6 
to formulas (1) and (2). The standard error of the corrections can be com 
puted according to the general law of error propagation. Confidence limits 
of the corrected coordinates can then be determined according to statistical 
procedures for a desired confidence level and for the degrees of freedom pres 
ent in the determination of the standard error of unit weight. 
In order to illustrate these principles and to determine a value of the standard 
error of the corrected image coordinates under well defined conditions, an 
example will be presented, where only algebraical procedures will be used. 
Assume that four stars are used for an interpolation procedure as schema 
tically shown in Fig. 1. The stars are assumed to be located in an approximate 
square around the principal point of the photograph, and the object is assumed 
to be somewhere within the square. 
The side of the square is assumed to be 2 a, and the image coordinates of 
the stars are consequently as follows. 
Star 
z 
1 
—a 
—a 
2 
—a 
+a 
3 
+a 
+a 
4 
+a 
—a 
The equations (5) and (6) are tabulated for the four stars in Table 1. 
TABLE 1 
Coefficients of the corrections 
V 
Star 
X 
z 
dx 0 
dz Q 
dc 
dx 
dtp 
dco 
dx 
dz 
v x 
1 
—a 
—a 
— 1 
— 
a 
+ - 
c 
—a 
a 2 
c 
a 2 
c 
—dx v 
— 
2 
—a 
+a 
—1 
— 
a 
+ - 
c 
+a 
a 2 
c 
a 2 
+ - 
c 
—dx 2 
— 
3 
+a 
-\-a 
—1 
— 
a 
c 
+a 
a 2 
c 
a 2 
c 
—dx 3 
— 
4 
+a 
—a 
—1 
— 
a 
c 
—a 
a 2 
c 
a 2 
+ - 
c 
—dx x 
— 
v z 
1 
—a 
—a 
— 
—1 
a 
+ - 
c 
—a 
a 2 
c 
a 2 
c 
— 
—dz x 
2 
—a 
+a 
— 
—1 
a 
c 
—a 
a 2 
+ - 
c 
1 
Î 
| a, 
— 
—dz 2 
3 
+a 
+a 
— 
—l 
a 
c 
+a 
a 2 
c 
a 2 
c 
— 
—dz 3 
4 
+a 
—a 
— 
—1 
a 
H 
c 
+a 
a 2 
c 
a 2 
c 
— 
—d?i