Geoscience Reference
In-Depth Information
Accordingly, this may be written
OC
AB
=DC
ABB
0
A
0
A
.
(4-44)
Thus, the orthometric correction from
A
to
B
equals the dynamic correc-
tion over the loop
ABB
0
A
0
A
, a curious, but practically completely useless
relation equivalent to (4-41). (
Question:
Why is this independent of
γ
0
?)
From (4-18), we find
=
B
A
dn
=
B
g
−
γ
0
γ
0
g
−
γ
0
γ
0
DC
AB
δn ,
A
DC
A
0
A
=
A
A
0
g − γ
0
γ
0
dH
=
g
A
− γ
0
γ
0
(4-45)
H
A
,
DC
B
0
B
=
B
B
0
g
−
γ
0
γ
0
dH
=
g
B
−
γ
0
H
B
,
γ
0
where
g
A
and
g
B
are the mean values of gravity along the plumb lines of
A
and
B
. Thus, the orthometric correction (4-41) becomes
OC
AB
=
B
g
−
γ
0
γ
0
δn
+
g
A
−
γ
0
g
B
−
γ
0
H
A
−
H
B
.
(4-46)
γ
0
γ
0
A
Here again we need the mean values of gravity along the plumb lines,
g
A
and
g
B
;
γ
0
is an arbitrary constant for which we always take normal gravity at
45
◦
latitude.
Accuracy
Let us first evaluate the effect on
H
of an error in the mean gravity
g
.From
H
=
C/g
, we obtain by differentiation
C
g
2
δg
=
H
g
δH
=
−
−
δg.
(4-47)
Since
g
is about 1000 gal, we have, neglecting the minus sign, the simple
formula
=
δg
[mgal]
H
[km]
,
δH
[mm]
(4-48)
the subscripts denoting the units;
δH
is the error in
H
,causedbyanerror
δg
in
g
.
For
H
=1km,
=
δg
[mgal]
,
δH
[mm]
(4-49)
