I. INTRODUCTION 
Theoretical and practical work concerned with the development and testing 
of analytical solutions for the reduction of photogrammetric records has, in 
the past, proven the feasibility of such a method. Such a project was initi- 
ated at the Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland. 
with the study of the orientation of & single camera followed by & solution 
for the problem of triangulation by a combination of two photogrammetric 
cameras, These two phases have been presented in the BRL Reports No. 800 ETS 
and No. 961 [2]. The phase logically to follow is the development of an i 
analytical solution for the n-camera case. The problem of triangulating, for 
example, the space-time coordinates of points of trajectories recorded simul- 
. taneously on more than two photogrammetric cameras belongs in this category, 
as well as the problems of strip and block triangulation. 
In [2] an approach was outlined which would have made it possible to 
extend the two camera solution to the treatment of the n-camera problem. The 
most serlous objection to that approach is the fact that, in such & case, the 
matrix, associated with the vectors of the residuals, loses more and more its 
diagonal character. Thus, the basis for the feasibility of the corresponding 
numerical solution is being impaired. (Compare [2], page 22 and schematics 
on page 48). Furthermore, the solution becomes cumbersome if additional 
information must be introduced expressing certain geometric conditions con- 
cerned with the coordinates of the points of the object to be triangulated, 
Last but not least, the "bookkeeping effort" in the preparation of the 
electronic computations would have been considerable, due to the necessity of 
distinguishing between, various kinds of control data and corresponding con- 
ditional equations, which, to make things worse, are of somewhat different 
character, depending on the number of cameras involved in any one specific 
triangulation. 
The following solution overcomes these objections. As an additional 
feature, this solution is based in its entirety on the simplest mathematical 
presentation conceivable, The use of matrix calculus for setting up a system 
of reduced normal equations ls especially suited for electronic computers, 
* Reference at the end of the paper, 
2