methods, do not at present have the potential for support 
ing or replacing classic first-order triangulation. Despite 
quite a number of optimistic dissertations and numerous 
constructive discussions on the subject, the fact must be 
acknowledged that in praxis aerial triangulation procedures 
have not provided a practical approach for satisfying the 
accuracy requirements for even second or third-order geo 
detic densification triangulations. 
Generally speaking, the method of aerial triangula 
tion has not, so far, realized its theoretical potential 
for establishing geodetic control; specifically, it has not 
produced results in large-scale applications which are 
commensurate with the concepts of accuracy and statistical 
reliability that apply to the results of classic geodetic 
operations. 
These statements are made with full recognition that 
much progress has been made with numerical evaluation of 
aerial triangulation schemes for the establishment of mapp 
ing control and that high precision has been obtained in 
the domain of cadastral surveying by some agencies using the 
photogrammetric method. Economy in these methods has been 
obtained because computers have become faster by a factor 
of three to four during the past decade. This additional 
speed, together with increased word lengths, improved flexi 
bility of compilers and more efficient software, has dras 
tically reduced the costs of computing, even when considering 
the inversion of exceedingly large matrices. As a result, 
computing costs are but a small percentage of the total 
expenditures for aerial triangulation. 
There is every reason to believe that this trend 
will continue. Thus, further reduced computational costs 
should help to make the photogrammetric method economically 
attractive for determining geodetic control. 
Existing data generators permit the simulation of any 
conceivable topography in connection with any contemplated 
triangulation scheme. Associated computer programs enable 
the computation of artificial raw data and randomly-distributed 
residual errors, thus making it possible to verify, by 
computational means, the theoretically-derived effects of 
error propagation, including the influence of uncompensated 
systematic errors, as well as the impact of auxiliary data 
on both the accuracy and economy of specific triangulation 
configurations. 
From a theoretical standpoint, the photogrammetric 
triangulation method can be numerically investigated and