aerial triangulation would have by now overcome one of the main 
obstacles to its diffusion. 
Assuming the hypothesis, proved by experience, that the correc 
tions to be attributed to the transformed X* and Y* coordinates of the 
points not included in the first stereogram to obtain the actual X, Y 
coordinates, to be a function of parameters k and 0 or of others con 
taining them, which in turn may vary from point to point with a certain 
continuity, one can certainly operate as follows. 
Therefore, by simplifying the (1) considering 
(2) r = k. cos 0 and s = k. sen©, 
which may be written out as 
(3) X = rx + sy + a 
Y = — sx + ry + b 
from which we can arrive, by differentiation with regard to the new 
parameters r and s, to the expression in finite terms of the differences 
(4) AX = x Ar + y As 
AY = y Ar — x As 
produced by effect of the variation A r and As. 
It is superfluous to observe that, once we know the differences 
between the actual topographic coordinates and the transformed co 
ordinates 
(5) AX i = X I — x; 
A Y { = Yj — Y*, 
the (4) can provide, for each point considered, the actual variations 
A r i and A s.. In fact, considering the system defined by (4), we 
have the result: 
(6) = x, A X; + y, A Yj 
x 2 , + y* 
= y , A Xi - x, AY, 
S i 7 ■ 2 
Xi + yr 
Whereby, implicity resulting what we have already said, we have 
5