the simplicity of the mathematical model on which the gener&l photogrammetric
solution is based. Thus, the least squares solution, can be considered an
economical technique for intersecting corresponding rays of various bundles.
A comparison of this report with [2] ; Shows that the present approach
distinguishes itself from the former one only by the way in which the elimi-
nation of the unknown coordinates of the model X is &ccomplished. In the
present solution, this elimination of unknowns is not performed algebraically
before the observation equations are formed but during the process of forming
the reduced normal equations. Consequently, the system of reduced normal
equations (formula (37)) agrees, to all but second order terms, which have been
neglected during the process of linearization by the Taylor series, with the
corresponding normal equation system of the formerly published solution. The
advantage of the present solution can be seen in the simple and systematic flow
of the computations. It is possible to treat all casesvof practical analytical
photogrammetry with but one basic computing scheme, thus simplifying consider-
&bly the "bookkeeping effort" in the electronic computer.
A critical study of the individual steps of the presented solution leads
to a conclusion which, although somewhat discouraging for the author, may en-
courage the application of analytical photogrammetry. It becomes obvious that
the analytical treatment of photogrammetric problems does not call for any new
manipulations in photogrammetric theory or statistical treatment of errors.
The expressions, representing the basis of the whole solution, derived in
equations (11) and (12), as they exist between the coordinates of the model and
the corresponding coordinates of the images, are the well-known formulas derived .
by v. Gruber in [14] and the corresponding inverse functions. The partial differ-
ential quotients necessary to form the observation equations (15), given with‘
formulas (40) and (41) are the same expressions that are found in [1] or [?] ;
the unmodified use of these expressions appears justified due to the simplicity
of their construction. The system of normal equations (21) resulting from the
system of observational equations (18) 1s identical, as mentioned before, with
the solution given by Helmert in [4] . The elimination of the vectors, K in
the system of normal equations (21), Ay in the system (35), and the reduction
78
Pp ae. *
