WORKING GROUP 2 
MARKOVIODIMITRIJEVIC-PETROVIC 
131 
The error of the radial triangulation-sketchmaster process is a function of 
many factors, such as, for instance, relative height of triangulation points, 
relations of flying height, relief, focal length, and others. It will be useful to 
avoid this step in the statistical drainage analysis, especially in mountainous 
regions. This can be avoided by analysing the prints themselves, and not the map. 
In this case, only one group of errors remains - the errors due to central 
projection, and they can be mathematically predicted. 
The central projection of a non-horizontal line does not have the same 
pitch, direction or length as the line itself. If the line has a pitch azimuth 
v = v r -\-[x, and a length m (orthogonally projected as mi, centrally as m'), its 
projection will have an azimuth v r -\~n' (where v r is the azimuth of the radial 
line r, which passes through the projected point A', ¡x the horizontal angle be 
tween this line and mi, and ¡x the horizontal angle between line r and m'), and 
a length m'. The differences between ¡x and ¡x, and between m and m' are 
functions ol the focal length/, the radial distance of the projected point A' (r), 
the pitch a and length m of the line, and the angle between r and m' (/a). These 
relations are shown in fig. 1. From the photographs ¡x' can be read off, as can 
m', r and/ The key-datum is therefore the pitch angle a, so we shall assume 
that it is known for the further theoretical treatment. 
Bearing deformation 
Fig. 1 shows the relation: 
As fx = [x—<5, the true azimuth can be found knowing r, / and ¡x . For 
varying values of these parameters, the change of ò has the form of a sinusoid 
of a variable amplitude but of constant wave length. The graphical solution 
of equation (2) is given in fig. 2. 
In a statistical treatment, the stream bearings are divided into classes with 
intervals of 10°. The exact position of each datum in its class has no importance; 
thus the measurement errors must be so small that a large number of data 
could not pass into an adjacent class. If we know that the error in field dip- 
measurements is about 2-3° and assume that the measurements on the photo 
graphs cannot be more accurate, we could adopt 3° 36' (1% of 360°) as the 
maximum permissible error. By introducing this value into equation (2) we get: 
(i) For a given a, the error will be, for every ¡x in the permitted limits, 
within a circle with its centre at the principal point and radius: 
A r m\ 
(1) 
sin ò sin Cp 
where: cp — 180°—//, mi = m cos a and Ah — m sin a 
r 
Also : Ar = — m sin a 
r 
By substitution we obtain: sin <5 = — tan a sin /x' 
or 
(2)