LAND MEE TKEN DE
Dr. P. RICHARDUS Ph.D. x),
The Precision of an Intersection
Summary
A number of orientation bearings have to be observed for the
calculation of the bearing of the intersecting line at an occupied
station to a station P of which the coordinates are to be determined.
It is usually assumed that these bearings have equal weights and
are free of correlationit is also assumed that the coordinates of
station P will have smaller variances if the so called centroid
condition (explained in section 2) is satisfied. In this paper it is
derived that only specific bearings satisfy these requirements.
They are given by formulae developed in sections 3 and 4.
The requirement of the centroid condition is very stringent in
a special type of control survey mentioned in section 3, but it
appears to be without significance in the general case where the
influence of the precision of the orientation stations and that of
the occupied station are balanced.
New guiding rules for the reconnaissance are suggested in
section 6.
The variance of the observed intersecting bearing at the occupied
station to P is also derived (formulae 45, 46 and 48).
Use is made in these derivations of the modem (and very satis
factory) method of expressing the relative accuracy of the position
of two coordinated stations by the relative standard ellipse and its
simplification to a circle with radius
gr c 2d
where c is a constant and d the distance between the stations.
x- Suppose that a point P is to be coordinated by intersection
from the stations I, II, III etc. (more than two) with known
coordinates, as indicated in the figure 1.
The usual procedure is to observe a few arcs at each station
to other coordinated orientation points and the direction to the
unknown point P, and to perform a station adjustment. The
bearings say <pI)f are calculated from the coordinates of the stations
I and 1 (i is a running index 1,1). The orientation is then
obtained by the formula
Senior Lecturer of Surveying—The University of New South Wales:
b Dr. ir. Richardus verblijft thans met verlof in Nederland en is werk
zaam aan de Onderafdeling der geodesie van de Technische Hogeschool
