Substituting this in (22) and (23) it is found that
tan cp2 tan cpj Ï- or <p2-
V c
It is clear that with this type of intersection for deformation
measurements the centroid condition has to be satisfied as rigor
ously as possible. The triangulations for these measurements
include generally only a very limited number of stations, so that
the weight coefficients of the coordinates of the occupied stations
Qxx> Qyy ar|d Qxy can b® calculated without major effort.
4. We will now consider the more general case that the coordi
nates of the orientation stations are not without error.
The law of propagation of errors is now to be applied to equation
(4), which yields in symbolical notation:
Qvn ai.iQyl h.i Qxj ai.iQvi KiQxi Q«.u (31)
or worked out:
Qvl.ivl.i aI-» (Qy*V» 2QYiY1 Qy^^i
bf.i {QxiXi 2Qxixl Qx^if
2al.ibl.i {QxiYiQyiX1QxiY-i Qxjy,} öaj faj j (32)
and the covariance
It is seen in equation (32) that the coefficients of the a\ i, b\i
and anbn are the respective elements of the relative standard
curves of the points i and I. It is unfortunately necessary to in-
(32) and (33) manageable.
It will be assumed that the relative standard curves (indicated
by Qxx< Qyy an<^ Qxy) are equal and in addition that the correlation
between the coordinates of the station involved is symmetrical
in the following way:
Qxi.Yj Qxj.Yi
QxltYi QxltYj
QyvXi QyvXj.
The weight coefficients (32) and (33) can then be written in the
somewhat simplified manner:
247
QvLiVLj auau {QxiYi QyjYj QyiYj}
{Qx1Y1 QxiXj QxiXi QxxXj)
ai.ih.j {Qx1y1 Qy^xj QyiXj QyiXj}
ai.jbu Qxsy1 Qx1y1 QxiYj QxiYj}- (33)
