The precision of a level run is usually prescribed in terms of a maximum error of closure. This is obtained by multiplying a constant factor by the square root of the length of the run in miles or in kilometers, depending upon the system of measurement being used. The Federal Bureau of Surveying and Mapping specifies certain requirements and the maximum closing errors, such as those shown in table 14-1. You may refer to this standard if the order of precision is not specified for a particular survey project.

A level run that begins at a particular BM and is carried back again to the same BM is called a level loop. A run that does not close on the initial BM is called a level line. A level line closes on another BM; but when a level line is carried back to its origin, it becomes a level loop. Usually, a level line is carried back to the initial BM to determine the error of closure.

Error of closure is simply the difference between the known elevation of the initial BM and the elevation of the same (BM) as computed in the level run.

The error of closure that can be allowed depends on the precision required (first, second, or third order). The permissible (or allowable) error of closure in accuracy leveling is expressed in terms of a coefficient and the square root of the horizontal length of the actual route over which the leveling was done.

Most differential leveling (plane surveying) is third-order work. In third-order leveling, the closure is usually made on surveys of higher accuracy without doubling back to the old BM at the original starting point of the level circuit.

The length of the level circuit, therefore, is the actual distance leveled. For third-order leveling, the allowable error is as follows:

By adding the sight distances in the sixth and seventh columns of the differential level circuit shown in figure 14-14, you will find that the length of the level circuit is 2,140 ft. The length in miles is

Since the actual error is only 0.015 ft, the results are sufficiently accurate.

First- and second-order levels usually close on themselves. The leveling party runs a line of levels from an old BM or station to the new BM or station, and then doubles back to the old BM for closure. The actual distance leveled is twice the length of the level circuit.

For second-order leveling, the allowable error is

First-order leveling is still more precise. The allowable error cannot be greater than