248
Qvjjru al'Qyy 2ai.fil.iQxV b\.iQxX Qcq ^aj f
QviPU aI 'QYY 2al-fil.jQxY b'l.iQxx Qa\ j«.\ j j>. (34)
QvLiVi j i {ai.iauQyY (ai.fii.j ai.fii.i) Qxy bi.fii.jQxx
If the distances between the orientation points mutually and
between the occupied station and the stations are chosen so as to
be approximately equal, these assumptions would be less sweeping
than the immediate introduction of the relative standard circle
as an estimate of the relative precision of two points.
The same reasoning as in the preceding section can now be applied
to the equations (34), this time considering the relative standard
curve of the occupied station I and the orientation stations instead
of the standard curve of the occupied station I only. The same
formulae (23) to (30) inclusive would apply.
In practice there are mostly no other means to estimate the
relative standard curves than as circles of a radius
R c ][2d (35)
where the correlation can be ignored.
The c is a constant pertinent to the region of the control survey
and d the mean distance between the occupied station and the
orientation stations (numbered I and i, j respectively). It is then
seen by substitution of c 1 and D o in (23) and (24) that
A B A +B
tan <pt A +B and tan <p2 _g
since now Qxx Qyy and Qxy 0.
Consequently
9i 9i 7 9a 9i- (36)
4
The expressions (25), (26), (29), (30) and (31) can be simplified
accordingly. They become respectively
*1 d, yi (37)
and
dl d2 ds dy (i y 2). (38)
Referring to formula (12) it is seen that all terms vanish where the
coefficients ca and Cj occur.
We still have to attend to the influence of the third term of
formula (11) viz.
TZ
91 92 -
and also