and the whole plane-table survey thus be reduced after the completion of the field-work to any desired map scale.

54. Reconnaissance and Execution of Plane-table Triangulation. Having located on the plane-table sheet (Art. 188) two intervisible and well-defined points, the topographer should visit one of these and erect a signal of sufficient size to be visible from the most distant part of the territory cor

responding to the plane-table sheet. Then selecting a number of points visible from his position which may furnish satisfactory stations, a hasty reconnaissance trip is made over the territory, covering it all, if convenient, in the first reconnaissance, or perhaps only a portion, and returning to the reconnaissance after the plane-table work has caught up with it.

This reconnaissance should consist in the selection of a few commanding and well-distributed stations, preferably on the highest eminences in the region under survey, and on each of these a signal must be erected on the point from which the greatest command of the surrounding country may be had. The distance apart of such secondary stations is chiefly dependent on the character of the topography and upon the scale of the map, and may be such as to correspond for the scale of the map chosen to a distance on the paper of five or six inches. In the course of this reconnaissance, a number of other stations may be selected by merely noting their positions and appearance, these being on prominent cleared points, such as bare rocks on mountain summits or slopes, a high lone tree, a building in a field, etc., or a few signal-flags may be placed, providing a sufficient number of such objects are not discovered.

The topographer then begins his plane-table triangulation by occupying one of the two primary points and orienting on the other, lines being drawn to the secondary stations and to such other possible tertiary points as may be easily recognized (Fig. 1). He then occupies the second of the primary stations and orients from the first, intersecting on such of the flags established as are visible from his position. Or, he may make his second station on one of the points sighted from the first, determining his position by resecting (Art. 74) from the second primary station. He continues thus until he has carried a secondary or skeleton triangulation over the entire area under survey, taking care not to spend too much time in sighting and attempting to locate minor and unimportant objects, but