variable indépendante. On repasse aux fonctions z cherchées par la transforma 
tion z = W u, la matrice W étant sa propre inverse. 
Enfin, dans l’une et l’autre méthode, les corrections en inclinaison transversale 
s’obtiennent aisément à partir des z et des équations de raccord entre rubans. 
Relaxation methods for the altimetric adjustment of photogrammetric blocks 
The paper completes two previous publications of the author in the »Bulletin de la Société 
Beige de Photogrammétrie», nrs 39 and 40 (1955). 
In normal conditions of aero triangulation, two sets of quantities can be considered as »measures», 
which affect altimetry, i. e. transfer in both fore-and-aft and lateral tilt. Supposing all available 
means have been used to eliminate non-accidental errors, a least squares principle may be applied 
on these quantities. 
In the previous publications, the author has given a solution for this problem by transforming 
it in a »continuous» one and applying the calculus of variations. He obtains a system of differential 
equations, but the system is to be solved numerically by discrete values, so that continuity no 
longer remains in the practical calculation. Therefore a mean must be found to solve the problem 
without introducing continuity. 
Relaxation methods, due to R. V. Southwell, actually provide at least two solutions in that way. 
One solution consists in applying relaxation technique similar to the integration, of partial 
difference equations of the second order with two independent variables. Another solution makes 
use of a linear transformation, the coefficients of which are functions of the number of strips only; 
the numerical values of these coefficients will be given in the paper. Relaxation can then be 
applied to separate difference equations with a single independent variable. 
Both solutions give the altitude corrections on the axis of each strip. The corrections of the 
transversal tilt are calculated afterwards, from the axial altitude corrections and the altitude 
discrepancies between strips. 
Il n’y a pas de discussion. 
M. A. J. van der Weele (Pays-Bas) occupe ensuite la tribune. Son sujet est 
intitidé: »Rational Adjustment of Blocs of Aerial Triangulation.» 
The method which is proposed in this paper is specially meant for the adjust 
ment of those triangulations where ground control is sparse and vast terrains 
have to be covered. In most of those cases maps on small scales (1: 100.000, 
1:250.000) are desired and photographs are made on scales 1:30.000—1:50.000 
to meet at the same time the needs for mapping and interpretation purposes. 
It is assumed that it will be necessary to apply aerial triangulation in a first 
or second order instrument to meet the requirement for the precision of the 
heights. The adjustment of planimetry is considered separately from that for the 
elevations since the determination of supplementary height control is much 
easier than that of planimetric control. 
The machine coordinates, obtained from the aerial triangulation have a rela 
tive precision which is much better than necessary for the map. By simple linear 
transformation, approximately squareformed blocs are computed in one coordi 
nate system consisting of so many models that the internal accuracy is kept 
within the limits, prescribed for the job (e. g. 0.1 à 0.2 mm on map scale). 
These blocs are now considered as units for an adjustment by means of slotted 
templets. For each bloc, two templets are made with their respective radial 
centres in the midpoints of opposite sides of the squares. 
Since the radial lines, realised in those templets, have no errors caused by tilts 
of camera-axis nor by terrain-elevation differences, the result of the adjustment 
will be a set of point-positions showing only small deformations compared with 
the positions computed originally in each bloc. 
These deformations can be taken into account by a simple linear graphical 
correction. The relative precision within a bloc is therefore not disturbed by this 
correction and remains on an extremely high level. The absolute precision of the 
map, which is less important for the average user, will still be reasonably good 
since during the lay-out, all theoretical conditions for the adjustment are auto 
matically taken into account. 
A. J. van der Weele: 
Rational Adjustment 
of Blocs of Aerial 
Triangulation. 
(Publ. Ill W 3) 
15 
225