28o
stant, e, is accurately known, absolute v's, (va)i, at point A, can
then be obtained, for example, from
(Va)i (<>>AB)i (G-Wi s 180°) Qab (t T) a, I>2, ,m
where m is the number of GIN determinations at A
<x>ab is the mean observed RM reading at A
%ab is the bearing A to B calculated from the Gauss Conform
projection co-ordinates (this is the projection used in South
Africa and bearings are conventionally referred to south)
Figure 3 shows the relationships between the respective quantities.
From point B, the absolute v's would be
(vb)i={o>BA)i+{GIN2 £+y 1800) 02M {t—T)B, 1,2k)
where k is the number of GIN determinations at B
Y is the meridian convergence at B relative to A
The weighting of the results of individual sets of observations
would be in accordance with the form described in the preceding
paragraph.
The standard error for an azimuth determination for a single
set, calculated from all the test observations summarised in Table I,
was found to be 6".3 for the tracking method and 7".5 for the transit
method, at either end of the test line. If the azimuth was determined
at each end of the test line and the mean result accepted, the
standard error for the mean azimuth would be (6.3/]ft) 4".5
and (7.5/^2) 5".3 for the tracking and transit methods, re
spectively, using the GAK1/T2 configuration. The results presented
in this way give the prospective user a better insight into the po
tential capability of the instrument than does the information
in Table II, which tabulated data reflects approximately twice
the mean error to be expected from an azimuth determination at a
point.
The above results, which represent some fifty hours of contin
uous observation, give a succint comparison of the accuracy of the
two observing procedures. This evidence confirms previous beliefs
that the techniques yield comparable results. Both methods pro
duce directions which agree to within about 5 seconds of arc of
the true azimuth, and almost exactly with each other. A fair con
clusion, in view of the number of observations taken, therefore,
would be that the accuracy of the GAKi gyro-attachment and T2
theodolite, used in the tests herein described, is at least of the order
of 10 seconds of arc.
The summary presented in Tables I and II does not, however,
reveal the previously mentioned behaviour patterns of the spinning
gyroscope during protracted oscillation. In all cases of extended
tracking during the experiment the secondary harmonic (or SHAR)
manifested itself in the sets of consecutive Schuler means. Figure
