in which 
fee = C - 000 G (2.6) 
is the variance covariance matrix of: 
1 
= 2 2 21 214 «LÀ 
XX - GS GC X (2.7) 
2 2 i 
So, Xe means Xs orthogonalized with respects to Xe . 
When, after the free adjustment, both the coordinates of the free network X, and 
f 
the known coordinates X are defined in the same S-system, the second phase of 
the adjustment can be carried out with the condition equations: 
: 2 1 
However, for practical reasons the known coordinates X. 
H 
Consequently the coordinates X, from the free adjusment get a correction 
des 
Red if 
Then, because of the correlation af! between xd and x: in (2.5), x: has to 
are not to be changed. 
be corrected by 
1 
GE A RT) (2.8) 
k f 
Coordinates X , after constraint of the results of the free adjustment to the 
4 
known coordinates X, are then computed as: 
k 
1 
1 X 
X I 0 0 : 
z -1 -1 X (2.9) 
e nil ld e ici f 
c f "Vt dud 2 
X 
f 
or with (2.7) 
xi I 0 x 
e = in^ 2 2.1 
X. Gr Gr I X. 
= 332