though that coincided with the geoid. Angles of triangulation,
astronomical observations for latitude and longitude and pendulum
observations for gravity were so treatedbut some doubts remain
as to the precise significance of these reduced values and whether
the topography has been tampered with and in what way.
I consider that such reductions no longer remain acceptable
for Geodesy of 1961. In the course of geodetic enquiries it is per
missible to propose any re-distribution of topography which may
assist the handling of observational results: but it is essential that
all relevant consequences be traced and assessed.
Consider the "Free air Gravity reduction". This in no way
converts a ground-surface observation to one at geoidal level.
The International Gravity expression for y0 applies to geoidal level.
It also implies values throughout external space, assumed free
of matter: say y. It is the value of y corresponding to the "g"
observed at the gravity station which is the proper basis for ex
pressing the anomaly, Ag gy: and y y0 (1 2h/R). No
vertical displacement of the gravity station arises.
But I remember 50 years ago hearing discussions as to whether
the Free Air Anomaly implied underground regions of no mass:
and indeed Laplace spoke of "underground caverns" in connection
with Bouguer's results in the Peruvian Andes. The Free Air
Anomaly is a misnomer, which certainly misled people in the past,
and probably continues so to do. It suggests that in some way a
reduction has been made from one. level to another, separated only
by air. In actual fact the anomaly applies to the point where it was
observedin general it is a "ground-level anomaly", the difference
between observed g and reference system value of y for the same
level. I shall refer to the Reference System a little later.
3. Heights and Potential. When the external level surfaces
close to the Earth are considered it is at once apparent that the
vertical separation of a pair of surfaces is not constant. Before they
can be properly combined in a continuous sum, the elements of
height measured in Spirit Levelling require to be expressed as
elements of potential by application of a factor g. Only thus the
difference of potential of two points, A and B, can be found with
a unique value, independent of the intervening route followed.
In this way the difference of potential from that at geoidal level is
consistently found for all points connected.
Strict consideration of the reduction of vertical angles in triangu
lation operationsthough embarassed by vagaries of atmospheric
refractionshows that it is the vertical separation of the equipoten-
tials through the terminals, at a point midway between the stations
where the vertical angles are measured, which is found by the usual
processes. This should be multiplied by g at the mid point to give
the potential difference. The separations at the terminals A or B
is then obtained by division by g at A or B as the case may be.
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