249
{«„AY* bLiAXi}.
(39)
One derives from this equation in the usual way that the weight
coefficient pertinent to this influence would be (two orienting
bearings)
Qt 1 («i.iQy1 fo.iQxj)2 i («i.2<?y2 bi.2<2at2)2
I (ai.iQYl bi.iQxj) («1.2Qy2 fo.zQxJ- (40)
Again using the relative standard circle (35) of the points 1 and 2,
it becomes after some calculation
Qtt Qrr- (41)
The same procedure applied for three orientation bearings yields
Qtt p Jlp Qrr °"5 5^ Qrr- (42)
When these results are inserted in the formula (12) the precision
of the bearing at station I to station P may be estimated by
2 ct«2i dlp Cr (43)
in the case of two orientation bearings;
a"d ^-p"i (44)
in the case of three orientation bearings, where aj is the variance of
the observations. is the square of the radius of the relative stand
ard circle of all coordinated stations involved per occupied station
di p is the distance from station I to P and p 206265 sec of
arc or 636620 cc.
Similar formulae are used for the other occupied stations whilst
the correlation between stations "^v11 etc. may be ignored.
5. It will be shown in this section that the estimates of <r?q of
the formulae (43) and (44) are not minimal for reasons explained
at the end of section 2.
The orientation bearings can still be of equal weight and free
of correlation according to formula (18c) if the directions indicated
by (23) and (24) are maintained but not the corresponding lengths.
The centroid condition however would be disturbed. Consequently
the terms with the coefficients ca and c*, in formula (12) and in all
other expressions of avivn, ovivm etc. will not disappear. In the
case of three orientation bearings it is seen readily by writing out
the equations (34) that the weight coefficients QvIivli and also
the correlation Qv11vl a Qv12vVa (QvLlvl 2 o) become smaller
«1 .p
-2 3 2 P2
