CALCULATION OF A BLOCK OF STRIPS, ETC. 
I y o + «>yj-pi^-y M 
. . ' + A9 1 A'' 1 + Am 1 ¥’■ + (s 1 Z' h ' — Zt,h) 
1 j K + «’ X? + P 1 Y? - X>„ - a> X2 - {S' Y? 
I + 011 y k — P 1 - Y k — Y ‘o ~ «’ Y 'i + P 1 - V i j 
Z‘ + A91 X'i + Ac,1 Y'i — Z< — A 9 1 x'i - Ato! V 'i + ( S i Z’ k ' 
where X' \ ' Z' indicate the coordinates in the relative system; X t Y t Zt the 
ground coordinates; by the ij ... indices we show the M models to which the 
point under consideration belongs ; by the h and k indices the points providing 
the external and internal constraints, respectively. Assuming the block to consist 
of n stretches, and to include p points whose planimetry and elevation are known, 
and that we have observed q points common to two stretches at least, system (1) 
consists of not less than 3 {p + q) equations with 7 n unknowns. 
6. — Theoretically, the rigorous solution of system (1) using the least squares 
method does not present any difficulty ; from a practical point of view, however, 
the difficulties are quite noteworthy, due to the great number of equations in 
the system. For a block of 10 stretches only, each consisting of 5 models, based 
on a total of 20 known points, and assuming a single common point in the trans 
versal overlap between two adjacent pairs, we have n = 10, p = 20, q = 40 ; 
this means that we should resolve a system of 180 equations with 70 unknowns. 
Calculations may be simplified separating planimetry from altimetry, but 
its complexity remains all the same quite evident; even for blocks of a very modest 
size, we should make recourse to great computers of the 700 and 7000 I.B.M. type. 
I.G.M. has at present realized and experimented the relative calculation pro 
gram for the I.B.M. 704 computer (see para. 13), with good results. 
7. — We point out the great flexibility of this procedure, and its full suita 
bility to any situation — even is locally anomalous — of coverage and control. 
This, essentially, for the following reasons : 
a) no hypothesis is made about the nature and the way of action of the 
errors involved, except the hypothesis — fully justified by practical results — which 
states that, in sufficiently short stretches, the deformation of the M> models re 
mains practically negligible. Therefore, it is not necessary to know the closure 
errors of the single strips, nor to distribute them on the intermediate pairs accor 
ding to hypothetical laws ; 
b) each strip is not considered as a continuous and indivisible unit, but 
as an ensemble of stretches, each one of them existing in its own relative reference. 
The subdivision into stretches cuts at regular intervals the propagation of errors ; 
this permits to use even bad flights, and offers a large tolerance as for imperfec 
tions of instrumental adjusting, of internal and external orientation, and of obser 
vation ; 
= ^x,h 
= Vy,b 
== 5^z,h 
= r» x ,k 
— r’y,k 
— Si Z'i) = Vz,k