‘ + x)
2
The two readings are:
S1 = (S
‘ + x) and S2 = (S
‘ are the staff readings that would have been obtained if the line of collimationwas horizontal, x is the error in each reading due to the collimation error, the effect of
will be the same. The difference
2
and S
1
2
1
‘ and S
which is to tilt the line of sight by angle α.
Since AC = CB, the error x in the readings S
‘
2
gives:
‘ - S
1
2
and S
‘ + x) = S
2
1
between readings S
‘ + x) – (S
This gives the true difference in height between A and B. This demonstrates that if a
collimation error is present in a level, the effect of this cancels out when height
differences are computed provided readings are taken over equal sighting distances.
1
= (S
2
- S
1
1
S
S