The columns

Column Meaning
B.S. (back sight) The first reading after the instrument is set up, taken on a point of known level: the bench mark, or a change point.
I.S. (intermediate sight) Any reading between the back sight and the fore sight, such as each offset of a cross-section.
F.S. (fore sight) The last reading before the instrument is moved, or the closing reading.
H.I. (height of instrument) The level of the line of sight: the R.L. of the point the back sight was taken on, plus the back sight.
R.L. (reduced level) The level of each staff point above the datum.
C.P. (change point) A point read twice: a fore sight from the old set-up, then a back sight from the new one.

The method in three rules

  1. Start of a set-up: H.I. = R.L. of the point + B.S. On the first line, the point is the bench mark.
  2. Every other reading: R.L. = H.I. − the reading (I.S. or F.S.).
  3. At a change point: first R.L. = H.I. − F.S. using the old H.I., then the new H.I. = that R.L. + the new B.S.

Worked example

Bench mark on a culvert, R.L. 100.000. The leveller reads the cross-section at chainage 0+000, moves the instrument through a change point, reads three offsets at 0+030 and closes on a temporary bench mark.

Point B.S. I.S. F.S. H.I. R.L.
BM on culvert 1.450 101.450 100.000
CH 0+000, −10.0 1.820 99.630
CH 0+000, −5.0 2.105 99.345
CH 0+000, 0.0 2.640 98.810
CH 0+000, +5.0 2.230 99.220
CH 0+000, +10.0 1.905 99.545
CP 1 0.985 3.415 99.020 98.035
CH 0+030, −5.0 1.210 97.810
CH 0+030, 0.0 1.465 97.555
CH 0+030, +5.0 0.870 98.150
TBM 2 1.125 97.895

Line by line:

  • BM: H.I. = 100.000 + 1.450 = 101.450.
  • CH 0+000, −10.0: R.L. = 101.450 − 1.820 = 99.630. The other four offsets at 0+000 are worked the same way from 101.450.
  • CP 1: R.L. = 101.450 − 3.415 = 98.035 (old H.I.). The instrument moves; the new H.I. = 98.035 + 0.985 = 99.020.
  • CH 0+030: each R.L. = 99.020 − the reading, for example 99.020 − 1.210 = 97.810.
  • TBM 2: R.L. = 99.020 − 1.125 = 97.895.

Check 1: back sights against fore sights

The difference between the sums of the back sights and the fore sights must equal the difference between the last and the first R.L.:

  • Σ B.S. = 1.450 + 0.985 = 2.435
  • Σ F.S. = 3.415 + 1.125 = 4.540
  • Σ B.S. − Σ F.S. = −2.105
  • Last R.L. − first R.L. = 97.895 − 100.000 = −2.105 ✓

This check proves the change points and the closing R.L. It does not check the intermediate sights: a slip in any I.S. line leaves it unchanged.

Check 2: every reduced level

To check the intermediate sights too, multiply each H.I. by the number of readings reduced from it (intermediate and fore sights), add them up, and take away all the I.S. and F.S. readings. The result must equal the sum of every R.L. except the first.

  • 101.450 was used for 6 readings (five offsets at 0+000 and the fore sight on CP 1): 6 × 101.450 = 608.700
  • 99.020 was used for 4 readings (three offsets at 0+030 and the fore sight on TBM 2): 4 × 99.020 = 396.080
  • Σ (H.I. × readings) = 1004.780
  • Σ I.S. = 14.245, Σ F.S. = 4.540
  • 1004.780 − 14.245 − 4.540 = 985.995
  • Σ R.L. except the bench mark = 985.995 ✓

Height of instrument or rise and fall?

Both give the same reduced levels. The height of instrument method is quicker when a set-up has many intermediate sights, which is exactly what a cross-section survey has: one subtraction per reading. The rise and fall method compares each reading with the one before it, so its check (Σ rise − Σ fall = last R.L. − first R.L.) covers every reading, at the cost of more arithmetic.

Mistakes that are easy to make

  • Keeping the old H.I. after a change point. Every reading after the C.P. must be reduced from the new H.I.
  • Booking the change point once. It needs both the F.S. (old set-up) and the B.S. (new set-up) on the same line.
  • Mixing up left and right. Book offsets left of the centre line as negative, consistently, or the cross-section is drawn back to front.
  • Not closing. Always finish on a bench mark or a point of known level; check 1 only means something when the last R.L. can be compared with a known value.