13
I: 1.2 Linear Functions of the Basic Measurements
All parameters of the adjustment procedure are linear functions of the basic
observations and the standard errors of such functions can, consequently, be
computed from the standard error of unit weight and the laws of error propa
gation. Similarly the standard error of residuals after the adjustment can be
computed from the basic expressions of the residuals (the correction equations).
Some examples from test measurements in stereocomparators and autographs
will be shown.
Stereocomparator.
Among the most important regular errors of a stereocomparator are the lack
of orthogonality ¿//3 and the affinity dm x —dm y , which can be expressed as
direct functions of the observed coordinate discrepancies, see Hallert 1963 a
and 1963 b.
From adjustment of test measurements in 25 grid points as indicated in
these references, the standard errors of the corrections d/3 and dm x —dm y can
be computed as
s f =s^ m =-s 0
For a = 50 mm and y 0 — 1 micron is found
s p = 2 cc ,5 (centesimal seconds)
V x - my = 4.o • 10“ 6
In both cases the ideal value of the parameter should be zero. Deviations
from this figure are, consequently, to be regarded as defects of the adjustment
of the instrument and can therefore be mechanically corrected if the values
obtained are significant. For 44 degrees of freedom in the determination of the
standard error of unit weight and the level 5 percent the f p -factor is found to
be 2.oi and the confidence limits are consequently, in this case (for s 0 = 1
micron)
for dp=±5 cc
and for dm x —dm y — + 8 * 10“°
Autographs A7 and A8.
The autograph A7 No. 310 has continuously been tested according to these
principles and in particular the regular errors x-deviation and ^-deviation
(dt and dl resp.) have been mechanically adjusted when the confidence limits
have been reached. 1 ) The principles from Kaasila 1961 have been applied to
*) According to the Wild A7 operating instructions dt and dl are also called x-obliquity
and width error respectively.
