Note that the sign of the "Rod Correction" is the same as in leveling.
‘Vhen the line of sight is level, the stadia arc reading is so, and hence the multiple is o, which gives a "Product" o. The only entry is, therefore, the "Rod Correction," or the final rod reading, whose sign follows the above rule.
Take the "Product" and the "Rod Correction" by pairs, and add algebraically; e.g., —16.8+8.2= —8.6, the "Differ ence of Elevation." This, applied algebraically to the last known elevation, gives the elevation desired.
Upon the drawing board, or plane table, a sheet of drawing paper is firmly attached, on which the observations in the field are to be recorded at the time they are made. The table is set up in its proper position (oriented) over a known or unknown point. By keeping the ruler on the point representing the occupied station, the telescope is turned upon other objects and lines are drawn towards them. This will give the direction of the desired point from the table, and its horizontal distance or the difference in elevation determined by stadia. Horizontal distances are sometimes measured with chain; and quite often points are located by means of triangulation from two known points. As it is almost impossible to keep the table perfectly level, the bubble of the instrument is to be kept level and the error of the vernier reading determined and which is to be accounted for in each vertical reading.
The plane table is the instrument used to a great extent in geological surveys. By means of it topographic and geologic mapping of a territory may be made simultaneously. The principal methods used are: radiation, traversing, intersection and resection.
Radiation. In this method a convenient point on the paper is set over a selected point, the table oriented and clamped, each point which is to be located is sighted and a line is drawn along the fiducial edge towards them in turn. The distance and elevation measured by stadia (or by chaining for distance). (Fig. 26.) Traversing. This method is similar to traversing as done with a transit, and consists in moving the plane table from one point to another, then back sighting to the station just left, so the table is always carefully oriented. This is one of the simplest methods
in use and is most generally combined with the method of radiation. (Fig. 27.) Intersection. When points are located by a system of triangulation from a carefully measured base line, or any known line, the points are located by intersection. The method employed necessitates the orienting of the plane table at one end of a known line, then the point required is sighted and the direction drawn by means of the fiducial edge; the table is then moved to the-other end of the line, the table oriented, and the point previously sighted from the first point is again sighted from this second point, the line drawn again, and the intersection of the two lines will determine the location of the point sighted.
This system is best employed in finding of distant and not easily accessible points, and may be used in keeping a check on the progress of the work, with previously determined stations. (Fig. 28.) Resection. The previous method necessitates the setting of the instrument over a known point, but in the course of work it may sometimes be more convenient to set over a point that has not been previously located. This may be done by resection. which consists of setting up the plane table at a random point and orienting it with respect to either three or two known points, which may be done by means of special problems, and in orient ing with respect to three points it is accomplished by the three point problem, and in case of two points, by the two-point problem.
Three-point Problem. There are several variations of this solution, known as the mechanical solution, the Coast Survey solution, Bessel's solution and the analytical solution. The problem is indeterminate if a circle can be passed through the three points and the selected fourth point.