136.442 ft. The elevation found through differentialleveling was 136.457 ft. The error of closure of the levelcircuit is 136.457 – 136.442 = 0.015 ft.therefore, is the actual distance leveled. For third-orderleveling, the allowable error isAssume that errors have occurred progressivelyalong the line over which the leveling wasaccomplished. You make adjustments for these errors bydistributing them proportionally along the line as shownby the following example. If you refer to figure 7-4, youwill notice that the total distance between BM 35 andBM 19, over which the line of levels was run, is 2,140ft. The elevation on the closing BM 19 is found to be0.015 ft greater than its known elevation. You musttherefore adjust the elevations found for theintermediate BMs 16, 17, and 18.The amount of correction is calculated as follows:BM 16 is 440 ft from the starting BM. The total lengthdistance between the starting and closing BMs is 2,140ft. The error of closure is 0.015 ft. By substituting thesevalues into the above formula, the correction is asfollows:Since the observed elevation of the closing BMis greater than its known elevation, the adjustmentsare subtracted from the intermediate BMs.Therefore, for BM 16, the adjusted elevation is134.851 – 0.003 = 134.848. The adjustments for inter-mediate BMs 17 and 18 are made in a similar manner.Calculating the Allowable ErrorThe error of closure that can be allowed depends onthe precision required (first, second, or third order). Theallowable error of closure in leveling is expressed interms of a coefficient times the square root of thehorizontal length of the actual route over which theleveling was accomplishedMost differential leveling (plane surveying) isthird-order work. In third-order leveling, the closure isusually made on surveys of higher accuracy withoutdoubling back to the benchmark at the original startingpoint of the level circuit. The length of the level circuit,Refer again to figure 7-4. By adding the sight distancesin the sixth and seventh columns of the figure, you willfind that the length of the level circuit is 2,140 ft (or0.405 miles). The allowable error of closure, then, isSince the actual error is only 0.015 ft, the results aresufficiently accurate for third-order precision.First- and second-order levels usually close onthemselves; that is, the leveling party runs a line of levelsfrom an old BM or station to the new BM or station, andthen doubles back to the old BM for closure. The actualdistance leveled is twice the length of the level circuit.For second-order leveling, the allowable error isFirst-order leveling is even more precise. Theallowable error cannot be greater thanAdjusting Level NetsWhen a level survey system covers a large area, you,in turn, adjust the interconnecting network in the wholesystem. Adjustment of an interconnecting network oflevel circuits consists of adjusting, in turn, each separatefigure in the net, with the adjusted values for each circuitused in the adjustment of adjacent circuits. This processis repeated for as many cycles as necessary to balancethe values for the whole net. Within each circuit the errorof closure is normally distributed to the various sides inproportion to their lengths. Figure 7-5 represents a levelnet made up of circuits BCDEB, AEDA, and EABE.Along each side of the circuit is shown the lengthof the side in miles and the observed difference inelevation in feet between terminal BMs. The differencein elevation (plus or minus) is in the direction indicatedby the arrows. Within each circuit is shown its totallength (L) and the error of closure (Ec) that is determinedby summing up the differences in elevation in aclockwise direction. Figure 7-6 shows the computationsrequired to balance the net. The circuits, sides, distances(expressed in miles and in percentages of the total), anddifferences in elevation (DE) are listed.7-6

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