(f) Astro-geodetic datum orientation is obtained from the deflections of the vertical at a

number of selected Laplace stations (Figure 1-19). In this orientation method, the geoid and the

ellipsoid are oriented so that the sum of the squares of the deflections of the vertical at the Laplace

stations is made as small as possible. One of the Laplace stations in the adjustment is arbitrarily selected

as the origin. Consequently, instead of having a zero deflection as with the single-point orientation,

there is a deflection of the vertical at the origin point. Through a similar process, the geoid separation at

the starting point can be found. This procedure reorients the ellipsoid so that it provides the best average

fit at all the Laplace stations. The use of geodetic data produced by this method is still limited to

relatively small areas since the deflections of the vertical still remain relative. They are not comparable

with similar deflections derived from another adjustment. As in the single astronomic method, the

datum is not earth-centered and the rotational axis of the ellipsoid does not coincide with the axis of the

earth.