page thirty-two

The Benchmark

The Heartwood found a year. This room finds a height. Every hillside hides the one question a village needs answered before it spends money on a water pipe: is the spring really higher than the place the water has to reach, and by how much? The eye is no good at it. Measuring it means a level, a staff, a notebook and a morning of walking. The day's number lays out the village and the hill, and hands you the telescope.

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The line

You start with the staff on the benchmark, whose height is published, and walk the level up the hill in short hops. At each set-up you take a back sight to the staff where you have just been, intermediate sights to anything you want the height of, and a fore sight to a change point, where the staff stays while the level moves on past it. The last fore sight lands on a second mark of known height, and that is your check.

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m
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Reading an E staff. The big figure is the decimetre, and the small red one beside it is the metre, so a big 4 with a little red 1 is 1.4 m, printed just above the 1.400 line. Each black band and each white band is one centimetre: the E fills the bottom half of every decimetre, and two loose bars fill the top half. Find the figure just below the horizontal hair, count the bands up to the hair, and estimate the millimetres. The short hairs above and below are stadia hairs, for measuring distance, and you can ignore them here.

Village
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Away from the reading box, the arrow keys walk to other days. Every day is a different village and a different hill.

The level book

Booked the rise-and-fall way. Each reading is compared with the one before it in the same set-up: a smaller reading means the ground has risen, a bigger one that it has fallen. The reduced levels are carried along from the benchmark. The yellow cell is the sight in the telescope now.

Closing the loop

m

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Route
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Set-ups
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Sights
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Pipe run
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Allowed misclosure
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Instrument
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What is real here and what is not

The method, the booking and the tolerances are the ones surveyors are taught. The village, its hill, its well and its benchmarks are the day's number, so nobody should go looking for any of them.

  1. 01

    Benchmarks are real

    Britain is scattered with them: a horizontal bar cut into a church, a bridge or a milestone with a broad arrow, the crow's foot, pointing up at it, and flush brackets set into walls. Their heights are above Ordnance Datum Newlyn, which is mean sea level at the Newlyn tide gauge in Cornwall from 1915 to 1921. The Ordnance Survey stopped maintaining most of them decades ago, but hundreds of thousands are still there.

  2. 02

    So is the staff

    The E-pattern staff, with centimetre bands grouped into an E over each half decimetre and figures at every decimetre, is the standard British levelling staff. Readings are taken to the millimetre by estimating inside the centimetre band, and good observers agree to within a millimetre or two at these distances.

  3. 03

    The booking is real

    Rise-and-fall booking, with the three-way check that the sum of back sights minus fore sights, the sum of rises minus falls, and the last reduced level minus the first all agree, is how levels have been booked for more than a century. It only checks the arithmetic. Closing on a second known mark is what checks the readings.

  4. 04

    So are the errors

    A level whose line of sight is not quite horizontal adds an error in proportion to the sight length, so it cancels when back and fore sights are equal. That is why surveyors pace them out, and why the two-peg test exists. 12√K mm, with K in kilometres, is a common allowance for ordinary engineering levelling. Sharing the misclosure out in proportion to the set-ups is the usual adjustment.

  5. 05

    The rest is invented

    The hill is a sum of smooth waves, and the reading errors are a tidy normal millimetre. The real field is worse. Heat shimmer makes the staff dance, the staffman does not hold it quite upright, sinking tripods and soft change points creep, and long sights near the ground bend with refraction. The 1 in 200 the parish wants is a rule of thumb for this page, not a water engineer's design.

Thirty-two rooms, and one number doing all the work. Today it raises a hill, lets a spring out halfway up it, puts a village at the bottom and leaves you a telescope to find out whether the water can get down on its own.