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vations containing the greatest number of repetitions of the SHAR
effect does not necessarily produce the best result. This is almost
certainly due to the presence of other significant but still undetected
systematic errors.
It is with a realisation of this fact then that weighting for relative
precision comparisons between observation sets is suggested as
being directly proportional to the number of repetitions of the
SHAR effect (rather than to the total number of observations, n,
itself, even although the bisection and reading errors relative to
the extremal positions, or timing errors, will be minimised as n
increases) and inversely proportional to the square of the standard
error, cr, of the apparent gyro-indicated north, 0O, where a is obtained
from Schuler's formula [5]
ere, 2 [yv]j(n1) n3) which gives the standard error for the
mean of the individual Schuler means. Here the v's are given by
n 0O Li Li+2)l4 I Li+1, (i 1,2, n—2)
for the tracking method, and
vi 0O N' c.a.dti, i 1,2, n2)
for the transit method, if c is assumed to have been previously
determined. In these cases n is the total number of turning points
or transits, respectively, observed. N' is the approximate north
setting of the gyroscope for the transit method, which should be
good to 10 minutes of arc for effective results. Because of the pres
ence of the SHAR effect all the v's should be corrected accordingly,
a task which can be done graphically (this has been found to be
quite adequate) or by means of least squares curve fitting pro
cedures applied to the unit Schuler means.
The contribution of the pointing and reading errors to the
reference mark (RM) to the standard error of angle a (say), see
Figure 3, has to be taken into account. Here again no balance be
tween the RM readings and the number of oscillations observed,
occurs in general. Observing on one face of the theodolite only,
it is unlikely that more than four RM observations before and four
after the gyro-set will be taken. The appropriate standard error
from eight such readings would then be of the order of 2 seconds
of arc. Considering Case 5, Figure 5, as an example, (r6o 2".3,
which gives oa 3".i. The corresponding weight of the deter
mination of a, the angle at University Pillar in this instance, be
tween the reference line and gyro-indicated north, would be
proportional to 2/9.3, the 2 in the numerator being the number of
half-period secondary harmonics which occurred in the observa
tional set.
Relative precision comparisons are, however, not sufficiently
meaningful when describing the azimuth determining ability of the
gyrotheodolite. Assuming that the instrumental calibration con-
