An individual Pi matrix designates the weights of the plate measurements and 
of the control data, as they pertain to a specific ray. The introduction of 
weighting factors for the plate measurements may become necessary to express 
varying degrees of precision associated with the original observations. Such 
variations may arise from the method of measuring, the varying image quality 
caused by loss of definition towards the edges of the photograph, or from a 
decrease of accuracy with which the distortion correction is known for image 
points at increasing radial distances from the center of the plate. Various 
degrees of dependability of the given control data can be considered, as well, 
by the introduction of corresponding weighting factors. Infinitely large 
welght with respect to the given control data will eliminate the V from the 
solution, thus distributing the unavoidable discrepancies among the plate co- 
ordinate measurements only; however, infinitely large weight assigned to the 
plate coordinate measurements will make the given control data absorb all the 
discrepancies present in connection with a certain ray under consideration. 3 
While the boundary conditions that were just mentioned are only of secondary 
importance, the choice of suitable weighting coefficients makes it possible 
to prevent an undue deformation of the model obtained photogrammetrically by 
possible strain in the configuration of the given control data. In case the 
original observations (image point or control coordinates) are not independent 
from each other, the corresponding correlations can be allowed for by intro- 
ducing the corresponding correlation coefficients into the P matrix. In 
  
case all the p-values are equal, it is convenient to consider P as the unit 
A 
matrix. 
In setting up the corresponding normal equations, one has to take into 
account the fact that in the most general case each observational equation 
contains more than one measurement, Furthermore, in such a case, certain 
measurements and their residuals appear in more than one observational 
equation. Helmert in 4 , (pp 215-222), has shown a direct solution of the 
| general problem of a least squares adjustment. (Compare 2 , paragraph IV). 
| Accordingly, we obtain in our case a set of normal equations as shown in 
| formulas (21): LT 
| AP A K-BA=-Q 
-DK o : 0 (21) 
20 
“EN