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Since these anomalies refer to a level surface , Vening Meinesz' formula can
now be applied directly and gives (8-77).
Relation with the ellipsoidal geodetic coordinates
The deflection components ξ and η as given by the above expressions rep-
resent the deviation of the actual plumb line from the normal plumb line at
the ground point P . Therefore, they are defined by
ϕ ,
ξ
(8-79)
λ )cos ϕ.
η =(Λ
The symbols Φ and Λ represent the astronomical coordinates of P referred to
the ground. The symbols ϕ and λ represent the “normal coordinates” of P ,
defining the direction of the normal plumb line at P ; they are not identical
with the ellipsoidal coordinates ϕ and λ of P , which are the coordinates of
the foot point Q 0 of the straight perpendicular to the ellipsoid (Fig. 8.8).
ellipsoidal normal
normal
P
plumb line
earth's
surface
parallel to
equator
'
*
''
'
ellipsoid
Q 0
Q 00
Fig. 8.8. Normal latitude ϕ and ellipsoidal latitude ϕ
The normal coordinates of P , ϕ and λ , differ from the normal coordi-
nates of Q 00 , ϕ and λ , by the correction for the normal curvature of the
plumb line (see Sect. 5.15). Formula (5-147) gives
h
R
ϕ = ϕ + f
sin 2 ϕ,
(8-80)
λ = λ .
Because of the rotational symmetry, we have rigorously
λ = λ,
(8-81)
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