## On Helmert's 2nd condensation method

**Zdenek Martinec** ** , **
**Ctirad Matyska** ** , **
**E.W. Grafarend** ** & **
**P. Vanicek**
### Summary

In the past, two different methods were proposed to consider the effect
of the terrain in Helmert's 2nd condensation method. In Vanicek and
Kleusberg (1987) approach the attraction of the topographical masses
is evaluated at a point on the topographical surface. By analogy with the
Molodensky's theory, Wang and Rapp (1990) claim that the free-air anomaly
should be reduced by the terrain correction. They also state
that the attraction of the topographical masses should be referred to a
point on the geoid.

This paper shows that key to solve this discrepancy
is hidden in the way how
the downward continuation of the anomalous gravity is treated
in the particular methods. In the Vanicek and Kleusberg approach (1987)
the downward continuation of the anomalous gravity
from the topographical surface to the geoid is completely neglected,
whereas Wang and Rapp (1990) evaluate this term under implicit assumption
that there is a linear relationship between free-air gravity anomaly and
the elevation of topography. As Moritz (1966) showed such an assumption
comes from a simplified view of the compensation of topographical masses;
it has not been proved yet that this assumption is acceptable for a precise
geoid determination.
In other words it means that both methods, Vanicek and Kleusberg (1987)
as well as Wang and Rapp (1990), are for different reasons only approximate.
We will not be able to decide which method yields more accurate results
until a correct procedure of computing downward continuation of anomalous
gravity will be employed. Let us emphasize that this paper does not aspire
to provide such an accurate procedure.

Manuscr. Geod., **18** (1993), 417-421.