43 
Thus it would appear that the final correction curves for the block are of the 
second degree in x only. The above formulae for Ax and Ay, however, strictly 
apply to strip co-ordinates only. They are such that the scale and azimuth correction 
dax d 
Ay : : : 
JE and T respectively) are linear in x. But 
across the strip the scale and azimuth corrections ( 
  
  
in the direction of the strip ( 
  
D and d ^x 
for variable y. This does not create a significant distortien in the lateral sense 
because the width of the strip is negligible compared to its length. However, when 
the runs have been connected laterally to form a nearly square block, it is evident 
that if the scale and azimuth corrections increase as linear functions of x, they will 
do the same for y. Integration over x and y gives expressions for Ax and A» both 
of the second degree in x and y. 
For an entirely graphical approach the following disposition of nine control 
points appears to be the minimum; vide Fig. 2: 
) are constant 
  
  
  
  
  
  
  
  
  
d pass peiuts, 3 + 5 : 1,500 
ds pies Ei 
zr P qu — — - B Run 1H- Ts re UE +—>1,100 
tie points Y e- e + 1.000 
100 2 
À Run 2H Ou mM En 900 
200 
| tie points| i —9- *- * ç 700 
| 206. > 
Run ge LEAD ko 
A pass points © e v = 300 
| ! , 1 2 3 4 5 
I II [11 
Fic. 2 Fic. 3 
Each cross-section contains three points which makes it possible to construct a 
parabola for the corrections AX and AY along I, IT and III. For any longitudinal 
section (e.g. A and B) three points for the construction of a parabola are found 
by reading from the lateral curves. By taking the longitudinal sections through the 
tie points between runs, the corrections to those points are found by reading 
directly from the curves. The corrections to points not common between runs are 
found by linear interpolation between longitudinal curves. 
COMPUTATIONS 
The computations for the actual adjustment, demonstrated here for a block of 
three runs (see Fig. 1), include the following steps. 
I. The connection of the individual runs by linear transformation of the 
machine co-ordinates é and n, 
X — a.E+b.n+c l (16) 
y — —b.é-- a.9 4- d t : « * : : ; 
The parameters are determined from two points known in both systems, preferablv 
a tie point at the beginning and at the end of two adjacent strips. First the co- 
ordinates of run 2 are transformed into the system of run 3, thereafter run 1 is 
connected by means of two points in run 2 which have already been transformed 
into the system of run 3.