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The basic cycle of differential leveling can be summarized as follows:

                            HI (Height of Instrument) = H A (Known elevation) + BS (backsight)

                                          H B (New elevation) = HI – FS (foresight)


                     Frequently,  the  elevations  of  points  over  a  relatively  long  distance  must  be
                  determined. A process of measuring two or more widely separated points simply
                  involves several cycles or repetitions of the basic differential leveling operation.
                  More specific terms for this are benchmark, profile, and topographic leveling.


                     5.4 Benchmarks and Turning Points
                     Suppose it is necessary to determine the elevation of some point C from point A.
                  But in this case, let us assume that it is not possible to set up the level so that both
                  points  A  and  C  are  visible  from  one  position.  The  line  of  levels  can  be  carried
                  forward towards C by establishing a convenient and temporary turning point (TP)
                  somewhere between A and C. The selected TP serves merely as an intermediate
                  reference point; it does not have to be actually set in the ground as a permanent
                  monument.












                    Fig.5.2. Temporary turning points are used to carry a line of levels from a benchmark to some
                   other station or benchmark; the process of differential leveling is repeated at each instrument set
                                                                up

                     The elevation of the turning point is computed from the first pair of BS and FS
                  readings.  The  BS  is  on  point  A,  which  is  the  end  point  of  known  elevation.  A
                  secure and permanent point of known elevation  is called a  bench mark (BM); a
                  leveling survey should begin with a back sight on a benchmark. The BS is added to
                  the elevation to give the HI at the first instrument position.
                     The elevation of the turning point is obtained by subtracting the FS from the HI.
                  Once  the  elevation  of  the  turning  point  is  known,  the  level  instrument  can  be
                  moved to another location, one closer to C but still in sight of the turning point.
                  Then  another  back  sight  is  taken,  this  time  on  the  turning  point,  in  order  to
                  determine the new height of instrument. Finally a foresight is taken on point C, and
                  its elevation is computed.




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