A levelling sheet, reduced twice, with the check LEVEL

Levelling is the one piece of site arithmetic that proves itself

Reduce the readings by the height of the instrument and you get a column of levels. Reduce the same readings by rises and falls and you get another. If the field work and the arithmetic are both sound, three things are equal:

Σ backsights − Σ foresights
      = Σ rises      − Σ falls
      = last level        − first level

That is not a nicety, it is the point. Almost no other calculation on a site tells you it is wrong. This one does, and it tells you now, while the instrument is still set up and the staff is still there, rather than in three weeks when a drain runs the wrong way.

So both reductions are done here and the check is shown. If the three do not agree, stop and find out why before anybody leaves.

What the check catches and what it does not

It catches arithmetic. A transposed digit, a reading entered in the wrong column, a line added twice: any of those breaks the equality and is found in the moment.

It does not catch a reading that was written down correctly and taken wrongly. A staff not held plumb, a staff on soft ground, a bubble not centred, a collimation error in the instrument, the bottom section of the staff not fully extended: all of those produce a sheet that balances perfectly and levels that are wrong. The check is a proof of the arithmetic, not of the survey.

Which is why the field discipline is separate and not optional. Keep backsight and foresight distances roughly equal, so a collimation error cancels. Close the run back to the benchmark you started from, or on to another known one, so the misclosure is a number you can look at. Change point on something solid, and describe it, so the run can be rerun.

Booking it so it can be read afterwards

Write the benchmark down properly: its value, where it is, and where the value came from. A sheet of levels with no stated datum is a sheet of relative numbers, and it cannot be joined to anybody else's work.

Describe every change point and every station in words. “CP1 on the manhole cover, NE corner of the yard” is what lets somebody stand where you stood. “CP1” is not.

Keep the misclosure and say what you did with it. A run that closes within tolerance and is distributed is honest work; a run that closes badly and is quietly adjusted is not, and the difference is only visible if the raw figures are still on the sheet.

And book it as you go rather than reconstructing it in the van. The reason the check exists is that levelling is done by tired people writing numbers in a notebook in the rain, and every part of the procedure is designed around that being true.

The arithmetic runs here in the tab and nothing is uploaded. Nearby: CUT turns a cutting list into which bar each piece comes off, CONCRETE works out what a pour actually needs, RAMP handles gradients and the landings people forget, and FIGURES keeps the rounding honest.