Two peg test and permanent adjustment

Two peg test is the field test used to find the collimation error of a level: the error caused by the line of collimation not being exactly parallel to the axis of the bubble tube when the bubble is central. The line of sight is then inclined up or down, and the staff readings contain an error proportional to the sight distance.

When permanent adjustment is required: when the test shows a collimation error larger than the permissible limit (about 10 mm in 100 m for ordinary levelling; 5 mm or less for precise work), or when the instrument has been damaged or dropped. If the error is small, it is eliminated in the field by keeping the backsight and foresight distances equal.

Field procedure

1. Choose two points A and B about 60–100 m apart on level ground. Drive pegs or mark them.
2. First setup: set up the level at the mid-point F of AB. Level it and read the staff on A ($a_1$) and B ($b_1$). Equal sights cancel the collimation error, so the true difference of level is $h = a_1 - b_1$.
3. Second setup: move the level to a point O on the line AB produced (or between A and B), about 2–5 m from one peg, say B. Level it and read the staff on B ($b_2$, near) and on A ($a_2$, far).
4. The apparent difference is $a_2 - b_2$. The error in the far staff reading is $e = (a_2 - b_2) - h$.

 Setup 1:       A       F       B      equal sights
                |  <----+---->  |
 Setup 2:       A                O B    near B
                |  <------------>|-|

5. If the apparent difference equals the true difference, there is no error. If $e$ is positive, the line of collimation is inclined upward; if negative, downward.

Adjustment

• Let $d_A$ and $d_B$ be the distances of the instrument from A (far) and B (near). The error per metre of sight is $k = e/(d_A - d_B)$. The correct readings for a horizontal line of sight are $a_2' = a_2 - k\,d_A$ on A and $b_2' = b_2 - k\,d_B$ on B (check: $a_2' - b_2' = h$).
• Without moving the instrument, bring the horizontal cross-hair to the correct reading $a_2'$ on the far staff A with the vertical capstan screws of the diaphragm (top and bottom screws: loosen one and tighten the other).
• Check that the bubble stays central, and repeat the test until the error is within the limit.

Collimation error $= \dfrac{e}{\text{difference of distances}}$ (for example 0.004 m in 60 m).