24 ANALYTICAL AERIAL TRIANGULATION, DISCUSSION 
the additional measurement of the length of any 
one ray in each of the bundles. (Heavy lines 
refer to the center, thin lines to the edge position 
or the strip.) In other words, a differential scale 
determination is carried out at each station. 
Such a method has been introduced in conven- 
tional aerial triangulation with the execution of 
ARP-measurements. The results indexed by 
mo / 
my[ml -K uM 107° / 
100| mytmi-K,u M10? 
mylmi -Kz uM: 1079 v 
u=-mean square error of unit weight 
$04 in microns 
M H (scalefactor) 
80 | 
70] 
60 | 
50 
40] 
30 
20] 
  
  
5 7 9 " 13 15 17 19 21 23 
No of photographs in the strip 
Fig. 7 
*h" show that the scale along the strip (X;) is 
decidedly improved, but at the same time it is 
seen that only an insignificant improvement on 
both the Y- and Z-coordinates is obtained. 
If both types of auxiliary data, namely dif- 
ferential scaling and celestial orientation are 
introduced, the laws of error propagation can be 
decidedly improved for all three coordinates. 
Such a result is shown in Fig. 7 where the cor- 
responding curves are indexed by "st h^". 
Prof P. WisER: Je remercie vivement Mon- 
sieur Schmid pour cette trés intéressante inter- 
vention. Il est vraiment fort regrettable que le 
temps nous soit tellement compté, mais trois 
orateurs sont encore inscrits au débat. Je vais 
donc passer la parole à Monsieur Inghilleri. On 
m'a informé que Monsieur Solaini, orateur in- 
scrit ensuite, ne prendra pas la parole en ce 
moment, et par conséquent Monsieur Inghilleri 
aura à sa disposition le temps destiné primitive- 
ment à Monsieur Solaini. 
Mr G. INGHILLERI: In Mr Schut's paper it is 
not mentioned at all the method studied and 
chosen by the Institute of Geodesy and Photo- 
grammetry in Milan, most probably because at 
the time when the aforesaid report was issued 
only a short publication had appeared in the 
Lincei Academy magazine and a technical paper 
in the ASTIA bulletin. 
The above-mentioned method is a typical 
cantilever one: each photograph is orientated in 
respect of the preceding one; since with very 
small modifications of the computation pro- 
gramme it is possible to orientate also the first 
photographs of the strip in respect of the known 
ground points, the relative orientation of each 
photograph coincides with the absolute orienta- 
tion. At the same time the model scaling is 
determined by imposing that a direction passes 
through a point of a known altitude. 
The equations through which we can com- 
pute the relative orientation are the Y-parallax 
equations: if we use six points on each model we 
may write six transcendental equations in the 
unknown orientation parameters imposing the 
parallaxes vanishing, and one more transcenden- 
tal equation for the computation of b,. By 
simple programme variations we can vary the 
number of points considered in each model. 
For the solution of the equations system we 
use the parallel hyperplanes method; that is we 
carry out the linearisation of the system and 
introduce the approximate values of orientation 
parameters; we then obtain the normal equa- 
tions according to the proceeding of least 
squares and we invert the matrix. At each itera- 
tion a simple sum of products gives the correc- 
tion to be added to the orientation parameters 
until the values of the residuals are small 
enough. 
We must still mention a detail. The reference 
system for the strip is a geodetic line connecting 
one point in the first model with a point in the 
last one; the co-ordinates of the strip points that 
we compute are rectangular geodetical co-or- 
dinates which refer to the above-mentioned 
geodetic line. 
Of course, the computations relative to each 
photograph are referred to a rectangular system, 
but after bridging this system rotates and trans- 
lates so that the X-axis will be tangent to the 
reference geodetic line in a suitable point and 
the Z-axis will be parallel to the vertical through 
that same point. This point is taken on the 
geodetic line and is always very near to the 
nadiral point of the preceding photograph. With 
the use of the variable reference system we can 
automatically solve the problems of the earth 
curvature since with very simple formulae we 
can obtain the true height of the points and well 
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