12 
Close to the image center (c=150 mm) this value corresponds to a standard 
error in each of the two angles of direction of about 12 cc (centesimal seconds) 
or 4" (sexagesimal seconds). 
Under the conditions stated, approximately the same geometrical quality 
may be expected throughout the photograph. 
In estimating the confidence limits of the computed values of the angles 
the derived standard errors are essential. 
According to the ¿-distribution on the five percent level the following factors 
t p are found for varying degrees of freedom (see Cramer 1946) 
d.f.= 2 t p =4,3 
d.f.= 5 t p = 2,6 
d.f.= 10 t p = 2,2 
d.f. = 60 t p =2,o 
The great importance of many redundant observations in the determina 
tion of the standard error of unit weight is obvious. If only two degrees of 
freedom are available, as in the case of only four stars, possible deviations of 
the computed direction from its correct value of more than four times the 
standard error have to be accepted because of the irregular fluctuations of 
the standard error itself. From about ten redundant observations the factor 
t p becomes stabilized near two, and the decrease with increased number 
of observations is then very small. For the determination of the confidence 
limits of the standard error of unit weight itself the chP-distribution has to be 
applied, as shown in most textbooks on statistics, see for instance Cramer 
1946. 
1.2. A simplified interpolation procedure 
In many cases the angles cp and co may be so well determined from the photo 
graphy that the influence of their non-linear errors upon the image coordinates 
can be neglected. In such a case the interpolation may be performed with 
four parameters only: two translations dx 0 and dz 0 , one rotation dx of the 
ds 
plate and one scale change—. 
s 
The discrepancies dx = x meas —x given and dz=z meas —z given are interpreted 
as caused by these regular errors according to the error equations 
ds 
dx = dx 0 + x zdx 
s 
(31)