We previously described a modified surveying theodolite in which the head can be set in a second more elevated position by means of a sliding calibrated extension rod, thus allowing through triangulation the measurement of otherwise inaccessible distances or heights of objects. The recommended sequence of operations required the tilting of the extended rod of the instrument away from the plumb line in order to determine such a distance or height. Unfortunately, this tilting adversely affects the mechanical stability of the instrument. However, it is possible to make triangulation measurements without tilting the rod away from the normal. A new sequence of operations is presented in which the height of a distant object, horizontal distances, and slope distances can be calculated as functions of two measured angles of elevation and the length of the extended rod (along the normal, or plumb line) only. This operational modification has the advantages over the earlier-described procedure of simplicity, lower cost, convenience, greater mechanical stability, and increased precision of measurement.
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