195
I contributed a note entitled "The Vertical Dimension in Geodesy"
to the I.A.G., Section I, at the General Assembly in Helsinki, i960.
While potential difference has already been adopted in Spirit
Levelling, the same has not yet been done for Triangulation. A
precisely similar variation of the weight of unit mass with g has
long been recognised.
4. The Reference System. For a century it has been ap
parent that no ellipsoid would precisely agree with the geoid. The
International Ellipsoid, Madrid 1924 is a Reference Figure,
from which geodetic anomalies may be reckoned. In conjunction
and consistent with this, the International formula for gravity,
Stockholm 1930, gives a Reference Value for Gravity at geoidal
level. As already mentioned, this implies corresponding Reference
values of gravity for all external points. But the ingrained idea of
"reduction to geoid" has usually led to observed value g being
"corrected" to g (1 2h/R) and reduced by y0 to obtain the
anomaly, instead of this g being reduced by the value of y. The
difference in amount of anomaly is negligible: but the impression
given, that it applies to geoidal level, is thoroughly bad and has led
to misinterpretations.
The fundamental quantity, for Reference Figure or Gravityas
also for their actual counterparts in natureis Potential. The
Reference Potentialfrom which the actual potential will
usually diifer by an Anomaly of Potentialmay be expressed
U 1-coV sin2 0 f (1 W
(vide page 201, equation (1)) to which correspond the family of
equipotential or level surfaces
r a 1 s cos2 0 p2 cos2 0 sin2 0) 8a
(vide page 201, equation (3)) and gravity at that surface
y G (1 p2 cos2 0 p4 cos2 0 sin2 0) -j- 8y.
In these equations, s, p2, G, [32, (34 are related to "a", through the
constants to, E, B, C.
Also 8a and 8y are connected with 8F.
The observations of geodesists are all metrical and liable to
observation errors. They should not depend on hypotheses: and
so should have no errors on such accounts. They lead to values
of the coordinates <j>, X, U and of g at a surfacepoint P, displaying
anomalies A<f>, AX, AU v, Ag g y, subject to observation
error only The coordinate U U0 Udh, replaces the custom
ary height above an elusive geoid; elusive in that its location with
reference to ground level depends on unknown interior masses.
Geodesists, as such, are concerned only with the Earth's surface
and regions exterior thereto. The internal level surfaces cannot be
