Geoscience Reference
In-Depth Information
4Heights
4.1
Spirit leveling
The principle of spirit leveling is well known. To measure the height difference
δH
AB
between two points
A
and
B
, vertical rods are set up at each of
these two points and a level (leveling instrument) somewhere between them
(Fig. 4.1). Since the line
A B
is horizontal, the difference in the rod readings
l
1
=
A A
and
l
2
=
B B
is the height difference:
δH
AB
=
l
1
−
l
2
.
(4-1)
If we measure a circuit, that is, a closed leveling line where we finally return
to the initial point, then the algebraic sum of all measured differences in
height will not in general be rigorously zero, as one would expect, even if we
had been able to observe with perfect precision. This misclosure indicates
that leveling is more complicated than it appears at first sight.
Let us look into the matter more closely. Figure 4.2 shows the relevant
geometrical principles. Let the points
A
and
B
be so far apart that the pro-
cedure of Fig. 4.1 must be applied repeatedly. Then the sum of the leveled
height differences between
A
and
B
will not be equal to the difference in the
orthometric heights
H
A
and
H
B
. The reason is that the leveling increment
δn
, as we henceforth denote it, is different from the corresponding increment
δH
B
of
H
B
(Fig. 4.2), due to the nonparallelism of the level surfaces. De-
noting the corresponding increment of the potential
W
by
δW
,wehaveby
(2-21)
−δW
=
gδn
=
g
δH
B
,
(4-2)
_
_
A
B
l
2
l
1
B
±
H
AB
A
Fig. 4.1. Spirit leveling
