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elevations H are due to sub-normal underlying density. To my
mind it also shows that computation of simple topographic attrac
tions is worthless. What is useful is the effect of topography dif
ference h H, which will relate actual astro-observations to the
Mean Earth. Computations need not be carried very far (say 2°)
from the central point.
6. The Shape of the Earth's Surface. The true aim of
geodesy is the accurate relative location of all points on its surface.
For this it suffices to locate points on the M.E. surface, whose re
lation to the Actual Earth is easily found.
A well known theorem of Green allows the anomaly of potential
at M.E. surface points to be expressed in terms of Ag. There is a
paper of mine in Bull. Geod. No. 56 "The Shape of the Earth's
Surface" which shows the development.
I imagine a surface, which I have called the Terroid. This is part
of the Reference System, and is such that to any point P on the
Earth there corresponds Pi on the Terroid having the same potential
and angular coordinates: and accordingly the location of Py is
determinate. The actual point P lies on the radius vector CP
(from the Centre of Gravity) at distance (yjg) p below P, if v is the
potential anomaly. Equation (5.5) loc- cit. shows that, to a first
approximation
a relation of the same form as that of Stokes, but applicable to
the M.E. surface. Thus the gravity anomaly has not required any
"reduction to geoidal level". To the accuracy of the formula, the
radius R may be replaced by a constant.
For a second approximation, which my formulae permit, the
argument under the integral requires the correct R.
7. The Practical Problem of Earth Shape. The M.E. plan
provides a practical means of stating the answer to the question
of Earth Shape in terms of gravity measurementsthat is the Shape
of the Bounding Surface of a Smoothed Earthfrom which the
surface features have not been removed, as in the older plans of
reduction to sea level and obliteration of topography. The form is
very similar to that given by Stokes, but gives Potential Anomaly
at M.E. surfaceand admits of a second approximation, should that
be wanted later.
But for practical use the formula, like that of Stokes, requires
values of AgE over the entire surface of the globe. At present only
a small fraction of the total surface has been gravimetrically sur
veyed in spite of great increase in observing facilities combined with
increase of workers. The oceans still offer especial difficulties and
