Then, you should check on the arithmetical accuracy with which you added BSs and subtracted FSs. The difference between the sum of the BSs taken on BMs or TPs and the sum of the FSs taken on BMs or TPs should equal the difference in elevation between the initial BM or TP and the final BM or TP.

Balanced BS and FS distances are shown in figure 14-14. The distance used for the first instrument setup was 220 ft. The first BS (rod reading on El 35) was 6,659 ft. The first FS (rod reading on 0 16) was 4.971. Notice that the plus sign (+) appears at the top of the BS column and that the minus sign () appears at the top of the FS column in the field notebook. This helps you to remember that BSs are added and FSs are subtracted as you compute the new elevations. The BS taken on a point added to the elevation of the point gives the HI. This establishes the elevation of the line of sight so that an FS can then be taken on any point (BM, TBM, or TP). The level line is extended as far as desired with as many instrument setups as may be necessary by a repetition of the process used in the first setup.

The elevation of El 35 is 133.163 ft. The first HI is

gives the elevation of 0, the first established. Following through with a similar computation for each setup, notice that the elevation of El 19 was found to be 136.457 ft.

Look now at the notes in figure 14-14. The sum of all the BSs is 24.620 ft. The sum of all the FSs is 21.326 ft. The difference between the sum of the BSs and the sum of the FSs is 24.620 21.326 = 3.294 ft.

This difference should agree with the difference between the actual elevation of BM 35 and the elevation already found for BM 19; that is, 136.457 133.163 = 3.294 ft.

This provides a check on the step-by-step computation of elevations.

ADJUSTMENT OF INTERMEDIATE BENCH MARK ELEVATIONS. Level lines that begin and end on points that have fixed elevations, such as BMs, are often called level circuits. When leveling is accomplished between two previously established BMs or over a loop that closes back on the starting point, the elevation determined for the final BM will seldom be equal to its previously established elevation. The difference between these two elevations for the same BM is known as the ERROR OF CLOSURE. The Remarks column of figure 14-14 indicates that the actual elevation of BM 19 is known to be 136.442 ft. The elevation found through differential leveling was 136.457 ft. The error of closure of the level circuit is

It is assumed that errors have occurred progressively along the line over which the leveling was done so that adjustments for these errors are distributed proportionally along the line as shown by the following example: Referring to figure 14-14, you will notice that the total distance between BM 35 and BM 19, over which the line of levels was run, was 2,140 ft. The elevation on the closing BM 19 was found to be 0.015 ft greater than its known elevation. You must therefore adjust the elevations found for the intermediate

The amount of correction is calculated as follows:

TBM 16 is 440 ft from the starting BM. The total length distance between the starting and closing BMs is 2,140 ft. The error of closure is 0.015 ft. The adjusted elevation of TBM 16 is

The adjustments for intermediate TBMs 17 and 18 are made in a similar manner.