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RADIAL TRIANGULATION, AUTHOR'S PRESENTATION 75 
schliesslich der Beobachtungsfehler, wird durch die Tafel illustriert. Neue Re 
methoden und die Möglichkeit von Anwendung der I.T.C.-Jer 
thode werden signalisiert. Auf dem Gebiet der mechanischen 
genannt die Verwendung von astronomisch orientierten, nicht lokalisierten, 
Punktegruppen und die Anwendung der Bildschlitzmethode 
Schliesslich erwartet man eine Anwendung der rezent entwie 
lisierungsmittel in der Radialtriangulation. 
chnungs- 
ie Blockausgleichungsme- 
Radialtriangulation wird 
örtlichen 
auf Konvergentaufnahmen. 
kelten sehr genauen Stabi- 
Author’s Presentation of the Paper 
I propose just to give a short introduction as 
we are already behind‘ time, and first of all I 
would like to point out that, as most of you may 
know, radial triangulation has a certain limita- 
tion, in that it gives only the planimetry as con- 
trasted with spatial triangulation which gives 
planimetry and height. This means that the 
application of radial triangulation is restricted 
to special cases which, by the way, occur rather 
frequently. 
Among these special cases I will mention a 
few. First of all, the case when only the plani- 
metry of flat, or rather flat, country is required, 
as for instance for a cadastral or statistical map. 
These may be maps of rather flat terrain, as I 
said, but it is equally possible that also maps of 
more undulating regions, or even hilly country, 
may be made and can be made by radial trian- 
gulation. 
The second case is, when for showing the 
shape of terrain, it is sufficient to use form lines 
instead of contour lines, and these form lines 
could be put into the map by using very simple 
methods, such as table stereoscope, and the 
like. 
The next case is rather an important one, 
and a frequently occurring one, and one which is 
more or less the opposite of the second case: 
that is, when the requirements for height ac- 
curacy are so high that it is impossible or un- 
economical to determine these heights photo- 
grammetrically, so that they have to be deter- 
mined by classic ground survey. This may be the 
case for special maps for irrigation and drainage 
purposes. 
On the other hand, apart from these natural 
limitations of the radial triangulation method, 
there are certain advantages of the method. In 
the first place, the equipment which is necessary 
to carry out radial triangulation is inexpensive 
as compared with the equipment for spatial 
triangulation. This is quite evident in the case of 
mechanical radial triangulation, but it also 
applies in a more restricted sense to the in- 
Strumental, or what is called numerical, radial 
triangulation. 
The second advantage — a little one but I 
should mention it for the sake of completeness — 
is that there is no need to compensate for radial 
distortion. 
A third advantage, which is rather important, 
I think, is that it has a greater speed of opera- 
tion, no relative orientation having to be carried 
out. To give you an idea of the speed of opera- 
tion, the observation or rather the measurement 
of one pair of photographs in the radial trian- 
gulator — I am referring to numerical radial 
triangulation — takes only twenty minutes, 
whereas relative orientation in spatial triangula- 
tion normally takes at least one hour. 
Then there is the less high requirement of 
skill and experience of the operators, for the 
only thing they have to do is just to measure 
by applying the principle of stereoscopy, no 
relative orientation being carried out. 
The last advantage is that the computations 
in radial triangulation are very simple, so that 
if necessary they could be carried out just by a 
table computor, although it is preferable to use 
an electronic computor in order to speed up the 
work. ; 
There are two types of numerical radial 
triangulation: the principal point triangulation 
and nadir point triangulation. The principal 
point triangulation is mostly used because of the 
ease of determining the location of the principal 
point of the photograph which is then used as a 
centre for the radial directions to be measured. 
It has a disadvantage that these directions 
measured from this point are affected by sys- 
tematic errors which are a function not only 
of the inclination of the photograph but also of 
the ground elevation. The nadir point can be 
found if the inclination of the camera is known, 
for instance with the horizon camera or a gyro- 
scope. In the meeting just before this, we heard 
that it is now possible within an accuracy of 
about two to three minutes of an arc only. When 
measuring this nadir point the direction can be 
easily reduced for this remaining inclination, 
by a simple formula which does not contain 
ground elevation. This does not mean, of course, 
that these corrected directions are errorless, for 
the inclinations from which the corrections are