11 
FACTORS FOR ELLIPSOID HEIGHT, LATITUDE. AND LONGITUDE USING I TO 4 SCALARS 
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necessary ties and astronomical observations. The scalers 
are established by three-dimensional traverses with distances 
being measured by Geodimeter or electronic distance measur 
ing equipment. In combination with astronomical observations 
and precise angle measurements it is expected that these 
traverses provide the chord distances between pairs of sta 
tions in the world net to one part in one million. 
The need for these scalers is demonstrated by theoretical 
studies of the error propagation in photogrammetric satellite 
triangulation. In Figure 3 it is shown that, typically, the 
longest axes of the error ellipsoids are normal to the earth's 
surface. When considering two stations diametrically opposed 
to each other, these error components represent the uncertainty 
in scale of the world net. Consequently, additional scale 
lines provide the necessary information in order to reduce 
these errors. The situation is shown in Figure 4, in the 
upper portion of which the improvement in accuracy of the 
height component is shown as the number of measured scalers 
increases. Denoting the more or less equal amounts of the 
mean errors in latitude and longitude, as shown in the lower 
portion of Figure 4, by unity it can be seen that the mean 
error in the direction of height is roughly three when only 
one scaler is introduced. With four scalers these mean errors 
are reduced to 1.8. It is, therefore, reasonable to expect 
as the ultimate accuracy with the PAGEOS satellite, posi 
tional mean errors f*or the latitude and longitude components 
of ±6 meter, and +11 meter in the direction of height. 
Figure 5 shows the axes of the error ellipsoids for 25 
stations as obtained from the adjustment of the presently 
reduced data. The results are obtained from 730 photo 
graphs, representing about 33% of the ultimately expected 
raw data. Because the 25 incorporated stations represent 
about 55% of all stations it is obvious that the result of 
this adjustment still suffers from a deficiency of informa 
tion; this accounts for the larger mean errors. However, 
in areas where all of the necessary measurements have been 
obtained and reduced, the corresponding mean errors, indexed 
by are in reassuring agreement with theoretical expecta 
tions, particularly since only one scaler was used. 
A comparison of the results obtained so far with classic 
geodetic data and with results obtained by other systems of 
satellite geodesy, especially the results from dynamic geodesy, 
already provide interesting information, the value of which 
can be expected to increase qualitatively and quantitatively 
with the progress of the program. Such consideration would