29 
d. Analysis of the Accuracy of the Spatial Triangulation 
From the average values in the foregoing tabulation, one 
can derive a theoretical mean error of the spatial triangula 
tion procedure. Accuracy studies made in connection with the 
SAO catalog lead to the conclusion that the star field as a 
whole will not allow a statistical improvement below the ±0"2 
or ±0.5 micron level, even that being, at present, some what 
optimistic relative to southern hemisphere stars. Applying 
the square root law, the uncertainty in the photogrammetrie 
bundle reconstruction should be reduced, using an average of 
seven hundred star images, by a factor of 7*5? at least for 
the area at the center of the plate, resulting consequently 
in ±2.97/7-5 - ±0.4 microns random error contribution. Using 
an average of 308 satellite images per plate, the precision of 
a point interpolated near the center of the plate into the 
polynomial curve fit equation should be better by a factor 
of eight, compared to the average mean error of the curve 
fits. Consequently, the fictitious satellite position should 
contribute ±3.08/8 = ±0.4 microns. The total random noise in 1 
the triangulation must then be expected to be (0. 5 2+ 0. 4 2 + 0.4 2 ) s’ 
= ±0.8 micron. The least squares adjustments of the spatial 
triangulation have,typically, mean errors for a single observed 
direction of ±1.05 to ±1.06 microns. The last such adjust 
ment (lj June 1968) included 25 stations, 1534 observations, 1128 
unknowns and, consequently, 4o6 degrees of freedom. Three- 
hundred forty-nine satellite passes were used. Figure 12 
shows the distribution of the plate residuals of the most 
recent adjustment. The area under the normal curve equals 
the area under the histogram. These data indicate the 
presence of a slight systematic error source, as does the fact 
that the mean error of ±1.05 microns is larger than the 
expected mean error of ±0.8 micron. Presently, three sources 
of small systematic errors are known to exist. First, 
Universal Time (UT-l) furnished during the observational 
period was not a true measure of earth rotation. The neces 
sary additional corrections have now been obtained and will 
be applied. Secondly, and probably most important, the 
present reduction of the single cameras uses only a mean 
between the orientations before and after the satellite 
passage. The presently developed reduction techniques allow 
the elimination of any field instrumentation instability. 
Finally, the present reductions fail to take into account 
the difference of amount of earth rotation due to the dif 
ference in light travel time between satellite and observing 
stations. In order to produce a final result as free as 
possible from systematic error sources, we have decided to