1 from this equation and equation (4) 
Aiii el = Airr-li+iqyri CS) 
Equations (4) and (5) are linear. This means that no approximate . 
values for the scale factors are required. Equation (5) is evaluated 
for a pair of common points in each overlap and equation (4) for two 
points (in one and the same model) of which the distance 
13341 is determined by a geodetic measuring method. Any more 
distance 14441 gives a redundancy. 
(b) TILT AND HEIGHT DETERMINATION. 
If the scale factors are known, they are substituted in the equation 
of type (3) and next for each measured point an equation of type (3) 
is evaluated (height control points included). To improve modelling, 
equations containing only tilt elements can be added to a system of 
equation (3). 
We therefore consider again two points j and #1 in the model (i). 
For point jl, an equation of type (3) is written. Eliminating Zi 
and then A, from this equation, (3) and (4) give 
f 
ai = Í { = - + i x —7 
sim Yun 03 Sage Tag Uie 
The angle &jj+] is simply called "slope". It is the angle 
enclosed by the straight line connecting the measured points j and 
jtl in one and the same model and a plane parallel to the XY- plane. 
The angle Gjj+] must be determined by geodetic measuring. 
This is not necessary, however, if arbitrary pairs of points, for 
example of the shoreline of a lake (lake points), are measured, 
because in that case: aj5+1 = 0. 
y 2: 
1 
Equations (3) and (6) are Ron linear. If wl 
however, fhe tiit elements ay; and a3, are al 
element 834 is approximately equal to the uni 
in equations (3) and (53: 
nd $i are small, 
so small and the 
ty. We therefore put 
w 
i i+ 1 
Q4 7a = 2 2 9 Zi. 
33 35 
If the system of equations (3) and (6) is solved, transformed model 
coordinates u44, Vii, Wis (Lf) and (lg) are determined 
JJ + 
next for