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ints and well 
ANALYTICAL AERIAL TRIANGULATION, DISCUSSION 25 
defined planimetric co-ordinates which will be 
easily transformed into geographical co-or- 
dinates or in any other cartographic projections. 
Finally a few small variations of the programme 
allow the introduction of the statoscopic data, of 
the solar data and the radar profile, and also the 
simultaneous introduction of two or three of 
these elements. 
As we said before, we use the condition 
equation expressing the vanishing of the Y- 
parallaxes; this method in Mr Schut's paper is 
referred to as not sound. However, we wish to 
point out that the factor by which he multiplies 
the complanarity expression in order to obtain 
the parallax, varies according to the heights of 
the points; therefore, if there are redundant ob- 
servations, the factor becomes essential in the 
least squares method. Furthermore, it would be 
wise to check if the use of the parallax or similar 
expressions does actually cause a larger amount 
of work. 
Let us now examine the proceeding by 
which we solve the system of the orientation 
equations. The linearisation leads, at the first 
iteration, to the tangent hyperplanes and then, 
at the following iterations, to secant hyperplanes 
parallel to the preceding ones. In this connec- 
tion, we wish to note that the parallel hyper- 
planes method cannot be defined not sound. In 
fact, it leads to the same solutions which we 
would obtain with the Newton's method, avoid 
the computation of the coefficients and the solu- 
tion of a system at each iteration (ie a fairly 
large amount of computations). One might ob- 
ject that with the parallel hyperplanes method a 
large number of iterations is needed; however, 
our experience on several strips has shown that 
the solution is reached with an average of three 
iterations, provided that the deviation of the 
photograph axis from the vertical is not more 
than three sexagesimal degrees. Of course, the 
rate of convergency relative to the parallel 
hyperplanes method is much better than the one 
we obtain with predetermined or special solu- 
tions. 
As far as the method of strip triangulation 
is concerned, we believe it convenient to start 
the computations from the first photograph 
oriented on the known points. The advantages 
are quite evident if we consider both this method 
and the introduction of a variable reference 
system, since the only cause of disorientation 
derives from the errors of the strip; therefore, 
the models are almost oriented and in all the 
following operations we will be able to use the 
linear formulae. A further advantage will be an 
easier introduction of the solar data and of the 
gyroscopic data (which are local data) and also 
of the statoscopic and radar profile data. 
We believe that the comparison among the 
analytical triangulation methods should be made 
from the scientific and practical points of view. 
From the scientific point of view it is important 
to examine in detail the computation method: in 
other words, the expression and solution of the 
equations, the convergency of the iterations, the 
degrees of error sensibility, etc. 
On the contrary, from the practical point of 
view, we should examine the analytical trian- 
gulation methods as a whole, namely how many 
manual operations are required in order to 
obtain the data, what instruments are used, how 
many programmes we must perform on the 
computer before the final data are reached, the 
time requirements both in terms of the com- 
puter, instrument and man power, how many 
controls are needed, the ease with which a gross 
error can be detected and avoided during the 
computations, the characteristics of the com- 
puter which will be used, etc. 
I am afraid my time is up. 
Prof P. WisEn: Si nous voulons terminer dans 
le délai prescrit, il est indispensable que je puisse 
maintenant donner la parole à Monsieur McNair 
qui est le dernier orateur inscrit. Monsieur 
McNair. 
Prof A. J. McNarR: My remarks will be very 
brief, but I have two or three comments which I 
should like to make concerning the papers which 
have been presented and the comments which 
have been made so far. 
First, with regard to the paper which Mr 
Schut has produced. I feel that he has done a 
very good job and should be complimented on 
the keen analysis which he has made. In my 
own case, we discovered back in 1956 that there 
was a weakness in the Herget method of analyt- 
ical aerial triangulation in that the so-called 
weighting factor was, in fact, not a valid weight- 
ing factor at all. This has subsequently been 
eliminated from computations. 
At Cornell University in the United States 
we developed a method known as a general 
solution to analytical aerial triangulation. This 
was developed in 1957 and subsequently. has 
become known as the direct geodetic restraint 
method, on which the United States geological 
survey has worked. This method gives a general 
aerial triangulation problem to either strips or 
blocks. It gives a simultaneous solution to what- 
ever size you may have. 
At this point I would like to urge that we