is difficult to assume that 7-parameter transformation correctly 
describe the differences between the two coordinate systems. 
Using a similarity transformation on a large network may not be 
appropriate procedure, because it may distort local scale and 
orientation in the net, originating mostly from the systemtic 
errors in the measuring data reduction to the reference surface. 
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Figure 4: Residuals in the astrogeodetic network of Slovenia 
after the 7-parameter similarity transformation 
The neglection of the impact of the deflection of the vertical to 
the measured quantities and neglection of the geoidal heights 
are the most common source of the systemtic errors in the 
astrogeodetic network. However this type of transformation 
gives an overall impresión about the relative point positions in 
coordinate systems, and also serve as starting point for the 
detailed assessment of the coordinate system. 
The 7-parameter similarity transformation of the whole 
astrogeodetic network shows the residuals of the transformed 
point positions in the amount up to 1 m. The interesting fact is 
that the largest residuals occur at the points located on lower 
part of the country i.e. at the east and at the south-west. 
Residuals of the transformed coordinates are given in Figure 4. 
Interpolated displacements in the N-S and E-W directions, are 
sketched in Figure 5. 
With the 6-parameter coordinate transformation we compare 
coordinate systems under the presumption of equal scale in both 
systems. Such transformation is not very common procedure, 
since coordinate system which should be transformed, results 
from different measuring procedures or measuring techniques, 
what is also the reason for the need of transformation. In general 
it is much easier to accept that different measuring techniques 
produce coordinate systems which are rotated, shifted to each 
other and of different scale. 
Figure 6: Residuals in the astrogeodetic network of Slovenia 
after the 6-parameter similarity transformation 
The residuals after the 6-parameter orthogonal transformation of 
the ETRS 89 coordinate system to the national coordinate are in 
the amount to the 2 m.' The residual vectors are now increasing 
with the increased distance from the centre of the gravity ot the 
network. The residual vectors of the border points at the eastern 
and western part of the network exhibit large componets up to 2 
m in the E-W direction. Concerning the opposite direction and 
the almost parallel direction of the residual vectors at these 
points, it is possible to say that the distance between eastern and 
western part of the network are for about 4 meters too short. We 
can even say that the territory of the Republic of Slovenia, as 
presented in the official coordinate system, is for the same 
amount i.e. for 4 meters too short in E-W direction, and for 
about 2 m too short in N-S direction. Residuals of the 6- 
parameter transformation are given in Figure 6. 
The residuals in the Fig. 4 and in Fig 6. should be understood as 
the discrepancies between official and the true point positions. 
The same is valid also for the sketch in Fig. 5. 
Figure 5: Interpolated displacements in the astrogeodetic network of Slovenia after the 
7-parameter similarity transformation in N-S (left) and E-W (right) direction 
with the contour interval 100 mm 
At the end we tried to estimate the scale (the unit length) in the 
local coordinate system as a function of a position in the 
coordinate system. For the scale assessment we formed 37 
triangles connecting 27 points in the net. In each triangle the 
scale factor was estimated with the similarity 7-parameter 
transformation. Scale factor as function of the position in the net