CALCULATION OF A BLOCK OF STRIPS, ETC. 
13 
d) When the y} rotations are known, the corrected elevation for any ob 
served point may be calculated by means of the formula : 
7) z i,o = z l + X' Dl 
12. — It should be pointed out that the procedure outlined in para. 11, c) be 
comes defective when the line on which the T points approximately lie is the bi 
sectrix of the angle formed by the axes ; in such a case, in fact, the elevations 
from the two origins for the T points may coincide, though in an incorrect abso 
lute position, and remain undetermined. 
In practice, the total indétermination may be avoided by varying the posi 
tion of the axis points, or staggering that of the T points : a critical situation (more 
or less emphasized, according to the relative position of axes and T points) may 
nevertheless persist ; but it may eventually be corrected by a suitable differenti 
ation in the weights attributed to points A i and points 7M- in operation /) of 
para. 9. We think however that, when the points are rationally selected and 
employed, this may generally be avoided. 
The considerations concerning the critical situation of the axes are less im 
portant when the block consists not of two, but of several stretches transversally 
adjacent ; they should however not be neglected, and we should always try that 
the bisectrix of the axes does not coincide with the T points line. 
II — PRACTICAL APPLIANCE 
Electronic calculation. 
13. - In conformity with the above mentioned theoretical formulation, the 
calculation programs — for the rigorous procedure, employing the I.B.M. 704 
computer ; and for the simplified procedure, employing the I.B.M. 1620 computer — 
have been made out by Dr. Piero Bencini, whom the author thanks most warmly 
for his precious collaboration. Their general setting is resumed as follows. 
Rigorous procedure. 
a) BLR Program - it sets up and solves, by the method of least squares, 
the (1) generated system, computing for each stretch the values of the 7 unknowns 
of absolute orientation and dimension. Therefore this program transforms into 
absolute coordinates the relative coordinates of all observed points, and calcu 
lates the residuals of the observation equations. 
The computation of planimetry is kept separate from that of altimetry, so 
that two distinct normal systems are solved — of 4 n and 3 n order, respectively — 
instead of a single 7 n order normal system. This is undoubtedly convenient from 
the computing side, and is perfectly licit in the hypothesis that the correlation