114 
Conclusions 
In this paper the error propagation of three methods for aerial tri- 
angulation have been investigated in order to find general analytical 
expressions for the accuracy of the final results of the triangulations. 
The three methods are 1. The stereo-radial triangulation. 2. The 
model triangulation, and 3. The ordinary spatial triangulation. 
The investigations are based upon the real working procedures of the 
triangulation methods under well defined conditions. The fundamental 
operations of all three procedures are assumed to be carefully investi- 
gated concerning systematie errors, which consequently are assumed to 
be corrected in connection with the triangulation procedures. The 
error propagation deals exclusively with the irregular errors of image 
coordinate and parallax measurements. Such errors are assumed to be 
estimated statistically in connection with adjustments of discrepancies 
in conditions, especially in those of the relative orientation. 
The accuracy of the triangulation methods has been investigated for 
two cases viz. cantilever extension and bridging respectively. No 
redundant control points have been assumed in order to obtain as 
simple mathematical expressions as possible. Some approximations 
have also been introduced in order to simplify the final expressions for 
the accuracy. 
From the analytical expressions for the accuracy of bridging triangu- 
lation it is possible to determine the most favourable relation between 
the triangulation distance and the flying altitude. Such determinations 
have been performed for the three triangulation methods under well 
defined assumptions. It has been found that the aerial triangulation 
strips should consist of comparatively few models, of the order of magni- 
tude 5—6. For a certain density of the control points on the ground 
consequently the flying altitude must be chosen in a well defined man- 
ner. The density of the ground control as well as the flying altitude 
have to be chosen with respect to the actual tolerances for the mapping 
project, which have to be known. These conditions are of fundamental 
importance for the economy of the aerial triangulation and the mapping 
project. 
It seems most important that more attention be paid to the funda- 
mental operations of photogrammetry, primarily in order to determine 
systematic errors of the operations and to estimate the magnitude of 
the irregular errors. The more carefully this work is done, the better 
will the theoretically derived accuracy expressions agree with practice. 
For investigations of this agreement, confidence limits of the theoreti- 
cally derived standard errors are of great value. Such limits can be