executed with the electronic computer IBM 7040, using two points at the beginning and two at
the end of the strip. For the second degree adjustment we have employed 9 points, 3 at the
beginning, 3 in the middle and 3 at the end of the strip; for the computation, a Remington USS
computer.
After the linear and parabolic transformations, the coordinates of the check points have been
compared with the ground known coordinates. With these differences we have computed the
values contained in table no. 6, where, in columns 1, 2, 3, there are the number of points, the mean
and the mean square value of the residual differences on the check points of the planimetrie coordi
nates after linear transformation, in column 4 the m. s. v. of the planimetrie displacements com
puted with the formula
In columns 5 and 6 there are the points number, the mean and the m. s. v. of the discrepancies
between the Z coordinates of the check points. In the six following columns the values have iden
tical meaning, but they have been computed using the differences of the coordinates after the
parabolic adjustment.
The first and second horizontal sections of the table refer to the results of the independent
measures I and II. The third section {A) indicates the mean and the m. s. v. of the differences
of the check points coordinates computed in the I and II measure.
A summary analysis of this table suggests the following observations:
a) The remarkably large value of the means of the residual differences after linear transfor
mation, show the existence of a systematic deformation of the strip; such systematic deformation
disappears after the parabolic adjustment.
b) The agreement in value and sign of the means of the Z errors after linear transformation
in the two independent measures is quite meaningful; it is also in full accordance with the results
of other bridgings executed with other instruments and published in the provisional report of
Commission B of O.E.E.P.E., and is an evident indication that the errors depend on systematic
factors affecting the photographic material.
c) The m. s. v. of the differences between measures I and II after the parabolic adjustment
have the same magnitude as the m. s. v. of the residual differences with the coordinates of the
ground known points. This fact makes us suppose that the above mentioned differences should
be mainly ascribed to accidental errors of different origin.
The accidental error in the connection of the models is, perhaps, one of the main causes in
the formation of the residual errors, particularly in the Z coordinate. The column of the means
M of the AZ in table no. 5 shows very high values, whose mean square value is 34 cm for the first
measure and 22 cm for the second. Since these discrepancies do not undergo any change, in con
sequence of the adjustment by means of a second degree interpolation curve, it is evident that
these discontinuities between successive models don’t disappear, but remain as local errors of acci
dental character along the strip. It is obvious that these errors cannot be eliminated by assuming,
as final value of the coordinate, the mean of the values of the two successive models. In its turn,
the cause of these errors in the model connection can be found in the following fact: that the only
point used for the connection between two successive models and for the scale transfer, was indi
viduated by the operator by means of a photograph; which made uncertain the identification of
the same point in the two consecutive models. However, the sign agreement of the means of the
discrepancies, in the two measures, let us suppose that there may also be another systematic cause
for the model deformation, probably due to anomalies in the photographic material.
In figures 7 and 8 a graphical representation is given of the residual differences between the
control points coordinates after the linear transformation and after the second degree adjustment.
The graphs refer to the II measure. The points used for the linear and parabolic transformations
are marked with a triangle.
