caused by some elements of the adjustment procedure but this correlation is generally of minor im 
portance compared with the physical one. The effects of the algebraical correlation can be computed 
from the basic formula systems of the adj ustment. See reference 1.61:1. 
A detailed study of correlation effects in residuals after multicollimator tests has been made. See 
tables 1.61:5 through 10 in the Appendix. 
A further study of correlation within the same photograph has been made to find the relation between 
the correlation in residuals and the distance between the points in question. The figures of section 1.62 
(Appendix) show that in most cases the correlation increases with decreasing distance between the points. 
The tests were made with aerial photographs of the Oland test area, used for experiments until 1961. 
See reference 1.61:1. 
The procedure used was as follows: 
The points at which image coordinate residuals were determined were combined into squares of 
different size. The maximum was about 20 cm square and the minimum about 5 cm in the image. 
A correlation expression for each square was determined as a fraction of the sum of products of all 
x-residuals and of y-residuals in all combinations (numerator) and the products of the square roots of 
the sums of the squares of the x- and of the y-residuals (denominator). 
In formulas the correlation can be expressed as follows: 
corr x — 
corr v — 
[ r xp t xq ] 
[r x r x ] 
[ r yp r yq] 
i>y r y] 
(p, q cycl. diag.) 
(p, q cycl. diag.) 
r xp and r xq indicate the residuals in x of two points of the squares which can be combined in six ways. 
The expressions are similar for y. 
The limiting values of 1.5 for the expressions would occur with an infinitesimal square. 
One large, 9 medium and 16 small squares can be formed from a pattern of 25 regularly located points. 
The following averages of correlation were found: 
sides corr 
200x200 mm 0.39 
100x100 mm 0.42 
50 X 50 mm 0.58 
If the sides are denoted v and the correlation factor u the following analytical relation can be found: 
u = - 0.0000006633i; 3 + 0.0002515i; 2 - 0.02935t; + 1.5 
In fig. 1.63:1 the curve is plotted. Further correlation factor from multicollimator tests have been com 
puted and are indicated in the figure. The agreement is quite good. 
Although these tests are too limited for any general conclusions, they indicate the increasing correla 
tion with decreasing distance in the photographs. This fact is important for the determination of the 
accuracy of functions of image coordinates such as distances, angles and areas. More tests of this nature, 
particularly for different makes of film, glass plates etc., are desirable. 
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