(402) 
shape varies but very slightly from that of the rotating cylinder. However, 
these variations are practically negligible. 
At first, these considerations are of a purely projective nature and do not 
supply any information on the analytical character of the problem of uncer- 
tainty in the concrete individual case. Such information may only be derived 
from an analytical treatment of the critical surfaces which must start from the 
equation of errors of relative orientation. This analysis shows that the uncer- 
tainty consists in a linear interdependence of the 5 orientation elements. 
A y-parallax which is caused by errors of one or more orientation ele- 
ments, may be eliminated on the entire critical surface by modifications of the 
other orientation elements. On the orthogonal hyperboloid, all five orienta- 
tion elements are involved in this interdependence. On the rotating cylinder, 
which is practically the only important case, only three orientation elements 
are still involved, that is, — starting from the matching of consecutive pic- 
tures, — the displacements b, and b, of the right camera station and the tilt 
differential o. An investigation of the vertical section of the cylinder through 
the right camera station furnishes a very simple geometrical explanation for 
this uncertainty and for the interdependence of the three above mentioned orien- 
tation elements. 
A displacement by db, and db, of the right camera station, which returns 
it from its correct position to the cylinder, may be compensated in all points 
of the cylinder section and only in these points by one and the same do. For 
peripheric angles above the same arc are equal. A relief model free from y- 
parallaxes can therefore also be obtained in this manner with an orientation 
which contains errors in db, db, and do, for the parallaxes produced in the 
entire model by an orientation element that is in error, are always eliminated 
by changes of the other two orientation elements. 
However, this model does no longer bear resemblance to the terrain which 
has been photographed. It contains deformations in which errors of elevation 
are particularly prominent. Therefore if it should be possible to check the ele- 
vations with the aid of. surplus control points within the scope of absolute 
orientation, the observed elevations errors permit to correct relative orien- 
tation and thus eliminate the uncertainly of orientation. On general principle, 
elevation control in one additional point will be sufficient, 
The ascertained error of elevation permits to compute one of the three 
orientation errors. Owing to the interdependence of the orientation errors, the 
other two may be determined without an additional elevation control point. 
The corresponding formulas are very simple. They may be: 
xn 1 
do ee y—2m ‘ dh 
Asie dra aioe udh 
y —2m 
2m 
db, = ——— . dh, 
y —2m 
where y is the coordinate of the elevation control point in the base system, m 
and n the horizontal and/or vertical distances of the cylinder axis from the 
base, and dh the observed elevation error. 
The errors of the orientation elements are intrinsically differential values 
gun Yoga Ph BA 0A {SS As st