Line of position and errors of point position
Abstract
The general theory of lines of position and gradients provides great clarity and simplicity in matters of graphical adjustment and determination of point position errors. In geodesy, when determining the position of unknown points on a plane, we directly measure horizontal angles and distances, which can be considered as functions of two variables (coordinates). To a given measured value of a function there corresponds a certain geometric locus of points on the plane—a certain line, which we shall call the line of position. Let us turn to the errors of point position. The position of the projection of a point onto the horizontal plane is determined by the intersection of two lines of position of two measured functions. Graphical adjustment using gradients is highly expedient in repeated trigonometric determinations of moving points, for example in landslide areas, in areas subject to displacement due to underground mining, and the like. Once constructed, the error figure with the calculated gradients will serve as a convenient means for further studies of the movement of the point being determined.
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